m iniimniiiiiin i ^ BOUGHT WITH THE INCOME OF THE SAGE ENDOWMENT FUND THE GIFT OF HENRY W. SAGE 1891 Cornell University Library arV1112 Physical chemistry : 3 1924 031 195 062 olin.anx Cornell University Library The original of tliis book is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31 924031 1 95062 PHYSICAL CHEMISTET PHYSICAL CHEMISTRY • ITS BEARING ON BIOLOGY AND MEDICINE BY JAMES C. PHILTP, M.A., Ph.D., D.So. ASSISTANT PBOEESSOB IN THE DF.PABTMBNT OF CHEMISTKY, IMPEKIAL COLLEGE OF SCIENCE AND TECHNOLOGY, LONDON SECOND EDITION SHJCOND IMPRESSION NEW YORK LONGMANS, GREEN AND CO. LONDON: EDWARD ARNOLD Feinted in Great Beitain PEBFAOE The conc^tions and methods of physical chemistry have been extensively utilised during recent years in attacking biological and physiological problems, and the results which have followed this application of physico-chemical principles are not only of very great interest in them- selves, but are full of promise for the future. Students of biology and medicine, however, cannot truly appreciate or co-operate in this work unless they are familiar with the underlying principles. It is as a sketch of the physico- chemical basis for this modern treatment of biological and physiological problems that I have written the present volume. The book originated in a course of lectures delivered to biological students at the University of London in 1909, but since then much fresh material has been in- corporated. I have endeavoured to give a systematic exposition of physical chemistry so far as it has a bearing on the problems in question, and to illustrate the applica- tion of physico-chemical principles by examples taken fro^:!! the fields of biology, physiology, and medicine. Since the book is intended chiefly for students of these sciences, the use of mathematics has been avoided as far as possible, and the reader is assumed to have only an ordinary ac- quaintance with physios and chemistry. Numerous refer- vi PEEFACE ences to original papers are given for the use of those who may desire to follow up any particular line. Of larger works which have been frequently consulted in the preparation of this volume, the following may be mentioned : Fhysikalische Chemie der Zelle wnd der Gewebe, by E. Hober; Fhysikalische Chemie uvd Medizin, by Koranyi and Eichter; Grwndriss der Kolloid-chemie, by Wo. Ostwald. I desire to thank Professor Benjamin Moore for permission to reproduce Pig. 22, and Herr W. Engelmann for permission to reproduce Figs. 4, 6, 10, and 14. I must also express my indebtedness to Professor Groom, Dr. Harden, and Dr. Senter, who very kindly read parts of the MS. or proofs, and made many valuable suggestions. J. C. P. London, June 1910. PEEFACE TO THE SECOND EDITION The chief new feature of this edition is the addition of a chapter on electromotive force. The treatment of permeability in Chapter V has been extended by a short account of Czapek's researches on the surface tension of the cell membrane, while references to recent work have been inserted throughout. J. 0. P. LOKDON, October 1913* CONTENTS CHAP. PAGE I. Gases peom the Standpoint of Experiment and Theory. Diffusion Phenomena ... 1 II. Absorption of Gases by Liquids .... 20 III. Osmotic Pressure 33 IV. The Comparison op Osmotic Pressures. Isotonic Solutions 54 V. Permeability and Impermeability of Membranes 75 VI. Vapour Pressure, Boiling Point and Freezing Point op Solutions 86 VII. The Behaviour of Salts, Acids, and Bases in Aqueous Solution 114 VIII. Electrolytic Dissociation ; Physical and Bio- logical Applications 136 IX. Colloidal Solutions 177 X. The Separation op Colloids from their Solutions 201 XI. Adsorption 219 XII. Chemical Equilibrium and the Law of Mass Action 244 XIII. The Velocity op Chemical Reaction . . . 276 XIV. Electromotive Force 307 INDEX 322 vll PHYSICAL CHEMISTRY CHAPTEH I * GASES FROM THE STANDPOINT OF EXPERIMENT AND THEORY. DIFFUSION PHENOMENA The recent development of physical chemistry has been char- acterised very specially by the elaboration and application of new methods for the study of the phenomena exhibited by solutions. These methods are closely related to a theory of solution, which in its turn is rooted in the analogy ex- isting between the behaviour of solutions and that of gases. Any attempt, therefore, to expound the properties of solu- tions, and the interpretations of these properties that have been proposed, must be preceded by a glance at certain features which characterise the gaseous state, and at various theories which bear on the nature of gases. Fundamental Experimental Laws. — For physico- chemical purposes the fundamental facts in which the behaviour of gases is revealed are summed up in three laws, two of which are purely physical in character, while the third is more accurately described as chemical. It is perhaps necessary to emphasise the fact that these three laws are absolutely independent of any theories regarding the nature of gases ; they are simply the integrated ex- pression of experimental results. (a) Boyle's Law. — According to this law, the volume 2 PHYSICAL CHEMISTRY occupied by a given mass of gas varies inversely as the pressure to which it is subjected, provided the temperature is kept constant. The algebraic expression of this relation- ship is pv=G, where p is the pressure, ■;; is the volume, and is a constant. This is the equation to a hyperbola, and the curve therefore representing the corresponding changes of pressure and volume for a given quantity of a gas at constant temperature belongs to this type. If we represent by v^ the volume occupied by a given quantity of gas under the pressure p^, and by v^ its volume at the same temperature under the pressure p^ then we may express Boyle's law by the formula P^i — Vi^r' -^^ ^^ instance of the extent to which this law has been verified in work of the most accurate kind, Lord Rayleigh's figures for hydrogen, oxygen, and carbon dioxide may be quoted.^ He has shown that if the value of pv obtained for p=l atmosphere is taken as unity, then the value of pv for p = Q-Z atmosphere, instead of I'OOOO, is found to be 0"99974 in the case of hydrogen, 1*00038 in the case of oxygen, and 1'00279 in the case of carbon dioxide. For ordinary gases and under ordinary conditions, therefore, Boyle's law may be taken as an accurate statement of the corresponding variation of pressure and volume. Under certain conditions, however, the formula pv = G ceases to represent accurately the behaviour of a gas at constant temperature, and hence it must be regarded as of only limited validity. Such deviations from strict obedience to Boyle's law occur (1) wh«n the pressure applied to the gas is very high, and (2) when the gas is near its point of condensation. Amagat, for instance, in his experiments ^ on the compressibility of nitrogen at 22°, found that if the value of pv for p — 1 atmosphere 1 See Phil. Trans., A, 1905, 204, 351. 2 Arm. ohim.phys. (5), 1880, 19, 345. GASES 3 is taken as unity, the value for p = 62 atmospheres is as low as 0"986, while for ^ = 373'3 atmospheres it is as high as V207. Such deviations from Boyle's law, however, become in all cases less marked at highei temperatures. (b) Gay-Idissac's Law. — The volume occupied by a given mass of gas, kept under constant- pressure, increases as its temperature is raised, and the relative expansion is approximately the same for all gases. It is found that for 1° 0. rise of temperature the volume of a gas increases by ^-fg- of the volume which it occupies at 0° 0., subject to the condition that the pressure remains the same during the rise of temperature. If v,^ and v are the volumes occupied by a given mass of gas at 0° 0. and t° 0. respectively under equal pressures, and if a = -^}-g re- presents the coefficient of expansion common to all gases, then Gay-Lussac's law may be expressed algebraically by the equation v = Vf,{l + at). From the foregoing, taken in conjunction with Boyle's law, it is easy to show that the pressure exerted by a given mass of gas kept at constant volume must increase with rising temperature in the same proportion as the volume increases at constant pressure ; so that, if ^^ and p represent the pressure at 0° 0. and t° 0. respectively, p=PQ(l + at), subject to the condition that the volume of the gas remains the same throughout. This formula is not only deducible from the equations pv=G and v = Vg(l+at), but is also in harmony with the results of experimental work. The formula pv = is applicable only when the tem- perature is constant, and the formula v = VQ{l+af) only when the pressure is constant; but since the final con- dition of a gas may differ from its initial condition in respect both of temperature and of pressure, it is obvious that there must be also some one equation connecting the 4 PHYSICAL CHEMISTRY initial and the final volumes in this case. This equation may be deduced easily in the following manner. We may suppose that a given quantity of a gas, occupying the volume v^ at the pressure p^ and the temperature 0° C, occupies the volume v at the pressure p and the temperature t° C. ; the problem, then, is to find the algebraic relationship between v and v^. If we start with the gas at 0° and raise its temperature to t°, the pressure being kept constant, the new volume v-^ occupied by the gas can be easily calculated, for these simultaneous changes of volume and temperature are subject to Gay- Lussac's law; that is, v.^^=:v^(l+at). If now, at the temperature t°, we alter the pressure from p^ to p, the volume changes from v-^ to v, which we have chosen to represent the final volume. To simultaneous changes of pressure and volume at constant temperature Boyle's law is applicable, so that we have P'V=Pf,Vj^=PQ%{l+at). This equation, pv=p^Vf,{l + at), is the algebraical ex- pression both of Boyle's law and of Gay-Lussac's law. Its validity is not absolute, inasmuch as gases exhibit deviatipns from strict obedience to Gay-Lussac's law as well as Boyle's law. If the numerical value of the coefficient a is inserted in the equation it assumes the form pv=PfP^ „ - ; if, further, it is agreed to reckon temperature, not from 0° C, but from a point 273 degrees lower, and to take T as the symbol of temperature on this new scale, then the equation may be written pv=^j~T. Temperature reckoned in this way is known as ' absolute ' temperature, and —273° 0., the starting point of the 'absolute' scale, is termed the ' absolute ' zero. The equation pv = ^j^T sums up the physical be- haviour of gases so far as that is defined by the laws of Boyle and Gay-Lussac, but for certain purposes it is GASES 5 desirable to have the direct relationship Between v.^, the volume which a quantity of gas occupies at pressure jp^ and absolute temperature 2\, and v^, the volume which it occupies at pressure p^ ^^^ absolute temperature T^ A little consideration of the foregoing equation will show that the relationship required is ^^ =^P. -'1 -'2 (c) Gay-lMssa(is Law of Volumes. — This third experi- mental law, although associated with the same name as the second law, is purely chemical in its character, and deals with the relative proportions by volume in which chemical reaction between gases takes place. The law states that when two gases combine with each other to form a third gas, the volumes of the reacting gases are in a simple ratio to one another and to the volume of the gaseous product (all volumes being measured at the same temperature and pressure). Special cases of this will doubtless occur to the reader; it is, for instance, well known that 1 volume of hydrogen combines with 1 volume of chlorine to form 2 volumes of hydrogen chloride, and that 2 volumes of hydrogen combine with 1 volume of oxygen to form 2 volumes of water vapour. No gas is absolutely 'perfect,' that is, no gas con- forms rigidly to the first two laws, and hence it follows that the volume ratio of reacting gases found in the most accurate experimental work is less simple than the preceding paragraph woul^ seem to indicate. At 0° 0. and 760 mm., for instance, the ratio of the volumes of hydrogen and oxygen uniting to form water is 2 '0028: 1, according to Scott's accurate investigations.^ If, however, a correction is made for the slight extent to which hydrogen and oxygen deviate from Boyle's law (see p. 2), the volume ratio is almost exactly 2: 1. ^ Phil. Trams., 1893, A, 184, 543. See also Morley, Zeii. physikal. Chem., 1896, 20, 417. 6 PHYSICAL CHEMISTRY Theories bearing on the Nature of Gases. — (a) The Kinetic Theory of Gases. — A little consideration of the experimental laws wMch have just been enunciated shows that gases are characterised by simplicity and uniformity, both in their physical behaviour and in their chemical relationships. Various theories have been brought for- ward which offer an interpretation of this simple and uniform behaviour. According to one of these, the kinetic gas theory, the ultimate particles of a gas are rushing about at a high speed, the direction of their motion being altered only when they collide with one another or impinge on the walls of the containing vessel. The velocity of motion will vary somewhat from one particle to another, but so long as the temperature of a mass of gas remains the same, the average velocity of the constituent particles will be constant. The pressure exerted by the gas is due to the impacts delivered on the walls of the containing vessel by the moving particles. If it is further assumed that the volume of the particles themselves is negligible compared with the total volume of the gas, and that they are perfectly elastic, it follows by the principles of mechanics that at constant tem- perature pv=\'mnu^, in which equation m is the mass of an individual particle of the gas, n is the number of particles in volume v of the gas, and u is the average velocity of the molecules at the temperature considered. So long as the temperature is unchanged the product ^mnv? has a constant value, hence ji)v = const., which is the algebraic expression of Boyle's law. The assump- tions of the kinetic gas theory, then, involve the relation between pressure and volume required by the first fun- damental law of gases. If the temperature is changed, then the value of pv for a given mass of gas alters according to the formula already discussed — :pv=^dT, or, GASES 7 in words, the product of pressure and volume is pro- portional to the absolute temperature. But, according to the kinetic theory, pv = ^7iinu\ and, if we are dealing throughout with the same quantity of a given gas, the values of m and n are independent of temperature, so that u^ must be proportional to the absolute temperature. The kinetic gas theory involves therefore a definite con- ception of what happens when the temperature of a gas is raised; the kinetic energy of the molecules increases propprtionally to the absolute temperature. (b) Avogadro's Hypothesis. — According to this hypo- thesis, which bears especially on the third experimental law, equal volumes of different gases, measured at the same temperature and pressure, contain the same number of ultimate particles or molecules. If it is supposed that when two gases combine chemically one ultimate particle of the first gas reacts with one, two, or three ultimate particles of the second gas, then Avogadro's hypothesis is seen to offer a plausible and natjiral interpretation of Gay-Lussac's Law of Volumes. Bjit the essential point of the hypothesis, as it was enunciated by Avogadro, lay in the distinction which he drew between atoms and molecules. He suggested that the molecule of an element was not necessarily the same as the atom, and that the ultimate particle of a gaseous element might contain one, two, or more atoms of that element. Only when this suggestion is adopted is Avogadro's hypothesis capable of interpreting all the special cases which are summarised in Gay-Lussac's law. Avogadro's hypothesis was brought forward primarily as offering an explanation of the volume relationships of chemically reacting gases, but it obviously furnishes also a simple interpretation of the uniform behaviour of dif- ferent gases when exposed to changes of pressure and temperature. It is noteworthy also that the hypothesis 8 PHYSICAL CHEMISTRY is found to be in harmony with the consequences of the kinetic gas theory. The proppsition advanced by Avogadro has been adopted as a working hypothesis, and as such has stood the test of time ; it is, in fact, a necessary supplement to the Atomic Theory. Since the hypothesis is closely con- nected with much that is to follow, it is essential to indicate at this stage the results that flow directly from its acceptance. First of all, the acceptance of Avogadro's hypothesis leads to a definite conception of the relation between the atom and the molecule of the gaseous elements. The argument may be stated as follows. It is a recog- nised experimental result that 1 volume of hydrogen unites with 1 volume of chlorine to form 2 volumes of hydrogen chloride. If now we suppose that 1 volume of hydrogen contains n ultimate particles of hydrogen, then, according to Avogadro, the 1 volume of chlorine also contains n ultimate particles of chlorine, whilst the 2 volumes of the product contain 2n ultimate particles of hydrogen chloride ; that is, n ultimate particles of hydrogen unite with n ultimate particles of chlorine to form 2n ultimate particles of hydrogen chloride. Since we cannot conceive of an ultimate particle of hydrogen chloride which does not contain at least one atom of hydrogen, the n ultimate particles of hydrogen must have contained at least 2n atoms. Hence each ultimate particle, or molecule, of hydrogen must contain at least two atoms. There are grounds, which cannot be dis- cussed here, for supposing that the molecule of hydrogen does not contain more than two atoms; hence we must conclude that the molecule of hydrogen contains two atoms. The argument may be similarly stated in the case of other gaseous elements. Secondly, the acceptance of Avogadro's hypothesis GASES 9 leads to a definite relationship between density and molecular weight. Suppose that D is the density of a gas, and that M is the weight of one molecule : let Dg and Ms represent the corresponding quantities for hydrogen. Suppose also that in unit volume of the gas at N.T.P. (that is, at normal temperature and pres- sure — 0° 0. and 1 atmosphere) there are n molecules; then, according to Avogadro, unit volume of hydrogen at N.T.P. also contains ii molecules. Now the ratio of the densities of two gases is equal to the ratio of the weights of equal volumes of the two gases, measured of course at the same temperature and pressure; hence D _ Weight of unit volume of the gas at N.T.P. _ n.M _ M Dh~ Weight of unit volume of hydrogen at N.T.P. ~ n . Mji~ Mu' As has been already shown, the molecule of hydrogen contains two atoms, and therefore the value of Mu is twice the atomic weight. On the basis of = 16, the atomic weight of hydrogen is 1*008, so that Mb = 2-01Q. If, further, it is agreed to refer the density of gases and vapours to that of hydrogen taken as unity, then Db = 1, and we have M=2-01QJ). In words, the mole- cular weight of a gas is approximately equal to twice its density (relatively to hydrogen). Thirdly, the adoption of Avogadro's hypothesis permits us to cast the equation pv=^^^T into a more general form, although it should be borne in mind that in so doing we are introducing a hypothetical element into what is otherwise an expression of purely experimental laws. It is obvious that if we take weights of two gases in the ratio of their molecular weights, we are taking an equal number of molecules in the two cases, which means, according to Avogadro's hypothesis, that we _ are taking equal volumes (measured, naturally, at the same temperature and pressure). Hence, if we are dealing with the molecular weight in grams of any gas, a gram- 10 PHYSICAL CHEMISTRY molecule, or ' mol ' as it is called, the volume occupied at 1 atmosphere and 0° C. should always be the same. This gram-molecular volume must be the volume occupied at 1 atmosphere and 0° C. by 2-016 grams of hydrogen or 32 grams of oxygen, and that has been found to be 22'4 litres. If, then, it is agreed that in applying the equation pqjzzz'^^T the quantity of gas considered is always 1 gram- molecule, the value of v^ for ^^=1 is the same in all cases. Hence the equation may be written p) =B,T, where R= -^1 is a constant for all gases. The actual numerical value of R depends on the units in which the pressure and volume are measured; if, forinstance, pressure is measured in atmo- 1 X 22*4 spheres and volume in litres, then R= „ =-082. Thp equation pv = RT is termed the gas equation, and is of the utmost importance, not only in connection with gases, but also in relation to the behaviour of dissolved substances, as will appear later. Whenever the equation is applied, it is understood that 1 gram-molecule of the substance is being considered. Determination of the Molecular Weight of Erases and Vapours. — As has already been pointed out, the accept- ance of Avogadro's proposition as a working hypothesis leads to a definite relationship between molecular weight and density, expressed by the equation M= 2-016i?, D being the density of the gas relatively to hydrogen. The deter- mination of molecular weight resolves itself therefore into a determination of density, and it is necessary to consider at least two of the practical methods available for this purpose. Regnault's Method. — Two spherical glass bulbs, each provided with narrow tube and stopcock, and of appro?d- mately equal volume, are required. The one is used merely as a counterpoise on the balance, the other is weighed (a) when completely evacuated, (&) when filled GASES 11 at known temperature and pressure with the gas under examination. The volume of the second bulb having been deduced from the quantity of water or mercury ^ ?3 ^ 1^2 which it contains, the difference of the weights (a) and (i) is the weight of a known volume of the gas atknown tempera- ture and pressure. From these data it is easy to cal- culate the weight of 1 cub. cm. of the gas at N.T.P., and the result so obtained is com- pared with the cor- responding figure for hydrogen. Victor Meyei's Method. — While Eegnault's method is specially applicable to substances which are gases at the ordinary tempera- ture, this second method is employed in the case of Tig. 1. 12 PHYSICAL CHEMISTRY substances which are normally liquid, but can be vaporised without difSculty. The necessary apparatus is sketched in the preceding diagram (Fig. 1). The glass tube A with cylindrical bulb B and the two side tubes C and D is suspended in the wide vessel E, so that the end of the bulb B is a short distance above the surface of the liquid which occupies the bottom of E. The glass rod F, which is pushed through the side tube C, is kept in position by indiarubber tubing; the elasticity of the latter allows F to be temporarily pulled clear of A without any dis- turbance of its permanent position. The end of the other side tube D is placed under a graduated tube full of water standing in the vessel G. When the apparatus has been set up the liquid in E is boiled and the rate of ebullition is adjusted, so that ultimately the greater part of the tube E is filled with vapour; the liquid in B must have a boiling point at least 20° above that of the liquid the vapour density of which is being deter- mined. The boiling of the liquid in E will obviously expel a certain amount of air from the bulb B and the tube A, but ultimately, when the ebullition is steady, the expulsion of air will cease, and there will be tem- perature equilibrium between the inner vessel and the surrounding vapour. This state of equilibrium has been reached when after the insertion of a stopper in the top of the tube A no bubbles of air are expelled through D. A small bottle containing a weighed quantity of the liquid under examination is then dropped through the top of A on to the end of F, and the stopper is re-inserted. When the rod F is pulled back for a moment the bottle falls to the bottom of B, in which a little glass wool has previously been placed to prevent fracture. At the temperature which prevails in B the liquid is rapidly vaporised and a corresponding quantity of air is expelled GASES 13 in siiccessive bubbles from the end of D. The air thus collected in H is the exact equivalent of the Vapour produced in B, and when no more bubbles are expelled, its volume is found by transferring H to a cylinder full of water and measuring at known temperature and pressure in the usual way. Since this volume of vapour has been produced from the known weight of the liquid taken, the weight of 1 cub. cm. of the vapour at N.T.P. may easily be calculated ; the density is then obtained by comparing this result with the corresponding figure for hydrogen. An example may be taken to show how the data obtained in an experiment with Victor Meyer's apparatus are used to calculate the density, and from that the molecular weight. In a particular case 0*1 gram of a substance was weighed out and vaporised in a Victor Meyer apparatus. The expelled air was collected over water and found to measure 32 cub. cm. at 17° 0. and 750 mm. pressure. Now the tension of aqueous vapour at 17° is 14-4 mm., and the volume of air expelled, when allowance has , „ ^,. ^ . , 32 X 273 X (750 -14-4) been made tor this tension, becomes 290x760 = 29-16 cub. cm. at N.T.P. This, then, would be the volume of vapour produced if O'l gram of the substance were vaporised at N.T.P., and it follows that the weight of 1 cub. cm. of the vapour at N.T.P. would be ggTjg gram. The weight of 1 cub. cm. of hydrogen under these con- ditions is -00009 gram, and therefore the density of the vapour (relatively to hydrogen) is gg.iex-OOOOa '^^^"-^ ' *^® mole'oular weight is then 38-1 X 2-016 = 76"8. Gaseous Diffusion. — One characteristic feature of a gas as compared with a liquid or a solid is its ability to occupy f uUy any space which is offered to it ; it is capable of infinite expansion, and more than that, the occupation of any vacant space by a gas is accomplished with great 14 PHYSICAL OHEMISTEY rapidity. Again, when two vessels containing two dif- ferent gases at the same pressure are put into com- munication witii each other, a process of difEusion goes on until the composition of the gaseous mixture is the same at all points. Each gas moves from places where its concentration is high to places where its concentration is low, and equilibrium is not attained until the partial pressure of each gas is the same throughout. Such diffusion or mutual interpengtration is quite distinct from movement of the gas as a whole. A difference of gas pressure in two places may be equalised by mass move- ment — air currents, for example — ^but difEusion goes on where sach movement is excluded ; it is a molecular process. The kinetic gas theory, which has so far been discussed only in its bearing on Boyle's law and Gay-Lussac's law, supplies a plausible interpretation of these diffusion phenomena. If, as the theory supposes, each molecule is moving at a high speed (a mile per second, more or less, according to , the density and the temperature of the gas), it is intelligible that a gas brought in contact with a vacuous space should occupy the latter practically instantaneously. On the other hand, 'when one gas is diffusing into another gas the rate of advance is naturally much slower, for the forward path of each molecule, on account of the frequent collisions with the molecules of the other gas, is of a zigzag character. One of the conclusions which can be deduced from the assumptions of the kinetic gas theory is that the velocity with which a gaseous molecule is endowed is inversely proportional to the square root of the density of the gas. It follows from this, for instance, that the hydrogen molecule has a velocity four times as great as that of the oxygen molecule at the same temperature, for oxygen is sixteen times as heavy as hydrogen. If, then, we are correct in suggesting that diffusion pheno- GASES 15 mena are closely related to molecular velocity, we may expect to find a definite connection between the rate of diffusion and the density of a gas. In circumstances where the molecular movement alone comes into play, the rate of diffusion of a gas ought in fact to be inversely proportional to the square root of its density. This important relationship was verified by Graham i in his experiments on the rate of passage of different gases' through minute apertures into a vacuum. The experiments consisted in determining the times required for a given volume of various gases kept at steady pressure to pass throjigh a minute perforation in a metal plate into a" receiver which was being constantly eva- cuated. Graham found that the time required for the escape, or ' effusion ' as he called it, of a given volume of any gas was proportional to the square root of its density ; in other words, the velocity of effusion of a gas is in- versely proportional to the square root of its density. Some of Graham's resylts are recorded in the accom- panying table. The times necessary for the effusion of a certain volume of gas are given in the second column, while in the third column are the figures calculated on the assumption that the time of effusion is proportional to the square root of the density; in both cases the time required for the effusion of air is taken as unity. Time of Effusion. Gas. Experiment. Tlieoty. Air 1 1 Nitrogen 0-984 0-986 Oxygen 1050 1-052 Hydrogen 0-276 0-263 Carbon Dioxide .... 1-197 1-237 This relationship has been confirmed by Bunsen,^ who hag further based on it a method for the approximate deter- mination of the density of a gas. ' Graham, Chemical and Physical Researches, p. 95. " Oasometry, p. 121. 16 PHYSICAL CHEMISTRY The rate of passage of a gas through a capillary tube into a vacuum is not inversely proportional to the square root of the density ; the friction at the interior surface of the tube comes in as a disturbing factor. The velocity of diffusion of one gas into another through a porous diaphragm is inversely proportional to the square root of the density only when the diaphragm is extremely thin. Static Diffusion of Carbon Dioxide. — Another in- teresting phenomenon in the same field as the fore- going is the diffusion of a gas through a tube, at one end of which its concentration is kept either at zero or at some constant low value. This case is interesting because of its bearing on the absorption of carbon dioxide at the surface of a leaf. The gas exchange between the atmosphere and the assimilating <;ells of a leaf is at one stage simply a process of diffusion through the stomata alone, for Black- man has shown ^ that if these are blocked up no appreci- able diffusion of carbon dioxide into the leaf takes place. This being so, the diffusion of carbon dioxide through the stomata must be relatively rapid; indeed, in the case of a certain leaf examined by Brown and Escombe* the stomatic openings were fouiid to absorb per sq. cm. of their area as much as 7"77 cub. cm. of carbon dioxide per hour, a figure which is about fifty times as great as the absorption per unit area of a freely exposed solution of caustic alkali- The question whether this was possible led Brown and Escombe to study the free diffusion of carbon dioxide through small apertures into cavities with a comparatively large absorbing surface. These investigators found that if a tall cylinder com- municating freely with the atmosphere contains at the 1 PhU. Trans., B, 1895, 186, 485, 503. " Ibid., B, 1900, 193, 223. GASES 17 bottom a layer of caustic alkali, there is a regular flow or drift of carbon dioxide down the cylinder. Provided that the air outside the cylinder is of uniform com- position, and the air inside is free from convection currents, a static condition of affairs is established analogous to what is observed when one end of a metal bar is kept at a high temperature and the other end at a low temperature. When the steady condition of diffusion has been attained the rate of flow of the carbon dioxide, as deduced from the amount absorbed, is found to be inversely proportional to the length of the diffusion column. This is what might be expected on general" grounds, for the gradient of the line joining two points of fixed different altitude diminishes as the distance between the two points increases. When now a diaphragm with, a circular aperture is placed at the free end of the diffusion column, the pro- cess of diffusion and absorption is modified in a re- markable manner. As the size of the aperture is diminished, the diffusive flow per unit area of aperture increases rapidly, and when the area of the aperture has become small in comparison with the sectional area of the tube, the amount of diffusing gas is proportional to the diameter of the aperture, not, as' one might expect, to its area. This bare statement of results is illustrated by the following figures from Brown and Escombe's paper: — Diameter ofAperture in mm. 22-7 1206 5-86 3-23 2-12 Carbon Dioxide diffused per Hour in cub. cm. •2380 ^ -0928 •0556 •0399 ■0261 CO2 diffused per sq. cm. of Aperture per Hour in cub. cm. •0588 ■0812 •2074 •4855 •8253 Batio of Areas of Apertures. 1^00 •28 •066 •023 ■008 Katio of Diameters of Apertures. Batio of Total CO2 diffused per Hour. These figures make it plain that the 1-00 •53 •25 •14 •093 diffusive B 100 •39 •23 •16 •10 flow, 18 PHYSICAL CHEMISTRY especially in the case of the smaller apertures, is pro- portional, not to the area of the aperture, but to its diameter. A similar ' diameter law ' has been estab- lished for the diffusion of water vapour into flasks con- taining concentrated sulphuric acid as absorbent, and for the evaporation of water through narrow apertures into desiccated air. Diffusion through a Multi-perforate Diaphragm. — When a diffusion tube, such as that already described, is covered with a diaphragm containing many small apertures, the diffusive flow is checked to a remarkably small extent. In Brown and Escombe's experiments diaphragms were employed containing 100 perforations (0"38 mm. diameter) per sq. cm. of diaphragm surface. Although the area of the apertures was in this case only about one-ninth of the total area of the diaphragm, the amount of diffusion through the perforations was as great as when there was no diaphragm at all. The obstruction, therefore, which is offered to a diffusive flow by a multi-perforate diaphragm may be nil, and is certainly surprisingly small. This striking result is to be referred to the intensification of the diffusive flow which, as shown by the figures already quoted, accompanies the gradual decrease of aperture. Provided that the perforations in a multi-perforate septum are not too close, each aperture acts independently of the others, according to the diameter law. The surface of a leaf, regarded as a purely physical apparatus for the diffusion of atmospheric carbon dioxide to the assimilating centres, resembles a multi-perforate diaphragm. The amount of carbon dioxide, then, which enters the stomata will (1) depend on the gradient of density, and therefore on the extent to which the carbon dioxide concentration in the respiratory cavity apiDroaches zero, (2) be proportional to the linear dimensions of GASES 19 the stomatic openings. In view of the fact that the stomatic openings are elliptical in shape, the question may be raised, What is the linear dimension of such an aperture ? The answer is based on a study of evapora- tion from circular and elliptical surfaces of equal area, and is to the effect that, so far as diffusion is concerned, an elliptical tube is equivalent to a cylindrical tube having the same area of cross-section. As regards the gradient of density in connection with the absorption of carbon dioxide by a leaf, the conditions will be most favourable when the partial pressure of the atmospheric carbon dioxide at the surface of the leaf is kept constant by a movement of the air. If the leaf is in perfectly still air, there will be a density gradient for the carbon dioxide outside the stomatic openings also, and the maxi- mum possible absorption of the gas by the leaf will be somewhat diminished. From Brown and Escombe's researches on the leaf of Eeliaivthus annuus, it appears that the actual intake of carbon dioxide is only a small fraction of the amount which the diffusion mechanism of the leaf surface, re- garded as a multi-perforate septum, is able to deliver. It follows that the partial pressure of the carbon dioxide in the respiratory cavity can be only slightly less than in the atmosphere outside. The passage of carbon dioxide from the air to the assimilating. cells is probably most retarded at the walls of the latter. In order to penetrate these the gas must pass into solution in the water with which they are charged, and the subsequent process of liquid diffusion is very slow compared with gaseous diffusion. CHAPTER II ABSORPTION OF GASES BY LIQUIDS Solubility and Absorption. — It will be clear from the closing paragraph of the last chapter that in the gas exchange between an organism and the atmosphere there are other factors involved besides gaseous diffusion. The gases, both those which are being absorbed and assimi- lated and those of which the organism is ridding itself, pass into solution at some stage or other of the exchange, and the facilities for such an exchange will therefore depend on the extent to which the gases are soluble in the solvent fluid. The power of a liquid to dissolve a gas varies very markedly with the nature of the gas, and the solubility of a given gas in a given liquid depends on the tem- perature and the pressure at which the absorption takes place. As regards the first of these factors, it is found in almost all cases that the solubility of a gas in a liquid diminishes as the temperature rises. The relationship between the solubility of a gas and the pressure under which the absorption takes place is comparatively simple, and is embodied in Henry's law. Henry's Law. — According to this law, the quantity of a gas (either weight, or volume at N.T.P.) dissolved by a given volume of a given liquid at a given tem- perature is directly proportional to the pressure under which the absorption takes place; if, for instance, the on ABSOEPTION OF GASES BY LIQUIDS 21 pressure on the gas is doubled, twice as much of it will be forced into solution. With what accuracy Henry's law represents the facts may be judged from the numbers in the following table, which refers to the solubility of carbon dioxide in water. P is the pressure (in cm. of mercury) under which the absorption takes place, and V is the volume of carbon dioxide (measured at N.T.P.) which is absorbed by 1 cub, cm. of water at 15°; according to Henry's law the ratio — should be a constant. V p' 0-0135 0-0144 0-0145 0-0147 0-0146 0-0145 If we were to plot the weight of gas dissolved against the pressure under which the absorption takes place, then the curve obtained in the case of a gas which strictly obeys Henry's law would be a straight Una. Deviation from the law occurs when there is chemical action between the gas and any substance present in the absorbing liquid In such a case the relation between the pressure and the quantity of gas absorbed is not a linear one. If, then, the study of the mutual behaviour of a gas and a liquid shows that the quantity of gas absorbed by the liquid is not a linear function of the pressure, it may. safely be concluded that the gas is entering into chemical union with some constituent of the liquid. An instance of this will be quoted later on. The definite relationship between a gas and an ab- sorbent liquid is frequently expressed by means of the 'absorption coefficient.' This is defined as the volume p. 7. 69-8 0-944 128-9 1-865 200-2 2-908 236-9 3-486 273-8 4-003 311-0 4-501 22 PHYSICAL CHEMISTEY of the gas (reduced to N.T.P.) which is absorbed by unit volume of the liquid under normal pressure (i.e. 1 atmosphere). The statement, for instance, that the ab- sorption coefficient of oxygen in water at 20° is O'OSl, means that 1 cub. cm. of water at 20° absorbs under 1 atmosphere pressure 0-031 cub. cm. of oxygen (measured at N.T.P.). The following table shows the values of the absorption coefficient for some common gases in water : — Temperature. Oxygen. Nitrogen. Carbon Dioxide. 0° •0489 •0239 1-713 10' ■0380 •0196 1-194 20=' •0310 •0164 0-878 30° •0262 •0138 0-665 40° •0231 •0118 0-530 The figures quoted show that oxygen is more soluble in water than nitrogen, that carbon dioxide is much more soluble than either oxygen or nitrogen, and that in all cases the solubility diminishes as the temperature rises. Sometimes the relationship between a gas and an ab- sorbent liquid is expressed, not by the absorption coeffi- cient, but by the ' solubility,' defined as the volume of gas (measured at t° the temperature of experiment) which is absorbed by unit volume of the liquid under any pressure. If A represents the absorption coefficient and I the solubility, the relation between them is given by the equation l = A{l+at). Diffusion of a Gas through a Liquid Film. — The velocity of diffusion of a gas through a very thin porous septum is closely related, as we have already seen, to the density of the gas. But a new factor has to be taken into account when we are dealing with the passage or diffusion of a gas across a liquid film. The velocity of this diffusion depends on the power of the liquid to dissolve the gas, and is, as a matter of fact, directly pro- portional to the absorption coefficient of the gas in the ABSOEPTION OF GASES BY LIQUIDS 23 liquid. The direction of diffusion in such a case is natu- rally from the side of the film where the pressure of the gas is high to the side where it is low, the gas being taken into solution at the one surface and passed out of solution at the other. Other things being equal, the amount of gas diffusing across such a film in a given time wiH be proportional to the difference in the pressure of the gas on the two sides. That the solubility of a gas is all-important in deter- mining the velocity of its diffusion across a liquid film has been shown by Exner^ for soap bubbles, and by Wiesner and Molisch ^ for vegetable membranes impreg- nated with water. In both these cases carbon dioxide, although twenty-two times heavier than hydrogen, dif- fuses much more rapidly than the latter, for the absorp- tion coefficient of hydrogen is small, and of the same order of magnitude as those of oxygen and nitrogen quoted above. Similarly, carbon dioxide diffuses through moist vegetable membranes much more rapidly than oxygen, a fact which is of importance in relation to the gas exchange between the plant and the atmosphere. It should be noted that the presence of water is essential to the diffusion, for the air-dried membranes are almost, if not altogether, impermeable to" these gases.* The difference between an easily soluble and a spar- ingly soluble gas in connection with diffusion across a film of water is easily demonstrated. For this purpose the apparatus shown in Fig. 2 may be employed. The one end of a short, wide tube a is opened out slightly, and a piece of pig's bladder is tied over it and well sealed. The other end is closed by a rubber stopper » Sitmngsher. k. Ahad. Wiss. Wien, 1874, 70, ii. 465. ^ Ibid., 1889, 98, i. 670. ' Wiesner and Molisch, loc. dt. ; see also Steinbrinck, Ber. deviach, Bot. Oea., 1900, 18, 275. 24 PHYSICAL OHEMISTEY carrying a tube b, wMch. in its turn is connected with some arrangement for indicating changes of pressure. T In the apparatus sketched in Fig. 2, any increase of pressure in a is transmitted to the surface of the coloured liquid in c, and the liquid is forced up the tube d. If now, when the membrane has been impregnated with water and the apparatus has then been set up, a beaker is inverted over a and filled with hydrogen, no appre- ciable movement of the liquid in d is observed. A positive result, however, is obtained when the hydrogen in the beaker is replaced by a gas which is very soluble in water; with ammonia, for instance, a distinct rise of the liquid in d is ob- served in a very short time. The power of water to dissolve oxygen and carbon dioxide is an all-important fact in connection with aquatic plants. The possibility of gaseous interchange between the air and the cells of the submerged plant depends in the first place on the diffusion of oxygen and carbon dioxide through the medium surrounding the plant, for if the medium is freed and kept free from air the plant dies. In general the epidermis of the sub- merged leaf is not cuticularised, and is un- provided with stomata. It is, however, impregnated with water, and the exchange of oxygen and carbon dioxide between the surrounding medium and the interior of the leaf consists in a difEusion across this water- logged layer. It has been shown ^ that this diffusion across 1 Devaux, Ann. Sci. Nat., 1889, [vii.], 9, 35. Fig. 2 ABSOEPTION OF GASES BY LIQUIDS 25 the walls of submerged plants is subject to the same laws as regulate the passage of gases across a film of water. The gaseous interchange of aquatic plants must there- fore be a comparatively slow process, but in the character- istic development of intercellular spaces there is a mechanism which deals with this diificulty. By this means the oxygen and carbon dioxide liberated in the processes of assimilation and respiration respectively are kept available for future use. Thus it is that those parts of aquatic plants which lie in the mud at the bottom are supplied with oxygen without depending on the slow diffusion of this gas through the surrounding water.^ Another point of interest in connection with the gas exchange of aquatic plants is the fact that marine algas flourish more luxuriantly in arctic than in tropical waters* This is due to the greater solubility of carbon dioxide in water at low temperatures and the resulting increase in the facilities for gaseous interchange. Various investigators regard the gas exchange which takes place through the walls of the lungs as determined simply by the principles which govern the diffusion of a gas across a liquid film.^ It has been estimated th^,t the lung surface, regarded as a purely physical apparatus, would allow the diffusion of about 1450 cub. cm. of oxygen per minute in the case of an adult, and some physiolo^sts hold, therefore, that there is no need to assume the existence of a special secretive power in the lung membrane. This is a point, however, on which there appears to be considerable difference of opinion, many physiologists ' holding, on the other hand, that the lung membrane is the scene of a special secretive action. They maintain that the pressure of oxygen in the blood * See Goebel, PflanzenbiologisoJie Schilderwngen, ii. 252. 2 A. and M. Krogh, Slcand. Arch. Physiol, 1910, 23, 179. ' See Bohr, Nagel'a Handbuch der Physiologie, i. 142 ; Douglas and Haldane, Journ. Physiol., 1912, 44, 30B. 26 PHYSICAL CHEMISTRY is, under certain circumstances, higher than that in the lung cavities. If this is so, then the actual direction of diftusion is opposed to that which the physical law demands. The air-bladder of fishes is undoubtedly a case in which we must assume a special secretive activity. By keeping a fish alternately at the surface and at various depths below the surface it is possible to bring about varia- tions in the percentage of oxygen in its air-bladder. This organ is the scene of a secretion of oxygen, and the process is under the control of the nervous system.^ Solubility of Gases in Salt Solutions. — As a general rule, a gas is less soluble in a salt solution than it is in pure water at the same temperature, and the more concentrated the salt solution the greater is the lower- ing of the solubility. It is on an analogous principle that the ' salting out ' of organic compounds, sparingly soluble in water, is based. The lower absorptive power of salt solutions may be illustrated by the following figures for the solubility of oxygen at 25° in half-normal, normal, and twice-normal solutions of sulphuric acid and sodium chloride ; the solubility of oxygen' in pure water at this temperature, it should be noted, is 0"0308 : — Sulphuric acid 0-0288 0-0275 0-0251 Sodium chloride 0-0262 0-0223 0-0158 It is interesting to contrast with this the power of blood to absorb oxygen. Amongst other things blood contains in solution appreciable quantities of salts, and hence, in accordance with the general rule just discussed, one might expect the solvent power of blood for gases to be lower than that of water at the same temperature. 1 Bohr, loo. cit., 163. ABSOEPTION OF GASES BY LIQUIDS 27 Now at 15° 0. and 150 mm. pressure (that is, tte partial pressure of oxygen in the air) 100 cub. cm. of water can absorb about 0'7 cub. cm. of oxygen, but 100 cub. cm. of dog's blood absorbs under these conditions about 24 cub. cm. of that gas. If the blood is centrifuged, and the corpuscles are thus separated from the plasma, it can be shown that 100 cub. cm. of the latter take up under the afore-mentioned conditions 0*65 cub. cm. of oxygen. The solvent power of the plasma is therefore slightly less than that of water, and it is evidently the corpuscles which are responsible for the greater absorptive power of blood as a whole compared with water. This difference between the plasma and the blood as a whole is brought out also by a study of the way in which the quantities of oxygen dissolved in the two media are affected by altering the pressure under which the absorption takes place. In the case of the plasma the quantity of gas dissolved is proportional to the pressure — a behaviour in strict accordance with Henry's law. With the blood as a whole, 'on the other hand, there is no such proportionality. At low pressures the increase in the amount of gas dissolved for a given rise of pressure is much greater than at high pressures; the quantity of oxygen taken up by the blood at 760 mm. pressure is not very much greater than the quantity absorbed under 150 mm. pressure, although on the basis of Henry's law it ought to be about five times as great. The ac- companying figure (Fig. 3) will make clear the essen- tial difference between blood and plasma in relation to oxygen. As has already been pointed out, deviation from strict adherence to Henry's law means that the gas is entering into combination with the solvent or with something dissolved in the solvent. So it is in 'this case ; the absorption of oxygen by the blood is not merely a 28 PHYSICAL CHEMISTRY physical process; the gas is chemically fixed by the haenioglobiii in the corpuscles, and as the formation of the compound is tolerably complete at low pressures, the form of the upper curve becomes intelligible. The absorption of carbon monoxide and carbon dioxide by the blood is, it should be noted, subject to similar influences. A brief reference has already been made to the general Blood Oxygen Pressure Fig. 3, rule, that a gas is less soluble in a salt solution than in pure water at the same temperature. In addition to salts, acids, and bases, however, there are other substances such as sucrose (cane sugar), which have a similar effect in lowering the solubility of gases. The question as to the cause of this influence has lately attracted a gbod deal of attention, inasmuch as it appears to be closely related to the larger question of the possible hydration of dissolved substances, and therefore also to the im- portant problem of the nature of solution. One salient fact which has emerged in the .study of ABSORPTION OP GASES BY LIQUIDS 29 the influence of salts on the solubility of gases is, that the relative effects of different salts are nearly inde- pendent of the particular gas employed. It has been found that when a number of salts are arranged according to the magnitude of their influence on the solubility of one gas, the order is in general the same as when they are arranged according to the magnitude of their influence on the solubility of another gas. It follows, therefore, that the diminished solvent power of a salt solution as compared with water is mainly determined, not by the specific nature of the dissolved gas, but by some factor which is involved in the relationship of the water and the salt. In support of this conclusion a number of salts, acids, and bases are arranged in the following table ^ according to the magnitude of their influence at the same concen- tration on the solubility of carbon dioxide (I.), hydrogen (II.), and nitrous oxide (HI.)- The substances are so arranged that the influence increases from the top to the bottom of the column, and it will be observed that the relative positions are nearly the same in each case. L n. III. HNO3 HNO3 HNO3 HCl HOI HCl H2SO4 H2SO4 H2SO, CsGl LiOl OsOl KNO3 KNO3 KNO3 KI KOI KI RbCl NaNOg KBr KBr NaOl LiCl KOI KOH BbOl NaOl NaNO, KOI KOH Another important experimental result which must be kept in view by any one who attempts an inter- 1 See Geffoken, Zeit. pkysikal. Chem , 1904, 49, 284. 30 PHYSICAL CHEMISTRY pretation of these phenomena is, that the influence of a given salt in lowering the solubility is greatest in dilute solution. To extract this result from the actual experimental data, it is necessary to deal with what is known as the 'equivalent relative lowering of the solu- bility.' Suppose that Iq is the solubility of a gas in pure water, and that I is its solubility in a salt solution containing n gram equivalents per litre, then If^ — l is the lowering of solubility and -^P- is the relative lower- ing of solubility. As a glance at the table on p. 26 will show, the value of -^j— increases as the concentra- tion of the salt solution increases. If, however, we compare the values of - . A—, the equivalent relative lowering of the solubility, that is, if we take the values of the relative lowering per gram equivalent of salt, there is a decrease as the concentration of the salt solution increases. That means, to take a special case, that the efficiency of sodium chloride in lower- ing the solubility of a gas is in normal solution less than twice as great as the efficiency of this salt in semi-normal solution. The following data, relating to the lowering of the solubility of hydrogen at 15° by sodium chloride and potassium nitrate, will make this point clear ; the figures in the table are the values ««.'■ Concentration of Sodium Salt Solution. Chloride. Potassium Nitrate. 1-0 normal -22 •19 2'0 „ -20 •16 3-0 „ -18 •14 The fact that the value of - ' n • ^ — increases with dilution is a result of the utmost importance, for it shows that the cause which is at work in lowering the ABSORPTION OF GASES BY LIQUIDS 31 solubility is relatively most potent in dilute solutions. It has sometimes been suggested that the influence of salts on the solubility of gases is specially marked in concentrated solution, but the experimental evidence is distinctly opposed to this view. Interpretations of the Lowering of the Solubility of Gases. — It would be going beyond the scope of this volume to discuss in detail the attempts that have been made to interpret the effect which salts and some non- electrolytes have on the solubility of gases. It is, how- ever, desirable to indicate briefly what explanations have been suggested. First, it has been maintained that the influence exerted by a salt is connected with the internal pressure of the solution. When a salt is dissolved in water, there is an increase of the internal pressure, which is regarded as equivalent to a corresponding increase of the external pressure. This would mean an extra resistance offered to any increase in the bulk of the liquid, such an increase, for instance, as that which results from the absorption of a gas. Owing, then, to the increased resistance to expansion brought about by the salt, less gas will be absorbed by a salt solution than by pure water. Some workers who adopt this first line of explanation prefer to deal with compressibility instead of internal pressure, maintaining that the power of a liquid to dis- solve a sparingly soluble gas is quantitatively related to its compressibility.^ Attention is drawn to the paral- lelism between the lowering of compressibility and the lowering of gas solubility which are the result of add- ing salts to water. Secondly, it has been suggested that the lower solvent ' Ritzel, Zdt. phyaikal. Ohem., 1907, 60, 319. 32 PHYSICAL CHEMISTRY power of a salt solution as compared with water is due to the hydration of the dissolved salt.^ Part of the water in a salt solution is supposed to be in com- bination with the salt, the solvent which is thus appro- priated by the salt being no longer free to absorb gas. The influence of some non-electrolytes^ in lowering the solubility of gases may be regarded from the same point of view. If it is supposed that the non-electrolyte or electrolyte, as the case may be, is not responsible for any absorption, then the solvent powers of different salt solutions for gases can fairly be compared only when we put side by side the figures for a definite quantity of solvent in each case ; we must consider the quantity of gas absorbed, not by unit volume of the solution, but by that volume of solution which contains unit volume of the solvent. For it must be borne in mind that in many cases 1000 cub. cm. of a -concentrated aqueous solution do not contain anything like 1000 grams of water. A litre of a 10 per cent, sucrose solution, for instance, contains at ordinary temperatures only about 934 grams of water. On the basis of these assumptions, it is possible to calculate from the lowering of the absorption coefficient the ' average molecular hydration ' of a dissolved electro- lyte or non-electrolyte, that is, the number of molecules of water which on the average are attached to one molecule of dissolved substance. In the case of sucrose, to take a special instance, the average molecular hydration is about 6, a figure which agrees well with the values obtained by other methods.* 1 Rothmund, Zeit. physikcd. Chem., 1900, 33, 413 ; Philip, Trams. Faraday Soo.^WOl, 3, 140. " That is, substances like sucrose or dextrose, the aqueous solutions of which do not conduct the electric current to any appreciable extent. ' See Jones and Getman, Amer. Ohem. Journ., 1904, 32, 319 ; Callendar, Proc. Roy. Soc, A, 1908, 80, 499. CHAPTER III OSMOTIC PRESSURE Diffusion and Osmotic Pressure. — In a previous chapter reference has been made to the diffusion of gases, to the tendency they exhibit to move from places where the concentration is high to places where the concen- tration is low. Diffusion, however, is a phenomenon which is characteristic not only of gases but also of solutions, and in the latter case also is to be regarded as a mole- cular movement, not as a jpovement in mass. If a layer of strong sugar solution is put at the bottom of a tall cylinder, and water is carefully added, with as little mixing as possible, a process of diffusion commences which does not cease until the sugar concentration is the same at all points throughout the liquid. The sugar moves from places where its concentration is high to places where its concentration is low, although naturally, owing to the greater friction, the rate of movement is very much below that observed in gaseous diffusion. In addition to recognising this common characteristic of diffusion we may, in considering the analogy between gases and dissolved substances, go a step further, and regard the movement as due in each case to a pressure. Just as we speak of the pressure of a gas driving the molecules from places of high concentration to places of low concentration, so we may, by way of analogy at least, regard the molecules of a dissolved substance 33 C 34 PHYSICAL CHEMISTEY as diffusing under the influence of a pressure — ^the osmotic pressv/re, as it is called. Semi-permeable Membranes. — Gaseous pressure may be realised and measured at some surface interposed to prevent further expansion. Similarly, osmotic pressure might be realised and measured at some surface inter- posed to prevent further expansion, that is, diffusion, of the dissolved substance. If, however, this surface (some kind of membrane, for instance) is to reveal to us and enable us to measure the tendency to expansion of the dissolved substance only, then it must allow free passage to the solvent and block the further advance of the dissolved substance ; it must differentiate between solvent and solute ; it must be ' semi-permeable.' Given that a solution is separated from the solvent by a surface or membrane satisfying these specified conditions, then diffusion of the dissolved njbstance is impossible. Such a system, however, is not in equilibrium, for, so long as no hydrostatic pressure develops, equilibrium would be reached only when the concentration of the dissolved substance is the same on both sides of the membrane. Since diffusion of the dissolved substance is barred, the system seeks to get into the condition of equilibrium in the only other way which is possible, namely, by water passing through the membrane into the solution. This, then, would be the effect of interposing a semi- permeable membrane between solvent and solution, and the next question that arises is. Are such membranes known? The answer is in the affirmative, for certain membranes have been discovered which are readily permeable to water and are found to be practically 'impermeable to various dissolved substances. There is, for instance, the membrane which is formed when a drop of copper sulphate solution, on the end of a narrow OSMOTIC PEESSURE 35 glass tube, is introduced into a solution of potassium ferrocyanide. At the common surface qf the two solu- tions copper ferrocyanide is deposited as a thin trans- parent skin surrounding the drop of copper sulphate. Once the skin has been formed the precipitation of copper ferrocyanide ceases, the solutions on either side remaining clear; this obviously means that neither copper sulphate nor potassium ferrocyanide can penetrate a membrane of copper ferrocyanide. This membrane has been found to be impermeable also to various other substances, notably sucrose and dextrose; it may there- fore be described as semi-permeable in regard to (1) water and sucrose, and (2) water and dextrose. When an aqueous solution of sucrose, then, is separated from water by a membrane of copper ferrocyanide, we may hope to observe the passage of water into the solution, which has already been described as an inevit- able occurrence in such a system. For the purpose of quantitative measurement, and even for the purpose of qualitative demonstration, the easily ruptured membrane of copper ferrocyanide must be supported on some more or less rigid framework. It may, for instance, be de- posited in the walls of a small porous pot of unglazed porcelain. The pot which is to be used for this purpose must be well washed, and its walls must be thoroughly impregnated with water. It is then filled nearly to the top with a dilute solution of copper sulphate (2*5 grams per litre), and allowed to stand for a considerable time in a dilute solution of potassium ferrocyanide (2"1 grams per litre). Under these circumstances the salts diffuse through the walls of the pot, meet in the interior, and deposit a film of copper ferrocyanide. When the for- mation of the membrane is complete the pot is thoroughly washed and soaked in water; it is then ready for use in a way to be described presently. 36 PHYSICAL CHEMISTRY There is another method* of preparing a membrane of copper ferrocyanide for the purpose of demonstration — a method which is in some ways preferable to the first. One end of a glass tube, 50 mm. long and 10 mm. in diameter, is dipped in 20 per cent, gelatin^ to which a little potassium dichromate solution has been added. The gelatin film which is thus formed over the end of the tube becomes insoluble in water if allowed to dry in the light ; it may then be soaked in water to reraove the potassium dichromate. The glass tube is thus closed at one end by a diaphragm of insoluble gelatin, in which a serni-permeable membrane of copper ferrocyanide may be deposited. A solution of copper sulphate of the strength already specified is put inside the little cell, which is then immersed in potassium ferrocyanide solution. The gelatin diaphragm, which of itself is practically colour- less, soon begins to assume a brown colour ; this gradu- ally deepens until the formation of the membrane is complete. The vessel carrying the membrane, either the porous pot or the glass tube with the gelatin diaphragm, is then charged with sugar solution, and a rubber stopper carrying a tube of narrow bore is inserted and made tight with a suitable cement. When the pot or glass tube is immersed in water, the level of the liquid in the narrow tube soon begins to rise slowly, and, if the membrane has been well made, ultimately attains a considerable height. If the membrane were strong enough, and no leaks were sprung, water would continue to pass through the membrane until the hydrostatic pressure of the liquid column balanced the tendency of the water to force its way in. In most cases, however, where no special precautions have been taken, the cell breaks down long before this condition of equilibrium has been reached. ' TammauD, Zeit. physikai. Ohm,., 1892, 10,700. OSMOTIC PRESSUEE 37 The Semi-permeable Covering of Barley Grains. — In addition to copper ferrocyanide and other similar preci- pitation membranes, there are numerous plant and animal membranes which are permeable to water but imperme- able to many dissolved substances ; they are therefore semi-permeable. An interesting case of a semi-permeable membrane in the vegetable world was described lately by Brown.^ He has shown that certain barley grains (Hordeuvi vulgare var. ccerulescens) have a covering which exhibits selective action when placed in aqueous solutions of sulphuric acid and various other substances ; water is absorbed by the grains, whilst the dissolved substance cannot gain an entrance. That sulphuric acid cannot penetrate the covering of the grain is shown by the fact that a blue pigment which is present in the aleurone cells, and which is turned red by acids, remains unaffected when undamaged barley grains are soaked in sulphuric acid. On the othei; hand, any grain the covering of which is imperfect or has been purposely perforated, at once begins to exhibit the colour change denoting the access of acid to the interior. Grains which have been exposed to the action of boiling water for thirty minutes, and which, after this treatment, have lost all power of germinating, behave in the same way as untreated grains, so that the semi-permeable character of the covering does not depend on the activity of living protoplasm. A sugar solution separated from water- by a membrane of copper ferrocyanide draws water through the membrane, and similarly the contents of barley grains steeped in pure water attract water (up to about 70 per cent, of their weight) through the semi-permeable covering with which they are surrounded. If it were possible to replace the contents of a barley grain by a solution of sulphuric acid, then on steeping in water the same phenomenon » Annda Bot , 1907, 21, 79; also Proc. Roy. Soc, B, 1909, 81, 82. 38 PHYSICAL CHEMISTEY would be observed as in the case of the actual barley grain — water would enter through the semi-permeable cover- ing. We may therefore regard the barley seed contents and a solution of sulphuric acid as both capable of attracting water across a semi-permeable membrane, and hence the steeping of barley grains in a solution of sulphuric acid results in a competition for water between the seed con- tents and the sulphuric acid. In this connection the experiments made by Brown with solutions of sodium chloride are interesting. This salt resembles sulphuric acid in being unable to penetrate the covering of the barley grain, and in the competition for water between the seed contents and a solution of sodium chloride the amount of water which the former can attract depends on the concentration of the salt solution. As this is raised, the barley grains absorb less and" less water : the amount absorbed from a 2 per cent, salt solution is about 41 per cent, of the weight of the seeds, while from a saturated salt solution it is only about 14 per cent. By way of contrast, it is instructive to find that when barley grains are steeped in a solution of a substance which can pene- trate the seed covering {e.g. acetic acid or ethyl alcohol) the amount of water absorbed is nearly the same as when they are steeped in pure water. There is in this case no competition for the water. Another illustration of the comparative impermeability of seed coverings to certain substances is found in the use of copper sulphate as a fungicide. This salt is highly poisonous for the vegetable organism, and yet it is possible to steep wheat in a solution of copper sulphate and so destroy any adherent fungus spores without affecting the vitality of the seed itself. Pfeffer's Work on Osmotic Pressure. — At the begin- ning of this chapter osmotic pressure has been referred to as the driving force under the influence of which the OSMOTIC PEESSUEB 39 molecules of a dissolved substance diffuse. Witli the interposition of a semi-permeable membrane between sol- vent and solution, diffusion of the solute becomes im- possible, and the corresponding reverse movement of solvent into solution is observed. The driving force be- hind this movement is opposite in direction to the osmotic pressure, but is equivalent to it. Hence if we can measure the tendency of water to pass into a solution through a semi-permeable membrane, if, in other words, we can measure the force of the attraction between solvent and solution, we are at the same time determining the osmotic pressure of the solution. There are various conceptions current with regard to the nature of osmotic pressure. Some regard it as being of kinetic origin, strictly comparable with the pressure exerted by a gas on the walls of the containing vessel ; others consider it simply as the expression of the attrac- tion between solvent and solution ; and others still believe it to be closely related to surface tension. But whatever views may be held as to the nature of osmotic pressure, there is no doubt that what is determined in actual measurement is the force with which the solvent seeks to enter the solution through a semi-permeable membrane. The pioneer work in the direct measurement of osmotic pressure was carried out in the seventies of last century by Pfeffer, then professor of botany in Basle. His ex- perimental results form part of the foundation on which the modern theory of solution rests, and demand therefore at least a brief- consideration. Pfeffer measured the pressure developed in an osmotic cell which was charged with a solution and immersed in water. The osmotic cell consisted of a small porous pot with a semi-permeable membrane of copper ferrocyanide deposited close to the inner surface. By means of various connecting pieces the pot communicated with a closed manometer 40 PHYSICAL CHEMISTRY which served to register the pressure. The relation of these various parts will be clear from Fig. 4. The necessity for using a closed manometer instead of an open one will be apparent when it is pointed out that with an open manometer so much water would enter the cell that the concentration of the solution would be materially altered. The pressure measured in an open manometer, except for a very dilute solu- tion, would be quite different from the osmotic pressure of the solution put into the cell. With a closed manometer, on the other hand, the en- trance of a trace of water develops such a pressure in the cell as prevents any more coming in. Pfeffer estimated that in a cell actually used by him, and capable of holding 16 cub. cm., the amount of water that entered the cell while pressure equilibrium was being attained was not more than 0"14 cub. cm. In all his experiments, moreover, the specific gravity of the contents of the cell was determined before and after the mea- surement of the pressure, so that, if necessary, allow- ance could be made for change in concentration. With the apparatus just described PfefEer measured the osmotic 'pressure of Evidence of the different osmotic Fig. 4. numerous solutions. OSMOTIC PRESSURE 41 power of different substances is found in his figures for the osmotic pressure of 1 per cent, solutions of sucrose, potassium nitrate, and potassium sulphate, the values being o3'5, 178'0, and 193"0 cm. of mercury respectively. It was found also that the osmotic pressure exerted by a given substance in solution increased with the concen- tration, as shown for sucrose in the first two columns of the following table. The concentration (c) is stated as percentage of sucrose, and the osmotic pressure (P) is given in cm. of mercury. The figures in the third column are the values of the ratio — - — v — r^ — , and inspection concentration '^ shows that they are approximately constant. p. P. 1 53'5 53-5 2 101-6 50-8 2-74 151-8 55-4 4 208-2 52-1 6 307-5 51-3 The experimental diflJculties encountered in the direct determination of osmotic pressure are very great, and if we ascribe to these the variation from constancy of the figures in the third column, we may conclude that the osmotic pressure of a .solution is proportional to the concentration of the dissolved substance. Since the con- centration of a given quantity of dissolved substance is inversely as the volume which the solution occupies, the foregoing proposition may be stated also in the following way : The osmotic pressure exerted by a given quantity of dissolved substance is inversely proportional to the volume of the solution. It will be observed that this very closely resembles Boyle's law. Pfeffer studied also the influence of temperature on the osmotic pressure of a given solution, and showed that the pressure increases as the temperature rises. His 42 PHYSICAL CHEMISTRY results for a 1 per cent, solution of sucrose are shown in the first and second columns of the accompanying table. The figures in the third column are those cal- Osmotic Pressure in Atmospheres. e C. Observed. Calculated. 6 8 0-664 0-665 13-7 0-691 0-681 15-5 0-684 0.-686 22-0 0-721 0-701 32-0 0-716 0-725 36-0 0-746 0-735 cnlated by the formula P=PQ(l+at), where Pg = 0-649 and a = ^T^ — calculated, that is, on the assumption that the osmotic pressure of a given solution is proportional to the absolute temperature. The agreement between the observed and the calculated figures is far from perfect, but the differences are ir- regular, sometimes positive, sometimes negative. In view of this and of the afore-mentioned experimental diffi- culties, we may with reservation assent to the proposition that the osmotic pressure of a given solution is pro- portional to the absolute temperature — a proposition closely corresponding with the statement of Gay-Lussac's law for gases. Theoretical Yalne of the Osmotic Pressure. — Much of the interest attaching to the subject of osmotic pressure is due to the remarkable parallelism between the pro- perties of gases and those of dissolved substances — a parallelism which is revealed in Pfeffer's erperimental data, and which was emphasised by van't Hoff in 1887. By a thermodynamical argument,'- based on the validity of Henry's law, this chemist reached the conclusion that the osmotic pressure of a dilute solution must be pro- portional (1) to the concentration of the solute, and (2) to 1 Pha. Mag., 1888, 26, 81. OSMOTIC PRESSURE 43 the absolute temperature. When these propositions were advanced the experimental material available for their verification was very scanty, and was, in fact, derived almost exclusively from Pfeffer's measurements. Never- theless, van't HofE was satisfied that his theoretical conclusions were amply verified, and that he was justified in extending Boyle's law and Gay-Lussac's law to solutions. Moreover, a further step was taken in the extension of Avogadro's hypothesis to solutions, and van't Hoff assumed that at a given temperature equal volumes of two dilute solutions which have equal osmotic pressures contain the same number of dissolved molecules. If this assumption is adopted as, a working hypothesis, then it follows that the behaviour of substances in dilute solution must be governed by an equation PY=R'T, exactly analogous to the gas equation ^-y = ^2'. In the equation P F= WT, P is the osmotic pressure, V is the volume of solution which contains 1 gram-molecule of solute, T is the absolute temperature, and Sf is a constant for all dissolved substances. The gas constant B has already been evaluated and found to be 0'082 when the pressure is measured in atmospheres and the volume in litres. Suppose now that we find the value of R', using Pfeffer's data. According to these, the osmotic pressure of a 1 per cent, sucrose solution at 0° 0. is 0'649 of an atmosphere; hence P = 0'649 and T—273. Since we are dealing with a 1 per cent, solution we may, with close approximation to the truth, regard 100 cub. cm. of the solution as containing 1 gram of sucrose ; V, the volume of solution which contains 1 gram-molecule of sucrose, that is, 342 grams, would then be 34200 cub. cm., or 34'2 litres. It follows that i2'=-y= '^^5^— = 0-0813, a value very nearly equal to that of B, the gas constant. It appears 44 PHYSICAL CHEMISTRY therefore that R' = R, and that we may employ the same equation to represent the behaviour of dissolved sub- stances as is used in the case of gases, except that what is gas pressure in the one case is osmotic pressure in the other, and that what is the volume occupied by 1 gram- molecule of gas in the one case becomes in the other the volume of solution which contains 1 gram-molecule of solute. As was pointed out by van't HofF, the equality of K and R leads directly to a conclusion of the utmost importance, namely, that the osmotic pressure of a dilute sugar solution is equal to the pressure which the sugar would exert if it were in the gaseous state at the same temperature, and occupied the same volume as the solution. Two remarks may be made in reference to this pro- position. Firstly, validity is claimed for it only in connection with dilute solutions. Van't HofE himself applied his argument to 'ideal' solutions only, that is, solutions so dilute that the mutual action of the dissolved molecules and their actual volume compared with that of the space they inhabit are negligibly small. Secondly, it does not follow from van't Hoff's proposition that osmotic pressure and gaseous pressure must be due to the same cause ; the origin of osmotic pressure may be something quite different from the molecular impacts with which, according to the kinetic theory, the pressure of a gas is associated. Eeference has already been made (p. 39) to the various current views of the origin of osmotic pressure, but it ought to be borne in mind that the quantitative relation between the osmotic pressure, temperature, and concentration of a dilute solution is independent of the particular view which may be held in regard to the origin of osmotic effects. In this connection Larmor's views ^ are noteworthy. He supposes that 'each molecule of the dissolved substance > Nature, 1897, 55, 545. OSMOTIC PRESSUEE 45 sensibly influences the molecules around it so as to form a loosely-connected complex, in the sense, not of chemical union, but of physical influence. Provided the solution is so dilute that each such complex is out of range of the influence of the other complexes, then the principles of thermodynamics necessitate the osmotic laws. It does not matter whether the nucleus of the complex is a single molecule, or a group of molecules, or the entity that is called an ion; the pressure pheno- mena are determined merely by the number of complexes per unit volume.' Just as the acceptance of Avogadro'S; hypothesis leads to a relationship between molecular weight and density, and therefore to a method of determining the molecular weight of gases, so the extension of that hypothesis to solutions may be shown to have a similar result for dissolved substances. The connection between the equation PV=IiT, in which the hypothesis is incor- porated, and the determination of molecular weight is easily traced. For, supposing that a solution of a sub- stance containing g grams per litre is found to have the osmotic pressure F at the absolute temperature T, a simple calculation gives the value of M, the molecular weight of the substance. It must be remembered that V is the volume of solution containing 1 gram-molecule of solute: we have therefore V=—, and p¥=RT. 9 9 Since P, g, R, and T are known, M can be calculated. The determination of osmotic pressure, however, is not a practical method for ascertaining the molecular weight of a dissolved substance, because of the experimental difficulties to which reference has already been made, and which, as experience has shown, are solved only after much patient labour. There are other and simpler methods for determining the molecular weight of dis- 46 PHYSICAL CHEMISTRY solved substances, methods based on certain properties of solutions that are intimately related to osmotic pres- sure. These wUl be discussed later. Recent Work on the Direct Determination of Osmotic Pressure. — At the time when van't Hoff's theory of osmotic pressure was brought forward, the ex- perimental material available for its verification was ex- ceedingly scanty. Indeed, it is only within recent years that serious and sustained efforts have been made to confirm and extend Pfeffer's work on the direct measure- ment of osmotic pressure. The result of these efforts has been to throw much light on the relation of osmotic pressure to gas pressure. Morse, Frazer, and others, in a lengthy investigation,* have determined the osmotic pressures of sucrose and dextrose solutions of various concentrations and at various temperatures. The method employed is practi- cally the same as that used by Pfeffer, but the quality of the membranes and the manipulation of the apparatus have been so improved that pressures up to and over 2(f atmospheres are regularly recorded with great ac- curacy. The uncertainties of the measurements are, it is estimated, confined to the second decimal place of the figures expressing the osmotic pressure in atmospheres. The copper ferrocyanide membranes are deposited electrolytically. The porous pot, thoroughly impregnated with water, is filled with potassium ferrocyanide solution, and placed in copper sulphate solution ; a current is then passed from a copper electrode in the copper sulphate to a platinum wire in the ferrocyanide. The copper ferrocyanide is thus deposited in the walls of the pot, 1 See Amer. Chem. Journ., 1905, 34, 1 ; 1906, 36, 1, 39 ; 1907, 37, 324, 425, 558; 38, 175; 1908, 39, 667; 40, 1, 194; 1909, 41, 1, 257; 1911, 45, 91, 237, 383, 517, 554 ; 1912, 48, 29. See also Professor Findlay's monograph on Osmotic Pressure. OSMOTIC PEESSURB 47 the current being continued until the electrical resistance has reached a maximum. The cell is then rinsed out and soaked in water for several hours. This is followed by repeated electrolytic treatment until the resistance ceases to increase. The cell is now filled with a sucrose solution, placed in water, and allowed to develop pressure. When the maximum pressure has been reached the cell is taken down, rinsed, soaked in water, and again sub- jected to the membrane-forming process. The development of pressure discovers the weak places in the membrane, and these are subsequently mended by the electrolytic treatment. By repetition of these two operations the membrane ultimately reaches a maximum of resistance beyond which it cannot be forced, and the cell gives normal maximum osmotic pressures with sucrose solutions. The membranes prepared in this way are perfectly im- permeable to sucrose, even in contact with a solution containing 1 gram-molecule in 1000 grams of water. Besides effecting this improvement in the quality of the membrane, Morse and his co-workers have perfected (1) the connection between cell and manometer, (2) the means of accurately measuring the pressure. A descrip- tion of these details, however, lies beyond the scope of this volume. In considering the results of this recent- work on osmotic pressure, we may inquire how far they show that osmotic pressure is proportional to the concentration and to the absolute temperature, how far also they bear out the contention that osmotic pressure and gas pressure are equal. In regard to the first point, it has been found that the osmotic pressure of a sucrose or dextrose solution is proportional to the concentration, provided the coTvcen- tration is referred, not to unit volume of the solution, but to unit volume of the solvent. In the actual work, solutions were made up containing from 0*1 up to I'O gram- 48 PHYSICAL CHEMISTRY molecule of sugar dissolved in each case in 1000 grama of water ; these are described as weight-normal solutions, in contrast with the volume-normal solutions made by dissolving 0"1 or some other fraction of a gram-molecule in water and making the solution up to 1 litre. The following table will show that the osmotic pressure is proportional to the concentration as just defined; the figures are those for dextrose solutions at 10° C. : — Per 1000 gm. Water. of 0-1 0-2 0-5 1-0 -molecules. Osmotic Pressure. Per litre of Solution. In Atmospheres. Kelatively to the first taken as Unity. 0-099 2-39 1-00 0-196 4-76 1-99 0-474 11-91 4-98 0-901 23-80 9-96 It is obvious that the pressures for the four solutions increase in a ratio which is very nearly that of the con- centrations as given in the first column, but diverges widely from the ratio of the concentrations when these are stated in gram-molecules per litre of solution. As regards the applicability of Gay-Lussac's law to solutions, Morse and his fellow-workers conclude from their numerous experiments between 0° and 25° that the temperature coefiicients of osmotic pressure and gas pressure are practically equal. They find, for instance, that the osmotic pressure of a 1-0 weight-normal solution of sucrose is 25*06 atmospheres at 10°, and 26-33 atmos- pheres at 25°. If the temperature coefficients of osmotic pressure and gas pressure were equal, the osmotic pressure at 25°, calculated from that at 10°, ought to be — ggo = 26-38 atmospheres, in good agreement with the value actually recorded. The results obtained by Morse and his fellow-workers are of great interest also in relation to van't Hoff's proposition, that the osmotic pressure of a dilute sugar OSMOTIC PEESSURB " 49 solution is equal to tlie pressure which the sugar would exert if it were in the gaseous state at the same tem- perature and occupied the same volume as the solution. The bearing of the newer experimental data on this proposition will be best appreciated by a study of the following table. It refers to the osmotic pressures of sucrose solutions at 15°, and allows a comparison of the observed osmotic pressures with the values of the gas pressure calculated (I.) on the supposition that the gasified substance occupies the same volume as the solution, (II.) on the supposition that it occupies the same volume as the solvent in the solution. Oram-molecules of Sucrose. Osinotic Pressure in Atmospheres. Per 1000 gm. ot Water. Per litre of Solution. 0-1 0-098 0-2 0-192 0-4 0-369 0-6 0-5.33 0-8 0-684 1-0 0-825 Observed. Calc. I. Calc. n. 2-48 2-30 2-35 4-91 4-51 4-70 9-78 8-67 9-40 14-86 12-51 14-09 20-07 16-07 18-79 25-40 19-38 23-49 The values recorded in the last column are much closer to the experimental figures than the values under calc. I., and it follows, therefore, at least for sucrose solutions at 15°, that the osmotic pressure is approximately equal to that which the sucrose would exert if it were gasified at the same temperature^ and the volume of the gas were reduced to that of the solvent in the pure state. Similarly, for sucrose solu- tions at other temperatures between 0^ and 25° the observed osmotic pressure is somewhat greater (6-11 per cent.) than the gas pressure at the same temperature calculated on basis II. The results, then, of Morse and Frazer's work show that Boyle's law is approximately applicable to solutions of sucrose and dextrpse up to weight-normal strength, V 50 PHYSICAL CHEMISTRY provided the concentration is referred not to 1 litre of solution,, but to 1000 grams of solvent ; . it has been further shown that from 0° to 25° Gay-Lussac's law applies to solutions, that is, the temperature coefficients of osmotic pressure and gas pressure are equal. The theoretical equality between gas pressure and osmotic pressure is not strictly confirmed in the cases investigated. The excess of osmotic pressure over gas pressure may be due to hydration of the dissolved substance, but the question cannot yet be regarded as settled. The osmotic pressures of concentrated solutions of sucrose and dextrose have formed the subject of recent investigation also by Lord Berkeley and Mr. Hartley.* Except in one or two instances, the solutions examined by these investigators were still more concentrated than those which Morse and Frazer studied. They have also employed another method of determining the pressure which is required to hold in check the tendency of water to enter the solution through a semi-permeable membrane. In Lord Berkeley's experiments the copper ferrocyanide membrane is deposited as near as possible to the outside surface of a porous porcelain tube 15 cm. long, 2 cm. external and r2 cm. internal diameter. The means adopted to produce a satisfactory membrane are very similar to those employed by Morse and his fellow-workers. The tube carrying the membrane fits axially into a gun-metal vessel which holds the solution (about 250 cub. cm.) ; by various devices an absolutely tight joint is secured between the gun-metal vessel and the tube, the open ends of which are exposed. When a determination of osmotic pressure is to be made, a rubber stopper carrying a capillary tube bent at right angles is inserted into each end of the porcelain tube ; water is then introduced so as to fill the porcelain 1 Phil. Trans., A, 1906, 206, 481. OSMOTIC PEESSUEE 51 tube completely, and the vertical capillary tubes up to a certain level. The gun-metal vessel surrounding the porcelain tube is now filled up with the solution, and immediately connected with an apparatus by means of which a measured hydrostatic pressure can be applied. It is obvious that i£ this connection were not made and the solution were left in contact merely with the atmos- phere, water would pass from the porcelain tube through the membrane into the solution; this would be accom- panied by a fall of the water in the capillary tube.^ In actual work, however, as soon as the gun-metal vessel is full it is connected with the afore-mentioned apparatus ; by means of it pressure is applied to the solution, and so adjusted that water is prevented from entering. If the applied pressure is too great, water is squeezed out of the solution, and this is indicated by a rise of the water in the capillary tube. When the apparatus is so adjusted that the water in the capillary tube remains at a constant level, the registered pressure is the equili- brium pressure of the solution for a pressure of 1 atmosphere on the solvent. In this way Lord Berkeley and Mr. Hartley have obtained the following values for the osmotic pressures of sucrose and dextrose solutions at 0° 0. : — Sucrose. Dextrose. Grams Sucrose per litre of Solution. Osmotic Pressure in Atmospheres. Grams Dextrose per litre of Solution. Osmotic Pressure in Atmospheres. 180-1 13-95 99-8 13-21 3f00-2 26-77 199-5 29-17 420-3 43-97 319-2 53-19 540-4 67-51 448-6 87-87 660-5 100-78 548-6 121-18 750-6 133-74 One of the most remarkable things about these figures is the mere magnitude of the pressures which have been ' Only one of the capillary tubes is used for observation ; the other is closed by a glass stopcock. 52 PHYSICAL CHEMISTRY realised and measured. It is indeed a striking result that copper ferrocyanide membranes have been so pre- pared as to withstand a pressure of 100 atmospheres and over. Even in the cases where the pressure applied to the solution was up to this high figure, only the merest trace of sugar as a rule leaked through the membrane. A cursory glance at the foregoing tables will show that there is no proportionality between osmotic pressure and concentration, so long, at any rate, as concentration is referred to unit volume of the solution. It is easily seen from a comparison, for instance, of the figures for the first and fourth sucrose solutions and for the first and second dextrose solutions, that the pressure increases much more rapidly than the concentration. Even when the concentration is referred to I litre of the solvent, as was done by Morse and his fellow- workers, the osmotic pressure still increases more rapidly than the concentration. These relationships are best brought out by a diagram, in which the osmotic pressure of sucrose solutions is plotted against the concentration (Pig. 5). Curve I. represents the actual data recorded by Lord Berkeley and Mr. Hartley; curve II. is a straight line, traced on the assumption that the osmotic pressure may be calculated by the equation PV=RT, where V is the volume of solution containing 1 gram- molecule of sucrose ; curve III. is traced on the assumption that the osmotic pressure may be calculated by the equa- tion PV=RT, in which Fis the volume of solvent which goes to 1 gram-molecule of sucrose. The observed os- motic pressure is, it will be seen, always greater than the calculated pressure, even when the latter figure has been obtained by reducing the volume to that of the solvent present. It is, however, obvious that as the solu- tions become dilute the observed and calculated values approximate more and more closely to each other. OSMOTIC PEESSUEE 53 The abnormally high values recorded by Lord Berkeley and Mr. Hartley for the osmotic pressures of sucrose and dextrose solutions have been discussed by Callendar,^ who finds that the discrepancy between observed and calculated values disappears when it is assumed that the dissolved substance is hydrated. The theory which he develops leads him to conclude that in concentrated nlOO O80 « 10 o ■a o S O20 1 / / o III ^ / ^-^u ^ ^ ^ ^^ 100 200 300 400 500 600 Grams sucrose per litre of Solution Fia. 5. 700 sucrose solutions, such as those employed by Lord Berkeley and Mr. Hartley, each molecule of sucrose has attached to it on the average five water molecules. This figure is in good agreement with the value for the average molecular hydration of sucrose deduced from the influence of this substance on the solvent power of water for gases (see p. 32). ' Proc. Eoy. Soc, A, 1908, 80, 466. CHAPTEE IV THE COMPARISON 01" OSMOTIC PRESSUEE8. ISOTONIC SOLUTIONS Water Exchange between Two Solutions of Unequal Osmotic Pressure. — Although the direct determination of osmotic pressure is no easy matter, there are several methods available for the comparison of the osmotic pres- sures of different solutions. These methods depend on the exchange of water which takes place across a semi- permeable membrane separating two solutions. For two solutions of different osmotic pressure, separated by a semi-permeable membrane, .are no more in equilibrium than solvent and solution in the same circumstances. The osmotic exchange of water will always be such as to equalise the pressures on the two sides of the membrane ; the water, that is, will pass from the solution with smaller osmotic pressure to the solution which has the greater osmotic pressure. A simple experiment which demonstrates the existence of this water transport can be made with copper sulphate and potassium ferrocyanide solutions. A tall glass jar is filled with copper sulphate solution of medium strength — say 1 gram-molecule per litre. A Kttle potassium ferrocyanide solution (nearly saturated) is slowly run out from a narrow glass tube, the end of which dips below the surface of the copper sulphate solution. . As the potassium ferrocyanide runs out a transparent membrane of copper ferrocyanide is formed where the solutions COMPAEISON OF OSMOTIC PRESSURES 55 meet. A bag containing potassium ferrocyani^e solution is thus obtained attached to the end of the tube. When it has become- 1-2 cm. in diameter it is detached by jerking the tube, and it then slowly sinks to the bottom of the jar. If the relative concentrations of the copper sulphate and potassium ferrocyanide solutions have been rightly chosen, the latter has not only the greater density' but also the higher osmotic pressure. In virtue of this water enters the bag, dilutes its contents, and distends the membrane. The density of the contents of the bag is thereby diminished, and as the water continues to enter, it ultimately becomes equal to and less than the density of the surrounding copper sulphate solution. That this has taken place is shown by the spontaneous ascent of the bag to the top of the jar. Another experiment which shows even more distinctly the transport of water which takes place across a semi- permeable membrane between two solutions of .different osmotic pressure is the following. A small gas jar is half filled with a copper sulphate solution of the same strength as that described in the foregoing experiment. A narrow straight tube, into which some saturated potas- sium ferrocyanide solution has been sucked up, is closed at the top by a small piece of rubber tubing and a plug of glass rod. The tube is then lowered into the copper sulphate, and the ferrocyanide solution is pushed slightly beyond the end of the tube by compression of the rubber tubing with a screw^clip; a membrane is thus obtained hanging from the end of the tube and separating the concentrated potassium ferrocyanide solu- tion from the weaker copper sulphate solution. In these circumstances water passes from the copper sulphate to the potassium ferrocyanide. One result of this is that the layer of copper sulphate solution which is in im- mediate contact with the membrane is concentrated, and 56 PHYSICAL CHEMISTRY becomes denser than the rest of the solution; it there- fore sinks, and, on account of the difference in refractive power, the flow or ' trickle ' of this denser solution can be readily detected by the naked eye. It is instructive also to make a parallel experiment, in which the ferro- cyanide solution is weak and the copper sulphate solution is strong. The ferrocyanide solution is put as before into the tube, which for the purpose of this experiment is bent so that the end immersed in the copper sulphate solution points upward. The water transport in this case is in the opposite direction, from the inside of the membrane to the outside. The copper sulphate solution in immediate contact with the membrane is diluted, and the ascending current or ' trickle ' of this lighter solution is easily detected. On these phenomena Tammann^ has based a method for finding isotonic solutions of two membrane-forming salts — solutions, that is, which have the same osmotic pressure. With the help of an optical apparatus which permits the detection of the slightest irregularity in the refractive power of a medium, it is possible to determine which one of a series of potassium ferrocyanide solutions is isotonic with a given solution of copper sulphate. For when a drop of ferrocyanide solution is introduced into a copper sulphate solution and has surrounded itself with a membrane there is a change of density, and therefore of refractive power, at the top or bottom of the drop, according as the copper sulphate or the potassium ferrocyanide solution has the greater osmotic pressure. Only when the two solutions are isotonic does no irregularity occur in the refractive index either at the top or the bottom. In this way Tammann has found the concentrations of the potassium ferrocyanide solutions which are isotonic with various ' Arm. Phydk., 1888, 34, 299. COMPAEISON OF OSMOTIC PRESSURES 57 copper sulphate solutions. Some of his results are quoted in the following table, the numbers in which represent gram-molecules per 1000 grams of water. The two figures in the same horizontal line are those of isotonic solutions. CnS0«. E £ot. Gazette, 1908, 46, 53. COMPAEISON OP OSMOTIC PRESSUEBS 69 the case of water ; after sufficient time has been allowed for sedimentation, it is seen that while the bottom of the tube may have a deposit of corpuscles or their transparent envelopes, the supernatant liquid is red. In all the solutions, on the other hand, which are above the limiting concentration, the corpuscles have settled to the bottom, and the supernatant liquid is colourless. Similarly, a limiting conipentration may be discovered for another salt,- that solution being found by trial which is just dilute enough to lake the corpuscles. The solu- tions then of the two salts which are equivalent in osmotic effect, as indicated by the incipient laking of the cor- puscles, are to be regarded as isotonic solutions. Hamburger, who is responsible for this method of determining isotonic concentrations, records the following figures,^ which show how far it is possible in ordinary work to draw a definite line between solutions which lake the corpuscles and those which do not. The figures in Column I. represent the lowest percentage concen- tration at which the corpuscles sink to the bottom and leave the supernatant liquid absolutely colourless; the figures in Column. II. are the highest percentage con- centrations at which the corpuscles when they settle leave the supernatant liquid red. Bullock's blood was used in these experiments. Substance. I. n. KNO3 1-04 0-96 NaCl 0-60- 0-56 K2SO4 116 1-06 O12H22O11 6-29 5-63 CH3.COOK .... 1-07 1-00 MgSOi.THjO .... 3-52 3-26 CaClj 0-85 0-79 By careful work it is possible to bring the limits even 1 Zeit. phyaihd, Chem., 1890, 6, Sl9. 70 PHYSICAL CHEMISTRY closer than is shown in the table, but for ordinary pur- poses it is sufficient to take as the critical concentration for each substance the mean of the two figures quoted above. It is perhaps necessary to point out that a 1 per cent, solution of potassium nitrate, which is a critical con- centration so far as the corpuscles of bullock's blood are concerned (see above table), is not isotonic with the contents of these corpuscles in their normal condition. If the- corpuscles are immersed in a salt solution which is isotonic with their contents, and if the salt solution is then gradually diluted, the corpuscles undergo a corresponding increase in bulk, until at last the limit of resistance of the membrane is reached; the bursting is the final stage in the progressive distension of the corpuscle membrane, and occurs at a concentration con- siderably below that which is isotonic with the corpuscle contents in their normal condition. Light is thrown on this question by determining the concentration of the potassium nitrate solution that is isotonic with blood serum. Hamburger showed that a mixture of 10 cub. cm. horse blood serum with 7 cub. cm. of water was unable to lake certain blood corpuscles, although laking took place when 7*5 cub. cm. of water was mixed with 10 cub. cm. of the serum- Corpuscles from the same source were laked by 0"96 per cent, potassium nitrate solution, but not by 0'97 per cent, solution. Hence a mixture of 10 cub. cm. serum i- 7*25 cub. cm. of water is isotonic with a 0'965 per cent, solution of potassium nitrate, and we may conclude that the potassium nitrate solution which would be isotonic with the undiluted serum would contain 17"25 0'965-jQ-=l'66 per cent, of the salt. The corpuscles of horse blood are in osmotic equilibrium with the serum, COMPARISON OF OSMOTIC PRESSURES 71 so that no great error can be made in regarding the contents of these corpuscles as isotonic with a 1"66 per cent, solution of potassium nitrate. This is quite different from the most concentrated solution of potassium nitrate that is able to lake horse blood corpuscles; that solution contains about 1'17 per cent, of the salt. It is noteworthy that the limiting concentrations of a salt which produce laking of blood corpuscles are different for different kinds of blood. Thus, for example, the highest concentration of sodium chloride which causes laking is 0"21 per cent, for frog's blood, 0'47 per cent, for human blood, and 0"68 per cent, for horse blood. It is probable that these differences are connected not so much with the varying osmotic strength of the corpuscle contents, as with the different resisting power of the membrane. Isotonic Solations found by the Hsematocrit. — Blood corpuscles may be used in another way for the purpose of finding isotonic solutions. It has already been pointed out that corpuscles immersed in solutions of gradually diminishing concentration increase in bulk, until ulti- mately the membrane gives way. If, on the other hand, they are immersed successively in solutions of higher and higher concentration, more and more water passes out through the membrane, and the volume of the cor- puscles diminishes. It is evident that there must be for each salt which cannot penetrate the membrane some concentration such that corpuscles immersed in the solu- tion undergo no change of volume. This solution is discovered with the aid of the hsematocrit,^ a graduated thermometer tube which can be fitted to a centrifuge, and in which the corpuscles collect when blood, either alone or mixed with salt solution, is centrifuged. A 1 See Hedin, Zeit. physikal. Chem., 1896, 17, 164. 72 PHYSICAL CHEMISTRY definite quantity of blood, say 10 cub. cm., is treated in this way, and the operation is continued until no further diminution in the volume of the corpuscles in the hsemato- crit can be detected. The same quantity of blood is then mixed ■ with each of a series of salt solutions of graded strength, and the volume of the corpuscles in each mixture is determined as before. That solution in which the volume of the corpuscles is the same as in the blood itself is thus discovered; let it be designated as A. Similarly, out of a series of solutions of another salt one B is found, in which also the volume of the corpuscles is unaltered. This being so, A and B are isotonic solutions, and from the isotonic concentrations the isotonic coefficients may be calculated as already shown. It is interesting to compare the values of the isotonic coefficients obtained by different methods for various substances. This is done in the following table, where the isotonic coefficients are referred to that of sucrose taken as unity : — Plasmolytio ^^"Se"' Hematocrit Method. *Se?hod Method. MgSO^ . KNO3 . NaCl . CH3.C CaCL 1-00 1-00 1-00 1-09 1-27 I-IO 1-67 1-74 1-84 1-69 1-75 1-74 1-67 1-66 1-67 2-40 2-36 2-33 The concentration of the sodium chloride solution in which the volume of the corpuscles is unaltered is ap- proximately the same for all mammalian blood, namely, 0-9 per cent. To this solution the term 'physiological salt solution ' may properly be applied, for it is the solu- tion in which the corpuscles of mammalian blood remain unaltered as to volume, and in which, therefore, they COMPAEISON OF OSMOTIC PEESSURES 73 may be preserved. The term ' physiological salt solution ' is sometimes understood to mean a 0"6-0'7 per cent, sodium chloride solution, but this is a solution in which mammalian blood corpuscles certainly undergo alteration. The lower figure has its origin in the fact that erperi- ments of this kind were first made with frog's blood, the osmotic pressure of which is equal to that of a 0'6 or 0"65 per cent, solution of sodium chloride. Some Effects produced by Hypertonic Solutions.— The facts discussed in the earlier part of this chapter show that when a plant or animal cell is immersed in a hypertonic solution of a substance which cannot enter the cell, water passes outwards, and the contents of the cell become more concentrated. Such a change of con- centration may markedly afifect the activity of the cell, as instanced by the following case. The formation of starch from sugar that occurs in many plant cells, takes place only when the concentration of the sugar has reached a certain limit. It is found, however, that even in cells in which the sugar concentration is just short of that limit, starch formation can be induced by plas- molysing with potassium nitrate. The efEect of the hypertonic potassium nitrate solution is to raise the con- centration of the cell contents beyond the minimum necessary for the production of starch. Another interesting example of an osmotic stimulus is found in the part which hypertonic solutions play in artificial parthenogenesis.^ Loeb has shown that when unfertilised eggs of the sea-urchin StrongyloccTdrotus pwrpuratvs are placed for l|-2 minutes in a mixture of 50 cub. cm. sea-water + 3 cub. cm. O'lN butyric acid (or other monobasic fatty acid), and are then put back ^ See Loeb, Die chcmische Entvdcldvmgsei-regung des tierischen Eies, 1909 ; also Zeit. physikal. Chem., 1910, 70, 220. 74 PHYSICAL OHBMISTEY in ordinary sea- water, a fertilisation membrane is formed in all cases, the appearance of which marks the firnt stage of development of the eggs. One method of continuing this artificial development is to place the eggs, after the formation of the membrane, in hypertonic sea-water {e.g. 50 cub. cm. sea-water + 8 cub. cm. 2-5N NaOl). When they have been allowed to remain 20-50 minutes in this hypertonic sea-water the eggs are placed in normal sea-water, and there develop into larvae. It is a very interesting fact that a hypertonic gucrose solution may be employed instead of hypertonic sea- water; the result is the same so far as the development of the eggs is con- cerned. It is not quite certain how the hypertonic solution exerts its influence in this case, but probably it facilitates the oxidation of certain substances which, if not removed, would lead to cytolysis. CHAPTER V PERMEABILITY AND IMPEEMEABILITT OF MEMBRANES How does a Semi-permeable Membrane Act? — The consideration of osmotic phenomena leads very obviously to the questions: Wherein lies the efficiency of a semi-permeable membrane? Why is a membrane permeable to one substance, impermeable to another? The answers to these questions have a direct bearing not only on the purely physical side of osmotic pres- sure, but also on the osmosis which, as indicated in the previous chapter, plays such an important part in the equilibrium between plant and animal cells and their surroundings. The best method, perhaps, of deal- ing with this problem is first to consider it in its physical aspect alone, and then see how far the infor- mation so obtain^ can help in the interpretation of the biological phenomena of osmosis. According to Traube,i who discovered and studied various precipitation membranes, such as copper fer- rocyanide and gelatin-tannin, the feature of a semi- permeable - membrane which enables it to differentiate between one substance and another is the size of its' molecular interstices. Acting like a sieve, the mem- brane prevents the passage of particles which have a relatively large volume. Traube indeed maintained that with the help of these precipitation membranes it would -1 Archiv. AruU. Physid., 1867, 87. 7fi 76 ^ PHYSICAi: CHBMISTEY be possible to estimate the relative size of the particles of dissolved substances. It is certainly the case that the substances which are suited for quantitative experiments on osmotic pressure, substances therefore which must be practically incapable of penetrating the membrane employed, are all charac- terised by a high molecular weight. The compounds which have figured in direct determinations are mainly carbohydrates or ferrocyanides, and this fact, if one assumes with Traube that the volume of a molecule depends on its weight and its complexity, seems to support his conception of the action of the membrane. There are however many other facts which are opposed to this sieve theory of the membrane. In an investi- gation of the permeability of gelatin-tannin, zinc ferro- cyanide, and copper f errocyanide, Tammann found ^ that of 17 dyes tested 11 penetrated the first membrane, 7 the second, and 5 the third. On the basis of the sieve theory this would mean that the interstices or pores were widest in the gelatin-tannin membrane and narrowest in the copper ferrocyanide membrane. But with individual dyes it was found that in some cases the copper ferrocyanide membrane was more permeable than the zinc ferrocyanide, in other cases the latter was more permeable than the gelatin-tannin membrane, a result quite inconsistent with the sieve theory.* Again, Eaoult* found that when methyl alcohol and ether are separated by a membrane consisting of pig's bladder, there is an osmotic flow from the alcohol to the ether. If, however, the two liquids are separated by a membrane of vulcanised caoutchouc, osmosis takes place in the opposite direction, that is, from the ether to the alcohol. There must, therefore, be some other 1 Zeit. physikal. Ohem., 1892, 10, 255. " See, however, pp. 199, 200. " Zeit. phydhal. Chem., 1895, 17, 737. PEEMEABILITY AND IMPERMEABILITY 77 factor involved besides the size of the pores in the membrane. The nature of this factor is clearly indicated by Tam- mann's experiments,^ which showed that pig's bladder absorbs ten times as much methyl alcohol as ether, and that caoutchouc absorbs about one hundred times as much ether as methyl alcohol. The direction of the osmotic flow is therefore determined by the preferential absoi-ption of one of the two liquids by the membrane. This result was established more definitely by Flusin.^ who measured the velocity with which water, methyl alcohol, and amyl alcohol pass through pig's bladder, when the other side is bathed by ethyl alcohol, and when the pressure remains equal on the two sides of the membrane. Ethyl alcohol was taken as the second liquid in all cases, because the bladder is practically impermeable to this liquid. Some of Flusin's results are given in the follow- ing table ; the figures under ' velocity ' represent the volume of the liquid in cub. mm. which passed per hour across 1 sq. dcm. of surface, and the figures under ' absorption ' are the volumes of each liquid absorbed by 100 grams of bladder in five minutes. Liquid. Velocity, Absorption. Water 4674 121-9 Methyl alcohol .... 1748 28-7 Amyl alcohol 646 7-2 The view that the comparative permeability or im- permeability of a membrane to different substances depends on its power to dissolve or absorb them to a greater or less extent finds support in the fact that it is possible to construct osmotic -^ells in which absorp- tion by the membrane is undoubtedly the ruling factor. Reference may be made in this connection to the experi- 1 Zeit. physikal. Chem.. 1897, 22, 490. a Compt rend., 1898, 126, 1497; 1900, 131, 1308. 78 PHYSICAL CHEMISTRY ment described on p. 24. This experiment; wMch fur- nishes an example of gaseous osmosis, showed that in a cell containing air and closed by a membrane im- pregnated with water, extra pressure is developed when the outside of the membrane is bathed by a gas soluble in water. More "definite shape is given to this argu- ment from gaseous osmosis by Sir William Ramsay's work on the pressure produced by the passage of hydrogen through a palladium septum.^ In these ex- periments the outside of a small palladium cell con- taining nitrogen was bathed by a current of hydrogen. The apparatus was kept at 280° by means of a vapour jacket, and the inside of the palladium tube was connected with a manometer to register the pressure. When the initial pressure in the cell was 1 atmosphere, and a current of hydrogen (at atmospheric pressure) had been passed for some time, the internal pressure rose to about 1"9 atmosphere. This increment of pres- sure in the cell, although just nine-tenths of what might be expected, is plainly connected with the well-known power of palladium to absorb hydrogen, as distinct from other gases; the palladium septum by its absorp- tive power diiferentiates between hydrogen and other gases, and so gives rise to osmotic phenomena. Another osmotic cell, the efficiency of which clearly depends on selective absorption or solution by the mem- brane, is one described by Crum Brown.* Phenol and water are shaken up together until two mutually satu- rated layers are obtained, namely, (1) a lighter layer containing excess of water, (2) a layer containing excess of phenol. In a portion of the liquid from layer (1) a quantity of nitrate of lime is dissolved sufficient to make the solution heavier than layer (2). This solution » PhU. Mag., 1894' 38, 206. » Proc. Soy. Soc. Edin., 1899, 22, 439. PEEMEABILITY AND IMPERMEABILITY 79 is then put at the bottom of a narrow cylindrical jar, and above it there is carefully poured a small quantity of layer (2), say about 6-8 mm. in thickness. Above this again is put a considerable quantity of layer (1). The bottom layer in the cylinder is to be regarded as the top layer + calcium nitrate, and the two are separated by a liquid septum in which phenol predominates, and in which calcium nitrate is very sparingly soluble. The medium, however, in which the calcium nitrate is dis- *solved is readily soluble in the liquid septum, as appears from the fact that phenol and water are appreciably miscible. Hence in the cylinder there is a solution separated from its solvent by a septum which is per- meable to the solvent, but nearly impermeable to the dissolved substance. The natural result is that the bulk of the solution gradually increases at the expense of the solvent, and the intervening liquid septum slowly moves up the cylinder. Here again we have a case in which osmosis undoubtedly depends on selective absorption by the membrane. The physical evidence which has just been quoted gives strong support to the view that the efficiency of a semi-permeable membrane depends on its ability to differentiate, by solvent or absorptive power, between the substances which seek to penetrate it. We may next inquire how far this view can interpret the infinitely more complex phenomena connected with the permea- bility and impermeability of living membranes. The attempt, however, to give any such interpretation de- mands first a more detailed discussion of the experimental evidence bearing on the problem, evidence supplied mainly by Overton's work.^ » Vierteljahrschrift Zilrioh, 1895, 40, 199 ; 1899, 44, 88 ; Zeit. physihal Chem., 1897, 21, 18?; Jahrb. wus. Botanik, 1899, 34, 669. 80 PHYSICAL CHEMISTEY Permeability of Living Membranes. — Overton's ex- periments on the permeability of living membranes were made chiefly with plant cells, but there is remarkable agreement between the behaviour of plant and animal membranes in this respect, and it is true generally that a chemical compound which can penetrate the protoplasm of a plant cell is capable of doing so in the case also of an animal cell. The first method employed by Overton in the systematic study of permeability was the plas- molytic one discussed in the previous chapter, but it is necessary to describe rather more in detail the procedure actually adopted; this is best done by reference to a particular case. When root hairs of Hydrocharis are immersed in a 7 "5 per cent, sucrose solution distinct plasmolysis occurs, although none is observed in a 7 per cent, solution. Further, if the 7"5 per cent, solution in which the hairs are immersed is prevented from becoming more concentrated by evaporation, the extent of plasmolysis remains unchanged over a period of twenty-four hours. The plasmolysis vanishes instantaneously when- the hairs are dipped in pure water, and reappears with equal readiness when they are replaced in the 7'.5 per cent, sucrose solution. The fact that the protoplasmic streaming continues un- abated while ibhe hairs are in this solution shows that sucrose exerts no injurious effect on the vitality of the cells. Similar results are obtained with solutions of other substances as well as sucrose, and the conclusion is that the protoplasmic membrane is strictly semi-permeable in these cases. There are however many compounds which, although without deleterious influence on the plant, are unable to produce plasmolysis, or, at the most, produce a temporary plasmolysis. Ethyl alcohol is an example of a chemical compound for which the protoplasmic membrane is highly permeable, and which therefore is PERMEABILITY AND IMPERMEABILITY 81 unable to produce plasmolysis. If a Hydrocharis root is placed in a solution containing 7 per cent, of sucrose + 3 per cent, of ethyl alcohol, no plasmolysis occurs, although this solution is isotonic with a 28 per cent, sucrose solution. The failure of the cells to make any plasmolytic response cannot be due to any injurious influence of the alcohol, for this compound in 3 per cent, solution leaves the majority of plant cells un- harmed, except after prolonged contact. Similar to alcohol in the power of rapid penetration are all monohydric alcohols, aldehydes, ketones, and esters. The dihydric alcohols and the amides of monobasic acids penetrate the cell membrane more slowly, and the per- meability is still less for glycerine and urea. In the case of the hexahydric alcohols, the hexoses, the amino- acids, and neutral salts of the organic acids, the permea- bility is inappreciable. In some cases another method of studying the permea- bility of the cell membrane was employed by Overton. The sap of many plant cells contains tannin, a substance which forms sparingly soluble precipitates with numerous chemical compounds ; hence when cells containing tannin are dipped in an aqueous solution of one of these com- pounds, the greater or smaller permeability of the proto- plasmic membrane betrays itself by the more or less rapid formation of a precipitate in the cell. In his ex- periments with caffeine Overton found that the quantity of precipitate formed inside Spirogyra cells increased with the concentration of the external solution, while Lf cells containing precipitate were placed successively in caffeine solutions of gradually decreasing concentration, the precipitate grew less and less. The caffeine, in fact, penetrates the protoplasm with ease, and this is the case also with ammonia, aliphatic amines, and free alkaloids ; for the salts of the alkaloids, however, the membrane 82 PHYSICAL CHEMISTRY is less permeable, and to this fact is probably due tlie weaker toxic action of these salts compared with that of the free alkaloids. Another large class of substances, the behaviour of which in relation to the living membrane is interesting, is that of the organic dye-stuffs. Emphasis was laid by Overton on the fact that the salts of the basic aniline dyes, e.g. methylene blue, are as a rule very readily taken up by the plant or animal cell, whereas those which are sulphonic acid salts, e.g. indigo carmine, either cannot penetrate the cell membrane at all, or do so with great difficulty. Consideration of all these facts led Overton to the view that, so far as the living membrane can be regarded from, the purely physical standpoint, it is selective absorption on the part of the membrane which deter- mines the ability or inability of any substance to enter the cell. The compounds to which the cell membrane is permeable are generally soluble in fatty oils, and it probably consists of a substance which resembles these in solvent power. Overton maintains that the surface layer of the protoplast is impregnated with cholesterol or a mixture of cholesterol with other compounds, such as lecithin, and that the ability of a substance to make its way into the cell depends on its solubility in cholesterol. In support of this contention it has been found that there is a distinct parallelism between the rapidity with which various substances penetrate the cell and the extent of their solubility in cholesterol and lecithin solutions. Overton finds, for instance, that the basic aniline dyes are readily dissolved by solutions of cholesterol and lecithin, but that the sulphonic acid dyes, to which the cell mem- brane is generally impermeable, are very sparingly soluble in these media. This theory of the lipoid nature of the plasmatic PEEMEABILITT AND IMPEKMEABILITT 83 membrane has been very widely accepted, but it is not in all respects satisfactory; it fails, for instance, to give a reasonable interpretation of the fundamental fact that the membrane of plant and animal cells is so readily permeable to water. If, in reply to this objection, it is maintained that some of these lipoids are able to take up appreciable quantities of water,^ one may ask : How is it, then, that simple inorganic salts are unable to penetrate the membrane, or that part of it which is so impregnated with water? In this connection it is noteworthy that Czapek's work on the surface tension of the plant cell (see p. 85a) is opposed to the view that the plasmatic membrane is a continuous lipoid film, and rather favours the conception of it as a very fine fat emulsion, permeable for water and substances soluble in water. The theory has been criticised adversely by Euhland,^ who contends that the parallelism between power to penetrate the protoplasmic membrane and solubility in cholesterol solutions is not so complete as Overton be- lieves. There are dyes which are readily soluble in lipoids, and yet are unable, or practically unable, to enter the living cell; while, on the other hand, there are dyes for which the plasmatic membrane is highly permeable, which, however, are almost insoluble in chole- sterol. Some workers contend that the plasmatic mem- brane is protein, rather than lipoid, in character.^ The statement that simple inorganic salts are unable to penetrate the protoplasmic membrane is not absolutely correct. The very fact that the cell sap contains salts ' Lanolin, for instance, which is obtained from wool oil, and con- tains appreciable quantities of cholesterol, takes up in the anhydrous state about an equal weight of water, 2 Jahrh. wiss. Bot., 1908, 46, 1. " See Robertson, J. Biol. Chem., 1908, i, 1 ; Osterhout, The Plant World, 1913, 16, 129. 84 PHYSICAL CHEMISTRY which are supplied to the plant in the nutrient medium in which it grows indicates that there must be provision of some kind for the absorption of these salts. Further, a direct proof of the penetration of some inorganic salts into living protoplasm has recently been described by Osterhout.1 His experiments were carried out chiefly with Dianthus harhatus, which can be grown in distilled water, and the root hairs of which during such growth remain free from calcium oxalate crystals. When, however, they are transferred from distilled water to a dilute solution of a calcium salt, the presence of calcium oxalate crystals in the root hairs is evident within a few hours. This shows that calcium salts may penetrate fairly rapidly into living protoplasm. The subsequent growth is normal, so that the penetration of the calcium salts is not due to any abnormal or injured condition of the cells. Difficulties of a Purely Physical Theory of Per- meability. — It must be recognised that the behaviour of the living cell membrane towards the substances with which it comes in contact is in many cases incapable of interpretation on a purely physical basis. Although this is not the place for a discussion of the problem of permeability in its physiological aspect, it is worth while to indicate one or two of the facts in the face of which any purely physical theory is found wanting. It is well known, for instance, that the permeability of a cell membrane alters on the death of the cell; certain dyes can enter the cell only when the latter is killed. Again, there is the very striking fact that the inorganic constituents of the blood corpuscle are notably different from those of the plasma: the corpuscle fluid is comparatively rich in potassium and phosphate, while the plasma is poor in these, but rich in sodium and > Zeit. physikal. Chem., 1910, 70, 408 ; Seimce, 1911, 34, 187 ; 1912, 35, 112. PERMEABILITY AND IMPERMEABILITY 85 chloride. From the fact that the cell receives its nutri- ment from the external medium, it appears that the mem- brane cannot be absolutely impermeable to potassium salts, and yet their retention in the cell would seem to be im- possible if permeability of the membrane is conceded. We are therefore driven to assume some specific intervention of the living membrane or some special affinity between the cell protoplasm and the potassium salts.^ There are cases also where the membrane surrounding an organ, or even a whole organism, behaves in a way which is incompatible with a purely physical theory of permeability and osmosis. In the processes of secretion it is found that owing to the specific activity of the secretory organs a substance may be transferred from a place where its concentration is low to a place where its concentration is high. In the kidneys, for instance, urea is transferred from the blood, which contains little of it, to the urine, in which the proportion of urea is much greater. This could not be effected by any purely osmotic agency. Reference may be made also to some interesting observations on tadpoles made by Overton. Immersed in a 5-6 per cent, sucrose solution or in a 0'6 per cent, sodium chloride solution, tadpoles are un- affected, and their activity is unimpaired. If they are transferred to an 8 per cent, sucrose solution or an 0'8 per cent, sodium chloride solution, they lose a consider- able quantity of water in the course of twenty-four hours, and shrink notably in size. A similar result is produced by immersion of the tadpoles in solutions of uninjurious substances which are hypertonic to a 6 per cent, sucrose solution. Immersion in a solution hypotonic to a 6 per cent, sucrose solution we should expect to be followed by an intake of water, and consequent increase in the size of the tadpoles. This however is not the case, and » See Moore and Eoaf, Biochem. J., 1908, 3, 55 ; 1911, 6, 110. 85a PHYSICAL CHEMISTRY it therefore appears that the epithelial membranes of the tadpole are permeable to water in the one direction, but not in the other. This fact, and the others which have just been quoted, will serve to show that a purely- physical theory of the exchanges which take place across a living membrane is inadequate ; there is a physiological permeability as well as a physical permeability. Permeability and Surface Tension of the Cell Mem- brane. — As indicated by the phenomena of plasmolysis, the plasmatic membrane of plant cells is normally im- permeable to the substances present in the cell sap. There are conditions, however, in which the membrane loses its power of. retaining these substances, and the manner in which this may be brought about artificially is of great interest and importance. The researches of Czapek^ have shown that, as a convenient test for the unimpaired character of the cell membrane, the reaction between tannin and caffeine (cp. p. 81) may be employed. In a very large number of cases tannin is a constituent of the cell sap, and so long as the impermeability of the protoplasmic membrane is intact, immersion of such cells in a dilute caffeine solution will lead to the formation of a precipitate inside the cell. If, on the- other hand, the cells have been exposed to such conditions as destroy the impermeability of the membrane, then the tannin will diffuse away, and after a time the reaction with caffeine will be very feeble, if not entirely absent. In his systematic study of the effect of different sub- stances (in aqueous solution) on the permeability of higher plant cells, Czapek found that for each substance there was a critical concentration, such that the imper- meability of the -cells was retained if they were immersed ' XJAtr eine Methode zur dArekten Bestimmmng der Oberfliichenspannung der Plasmahaut von PjkmzemeUen (Gustav Fischer ; Jena, 1911). PERMEABILITY AND IMPERMEABILITY 85J for some time in a weaker solution, but rapidly destroyed if they were immersed in a stronger solution. In tlie series of the fatty alcohols, for instance, these critical concentrations are about 14 per cent, by weight for methyl alcohol, 8-9 per cent, for ethyl alcohol, 4 per cent, for w-propyl alcohol, 1'5 per cent, for ?i-butyl alcohol, and 0'5 per cent, for amyl alcohol. Now the very significant fact has been established that all these critical solutions - critical, that is, for the impermeability of the cell membrane — have practically the same surface tension, the average value being 0"685 that of water. The conclusion may therefore be drawn that this figure represents the natural surface tension of the plasmatic membrane, and that the abnormal permea- bility exhibited by higher plant cells after immersion in solutions above the critical concentration, results from the displacement of those substances which are normal constituents of the membrane. Further, the significant observation has been made that the surface tension of the saturated emulsions of neutral fats (containing notably the glycerides of unsaturated fatty acids) has a minimum value of 0'68 relatively to water. The coincidence of this figure with that for the natural surface tension of the plasmatic membrane is suggestive in connection with the question as to the nature of this membrane. Attention may be drawn also to the fact that the power of substances, notably the fatty alcohols, to lower the surface tension of water stands in evident relationship to their physiological activity' and to their heemolytic power.^ ' Traube, Ber. deutsch. physikcd. Oes., 1904, 6, 326. ' Fuhner and Neubauer, Archiv exper. Pathol., 1907, 56, 333. CHAPTER Vi Vapour pressure, boiling point and feeezinq point of solutions Yapour Pressure of Solvent and Solution. — The direct determination of the osmotic pressure of a solution is no easy matter. There are however other properties of solutions which are quantitatively related to osmotic Temperature Fio. 7. pressure, and serve therefore for its indirect evaluation. The first of thesb is the vapour pressure. Investigation, chiefly by Eaoult, has shown that when the dissolved substance is non-volatile the vapour pressure of a dilute VAPOUE PEBSSURE 87 solution is lower than that of the pure solvent at the same temperature by an amount which is proportional to the concentration of the dissolved substance. The general relation between the vapour pressure of the solvent and that of the solution at different temperatures is represented by the curves in Fig. 7, the upper curve showing the variation in the vapour pressure of the solvent with rising temperature, the lower curve showing the corresponding variation in the vapour pressure of the solution. The relative position of the two curves is such that, if AC and BC represent the vapour pres- sures of solvent and solution at one temperature, A'O' and B'C the same quantities at any other temperature, BC B'C , . , Tn~'pG" which means simply that for a given solu- tion the ratio of the vapour pressures of solution and solvent is the same at all temperatures. Yapour Pressure and _ Osmotic Pressure. — The mere fact of the existence of osmotic pressure involves the consequence that the solution of a non-volatile substance must have a lower vapour pressure than the solvent at the same temperature. The connection between the two will be made evident by. consideration of Fig. 8. Suppose that A is a funnel and tube closed at the bottom by a semi-permeable membrane, and containing sucrose «-A WM//M///A Fig. 8. 88 PHYSICAL OHEMISTEY solution. Suppose also that osmotic equilibrium has been established between the sucrose solution and the pure water in the vessel B, that, in fact, the weight of the column CD is equal to the osmotic pressure of the sucrose solution. If the whole apparatus stands in a vessel from which the air has been removed, the space inside the vessel will be occupied by water vapour. Now in any gaseous atmosphere the density, and therefore the pressure, of the gas is greatest at the bottom, because there the weight of the overlying column is a maximum ; the pressure at a higher point is less in proportion as the weight of the gaseous column above is diminished. Hence the pressure of water vapour at 0, level with the top of the sucrose solution in A, is less than at D, the surface of the water. The pressure at D is the vapour pressure of water at the temperature of the apparatus, and, since there is equilibrium, the pressure at G must be equal to the vapour pressure of the sucrose solution, the surface of which is at this level; that is, ^the vapour pressure of a solution must be lower than that of the solvent at the same temperature. Further, it is apparent that the difference between the vapour pressures is equal to the weight of a column of water vapour of height equal to CD. When the relationship between the osmotic and vapour pressures of a solution is treated mathematically, it is found that P= -jrr- • log^ —,' where F is the osmotic pres- sure and p' the vapour pressure of the solution ; p is the vapour pressure, M the molecular weight, and S the specific gravity of the solvent ; T is the absolute tem- perature, and Ji is the gas constant. A glance at the formula will show that in order to calculate the osmotic pressure of a solution from its vapour pressure it is not necessary to know the absolute values of p and p' ; a VAPOUE PRESSURE 89 knowledge of the I'alio of the vapour pressure of the solvent to that of the solution is sufficient. It is, as a matter of fact, an easier matter to determine the ratio of the vapoiir pressures of solvent and solution than to determine their absolute values. One very simple method of finding the ratio in question when water is the solvent is that devised by Ostwald and Walker.^ A current of air is drawn slowly through (1) Liebig's bulbs charged with the aqueous solution under examination, (2) another set of bulbs similarly charged, (3) bulbs containing water, (4) a U-tube containing pumice moistened with concentrated sulphuric acid. When the air leaves (2) it is charged with water vapour up to the pressure of the solution; when it leaves (3) it is charged with water vapour up to the pressure of pure water at the same temperature. The air therefore takes up water during its passage through the bulbs (3), and the loss of weight which these bulbs show is pro- portional to the difference p—p'. In passing through the sulphuric acid tube the air is deprived of the whole of the water vapour which it has taken up, and the gain in weight of this tube during an experiment is therefore proportional to p^ A determination of the loss in weight of (3), and the gain in weight of (4), after a current of air has been passed for some time, gives the required ratio of the vapour pressures, for p—p'_ loss in weight of water bulbs -, p fb" £■ ~y gain in weight of sulphuric acid tube p' can be easily calculated. Since, as already stated, the value of -, is independent of temperature, it is not essen- tial in this method to keep the temperature absolutely constant throughout an experiment; it is necessary only » Walker, Zeit physikal Chem., 1888, 2, 602. 90 PHYSICAL OHEMISTEY to ensure that the variation of temperature, if any, shall be the satne for all parts of the apparatus. This method of finding the relative vapour pressures of solvent and solution has lately been modified and improved by Lord Berkeley and Mr. Hartley,^ who arranged that the current of air, instead of bubbling through the solvent and the solution, should pass over their surfaces in specially constructed apparatus; in this way equality of the air pressure is secured through- out the train of vessels. In order to ensure rapid and complete saturation of the air with water vapour the vessels containing the solution and the solvent are regularly rocked, so that the exposed surface of liquid is constantly being renewed. With this apparatus Lord Berkeley and Mr. Hartley have determined the value of -, for various solutions of sucrose and calcium ferro- P cyanide, the osmotic pressures of these solutions being then calculated from the vapour pressure ratio by a formula similar to that quoted above. It is interesting to com- pare the values thus indirectly obtained for the osmotic pressure of calcium ferrocyanide solutions with those determined by the direct method described on p. 50. Osmotic Pressure in Atmospheres. Calculated from Vapour Pressure. 41-24 70-61 86-61 112-96 131-45 Vapour Pressure and Molecular Weight. — Since there is this quantatitive relationship between vapour pressure and osmotic pressure, and since, as already- shown, a knowledge of the osmotic pressure of a solutiou ' Proe. Ray. Soc, 1906, A, 77, 156 ; PhU. Trans., 1909, A, C09, 177. Orams Anliydrous Salt per 100 grams of Water. Observed. 31-39 41-22 39-50 70-84 42-89 87-09 47-22 112-84 49-97 130-66 VAPOUR PRESSURE 91 permits a calculation of the molecular weight of the dissolved substance, there must be some way of de- ducing the molecular weight directly from the vapour pressure. The required relationship is given by the formula ^^=^^:^> where p and p' are the vapour pressures, as before, of solvent and solution, n is the number of solute molecules, and N is the number of solvent molcnles in the solution. A slight transformation of the formula gives ^^=S^, so that n = N^^^. In order to illustrate the use of this formula the following data may be considered. A solution of 11-35 grams of oil of turpentine in 100 grams of ether was found to have a vapour pressure of 36'01 cm., the vapour pressure of pure ether at the same temperature being 38'3 cm. The molecular weight of ether is 74, so that the value of iVfor ,, . . 1 ,. . 100 J 100 38-3 -36-01 „„„ the given solution is t.^-, and 'i=-sj X — ggTQj — ='086 ; that is, 11-35 grams is "086 of a gram-molecule, and the molecular weight of oil of turpentine is there- 11-35 fore -:Qgg = 132, in .agreement with the theoretical value 136. A glance at the formula connecting osmotic pressure and vapour pressure, viz. /' = -jg^ .loge -,, shows that when solutions of two non-volatile substances in the same solvent have the same vapour pressure at any temperature, their osmotic pressures must be equal ; the solutions are isotonic. Now it has already been shown on p. 62 that if we can find isotonic solutions of two substances, the molecular weight of the one can be deduced from that of the other. Hence it follows that if we can find solutions of two substances which have the same vapour pressure, the molecular weight of the 92 PHYSICAL CHEMISTRY second can be calculated, when that of the first is taken as known. An interesting microscopic method of finding isotonic solutions, and therefore also of determining molecular weights, has been described by Barger.^ During some experiments on the growth of fungi in concentrated solutions it had been noticed that when a drop of strong salt solution is kept for some time in a small enclosed space in which water also is present the size of the drop gradually increases. This is obviously due to the fact that the vapour pressure of the water is greater than that of the salt solution, and hence there results a slow distillation from the water to the solution. In Barger's method a solution B is made up of the substance of unknown molecular weight, as well as a number of solutions A.^, A^, &c., of a standard substance the molecular weight of which is known ; these last solutions form a series of gradually increasing concentration. Alternate drops of A-^ and J3 are now introduced into a capillary tube, and any variation in the size of the drops -is observed under the microscope from time to time. If the size of the £ drops increases at the expense of the Aj^ drops, it follows that the vapour pressure of B is less than the vapour pressure of A.^, and therefore that the osmotic pressure of B is greater that that of A^ The experiment is now repeated with the whole series of A solutions, when it will be found that there are two adjoining members of the series A^ and A^, we shall suppose, such that when alternate drops of A^ and B are put in a capillary tube, the B drops increase in size at the expense of the A^^ drops, while in a similar experiment with Ag and B, the A^ drops increase at the expense of the B drops. The solution of A which has the 1 Jornm. Chem. Soe., 1904, 85, 286. VAPOUR PRESSURE 93 same vapour pressure and the same osmotic pressure as B must therefore lie between A^ and A^. The appli- cation of this method may be illustrated by the following example. Drops of an alcoholic solution of azobenzene containing 30*94 grams per litre were alternated with drops (1) of an alcoholic solution containing 0"16 mole- cule a-naphthol per litre, (2) of an alcoholic solution of the same substance containing 0'18 molecule per litre. In the first case the drops of the azobenzene solution increased in size, in the second case they decreased. A solution of azobenzene containing 30'94 grams per litre is therefore isotonic with a solution containing between 0'16 and 048 molecule of a-naphthol per litre. If the azobenzene solution were isotonic with the weaker of these a-naphthol solutions, and if these two substances are assumed to have the same isotonic coefficient, then the molecular weight of azobenzene would be — r^^ — = 193. If, on the other hand, the azobenzene solution were isotonic with the stronger of the a-naphthol solutions, then the molecular weight of azobenzene would be — ^ =172. The conclusion, therefore, to be drawn from this experiment is, that the molecular weight of azobenzene lies between 172 and 193. The value corre- sponding to the formula for azobenzene is 182. In some ways the method which has just been de- scribed recalls the hsematoorit method of finding isotonic solutions. In both cases transference of the solvent takes place across a semi-permeable membrane ; in Barger's arrangement, provided that the dissolved substances are non-volatile, the space between two neighbouring drops is permeable only to the molecules of the solvent, and is therefore equivalent to a semi-permeable membrane. Osmotic Pressure and Boiling Point. — The boiling 94 PHYSICAL CHEMISTRY point of a liquid is the temperature at whiclfits vapour pressure is equal to the atmospheric pressure. Provided . that we are dealing with a non-volatile solute, the vapour pressure curve for the solution lies below 'the vapour pressure curve for the pure solvent; hence, as shown graphically in Pig. 9, the solution must be raised to a higher temperature before its vapour pressure becomes equal to the atmospheric pressure; that is, the boiling point of the solution is higher than that of the solvent. Temperature Fig. 9. Further, the rise or elevation of the boiling point, T— T^, is quantitatively related to the lowering of the vapour pressure, and therefore also to the osmotic pressure. The relation between the osmotic pressure of a moderately dilute solution and its boiling point is given by the formula P= „..o, ' y ° atmospheres, where S is the specific gravity of the solvent at its boiling point, I is the latent heat of vaporisation for 1 gram of the solvent, BOILING POINT 95 Tg is its boiling point, and T that of the solution. In the case of an aqueous solution »S'= 0-959, 1 = 536, and To = 373, so that the osmotic pressure of an aqueous solution which boils T—T^^ degrees above the boiling point of water is 56*8 (T—Tq) atmospheres. If the solution boils, for instance, 0'1° higher than water, its osmotic pressure is 5'68 atmospheres. Boiling Point and Molecular Weight. — In view of the existence of a quantitative relationship between the osmotic pressure and boUing point of a solution, it is obvious that there must be a definite connection also between the elevation of boiling point and the mole- cular weight of the dissolved substance. The nature of this connection may be deduced empirically in the following way. Experiments have shown that the extent to which the boiling point of a given solvent is raised by the addition of a non-volatile substance is proportional to the concentration of that substance. This is borne out by the numbers in the following table,^ those in the first column representing the weights of phenanthrene dissolved in each case in 22'75 grams of benzene, those in the second column giving the observed rise of the boiling point above that of pure benzene ; the third column contains the ratios of the numbers in the first and second columns : — " ' Ratio. 1-59 1-59 1-61 From these data, as well as from many others that might be quoted, it appears that the value of the ratio is practically constant, and we may therefore conclude ' Biltz, ZHe Praxis der Molekelgevfichtshestimmung. a Grams Phenanthrene. 0-619 Rise of Boiling Point. 0-389° 1-018 0-639° 1-648 1-023° 96 PHYSICAL CHEMISTRY that the rise of boiling point is proportional to the con- centration of the Bolute. Assuming that this rule is valid even for concentrated solutions, we may easily calculate what elevation would be observed if the solution under examination contained 1 gram-mol. of phenanthrene in some definite quantity (say 100 grams) of benzene. The first solution, for instance, quoted in the above table contains 0"619 gram of phenanthrene in 22'75 grams of benzene; this is the same as a solution containing — „__ — = 2'72 grams of phenanthrene per 100 grams of benzene. If this quantity of benzene contained a gram-mol. — 178 grams — of phenanthrene, the corresponding elevation would be — giss — - = 25'5°. Suppose now another set of data, relating to a solution of phenyl benzoate in benzene, is similarly treated. A solution containing 1'015 gram of phenyl benzoate in 33"38 grams of benzene boils 0'387° higher than pure benzene. In this case the solution is the ^ . . 1-015x100 „ „ . nil same as one contaming — ggTgg — = (3 "04 grams or phenyl benzoate per 100 grams of benzene. On the basis of proportionality between rise of boiling point and con- centration, the elevation calculated for a solution con- taining 1 gram-mol. — 198 grams — of phenyl benzoate in 100 grams of benzene would be — st^jt — = 25*2°. This is very nearly the same figure as that calculated from the data for the phenanthrene solution, and in- stances of similar agreement might be multiplied. It is found, in fact, that when experimental data for the boiling points of benzene solutions are used to calculate the elevation which would be produced by dissolving 1 gram-mol. of solute in 1 00 grams of benzene, the figures obtained in the majority of cases lie between BOILING POINT 97 25° and 27°. This quantity appears therefore to be a characteristic constant for benzene, independent of the particular substance which is employed as solute ; it is referred to as the ' molecular elevation -of the boiling point ' or as the ' boiling point constant.' In the case of benzene the figure which has been chosen as giving the best value for the molecular elevation of the boil- ing point is 26"7°. When the experimental data for . the boiling points of solutions in water, alcohol, chloro- form, &c., are treated in the same way as has been done for benzene, there is similarly obtained in each case a characteristic constant ; the value of the molecular elevation of the boiling point (Ic) is 5*2° for water, 11-5° for ethyl alcohol, 21-0° for ether, and 39'0° for chloroform. It is noteworthy that the values of h deduced by caU culation from the experimental data can be confirmed. 0'02r^ On theoretical grounds h = — —2-, where ^j is the boiling point of the solvent on the absolute scale, and I is its latent heat of vaporisation. The values of k calculated for various solvents by this formula are in good agree- ment with the figures quoted above. When a trustworthy value has been obtained for k for any particular solvent, it is possible to determine the molecular weight of any new substance in this solvent. Suppose that a solution of g grams of this substance in 100 grams of the solvent is found to boil t° higher than the pure solvent ; if the molecular weight of the solute is M, then the molecular elevation of the M boiling point will be —t, and this must be equal to k, ^ M ■ which is already known. We have therefore —t = k, or j^—-:!.. The following figures illustrate the appli- 98 PHYSICAL CHEMISTRY cation of this formula. A solution containing 0-939 gram of a certain substance in 30 grams of benzene boils 0-588° higher than pure benzene. As benzene is the solvent, A; = 26-7°; g, the weight of solute per 100 grams of the 1 , 0-939X 00 „i„ ., , ,, 26-7X3-13 , .„ solvent, = g^ = 3-13, so that M= — „ gg = 142. Practical Determination of the Rise ot Boiling Point. Beckmann's Method. — A thermometer registers the same temperature when surrounded by the steam from boiling water as it does when surrounded by the steam from a boiling sugar or salt solution. In order therefore to find the rise of boiling point for such a solution, the bulb of the thermometer must be immersed (1) in boiling water, (2) in the solution boiling under the same conditions. A similar statement, naturally, applies to other solvents than water. It is found, however, that a thermometer immersed in a boiling liquid will register slightly different temperatures accord- ing to the way in which the heat is applied and the rate at which it is boiled. If the boiling vessel is in direct contact with a flame it is hardly possible to avoid superheating, and this leads to oscillation in the readings of the thermometer. Beckmann's apparatus, which is commonly used in determining the rise of boiling point, is designed to minimise these irregularities and to permit the comparison of solvent and solution under the same conditions. One form of Beckmann's boiling point apparatus is represented in Fig. 10. The boiling tube A is provided with two. side tubes ^^ and t^, the former serving for the introduction of material into the boiling tube, the latter holding a condenser K. The lower end of A rests in a hole cut in the asbestos sheet L, which in its turn lies on the sheet of wire gauze D. The short glass cylinder G serves as an air jacket for A, and is covered with a BOILING POINT 99 sheet of mica S. The upper end of the t;ibe A is closed Fig. 10. by a stopper, which carries the Beckmann thermometer. 100 PHYSICAL CHEMISTEY When an experiment is to be made, the weight of the empty dry boiling tube is first ascertained. Enough solvent to cover the bulb of the thermometer is then introduced, and the tubq is weighed again ; the difference between the two weighings gives the weight of solvent taken. The apparatus is then set up, and the tube is heated by a small Bunsen flame. In order to ensure regular ebullition, and so avoid oscillations of temperature as far as possible, it is advisable to put some glass beads, garnets, or platinum foil in the boiling tube. According to Beckmann, platinum foil is most effective in promoting regular boiling, and he advises the use of 10-20 grams of platinum foil rolled up and cut so as to form small tetrahedra. The flame must be so adjusted that the liquid in the tube A boils freely; after it has boiled for 15-20 minutes the temperature ought to be practi- cally constant, and readings of the thermometer made at minute intervals ought not to differ from a mean value by more than 0'01°. The constant temperature thus reached is taken as the boiling point of the solvent. The burner is then put on one side, and after the apparatus has cooled a little, a weighed quantity of the solute is introduced into the boiling tube. If the solute is a solid substance, it is best to introduce it in the form of lumps, or pastilles made in a steel press; if the solute is liquid, a pipette shaped like a Sprengel pyknometer is employed. When the solute has been added, the burner is replaced under the boiling tube, the size of flame remaining unaltered. The solution is now boiled until a steady temperature is attained; the reading of the thermometer then recorded is taken as the boiling point of the solution. A fresh addition of solute may be made, and the corresponding boiling point determined in a similar manner. Since the boiling point of a liquid varies notably with the atmospheric pressure, BOILING POINT 101 it is advisable to complete such a series of experiments in as short a time as possible. The Beckmann Thermometer. — In a determination of the elevation of the boiling point it is not necessary to know the actual temperatures at which solvent and solution boil ; it is sufficient to know accurately the difference in their boiling points. There is ^ therefore no objection to varying the quantity of mercury in the working part of the ther- mometer, and thereby adapting it for use with solvents of widely different boiling points : the scale may then be made very open with- out the instrument becoming inconveniently large. In the Beckmann thermometer, which is commonly used for determining the rise of boiling point and depression of the freezing point, the tube is sealed at the bottom to. a large bulb, and at the top to a reservoir in which any excess of mercury is kept. The scale of the instrument covers a range of about 6° Centigrade; the length corre- sponding to each degree is 3-5 cm., and each degree is divided into hundredths. The form of the reservoir will be under- stood by reference to the accompanying diagram of the thermometer head (Fig. 11). When it is desired to alter the adjustment of the thermo- meter, the bulb is warmed so that the mercury expands a little way into the reservoir, as shown in the diagram. The mercury at the top of the reservoir may then be detached by tapping, so that the thermometer is now adjusted for a higher temperature than previously; or mercury may be jerked up from the bottom of the reservoir, so that the thermometer is adjusted for a lower temperature. Fig. 11. 102 PHYSICAL CHEMISTRY Landsberger's Apparatus for Determining Rise of Boiling Point. — When a liquid is boiled by direct contact with a flame, superheating to some extent is inevitable. In order to avoid this difficulty Landsberger suggested that a solution should be brought to its boiling point by passing in the vapour of the solvent. The vapour pressure of the solution, it must be remembered, is lower than that of the solvent at the same temperature, so that, for instance, when steam at 100° is passed into a salt solution at 100^ the steam condenses, and by its latent heat of vaporisation raises the temperature of the salt solution above 100°, ultimately bringing it to its boiling point. In this case all risk of superheating is avoided, by virtue of the remarkable fact that the heating agent is at a lower temperature than the solution which is being boiled. In Walker and Lumsden's modification of Lands- berger's apparatus (see Fig. 12) the graduated boiling tube N is first charged with a small quantity of solvent, and this is boiled by passing in vapour through the tubes B and R from the flask F, where a large quantity of the solvent is boiled by direct heating. When the solvent in N is boiling the excess of vapour escapes through the small hole H, fills the space between the tubes N and E, and finally passes out into the con- denser 0. When the condensed solvent is dropping regularly from the end of the condenser the thermometer T is read, and the reading gives the boiling point of the solvent. The current of vapour is now stopped, and the most of the solvent which has condensed in N is poured back into F. A weighed quantity of the solute is introduced into N, and the current of vapour is re- started; when the solution is in active ebullition, and the condensed solvent is dropping from the end of the condenser at about the same rate as before, the ther- BOILING POINT 103 mometer is read, and the current of vapour is stopped immediately. The thermometer T and the dehvery tube E are removed, and the volume of solution in N ascer- tained as rapidly as possible. The boiling points of v^ Fig. 12. solvent and solution have thus been determined under the same conditions, and as the composition of the solution is known, all the data necessary for the calcula- tion of the molecular weight are available. ^ ' For more details of this method, see Journ. Ohem. Soc, 1898, 73, 502 ; also Turner, iMd., 1910, 97, 1184. 104 PHYSICAL CHEMISTRY Osmotic Pressure and Freezing Point. — It is a well- known fact that the freezing point of a solution is in all ordinary instances lower than that of the pure solvent. That such must be the case can be shown by a con- sideration of the relative positions of the vapour pressure curves for solvent and solution; it is only necessary to take into account also the existence of a vapour pressure curve for the solid solvent. Below the freezing point the solid , solvent has a tendency to. pass into the state of vapour, and the measure of this tendency at each TJ, Temperature Fig. 13. temperature is the vapour tension or vapour pressure. The vapour pressure curve for the solid is not a mere continuation of the vapour pressure curve for the liquid ; the two are independent, as shown at PqS and F^L in Fig. 13. At the freezing point, however, the vapour pressures of solid and liquid must be equal, since that is the temperature at which the two are in equilibrium. The two curves must therefore intersect at the freezing point, and we may define the freezing point as the temperature at which the vapour pressure curve for the liquid inter- sects the vapour pressure curve for the solid. Similarly, the freezing point of a solution is the temperature at FREEZING POINT 105 which the vapour pressure curve for the solution cuts the vapour pressure curve for the solid solvent, and it appears from the relative position of the curves, as shown in Pig. 13, that F, the freezing point of the solution, must be at a lower temperature than Fg, the freezing point of the pure solvent. This argument assumes that when a solution freezes it is pure solid solvent which crystallises out. This assumption is justified in the great majority of cases, and for aqueous salt solutions it can easily be shown that when freezing takes place pure ice, separates out. A test-tube containing r— -KMnO^ is kept in a freezing mixture for a short time until the layer next , the glass has frozen; the tube is then set in a wider jacket tube and again immersed in the freezing mixture ; in this way the freezing of the permanganate solution proceeds more slowly. When the contents of the tube have solidified completely it is seen that the coloured salt has been concentrated in the centre of the test- tube, and is surrounded by an envelope of perfectly colourless ice. The extent to which the freezing point of a solution is lower than that of the solvent, the depression of the freezing point, as it is called, depends then on the vapour pressure of the solution, and must therefore be quantitatively related to the osmotic pressure. The relation between osmotic pressure P and freezing point is given by the formula P= „.„, • -^ — atmos., where S is the specific gravity, T^ the freezing point, and m the latent heat of fusion of the solvent, while T is the freezing point of the solution. If the solvent is water, then S=l, ft, = 79-6, and ^0 = 273, and g^ = 12-03, so that the osmotic pressure of an aqueous solution is 106 PHYSICAL CHEMISTRY given by the formula P=12-03{Tq- T) atmos. The mean value, for instance, which has been found by various investigators for the freezing point of a 1 per cent, sucrose solution is -0'0546°. The osmotic pressure of this sucrose solution at 0° 0., calculated by the fore- going formula, would therefore be 0'656 atmosphere, in good agreement with the value (0'649) found by Pfeffer. Freezing Point and Molecular Weight. — The relation- ship existing between the freezing point of a solution and its osmotic pressure involves another between the freezing point and the molecular weight of the dissolved substance. What there is to be said in this connection is very similar to what has already been said about the boiling point ; elevation of the boiling point and de- pression of the freezing point are comparable quantities. The depression of the freezing point for a solution is proportional to the concentration of the dissolved substance. This statement embodies the results of count- less observations, and may be illustrated by the following data for the depression of the freezing point in aqueous solutions of chloral hydrate : — Grama Chloral Hydrate in 100 grama Water. Depression of Freezing Point. Batio. 2-834 0-335° 8-4 4-878 0-575° 8-5 6-595 0-775° 8-5 If on the basis of proportionality between freezing point depression and concentration we calculate what would be the depression for a solution containing 1 gram- mol. (165'5 grams) of chloral hydrate per 100 grams of water, we obtain for the three solutions quoted the values 19-6°, 19-5°,, 19-4° respectively. If the experi- mental data for solutions of other non-electrolytes in water are similarly treated, the value found for the depression which would be produced by 1 gram-mol. FREEZING POINT 107 of solute in 100 grams of water is not very different from the figures just quoted. A solution, for instance, containing 0'-609 gram of ethyl alcohol in 100 grams of water freezes at — 0*243° ; the depression for a gram- mol. would be ■ „^ =18-4°. It appears therefore that the figure for the depression due to 1 gram-mol. of solute in 100 grams of solvent is a characteristic constant for each solvent, and it is described as the 'molecular depression of the freezing point,' or, shortly, as the 'freezing point constant.' The accepted value of this constant (7c) for water is 18-6°, for acetic acid 39-0°, and for benzene 50-0°. On theoretical grounds 7c = " , where T^ is the freezing point of the solvent on the absolute scale, and « is the latent heat of fusion. It is interesting to note that the values thus calculated for k are in good agreement with those deduced from the consideration of the observed depressions. The value of k which has been adopted for any solvent after a study of various solutes of known molecular weight may be employed in determining the molecular weight of a new substance. Suppose that for a solution of this new substanqe containing ^ grams per 100 grams of solvent the observed depression of freezing point is t° ; if the required molecular weight of the solute is M, then the M molecular depression of the freezing point would be — t, and this must be equal to k, which is already known ; that is, — t = h, or M=—^. An illustration of the appli- cation of this formula may be quoted. A solution con- taining 0"565 of a certain substance in 23*4 grams of water freezes at — 0'77°; it is required to calculate the molecular weight of this substance. The value of g in this 108 PHYSICAL CHEMISTRY V case is — ^^ — =2-415, and since Ic for water =18-6°, ilf=l§:^iL5 = 58-3. ° Experimental Determination of the Depression of the Freezing Point. — The ap- paratus chiefly employed for this purpose was devised by Beckmann, and is represented in Pig. 14. It consists pf a tube A, set in a jacket tube B, and provided with a Beckmann thermometer D, and a platinum or nickel wire stirrer. The jacket tube B rests in a metal plate, which forms the cover of the thick glass jar C. When an experiment is to be made the glass jar is filled with a suitable cooling mixture ; the mixture should be such that its tempera- ture is not more than 2°-3° below the freezing point of the solvent to be used. A known weight of solvent is put in the tube A, and the cork carrying thermometer and stirrer is inserted ; the ther- mometer has been previously adjusted, so that at the freezing point of the solvent the top of the mercury thread is somewhere on the upper part of the scale. The tube A is first immersed directly in the cooling mixture, and only when the temperature has fallen nearly to the freezing point of the solvent is it set inside the jacket tube. The contents Fig. 14. PEEEZING POINT 109 of A are stirred regularly, and the temperature falls steadily. Close observation of the thermometer shows that after a short time the mercury ceases to fall, then rises and remains steady at one point; the temperature thus marked is the freezing point of the solvent. The tube A is now taken out of the bath and a weighed quantity of solute is introduced through the side tube; after it has completely dissolved, the operation of taking the freezing point is carried out as before. . The amount of supercooling, that is, the interval of temperature be- tween the lowest point to which the mercury falls and the highest point to which it rises (the freezing point, in other words), should be noted; if it is greater than 0"4°-0'5°, the determination of the freezing point should be repeated, and the occurrence of excessive supercooling avoided by introducing, if necessary, a tiny crystal of the solvent. Excessive supercooling involves the separa- tion of a considerable quantity of the solid solvent when freezing occurs, and this would mean an appreciable increase in the concentration of the solution. When the freezing point of the first solution has been satis- factorily determined, a further quantity of solute may be introduced, and the new freezing point ascertained as before. For each addition of solute there is a cor- responding depression, and from each pair of values the molecular weight of the dissolved substance may be calculated by the formula M=—j^, already discussed. z The value obtained for M by this method ought not to differ from the correct value by more than 3-5 per cent. In the most accurate work it is necessary to adjust the temperature of the external bath so that it is only slightly below the freezing point of the solution in A. This is conveniently done for aqueous solutions by putting no PHYSICAL CHEMISTEY ether in tlie external bath and aspirating a current of air through it.^ By regulating the current of air, any desired temperature between 0° and —15° is easily main- tained. Biological Applications. — The difficulties involved in the direct determination of osmotic pressure have been repeatedly emphasised. In the depression of the freez- ing point, however, we have a measure of the osmotic pressure of a solution which is more accessible by ordinary experimental work, and the freezing point method has therefore been extensively applied in studying the osmotic power of various fluids occurring in the living organism It should however be pointed out that the indirect deter- mination of osmotic pressure by means of the freezing point is, in one sense, much less accurate than the process of direct measurement. For, as has already been shown, the osmotic pressure P of an aqueous solution is related to the freezing point depression T^-T hj the formula P=12'QZ{Tf,- T) atmos., and it appears from this that to a freezing point depression of 0'001°, which it is very difficult to measure with any approach to accuracy, there corresponds an osmotic pressure of 9 mm. of mercury, a quantity which can be accurately determined. In the absence, however, of trustworthy and rapidly acting semi-permeable membranes the more practical if less accurate freezing point method of studying osmotic pressure is used by the ordinary worker. In the ordinary form of the Beckmann freezing point apparatus 10-20 cub. cm. of liquid are required for a determination. It is sometimes difficult, however, if not impossible, to obtain this quantity of a fluid from an organism, and hence if the osmotic value for such a fluid is to be determined by the freezing point method, ^ Raoult, Zeit. physihal. 0/iem., 1898, 27, 617. PEEEZING POINT 111 an apparatus permitting the use of a smaller quantity of liquid is desirable. With this end in view, modified forms of apparatus have been introduced, such as that described by Guye and Bogdan/ which differs from the Beckmann apparatus chiefly in having a smaller freezing tube and a smaller thermometer bulb. An experiment can be carried out with 1'5 cub. cm. of liquid, and the authors claim that the results are nearly as accurate as those obtained with the usual apparatus under ordinary working conditions. The freezing point method has been extensively used in studying the osmotic pressure of the blood from different animals, and the variations in this pressure resulting from changes in the external conditions. It is immaterial whether defibrinated blood or blood serum is taken for the determination of the freezing point, since the corpuscles, like other suspended particles, have no influence on the osmostic pressure. Further, blopd plasma and blood serum have practically the same freezing point, a little proteid more or less making no appreciable difference. Numerous investigations have shown that the freezing point of mammalian blood does not vary much from one species to another. This is brought out by the following figures: — Animal. Freezing Point of Blood. Man -0-66 Ox -0-68 Horae . . . • • — 0'66 Eabbit -0-69 Cat -0-63 Dog -0-57 Sheep -0-62 Nor is there much variation from time to time in the ^ /ourn. ehim. phys., 1903, 1, 379. H 112 PHYSICAL OHEMISTEY osmotic pressure of the blood of one individual, a fact that may be contrasted with the behaviour of urine in this respect. Even in the case of a healthy person, the freezing point of the urine varies within very wide limits in the course of twenty-four hours, and, according to Bouchard,'^ while the normal freezing point of undiluted urine maybe taken as about — 1'35°, it may vary from — 0"50° to — 2'24° in different pathological conditions. Another direction in which the freezing point method has been applied is in the study of the relation between the osmotic pressure of the blood of fishes and that of the surrounding medium. In the case of all invertebrate marine animals the freezing point of the blood or body fluid is the same as that of the water in which they live. Further, these organisms are unable to preserve any difference between the osmotic pressure of their body fluid and that of the surrounding medium ; when the osmotic pressure of the latter is artificially varied by dilution or concentration the body fluid undergoes a cor- responding change^ as shown by the freezing point. This is illustrated by the figures in the following table, bearing on the behaviour of a species of crab (Maia verrucosa). The figures under I. are the freezing points of sea- water (normal and artificially modified), while the figures under II. are the freezing points of the body fluid of the crab after immersion for some time in the corre- sponding water: — I. I. Normal sea-water . . -2-3'' -2'3° Concentrated sea-water . -2-98° -2-9° Diluted sea-water. . -1-38° -1-4° It is obvious that the organism is unable to regulate the osmotic pressure of its body fluid. In the case, however,, of many marine vertebrates ^ Pompt. rend, 1899, 128, 64. PEEEZING POINT 113 the osmotic pressure of the blood or body fluid is quite different from that of the surrounding medium, and variation in the osmotic pressure of the latter is accom- panied by only a slight variation of the former. This point is well illustrated by some observations of Dakin ^ on the blood of fish taken from sea-water of naturally varying concentration. He determined the freezing pftint of the blood of plaice caught in Kiel harbour, in the open Baltic, in the Kattegat, and off Helgoland. The freezing points of the water in the four cases were respectively -1-09°, -1-30°, -1-66°, and -1-90°, while the freezing points of the blood of the plaice were -0-66°, -0■72^ -0-73°, -0-79°. The osmotic pressure, therefore, of the blood of the plaice is dependent only to a very limited extent on the osmotic pressure of the surrounding medium. The codfish is stiU more in- dependent, and any variation observed in the freezing point of the blood in this case is covered by individual differences. With elasmobranchs, on the other hand, the osmotic pressure of the blood is almost the same as that of the surrounding sea-water, and as this increases in density, so the osmotic pressure of the blood changes. It is found in general that the freezing point of the blood of marine teleosts taken from the North Sea is on the average about — 0"75°, whilst that of the blood of fresh-water teleosts averages about — 0'53°; in each case the organism is largely inde- pendent, so far as osmotic pressure is concerned, of the medium in which it lives. 1 Biochem. Journ., 1908, 3, 258, 473. CHAPTER VII THE BEHAVIOUR OF SALTS, ACIDS, AND BASES IN AQUEOUS SOLUTION Facts apparently Inconsistent with AYogadro's Hypo- tliesis. — The acceptance of Avogadro's hypothesis was retarded by the discovery of certain cases in which the molecular weight of a substance, deduced from its vapour density, was quite out of harmony with the formula which seemed probable on grounds of chemical analogy. The vapour density of ammonium chloride, for instance, is only about half what it ought to be if NH^Cl is the correct formula for this compound ; on the other hand, the vapour density of acetic acid has a value greater than corre- sponds to the formula CHg.COOH. In the extension of Avogadro's hypothesis to solutions similar difficulties have been encountered. Cases are known in which the molecular weight of a dissolved substance, calculated from the depression of the freezing point or one of the other osmotic properties, is greater than the value which corresponds with the ordinarily accepted formula. Just as the vapour density of acetic acid is abnormally high, so the molecular weight of acetic acid dissolved in benzene, deduced from, its influence on the freezing point of benzene, is nearly double the value which corresponds to the formula CHg.COOH. High values are similarly obtained for the molecular weight in benzene solution of all substances containing the —OH group, phenol and alcohol, for instance, A glance at SALT SOLUTIONS 115 the formula by wbich molecular weight is calculated from the depression of the freezing point, M = -^ (see p. 107), shows that an abnormally large value for the mole- cular weight is the result of an abnormally small depres- sion. Now the depression of the freezing point, like the osmotic pressure, is a measure of the number of dissolved units, and hence an abnormally small depression points to a reduction in the number of dissolved units below the figure .which we should expect from the amount of substance actually in solution. Such a reduction must be due to the clubbing together, or association, of the normal molecules to form larger aggregates. Abnormally Great Depressions of the Freezing Point. — More interesting perhaps are the cases, the deviation of which from the normal is in the opposite direction. There are very many substances the mole- cular weights of which, calculated from their influence on the freezing point of water, are quite inconsistent with the accepted formulas. A solution of sodium chloride, for instance, containing 1'135 gram of the salt in 100 grams of water, freezes at — 0'687°. Taking A=18'6° for water (see p. 107), and calculating the molecular weight of the dissolved substance in the usual way, we obtain — 0^687 — = 30-7, a value far below 58'5, which is the molecular weight for sodium chloride, on the assump- tion that it contains one atom of sodium and one of ■chlorine. In the case of other salts also, as well as for many acids and bases, there is an equally marked 'discrepancy between the accepted formula of the sub- 'stance and the molecular weight deduced from its osmotic behaviour. A more definite conception of the extent «of the discrepancy will be gained by a glance at the •Jfigures in the following tables. In the first column of Sodium Chloride. Sodium Sulphate. ion. t. . t Concentration. H- 0-424° 1-93 0-028 0-141° 2-66 0-687° 1-87 0-070 0-326° 2-46 1-135° 1-86 0-117 0-515° 2-33 1-894° 1-85 0-195 0-817° 2-21 116 PHYSICAL CHEMISTEY each table is recorded the strength of the solution in gram-molecules per litre ; the second column contains the observed depressions t, and the third column contains the values i = T • tg being the depression which would be observed if the solute behaved normally : — Concentration. 0-117 0194 0-324 0-539 These figures, and many others which might be quoted, show that the depression of the freezing point of water caused by salts is abnormally great, a fact that points to an increase in the number of dissolved units above the figure which we should expect from the amount of salt actually present in any solution. Prom the figures obtained by Arrhemus,^ it appears that for salts of the type of sodium chloride the values of i run up to 2, while for salts, such as sodium and potassium sulphates, magnesium, calcium and strontium chlorides, the values run up to 3. Evidence of this enhanced osmotic activity on the part of salts is found also in the values of the isotonic coefficients tabulated on p. 72. The isotonic coefficients, it must be remembered, repre- sent the relative osmotic pressures of equimolecular solutions, and the figures for the isotonic coefficients show that sodium chloride and potassium nitrate exhibit • an osmotic activity which is about 1-7 times as great, while calcium chloride exhibits an osmotic activity which is 2-3 — 2-4 times as great as that of sucrose taken as the normal substance. As already indicated, this enhanced osmotic activity > Zeit. physikal. Chem., 1888, 2, 491. SALT SOLUTIONS 117 on the part of salts points to an abnormally large number of dissolved units in their solutions. How is this to be explained? Eeference has been made to the fact that ammonium chloride and other substances are found to have vapour densities much below the values correspond- ing to their accepted formulae. This exceptional be- haviour has been reconciled with Avogadro's hypothesis by assuming a dissociation of the vaporised molecule into two or more simpler molecules; in the case of ammonium chloride, indeed, direct evidence is obtain- able, showing that when the substance is vaporised it breaks up into ammonia and hydrogen chloride, giving two molecules in place of one. Between the case of these abnormally low vapour densities and the case of abnormally great depressions of the freezing point of water there is a historical parallel in that a dissociation hypothesis has been brought forward also to account for the exceptional osmotic behaviour of salts (acids and bases) in aqueous solution. The Electrolytic Dissociation Hypothesis. — In 1887 Arrhenius propounded the view^ that acids, bases, and salts in aqueous solution are dissociated to a greater or less extent into positively and negatively charged particles or 'ions,' and that the increase in the number of units in solution which arises from this dissociation is re- sponsible for the abnormally high osmotic activity of these substances. Sodium chloride, according to this hypothesis, splits up to a large extent, when dissolved . . ■ + in water, into positively charged sodium ions Na, and negatively charged chlorine ions CI; potassium nitrate + — similarly dissociates into K and NO3. ^ In both these 1 Zeit. physikal. Chem., 1887, 1, 631. 2 Positive ions are very frequently indicated by dots, negative ions by dashes ; thus— Na", H', NH4-, CI', NO/. 118 PHYSICAL CHEMISTEY + — cases, as also in others, such as hydrochlbric acid (H, CI), + — potassium hydroxide (K, OH), potassium acetate + + — (K, CH3.COO), and ammonium chloride (NH^, CI), one molecule produces two ions, so that even on the sup- position of complete dissociation the abnormal osmotic effect of these compounds, whether measured by the lowering of vapour pressure, the elevation of the boil- ing point, or the depression of the freezing point of water, cannot be greater than twice the effect pro- duced by an equimolecular quantity of a normal sub- stance. In harmony with this it is found, as already stated, that the values of i for sodium chloride, potassium nitrate, and the like, run up to 2. According to Arrhenius, sodium sulphate in aqueous solution is more or less dis- + + sociated into three ions, Na, Na, and SO^, the last carrying a double negative charge; similarly, calcium chloride produces three ions, one with a double positive ++ _ _ _ — — charge Ca, and two with a single negative charge 01, CI. In both these cases, and in analogous compounds, one molecule produces three ions, and on the supposition of complete dissociation the abnormal osmotic effect would be three times the effect due to an equimolecular quantity of a normal substance. In harmony with this it is found that the values of i for sodium and potassium sulphates, magnesium, calcium, and strontium chlorides, and other analogous compounds, run up to 3. If this hypothesis of the ionic dissociation of salts, acids, and bases in aqueous solution is accepted, then we can deduce the degree or extent of the dissociation in any solution by comparing the observed depression t of the freezing point with the depression tg which would be observed were there no dissociation; {he latter value is calculated by the formula io — -Tr' ^^ which M is the SALT SOLUTIONS 119 normal molecular weight of the dissolved substance. Suppose that of 100 molecules of a dissolved salt the fraction a has undergone dissociation, each dissociated molecule producing n ions, then there remain in the undissociated condition 100(1 — a) molecules. The number of molecules which have undergone disso- ciation is 100a, and the number of ions so produced is 100a Xw; the total number of units in solution is therefore 100(1 — a) + 100ara, and the actually observed depression t of the freezing point must be proportional to this figure. If, on the other hand, there were no dissociation the number of units in solution would be merely 100, and to this figure there would correspond the depression t^^. Since the depressions are propor- tional to the numbers of units present in solution, t 100(l-a) + 100a»t. ,,, .v ,, , t-t^ tr 100 = l+(--l>,sothata = ^— ^^; t i — \ or if — be expressed by the symbol i, a= - — -. If this Vn 7h ^ ±. formula is applied to the data bearing on the freezing points of sodium chloride and sodium sulphate solutions (see p. 116), it appears that in a sodium chloride solution containing 0-2 of a gram-mol. per litre, 85-90 per cent, of the salt is dissociated into its ions, and in a sodium sulphate solution of the same strength about 60 per cent, of the salt is so dissociated. It appears also from the figures on p. 116 that the more dilute the solution the greater is the percentage of salt in the dissociated condition. Ionic Dissociation and Electrolytic Conduction. — The claim which the hypothesis of ionic dissociation makes on our consideration is greatly strengthened by the fact that it not only furnishes an explanation of the abnormal osmotic influence of acids, bases, and salts in aqueous solution, but gives also an intelligible interpretation of 120 PHYSICAL CHEMISTEY various other phenomena. It is well known that a solntion of sugar or alcohol in water is no better a con- ductor of the electric current than water itself; sugar and alcohol are non-electrolytes. On the other hand, there are many substances the aqueous solutions of which are relatively good conductors of the electric current. As Arrhenius pointed out, these are precisely the substances which have an abnormally great effect in raising the boiling point or lowering the freezing point of water. Sugar and alcohol are non-electrolytes ; their effect on the freezing point of water is normal. Sodium chloride, potassium nitrate, hydrochloric and sulphuric acids are' electrolytes ; their aqueous solutions conduct the electric current, and they undergo decomposition under the in- fluence of the current ; they are also among the sub- stances which produce an abnormal depression of the freezing point. All this becomes intelligible if it is supposed that this latter class of substances is liable to ionic dissociation. For, according to Arrhenius's hypothesis, a solution of sodium chloride, to take one of the substances which have an abnormal influence on the freezing point of water, contains a large proportion of dissociated mole- cules in the form of positively and negatively charged ions. Accordingly when two electrodes, one charged positively and the other negatively, are immersed in such a solution, an attractive force is exerted on the ions of opposite sign. Under the influence of this force the positively charged ions move towards the negative electrode, and the negatively charged ions towards the positive electrode. The passage of an electric current, then, through a solution of sodium chloride or any other electrolyte consists in a stream- ing of positive ions in one direction and of negative ions in the opposite direction. The neutral or undis- SALT SOLUTIONS 121 sociated molecules are unaffected ; ttey are not charged, and experience no impulse to move rather in one direc- tion than another; they are inactive so far as the transport of electricity through the solution is con- cerned. On the basis of this view, the efficiency of a given quantity of a salt in conducting the current must depend' on the extent to which the salt is dissociated; if the degree of dissociation is high, then the propor- tion of current-carriers will be high also, and the power of conducting the current, the conductivity as it is called, will be relatively great. A solution of a sub- stance, on the other hand, which is ionised only to a small extent, will be a relatively poor conductor of the electric current. It is further obvious that if we could compare the conductivity of an actual sodium chloride solution with the conductivity which the same amount of the salt would exhibit if it were completely ionised, we should obtain a measure of the dissociation in the actual solution. Increase of Conductiyity with Dilution. — The figures recorded on p. 116 for solutions of sodium chloride and sodium sulphate show that the degree of dissociation in- creases as the solutions become less concentrated, i.e. as the dilution increases, and this is a statement that applies to dilute aqueous solutions of all electrolytes, so far as the freezing point evidence goes. It is therefore to be expected, on the basis of the ionic dissociation hypothesis, that for a given quantity of a salt the conducting efficiency — the con- ductivity — should become greater as the concentration of the solution decreases. This is what actually takes place, as can be demonstrated by the following simple experiment : — A rectangular glass jar is procured, say about 25 cm. Mgh, 4 cm. wide, and 10 cm. long, and two strips of sheet 122 PHYSICAL OHEMISTEY copper are cut to fit the opposite ends of the jar from top to bottom ; the top ends of the strips should project somewhat beyond the mouth of the jar, and are provided with binding screws. The two strips are kept pressed up against the opposite ends of the jar by glass rods, the ends of which are inserted into rubber stoppers, the total length of the rods + the stoppers being adjusted to the distance between the strips. A little concentrated sodium acetate solution is introduced into the jar, and the latter put in series with a sulphuric acid voltameter, fitted with a delivery tube so that the gas liberated when a current is passing may be collected in an inverted tube filled with water. In this arrangement the rate at which the bubbles of gas pass up the tube is roughly a measure of the strength of the current passing through the volta- meter and any other piece of apparatus which is in series with it. A current is now sent through the jar and the voltameter, and is so regulated that a bubble of gas ascends in the water tube once in two seconds or there- abouts. As soon as the current is adjusted, distilled water is poured continuously into the jar until it is full. In this way the sodium acetate solution is diluted without altering the quantity of salt which is between the elec- trodes, and which is therefore available for conduction, of the current. This progressive dilution of the salt, solution is accompanied by a gradual increase in the rate^ of evolution of gas from the voltameter, which points^ to an increase in the strength of the current which i» passing. The resistance, therefore, which the current experiences between the electrodes in the jar is diminishe(J by dilution of the sodium acetate solution; that is, the- conducting efficiency of the salt which is between the- electrodes, and which is constant in quantity throughout the experiment, increases with dilution. If a concentratedl acetic acid solution is put in the jar instead of sodiunB SALT SOLUTIONS 123 acetate solution, and the current is suitably adjusted, a similar result is obtained, except that the increase in the rate of erolution of the bubbles with dilution is much more marked in this case. The increase of conductivity with dilution is therefore more rapid for acetic acid than for sodium acetate. Measurement of Condnctivity. — The experiment just described demonstrates quaUtativelythe increase of con- ductivity with dilution, but it is easy to get a quantitative Fig. 15. measure of this change by determining the conductivity. The determination of the conductivity of a solution resolves itself into the determination of the resistance, and this is effected by a modification of the ordinary Wheatstone bridge method. The arrangement of the apparatus necessary for the determination of the resist- ance of a solution is represented diagrammatically in Pig. 15, where B is a resistance box, is a cell containing the solution ; ab is the bridge wire. The ends a and b of the bridge wire are connected with the small induction coil I, which gives an alternating current. This is neces- 124 PHYSICAL CHEMISTEY "^a-v T-* r^ sary in order to avoid the polarisation effects which would make themselves felt if a continuous current, such as is usually employed in the Wheatstone bridge method, were passed through the solution in 0. The use of an alter- nating current necessitates the replacement of the ordinary galvanometer by an instrument which will respond to such a current. A telephone is usually employed, and, as shown at T in the diagram, it is connected on the one hand with the point d,, and on the other with the moving contact c. When the apparatus is ready, the in- duction coil is operated by the accumulator A, and the moving contact is so adjusted on the wire ah that there is no sound in the' telephone. It follows then, according to well-known principles, that Resistance in C _ Length he _ Resistance in B ~ Length ae ' as the resistance in B is known and the lengths ae and 6c are easily ascertained on the scale over which the bridge wire is stretched, the resistance of the cell can be calculated. Various types of cell are employed according as the resistance of the solution is high or low. One of the most generally serviceable is shown in Pig. 16. The electrodes E are made of stout platinum foil, and are in electrical connection with the mercury in the glass tubes TT by means of two pieces of stout platinum wire sealed through the ends of these tubes. Connection is made with the rest of the apparatus by copper wires which dip in the mercury. The tubes TT are fitted tightly in the ebonite lid of the cell, so that the electrodes may be lifted out, rinsed and dried without their relative ^T Fig. 16. SALT SOLUTIONS 125 position being altered in the slightest. Before the cell is used the electrodes are platinised, that is, coated with a fine deposit of platinum black. This is done by electro- lysing a solution of platinic chloride in the cell, the electrodes being made alternately cathode and anode. It is customary to compare the resistance and con- ductivity of solutions with the resistance and conductivity of a hypothetical liquid which, if enclosed in a centi- metre cube, would offer a resistance of 1 ohm between two opposite faces of the cube acting as electrodes. In dealing with the density of liquids and solids we take water as the standard, and speak then of the specific gravity of a substance; similarly, in dealing with the resistance and conductivity of solutions we take the said hypothetical liquid as the standard, and speak then of the specific resistance and the specific conductivity of a solution. The specific resistance of a solution there- fore is simply the number which represents the resistance in ohms of a column of the solution 1 sq. cm. in section and 1 cm. long. The actual conducting column in the cell C has the resistance r, and if we suppose that the distance between the electrodes is I cm., and that the section of the conducting column is s sq. cm., then B, the specific resistance of the solution, is obtained by the formula B = Tj. The conductivity of a solution is t the reciprocal of the resistance, so that if we take k to re- present specific conductivity, we have « = _ = _. -. The evaluation of the specific conductivity depends therefore on the dimensions of the cell used, as well as on the observed resistance r. For most ordinary cells it would be impossible to obtain the exact values of I and s by mere measurements of length, and the device is usually adopted of first charging the cell with a solution the 126 PHYSICAL CHEMISTRY specific conductivity k^ of whicli has been accurately determined by special experiments. Such a solution is ^KCl, for which «(,= 0-002768 at 25°, or -^KCl, for which a;q = 0'001412 at 25°. These exact values have been obtained by determining the resistance of the solutions in cells for which I and s could be accurately determined. Suppose, then, that in an actual experiment N the cell is charged first with — -KCl, and secondly with the solution, the specific conductivity («) of which is to be found ; further, that the resistances measured in the two cases are respectively r^ and r at 25°. Subject to the condition that the relative position of the electrodes has remained the same throughout the experiment, «„= — .- and « = -.-, whence it follows Tq s r s that K = Kg,—. The value of k^ is known, the values of Vq and r have been determined, so that k is obtained by a simple calculation. It ought to be pointed out here that all solutions used in determinations of conductivity are prepared with specially pure water. Ordinary distilled water is re- distilled under certain conditions, and thus freed from various impurities which add to its conducting power. The question as to how far this purification, of water can be carried will be discussed later (p. 170). Specific Conductivity and Equivalent Conductivity. — When solutions of a salt of gradually decreasing con- centration are examined, it is found that the specific conductivity regularly diminishes. This falling off in the specific conductivity with increasing dilution is illus- trated by the figures in the first two columns of the following table, which refers to sodium chloride. The SALT SOLUTIONS 127 figures in the first column are the concentrations of the salt in gram-equivalents per litre of solution, those in the second column are the corresponding values of the specific conductivity at 25° ; the significance of the figures in the third column will be explained presently. Concentration. K, X, 0-0312 0-00356 114-1 0-0156 0-00183 117-4 0-0078- 0-000938 120-1 0-0039 0-000476 122-0 That the specific conductivity should diminish with increasing dilution is only to be expected, for its value is in each case based on the resistance between two opposite faces of a centimetre cube filled with the solution. Now as the solution is gradually diluted there will be less and less of the salt in this centimetre cube, less and less therefore of the substance which acts as the carrier of the current, for the water is a non-con- ductor, or at all events an exceedingly poor conductor. It is quite natural, then, that specific conductivity, based as it is on the consideration of a definite volume of the solution, should diminish with dilution. If, however, we are to ascertain really how the efficiency of a given salt in conducting the current varies with dilution, we must obtain a set of figures which relate to the same quantity of the salt at each dilution. Such figures are directly deducible from the values for the specific conductivity. Suppose that we are dealing with a normal solution of sodium chloride, and that we have an electrolytic cell the sides of which are formed by electrodes 1000 sq. cm. in area and exactly 1 cm. apart. This cell would hold 1 litre of the normal solution, and the quantity of salt between the electrodes would be 1 gram-equivalent. Since this solution may be regarded as made up of 1000 centimetre cubes, the 128 PHYSICAL CHEMISTET figure which represents the conducting power of the 1 gram-equivalent of salt will be 1000 times the figure which stands for the conductivity of a centimetre cube of the solution, that is, IOOOac, where k is the specific conductivity of a normal sodium chloride solution. If, instead of a normal solution of sodium chloride, we are dealing with a half-normal solution, the volume of the latter containing 1 gram-equivalent of salt is 2000 cub. cm., and to bring this gram-equivalent between two electrodes which are 1 cm. apart, the area of each electrode would have to be 2000 sq. cm. The bulk of solution between the electrodes in such an imaginary cell might be regarded as made up of 2000 centimetre cubes, and the figure which represents the conducting power of the 1 gram-equivalent of salt will be 2000 times the figiire which stands for the conductivity of a centimetre cube of the solution, that is, 2000/f, where K is the specific conductivity of a half-normal sodium chloride solution. This argument might obviously be extended to cover any solution of sodium chloride or any other electrolyte, but enough has been said to show that a measure of the conducting power of 1 gram- equivalent of electrolyte at various dilutions is to be found in the product — specific conductivity x volume of solution in cub. cm. which contains 1 gram-equivalent. For this volume of solution the symbol <^ is generally taken, and the conducting power of a gram-equivalent, the equivalent conductivity as it is termed, is represented by the symbol X, so that X = « . ^. With increasing dilution, as already indicated, the specific conductivity diminishes; the equivalent con- ductivity, on the other hand, increases steadily. This statement is borne out by the figures in the third column of the table on p. 127, and in greater detail by the numbers contained in the following table: — KCl. CH8.C00Na. HCl. NaOH. CH3.COOH. 98-3 41-2 301 160 1-32 102-4 49-4 327 172 2-01 112-0 61-1 351 183 4-60 115-9 64-2 360 190 6-48 122-4 70-2 370 200 14-3 124-4 72-4 373 203 20-0 126-3 74-3 376 206 30-2 127-3 75-2 377 208 41 128-1 75-8 ■ >• • >• 57 128-8 76-4 • ■• • •• 80 129-1 76-8 ■ ■• • •• 107 SALT SOLUTIONS 129 EQUIVALENT CONDUCTIVITY AT 18°. Oram-eguivalents per litre. 1-0 0-5 0-1 0-05 0-01 0-005 0-002 0-001 0-0005 0-0002 0-0001 The cases quoted in the foregoing table are merely instances of the behaviour of aqueous solutions of electrolytes generally, and there is therefore no doubt that the efficiency of an electrolyte as a conductor of the electric current increases with dilution. The figures in the table supply the quantitative basis for tljp con- clusion of which a qualitative demonstration has been described on p. 122. A study of the tabulated values for potassium chloride, sodium acetate, hydrochloric acid, and sodium hydroxide shows that X is increasing only very slightly in the most dilute solutions, that, in fact, it tends towards a maximum value which could be found by extrapolating to zero concentration. This may be done on the basis of an empirical rule dis- covered by Kohlrausch, who showed that for most electrolytes in dilute solution there is a linear relation- ship between the equivalent conductivity and the cube root df the concentration. The value thus obtained by extrapolation is known as the equivalent conductivity at infinite dilution, and is indicated by the symbol X^. Such an extrapolation can be safely made only in those cases in which \ changes but slightly in the most dilute solutions examined; it would, for instance, not 130 PHYSICAL CHEMISTEY be permissible in the case of acetic acid, where \ is increasing rapidly even at the greatest dilutions. Where extrapolation is out of the question, another method of finding the value of \„ must be adopted, a method that will be referred to later (p. 152). It should be noted that in this matter of extrapolation acetic acid is in quite a different category from sodium acetate, and the fact that the relative increase in \ between I'ON and O'OOOIN solutions is so much greater for acetic acid than for sodium acetate, is in harmony with the experiment described on p. 122. What significance is to be attached to the values of \^? According to the electrolytic dissociation hypo- thesis, a dissolved electrolyte takes part in the con- duction of a current only in so far as it is ionised, and its efiiciency in conducting the current will from this point of view be a maximum when ionisation is complete. The conducting efficiency, however, is, as we have seen, at a maximum in infinitely dilute solution, and therefore the value of \^ for any electrolyte is to be taken as a measure of the total number of ions that can be produced by the dissociation of 1 gram- equivalent. Similarly, the value of \ at any finite dilution is a measure of the number of ions produced by the partial dissociation of 1 gram-equivalent of the electrolyte under these conditions. The extent to which the electrolyte is ionised, the degree of dissociation (a), is given therefore by the simple formula a=^. The values of \„ at 18° for potassium chloride, sodium acetate, hydrochloric acid, sodium hydroxide, and acetic acid are 129-9, 77-2,. 383-3, 217-5, and 351-7 respectively. On the basis of these numbers and of the figures quoted in the table on p. 129, the following values of a have been calculated for a few selected concentrations : — SALT SOLUTIONS 131 Gram-equivalents per litre. KCl. CHa.COONa. HCl. NaOH. CHa.COOH. 10 0-76 0-53 0-79 0-73 0-004 0-5 0-79 0-64 0-85 0-79. 0-006 0-1 0-86 0-79 0-91 0-84 0-013 0-01 0-94 0-91 096 0-92 0-041 0-001 0-98 0-97 0-98 096 0-117 This table shows very plainly that on the basis of the electrolytic dissociation hypothesis we must regard potassium chloride, sodium acetate, hydrochloric acid, and sodium hydroxide as being highly ionised in dilute solution, and a similar result would be reached by a consideration of the experimental data for all sodium and potassium salts of monobasic acids, for nitric acid and potassium hydroxide. Acetic acid, on the other hand, is only slightly ionised even in very dilute solution, and in this respect is typical of . many monobasic organic acids, as well as of ammonia. There are however many acids which, as regards degree of dissociation, are in- termediate between hydrochloric acid and' acetic acid, just as there are many bases similarly intermediate between sodium hydroxide and ammonia. Yalues of a Obtained by Different Methods. — Eefer- ence has already been made to the fact that the electrolytic dissociation hypothesis offers an explanation not only of the abnormal osmotic behaviour of acids, bases, and salts in aqueous solution, but also of the part which these compounds play in the conduction of an electric current. Our closer examination of the bearing of the hypothesis on these two classes of phenomena has shown that the degree of dissociation of a salt, acid, or base in aqueous solution can be estimated in two ways: (1) from the osmotic behaviour, specially from the freezing point, of the solution; and (2) from its conductivity. The vital question then arises : Are the values of a, based on determinations of the freezing point, in agreement with 132 PHYSICAL CHEMISTEY those based on measurements of conductivity? Tha answer is, that although discrepancies occur in individual cases, the general parallelism between the two sets of values is so remarkable as to furnish a strong argument in support of Arrhenius's hypothesis. It was indeed this parallelism on which Arrhenius laid the main emphasis when the hypothesis was first brought forward. The general agreement between the values of a calculated from freezing point data and those derived from con- ductivity measurements is illustrated in the following table,' which embraces also certain figures for the osmotic activity of salts based on de Vries's isotonic coefficients. The last three columns of the table contain the values of i calculated (I.) from the depression of the freezing point; (II.) from the conductivity ; (III.) from de Vries's figures. Salt. KCl . . Oa(N03), MgSOi . CaClj . . K,FeCy„ , More recent and more accurate investigations have shown that the agreement between the values of a de- duced from the freezing point and from the conductivity is in dilute solutions better than the foregoing table would indicate. This contention is supported by the following figures for potassium nitrate : — Gram-equivalenta per litre. I. II. III. . 0-14 1-82 1-86 1-81 . 0-18 2-47 2-46 2-48 . 0-38 1-20 1-35 1-25 . 0-184 2-67 2-42 2-78 . 0-356 ,,, 3-07 3-09 Gram-equivalents per litre. . t from Freezing Faint. Irom Conductivity. 0-02 1-90 1-91 0-025 1-87 1-89 0-05 1-84 1-87 0-10 1-79 1-83 van't Hoff and Reicher. Zeit. pkysikal. Chem., 1889, 3, 198. SALT SOLUTIONS 133 It ought to be borne in mind that the values of a derived from freezing point experiments are valid for temperatures in the neighbourhood of 0° C, while those derived from electrical measurements are valid at 18° or 25°, at which temperatures most determina- tions of conductivity have been made. The degree of dissociation, however, does not alter much between 0° and 25°. Utility of the Electrolytic Dissociation Hypothesis. — The evidence submitted so far shows that this hypothesis is capable of giving an intelligible interpretation of the abnormal depression of the freezing point on the one hand, and of the formation and behaviour of conducting solutions on the other hand. The remarkable parallelism between the values for the degree of dissociation deduced from the freezing points of salt solutions and those based on con- ductivity measurements creates a strong presumption in favour of the hypothesis, and it has therefore been widely adopted as a working theory of electrolytic solutions. Its utility in this respect cannot be denied, and although there are directions in which apparently the theory requires modification or extension, it has provided a satisfactory basis for the quantitative treatment of the phenomena exhibited by solutions of acids, bases, and salts. Evidence of the value of the theory from this practical standpoint will appear later. It is perhaps desirable at this stage to emphasise once more the distinction which the theory makes between electrolytes and non- electrolytes. Arrhenius contends that the substances known as electrolytes are ionised in aqueous solution, and that in virtue of this ionisation their solutions conduct the electric current. The fact that a solution has a definite conductivity is evidence that the dissolved substance is ionised, and the conductivity 134 PHYSICAL CHEMISTRY is taken as a measure of the ionisation. Non-electrolytes, on the o'ther hand, are not ionised; they have a normal effect on the freezing point of water, and their solutions do not conduct the electric current. This broad dis- tinction between electrolytes and non-electrolytes is not invalidated by the fact that there are many electrolytes which are close to the border line. Their aqueous solu- tions are very feeble conductors of the electric current, and their influence on the freezing point of water is nearly normal. This simply means that the degree of dissociation in such cases is extremely small. That there is, however, a fundamental distinction between a typical electrolyte, such as sodium chloride, and a typical non-electrolyte, such as sucrose, is clear from a consideration of their osmotic and electrical behaviour. One objection which has been frequently urged against the electrolytic dissociation theory may be considered here, and that is the absence of a motive for dissociation. It is well known that the elements sodium and chlorine combine with extraordinary vigour to form sodium chloride, and that a very large amount of heat is developed when the combination takes place. Yet, according to the electrolytic dissociation theory, this compound is no sooner dissolved in water than the molecule is split up into two ions. This separation of the electrically charged atoms must obviously require a considerable amount of energy, and the question at once arises : From what source is this necessary energy derived? A full discussion of the question cannot be undertaken here, but it may be pointed out that much evidence has lately been accumulated showing that the ions are hydrated, that they carry about with them an envelope of water molecules. On the basis of this experimental material, the view has been brought forward that the attraction SALT SOLUTIONS 135 of the ions for water is the real motive for dissociation in aqueous solution, and that the energy necessary for the separation of the ions is derived from the heat of their combination with water.^ ^ See Lowry, Trans. Faraday Soc, 1905, 1, 197; Bousfield and Lowry, ibid., 1907, 3, 123. CHAPTER VIII ELECTROLYTIC DISSOCIATION; PHYSICAL AND BIOLOGICAL APPLICATIONS In the foregoing chapter the behaviour of acids, bases, and salts in aqueous solution has been contrasted with that of non- electrolytes, and it has been shown how the study of electrolytic solutions led up to the theory of ionic dissociation. The evidence discussed so far has been of a purely physical kind, but the theory has a highly important bearing on many physiological problems, as well as on questions connected with the general behaviour of electrolytic solutions. As a preliminaryj therefore, to a further consideration of the ionic hypo- thesis in its various aspects, it may be desirable to mention one or two facts which indicate the part played by electrolytes in the living organism. The ConductiYity of Physiological Fluids. — The fluids which bathe the tissues of plants and animals are electrolytic solutions. They contain, it is true, large quantities of non-electrolytic material, such as proteins, but they contain also appreciable quantities of salts, in virtue of which they are conducting fluids. Blood, for instance, is relatively a good conductor, the conductivity of the serum being nearly the same as that of a 0*7 per cent, sodium chloride solution. The figure found for the specific conductivity, of ox blood serum at 25° varies between 0'0114 and O'OISI, and if the serum is diluted, the specific conductivity diminishes in the same way as that of an ordinary salt solution. If the quantity 136 ELECTROLYTIC DISSOCIATION 137 of mixed salts in 1 litre of the undiluted serum is taken as a standard, and the conductivity of the diluted serum is in each case referred, not to 1 centimetre cube of solution but to this standard quantity of the mixed salts, numbers are obtained 'which are analogous to the equivalent conductivities recorded in the case of an ordinary salt solution, and which, like these, increase with dilution. By comparing the figure for the un- diluted serum with the maximum figure obtained on dilution, it is possible to estimate the average degree of dissociation of the salts in the undiluted serum ; this turns out to be from 0'65 to 0"76. The serum proteins, however, which amount to about 8 per cent., lower the conductivity of the undiluted serum more than that of the diluted serum, in which their concentration is much reduced, so that the foregoing figure is certainly too low. It is worth while noting by the way that the conductivity of defibrinated blood is only about half that of the corresponding serum. This is due to the fact that the defibrinated blood contains the corpuscles, which are non-conducting bodies, and diminish the con- ductivity by obstructing the active carriers of the current. The extent by which the conductivity of a sample of defibrinated blood is less than that of the corresponding serum has in fact been employed to calculate the total volume of the corpuscles in blood. The phenomenon is analogous to the lowering of the conductivity of a sodium chloride solution which results from the suspension of quartz powder in the solution. Since blood and other physiological fluids are possessed of the characteristics of electrolytes, it is not surprising that the replacement of the fluids which normally bathe animal tissues by solutions of non-electrolytes should result in very marked modification of the activities of the tissues so treated. It has been found, for instance, 138 PHYSICAL CHEMISTRY that if a frog muscle is allowed to lie in isotonic sucrose or dextrose solution long enough, to extract all the salts from the fluid which bathes the muscle fibres, then the muscle gets into a condition in which it has no power either to transmit or respond to a stimulus; its contractility has disappeared. The power, however, is not destroyed; it is only rendered latent, for on the addition of sodium chloride or other sodium salts, the muscle is again able to respond to a stimulus. While it is true that the greater part of the con- ductiyity exhibited by physiological fluids is due to the presence of inorganic salts, yet there are other substances present which are partially ionised, and which therefore contribute to the conductivity of these fluids. Under the influence of enzymes changes take place in the organism, which result in the production of ionised from non-ionised substances. Proteins, for instance, are split up by the action of trypsin, an enzyme found in the pancreatic juice, and produce peptones and amino- acids, substances which are ionised to a certain extent. The course of such a protein degradation may therefore be followed by observing the increase of conductivity, or, what is the same thing, the decrease of resistance. The following figures supply an illustration of this phenomenon : they refer to the action of trypsin on a solution of casein ogen : ^ — Time in Sesistance Minutes, in ohms. 3330 4 325-5 12 308-2 30 286-1 131 230-0 466 ' 187-4 711 180-1 ' Bayliss, Joum. Physiol., 1908, 36, 221. ELECTEOLYTIO DISSOCIATION 139 The decrease in viscosity which results -from the action of trypsin in this case is quite inadequate to account for the increase in conductivity, and the latter must therefore be attributed to an increase in the number of current carriers, that is, the ions. The conductivity method of following the formation of ions which results from protein degradation has lately been employed in comparing the antiseptic value of disinfectants.^ The evidence quoted in the foregoing paragraphs may suffice to indicate in a prehminary way that in the processes associated with vital activity electrolytes must play no inconsiderable part. It is therefore desirable to con- sider the characteristic properties of electrolytic solutions in greater detail than we have as yet done, and to inquire how far the theory of ionic dissociation is capable of interpreting these properties adequately. One fact, for instance, which forces itself on all who study the be- haviour of salt solutions is, that their properties are additive in character. What is the evidence for this generalisation, and supposing the evidence to be satis- factory, how is it to be explained ? The Additive Character of the Properties of Salt Solutions.^ Evidence Based on their Chemical Be- haviour. — It is generally recognised that the chemical reactions of a dissolved salt are simply the sum of the reactions which are characteristic of the positive part of the salt and those which are characteristic of the negative part. The behaviour of calcium chloride, for example, in dilute aqueous solution is not that of a compound which has its own individual peculiarities; the reactions of a dilute calcium chloride solution are simply those which are common to calcium salts .plus ' Sohryver and Lessing, Journ. Soc. Chem. Ind., 1909, 28, 60. ^ The phrase ' salt solutions ' is to be understood as coyering solu- tions of acids and bases. 140 PHYSICAL CHEMISTRY those which are common to chlorides. The significance of this is apparent, in view of the fact that in a chemical compound the characteristics of the components cannot as a rule be detected ; the properties of a given element are modified to an extent which depends on the other element or elements with which it has com- bined. Sulphur, for instance, unites both with carbon and with oxygen, forming carbon disulphide and sulphur dioxide respectively, but it is quite impossible to regard the properties of these two compounds as the sum of the properties of the components; the characteristics of sulphurj which would in that case be exhibited by both compounds alike, are conspicuously absent. The additive character of the reactions of dilute salt solutions is emphasised by contrast with the behaviour of organic substances. The existence of a common atom or group of atoms in these substances cannot be proved by the simple precipitation reactions on which we rely for the recognition, say, of bromides or sulphates in aqueous solution. The reactions of an organic com- pound, even in solution, are as a rule not resolvable into the reactions of the component atoms or groups. For instance, an aqueous solution of potassium ethyl sulphate is not precipitated by the addition of barium chloride, and alcoholic solutions of silver nitrate and phenyl bromide may be mixed without giving any precipitate of silver bromide. The electrolytic dissociation hypothesis supplies an interpretation of the additive character of reactions in salt solutions. According to this hypothesis, dilute solutions of sulphuric acid, copper sulphate, and potassium sulphate are alike in this, that they all contain large -quantities of the SO^ ion, so that when barium chloride is added to each of these solutions the same result ELEOTEOLYTIO DISSOCIATION 141 follows. It is possible however for a compound con- taining the — SO4 group, such as potassium ethyl sulphate, to dissolve without being ioniged, or to ionise in a different way from ordinary sulphates, and in such a case the addition of barium . chloride may not cause any precipitation whatsoever. Similarly, the failure of silver nitrate to precipitate phenyl bromide in alcoholic solution is to be attributed to the non-ionisation of phenyl bromide. Prom the point of view, then, of the electrolytic dissociation theory, the reactions which are so largely employed in ' analytical chemistry are ionic reactions, and the behaviour of a salt in dilute solution may be regarded as the reactions of the positive ion plubs those of the negative ion. The observation' that a compound which is very reactive in dilute aqueous solution frequently loses this character when dissolved in a non-ionising solvent is instructive in this connection. Thus acids in aqueous solution are characterised by their power of acting on carbonates, and yet a solution of dry hydrogen chloride in benzene — a solution, it should be observed, which does not conduct the electric current — is unable to attack dry sodium carbonate.^ Since this solution is a non-con- ductor, we may conclude that the dissolved hydrogen chloride is in the un-dissociated or un-ionised condition ; it appears, therefore, that the reactions of hydrogen chloride in aqueous solution are quite different from its reactions in the un-ionised condition. It has some- times been suggested that all instantaneous reactions, such as those occurring in the precipitation of one salt by another, are ionic reactions, but this statement is too sweeping. Kahlenberg^ has found cases of double decomposition accompanied by immediate precipitation ' See Kahlenberg, Journ. Physical Chem., 1902, 6, 1, ' Zoc. oU. 142 PHYSICAL CHEMISTRY in solutions which are excellent insulators. Thus a solution of dry hydrogen chloride in benzene and a solution of dry ammonia in benzene are both non- conductors like benzene itself, and yet, when mixed, they give instantly a white precipitate of ammonium chloride. The Colour of Salt Solutions, — If we take a series of coloured salts the colour of which springs from the presence of a particular metal or a particular acid radical, it is found that dilute solutions of the salts of each series have all the same colour. This is the case even when the solid salts or their concentrated aqueous solutions differ in colour; any such difference tends to disappear with dilution. Concentrated cupric chloride solutions are green, and in this respect differ from concentrated copper sulphate solutions, which are blue ; the green solutions, however, turn blue on dilution, and are then indistinguishable, so far as the colour goes, from dilute copper sulphate solutions. The colour of a cupric salt in dilute solution is in fact independent of the acid radical, provided that the latter itself makes no contribution to the colour. The additive character of the colour of a salt in dilute aqueous solution is brought out very clearly by a study of absorption spectra. Ostwald has recorded photographically ^ the absorption spectra of solutions of the permanganates of lithium, cadmium, ammonium, zinc, potassium, nickel, magnesium, copper, hydrogen, aluminium, sodium, barium, and cobalt (in all cases 0*002 gram- equivalent per litre). The absorption bands are practically identical for all these solutions, and occupy the same positions in the spectrum. This striking result strongly supports the contention that the colour of a dilute salt solution 1 Zeit. physikal. Ohem., 1892, 9, 579 ELECTROLYTIC DISSOCIATION , 143 is an additive property based on the independent contributions made by the metallic and acidic parts of the salt. An intelligible explanation o£ this inde- pendence of the metallic and acidic parts of a salt is furnished by the electrolytic dissociation theory, according to which a dilute salt solution is mainly a mixture, in electrically equivalent quantities, of the two ions. The theory postulates that the spheres of influence of those ions are distinct, and that in regard to colour as well as chemical reactivity, each ion makes its characteristic contribution to the properties of the solution. Ionic ConduotiYity. — Evidence of a more definitely quantitative kind in favour of the view that the metallic and acidic parts of a salt are to a large extent inde- pendent of each other in dilute solution is obtained by considering the way in which the value of the equivalent conductivity varies from one salt to another. Suppose that for this purpose we deal with the figures recorded in the following table; they represent the equivalent conductivities found for half-a-dozen alkali salts at 18° in O'OOOl normal concentration:^ — Chloride. Ifitrate. Potassium .... 129-05 125-49 Sodium 108'06 104-53 Lithium 98-06 94-38 A glance at these figures will show that Xkci — ^NaCi = 20"99, and that Xkno, — ^NaNOa = 20-96, practically the same figure. Further, \Kci~''^LiCi = 30'99, while Xkxo, — XLiJN0, = 31"ll, practically the same figure. Again, Xkci — XkN03 = 3'56, XlfaCl — ^NalfO, = 3'53, and A-LiCl — ^LiNO,, = 3*68. "Expressed in words, these figures mean that the change in the value of the equivalent conductivity produced 1 Kohlrausoh and Maltby, Sitzungsber. Ic. Akad. Wiss. Berlin, 1899, 665. 144 PHYSICAL CHEMISTRY ... by substituting a sodium salt or a lithium salt for a potassium salt is the same whether the salt is a chloride or a nitrate ; that is, the metallic part of the salt makes a contribution to the conductivity which is in- dependent of the acidic radical with which it is associated. The values of the last three differences show similarly that the substitution of a nitrate for a chloride of equal concentration leads to a decrease of \, which is the same whether the metallic part of the salt is potassium, sodium, or lithium. Similar relationships would be found to exist if we dealt with the values of X^, obtained by extrapolation, instead of the values of X for O'OOOl normal solutions, and we may therefore conclude that the contribution which an ion makes to the equivalent conductivity of a highly diluted solution is independent of the other ion with which it is associated. Kohlrausch, who first detected the additive character of the con- ductivity of a highly diluted salt solution, expresses the independence of the ions in this respect by the equation X^=u + v, where u and v are the contributions which the cation and anion respectively make to the equivalent conductivity at infinite dilution. This equation is the expression of what is generally known as Kohl- rausch's Law of the Independent Migration of the Ions, and the terms u and v which appear in the equation are described as ionic conductivities. The value of u for a given cation remains the same for all salts which contain this cation, just as the value of v for a given anion remains the same whatever be the salt of which it forms part. The actual numerical values of u and v cannot however be obtained until some other equation is available which involves these quantities. The numbers recorded in the last table show very clearly that the contribution made to the conductivity by the lithium ion is less than that made by the sodium ELECTROLYTIC DISSOCIATION 145 ion, and this again is less than the contribution made by the potassium ion. In view of this the question at once suggests itself: Why should one ion contribute more than another to the conductivity of a solution? If, in accordance with the theory of electrolytic dis- sociation, we conceive the passage of a current through an electrolyte as consisting in the movement of elec- trically charged material particles, we might regard the superior efficiency of a given ion in the conduction of the current as due either to its carrying a greater charge, or to its moving more rapidly than other ions under the same conditions. The first explanation cannot be maintained, for Faraday has shown that the quantities of different ions liberated during electrolysis by a given current are in the ratio of their chemical equivalents ; that is, with a gram-equivalent of each ion there is associated the same definite quantity of electricity. All univalent ions — for example, K', Na*, CI', NOg', NH^' — must therefore carry the same charge. We are driven accordingly to the second possible explanation of the differ- ence in the contributions made by various ions to the con- ductivity, namely, that, exposed to the same electrical forces, different ions have different mobilities: one ion may be faster or slower than another ion. The accept- ance of this view involves certain conclusions as to changes of concentration which must accompany the process of electrolysis. We shall first deduce these conclusions, and then compare them with the results of experimental work. The assumption that the contribution which an ion makes to the equivalent conductivity depends on its mobility may be expressed more definitely by the equation ^^ speed of cation ^^g^ .^ .^ ^^ ^j^^^ ^-^^^ .^ ^^^ V speed of anion ■' ions of a salt move at different rates, the fall of con- 146 PHYSICAL CHEMISTRY centration round the anode due to electrolysis is different from the fall of concentration round the cathode. Suppose that the condition of an electrolytic solution before electrolysis commences is represented diagram- matically, as in Fig. 17. Between the anode A and the cathode C there is, we may suppose, only a limited number of fully ionised molecules. The electrolytic s s ©©©©©e©©©©©©©©©© 0e0e©©e0e©©000e© FlO. 17. cell may be conceived as divided into three parts, a compartment round the anode and one round the cathode, each containing six fully ionised molecules, as well as an intermediate compartment containing four fully ionised molecules. The compartments are separated from one another by the porous septa SS. Suppose, to begin with, that the positive and negative ions move at the same rate. If a current is passed just so long that two cations cross each of the septa SS from left to right, then in this time two anions will have crossed the septa from right to left, and the position of matters will be as represented in Fig. 18. In the ©@©©©©©©©©©©©©©© 0©00e00©00©©00e0 Fig. 18. . intermediate compartment there will still be four mole- cules as before the electrolysis; the concentration there is unaltered. The isolated ions are those which have been liberated at the electrodes during the passage of BLBCTEOLYTIO DISSOCIATION 147 the current: the number of these liberated ions is the same at each electrode, as required by Faraday's law. In the solution round the anode there are now four molecules — a loss of two molecules; in the cathode compartment there are four molecules left — ^likewise a loss of two molecules. Hence, when the ions move at the same rate, the fall of concentration round the anode is equal to the fall of concentration round the cathode. Suppose next that the speed of the cation is twice as great as that of the anion, and that the current passes just so long that two cations pass across each of the septa SS from left to right; in this time one anion will pass across each septum from right to left, and the position of matters will then be as represented in Fig. 19. s s ee©©e©©e©©©©e©ee eeeeeeeeeeesoee© Fig. 19. As before, the concentration in the intermediate com- partment is unaltered, while three ions have been liberated at each electrode. The number of molecules left in the anode compartment is now four — a loss of two; the number of molecules left in the cathode com- partment is five — a loss of one. We have therefore Fall of concentration round anode 2 speed of cation Fall of concentration round cathode " 1 ~ speed of anion This line of argument might be extended to cover other speed ratios, and a similar conclusion would be reached. On the basis, therefore, of the view that dif- ferent ions make contributions to the equivalent con- ductivity in proportion to their rates of migration 148 PHYSICAL CHEMISTRY under the action of the same electrical force, we have u _ speed of cation _ fall of concentration round anode V speed of anion ~fali of concentration round cathode' P vided that in any experiment carried out in order to determine the relative speed of the iona there is an intermediate zone of the electrolyte in which no change of concentration has taken place. If we adopt the view that during the electrolysis of a salt solution the ions are moving at different speeds, then it is obvious that of the electricity which is transported across any given section of the electrolyte, a greater fraction will be carried by one ion than by the other. If, for instance, the cation moves twice as fast as the anion, then two cations will cross a given section of the electrolyte from left to right, while one anion is crossing the same section from right to left; since the ions carry equal charges, this means that the quantity of positive elec- tricity transported across the section is twice as great as the quantity of negative electricity. To put it gene- rally, let us suppose that of the total transported elec- tricity the fraction ii is carried by the anions and the fraction 1—nhj the cations ; then 1— n u _ fall of concentration at anode n ~ v~ fall of concentration at cathode" Now there is a well-known algebraic theorem which states that if r=j, then —ri^^rgi if this theorem is applied to the foregoing equations, it is easily shown that 1 u fall of concentration at anode l—n= ——= and u + v total fall of concentration ' V fall of concentration at cathode u + v total fall of concentration Hittorf s Work. — So far we have simply attempted to deduce the conclusions that follow from the assump- tion of different ionic velocities, and we may now ask ELECTEOLYTIC DISSOCIATION 149 Do changes of conceiltration occur round the electrodes during electrolysis, and if so, is the fall of concentration at one electrode in some cases different from that at the other electrode? These questions were answered long ago in the affirmative by the classical work of Hittorf, who determined the values of n and \ — n, the transport or migration numbers as they are called, for various anions and cations. A particular example may perhaps be quoted to show the sort of experi- mental data which Hittorf obtained, and the way in which he employed these data to calculate the transport number. An electrolytic cell containing a solution of copper sulphate was put in series with one containing a solution of silver nitrate. After a current had been passed for some time, it was found that I'OOS gram of silver had been deposited on the cathode of the silver nitrate cell. According to Faraday's law, this amount of silver must be equivalent to the copper deposited on the cathode of the copper sulphate cell; this weight 31*8 of copper must therefore be 1-008 x ^^ = 0"2968 gram, a figure which is a measure, in terms of copper, of the total loss of concentration in the copper sulphate cell. Before electrolysis the solution round the cathode con- tained, as shown by analysis, an amount of copper sulphate equivalent to 2-8543 grams of copper oxide: after electrolysis the cathode solution gave on analysis 2-5897 grams of copper oxide. Electrolysis has resulted therefore in a fall of concentration at the cathode re- presented by 0-2646 gram CuO or 0-2114 gram Ou. This loss, however, is less than the weight of copper which has been deposited on the cathode out of the surrounding solution, namely, 0-2968 gram, and it is therefore obvious that the difference, 0-2968 — 0-2114 = 0-0854 gram, must have migrated from the anode com- 150 PHYSICAL CHEMISTKY partment into the cathode compartment. The figure 0"0854 represents, in terms of copper,- the fall of con- centration round the anode, and we have accordingly 1 ^_ fall of concentration at a node_ 0'0854 _j^,f)Qn _-l' i, ~" total fall of concentration ~0'2968~ ' is therefore the transport number for the copper ion in this solution. The transport number for the sulphate ion is 0'712, and a comparison of these figures shows that of the total electricity transported across any section of the electrolyte about seven-tenths is carried by the negative ions. Numerical Values for Ionic Conductivity. — From the work of Hittorf and others who have followed him, we know then the ratio of the contributions which the ions of an electrolyte make to the equivalent conductivity. The value of this ratio may not be the same in con- centrated and in dilute solutions of the electrolyte, but it is found on investigation that after a certain stage of dilution no further change in the value of the ratio takes place. As an illustration of this we may take the following figures obtained by Hittorf for the tran- sport number (1— w) of silver in silver nitrate solutions of different concentration : — Weight of Water to , IgramAgNOa. , ■'""• 2-48 0-532 2-73 0-522 5-18 ...... 0-505 10-38 ...... 0-490 14-5 0-475 49-4 0-474 247-3 0-476 These figures show that the transport number for silver in dilute solutions is 0-475, and that this value does not alter over a considerable range of concentration. ELECTEOLYTIO DISSOCIATION 151 So for other ions values of the transport numbers are obtained which are valid for highly diluted solutions, and which can be used in the following way to calculate ionic conductivities. We have seen that \^=u + v, 1 — n = — —.and n = — — ; henceitfoUowsthatw = (1 — n)\^ , and v = nX^. The value of X^ for a salt is ascertained, 00 CO ' as already shown, by extrapolating from the actually observed figures for \, while the values of n and 1 — n are given by Hittorf's work. As an example of the way in which ionic conductivities are calculated, the case of potassium chloride may be taken. For this salt \^ at 18° = 129"9, while the transport number for chlorine is 0-503. We have then % = 0-497 X 129-9 = 64-6, and ■y = 0-503x 129-9 = 65-3 ; that is, the ionic conduc- tivity of potassium at 18° is 64-6, and the ionic con- ductivity of chlorine is 65-3 at the same temperature. In a similar manner, by combining the values of n, 1 — n, and ^^^ior any electrolyte it is possible to calculate other ionic conductivities. It is noteworthy, however, that when one ionic conductivity has been evaluated, all others can be calculated from it by means of the formula \^=u + v, without any further determination of trans- port numbers. Suppose, for instance, that on the basis of the value 0-503 for the transport number of chlorine in potassium chloride the ionic conductivity of chlorine at 18° has been found to be 65-3, as just shown. Then since \„ for sodium chloride at 18° has been found to be 108-8, and since, according to Kohlrausch's law of the independent migration of the ions, X^for NaCl = Mifa+Vci, we have 1 08-8 = Mira + 65-3, whence MNa = 43-5. The following table records the values of the con- ductivity at 18° for various ions : — 152 PHYSICAL CHEMISTRY Cations. Anions. H . . . 318 OH. . . . 174 Li ... . 33-4 CI . 65-3 Na . . . . 43'5 I 66-4 K . . . . C4-6 NO, . . . 61-8 NHj . . . 64-4 CH3.COO. . 33-7 Ag . . . . 54-0 These figures, it should be noted, are based on the investigation of electrolytes for which \^"can be deter- mined by extrapolation from the measured values of \. So soon, however, as the values of 11 and v have been ascertained for various ions it becomes possible to calcu- late the value of \^ for electrolytes where an extra- polation cannot be made. Acetic acid supplies an instance of this. A glance at the figures for acetic acid recorded in the table on p. 129 shows that even at the highest dilutions the value of \ is still increasing so rapidly that an extrapolation is not permissible. But if Kohlrausch's law is valid for acetic acid at infinite dilution as it is for other electrolytes, then \^ =u^ + Vxa, where Mh is the ionic conductivity of hydrogen, and Vxe is the ionic con- ductivity of the acetate radical. The values of mh and v^e have been ascertained by a study of strong acids and of alkali acetates, and are recorded in the table of ionic con- ductivities. Hence for acetic acid \^ = 318 + 33'7 = 351"7, a figure which has been quoted already on p. 130. Actual Yelooity of Migration of the Ions. — The method employed in deducing the values of the ionic con- ductivities is based on the view that electrolysis consists in a streaming of positively charged ions in one direction and of negatively charged ions in the opposite direction, that the positive and negative ions may move at different rates, and that to this cause is due the difference in the contributions which the two ions of an electrolyte make to the equivalent conductivity. This view is con- ELECTEOLYTIO DISSOCIATION 153 firmed by the concentration changes which do occur during electrolysis, and by the relative magnitude of these changes round anode and cathode respectively. The values of u and V already quoted give, however, no direct information as to the actual speed at which the ions move under the action of a given electromotive force. They are measured in the same units as the equivalent conductivity, and enable us in the first place to deduce only the relative speeds of the two ions of an electrolyte under the same conditions. The actual speed of any particular ion will of course depend on the magnitude of the electric force which is acting on it, in other words, on the steepness of the potential gradient between the two electrodes. It is, however, possible to calculate from the ascertained values of ionic conductivity the actual rates at which the ions move when the fall of potential through the elec- trolyte has some definite value, say 1 volt per cm. The details of this calculation cannot be given here, but the results may be illustrated by the following figures. Pro- vided that the fall of potential in the electrolyte is 1 volt per cm., the hydrogen ion moves at the rate of 0-0033 cm. per second, the hydroxyl ion 0"0018 cm. per second, and the potassium ion 0'00067 cm. per second. If in some particular case the fall of potential were 10 volts per cm., then the rates at which the ions move would be ten times as great. Not only is it possible to calculate the actual velocity of the ions ; it can be determined by direct observation. The way in which this is possible is illustrated by the following experiment, first suggested by Nernst. A glass tube, about 1 mm. bore, is sealed at one end to a small tap funnel and at the other to a U tube, each limb of which is 5-8 mm. diameter. The capillary tube is then bent as shown in Fig. 20. A dilute solution of potassium permanganate (0*003 normal relatively to 154 PHYSICAL CHEMISTRY potassium), to which 5-10 per cent, of urea has been added in order to increase its density, is poured into the funnel, and the tap is opened until the capillary, tube is filled as far as its junction with the U tube. The tap is then closed, and the U tube is half or two-thirds filled with a O'OOS normal solution of potassium nitrate. The stop- cock is again carefully turned on, and the permanganate solution is allowed to occupy the bottom of the U tube slowly, pushing the potassium nitrate solution before it into each limb. When the U tube is completely full the stopcock is finally turned off. We thus obtain a column of potassium perman- ganate solution isolated between two columns of potassium nitrate solution. Two platinum wires connected with the terminals of a powerful battery, or say a 100-volt lighting circuit, are dipped in the solution at the top of each limb, the positive wire being placed in the right-hand limb. After the current has been running for a short time it is seen that the boundary \ V/y between coloured and colourless solu- ^~>/-^ tion is higher in the right limb I I than in the left; that is, the per- manganate ion which is responsible FlO 20 for the colour of the permanganate solution has visibly advanced towards the anode. If the advance of the boundary is measured, and if the potential difference between the electrodes, as well as their distance apart, is known, we may estimate the actual rate at which the permanganate ion would migrate if the fall of potential were 1 volt per cm. ELECTROLYTIC DISSOCIATION 165 The correctness of this estimate depends on whether the fall of potential is regular throughout the whole column of electrolyte between the electrodes. This would be the case only if the specific conductivity of the per- manganate solution were the same as that of the potas- sium nitrate solution. It is evident, therefore, that any determination of the rate at which an ion moves involves a knowledge not only of the distance covered, but also of the exact potential gradient. A discussion of the means adopted to ascertain the potential gradient, and of the conditions necessary to secure a sharp boundary between two solutions during electrolysis, is beyond the scope of this volume, but it may be mentioned that the advance of a boundary even between two colourless solu- tions can be followed by a method depending on the difference in refractive index.* Ionic Conductivity and Hydration. — Consideration of the numerical values of the ionic conductivity raises a point of great interest in connection with the theory of solutions. In the group of alkali metals, as recorded on p. 152, Mi,i = 33'4, Mifa = 43-o, and Mk = 64'6; the lightest metal furnishes, therefore, the most sluggish ion of the three, and the heaviest metal yields the most speedy ion. This curious result is now generally attri- buted to the different hydration of the ions.^ It is supposed that of the three the lithium ion is hydrated to the greatest extent, and that the size of the water •envelope,' of which the lithium ion is the nucleus, is responsible for the greater friction experienced by it in passing through the water, and therefore for its smaller mobility. The potassium ion, on the other hand, is pre- > Steele, Journ. Chem. Soo., 1901, 79, 414. ' See Kohlrausoh, Proo. Roy. Soc, 1903, 71, 338 ; Bousfield, Proo. Roy. Soc., 1905, 74, 563 ; PhU. Trans., A, 1906, 206, 101 ; Senter, Science Progress, Jan. 1907. 156 PHYSICAL CHEMISTRY. sumably hydrated to a less extent than either the sodium or the lithium ion. It is further noteworthy that for the three ions already mentioned the temperature coefficient oi the motility is greatest for the lithium ion and smallest for the potassium ion. This observation is at least in harmony with the view that the relative hydration is as suggested, for rise of temperature is bound to favour the breaking down of the hydrates, and the effect of a rise of temperature would probably be most marked in the case of the ion which is most highly hydrated. The view that the ions of an electrolyte are hydrated finds support in the observation that the temperature coefficient of the conductivity of a dilute solution is practically the same as the temperature coefficient of the fluidity of water ( fluidity = -^ rr— ). This seems ■' \ •' viscosity/ to show that the resistance which the ions experi- ence in their movements is the frictional resistance of the solvent, a result which becomes intelligible if it is supposed that each ion carries a water envelope along with it. Ionic ConductlYity and the Diffusion of Electro- lytes. — The difference in the contributions which various ions make to the equivalent conductivity of an electrolyte has been attributed to the difference in their speeds. The figures recorded in the table on p. 152 are therefore a measure of the speeds at which the ions move under the action of a given electromotive force ; they are proportional to the ' mobility ' of the ions. Now the mobility of an ion will come into play not only when it is in an electric field, but when it is involved in a concentration gradient, that is, when the salt of which it forms part is diffusing from places of high concentration to places of low concentration. ELECTROLYTIC DISSOCIATION 157 In the case of hydrochloric acid, for instance, the fact that the mobility of the hydrogen ion is about five times that of the chlorine ion must have a direct bear- ing on the rate of diffusion. Suppose that a solution of hydrochloric acid is in contact with pure water. Diffusion occurs, and it might be thought in view of their relative mobilities that the hydrogen ions would soon outstrip the slower chlorine ions. A little reflection, however, ,shows that such a separation of ions cannot take place except to an infinitesimal extent. In consequence of the greater mobility of hydrogen, the front rank of the diffusing acid will consist of positive hydrogen ions, while behind these there will be an excess of negative ions. Electro- static forces are thus called into action, which prevent anything more than an infinitesimal separation, and which have the effect of retarding the advance of the hydrogen ions and accelerating that of the chlorine ions. The net result is that the acid diffuses as a whole without any measurable separation of hydrogen and chlorine, the different natural mobilities of the two ions being compensated by the action of the electrostatic forces. Jt is evident, however, that the rates of diffusion of different chlorides will depend on the mobility of the positive ion, on its ability to push on in front and so accelerate the advance of the chlorine ion. We may therefore expect that when various chlorides are arranged in order according to their rates of diffusion in aqueous solution, the order will be the same as that of the conductivities of the positive ions ; similarly, we may expect that when various sodium salts are arranged according to their rates of diffusion in aqueous solution, the order will be the same as that of the conductivities of the negative ions. These expectations are borne out by the figures in the following tables, which give 158 PHYSICAL CHEMISTRY the diffusion coefficients of various chlorides and various sodium salts at 18° : — Diffusion Coefficient. Diffusion Coefficient. HOi . . . 2-30 NaOH . . . 1-40 KCl . . . 1-46 NaCl . . . 1-14 NaOl . . . M4 NaNOg. . . 1-03 LiCl . . . 1-00 NaCHaCOO . 0-78 Eeference to the table of ionic conductivities on p. 152 will show that in regard to mobility, H">K'>Na'>Lr, and that OH' > CI' > NO3' > OH3COO'. The. difference in mobility of various ions, then, is modified, so far as diffusion is concerned, by the electro- static attraction between the ions, and gives rise to a difference of potential at the common surface (1) of salt solution and water, (2) of differently concentrated solutions of the same salt, or (3) of solutions of different salts. It is in this direction that we must seek for an explanation of the electrical effects which, as found by physiologists, so frequently accompany vital activity. Differences of electrical potential in the tissues are probably due to a separation (infinitesimal in extent) of the positive and negative ions of the electrolytes which bathe these tissues. It will be apparent from the foregoing that the positive and negative ions of an electrolyte are not absolutely independent. The charges which the ions carry are responsible for the intervention of electro- static forces, and these limit the independence of the ions, so far at least as their separation is concerned. Another case in which the factor of electrostatic attrac- tion between the ions has a definite bearing is the problem of the permeability of living membranes to electrolytes. So far as reference has been made to this problem in the present volume, the behaviour of salts ELECTROLYTIC DISSOCIATION 159 only as indivisible units has been considered. We have however now adopted the view that salts are more or less ionised in aqueous solution, and that the ions are in many respects independent of each other. The questions then naturally arise : Is it not possible that the two ions of a salt are characterised by a different power of penetrating the living membrane ? If so, what would be the result if a solution of the salt were separated from pure water by such a membrane? If we assume for the moment that the ions of a salt do differ in their power of penetration, and, taking an extreme case, we suppose that the membrane is permeable to the anion but impermeable to the cation, then a little consideration shows that the salt as a whole cannot penetrate the membrane. For the passage of the anions through the membrane would mean a separation of the ions; this, as has been already shown, is opposed by the electrostatic forces, and can take place to an extent which, so far as analytical methods of detection go, is absolutely negligible ; the membrane would be practically imper- meable to the salt. It would, however, be the seat of a potential difference originating in the same manner as the potential difference at the common surface of salt solution and water, and the possibility of electrical effects arising in this way at the surface of a membrane bathed by an electrolyte has an important bearing on the problems of electro-physiology. ' In the case of the salt just described the anions are prevented from passing through the membrane by the inability of their positive partners. Actual transport of these anions through the membrane would be rendered possible however either (1) by adding to the salt solution another electrolyte the cation of which is able to pene- trate the membrane, or (2) by adding tg the water on the further side a salt for the anion of which the 1 See Donnan, Zeit. Elektwchem, , 1911, 17, 572. 160 PHYSICAL CHEMISTRY membrane is permeable. In the first case, the cation of the added salt and the anion of the original salt could cross the membrane together in electrically equiva- lent quantities ; in the second case, there would be an exchange of the two anions, also in electrically equiva- lent quantities. This is not an imaginary picture, for investigations by Hamburger, Koppe, and others '^ have shown that the plasmatic membrane of blood corpuscles is generally permeable to anions. Some of the facts which support this conclusion may be quoted briefly. When a current of carbon dioxide, is passed through blood, chlorine passes from the serum into the corpuscles, and the alkalinity of the serum increases. Again, if blood cor- puscles are separated by centrifuging, suspended in an isotonic solution of a neutral sodium salt and sub- jected to a current of carbon dioxide, the salt solution becomes strongly alkaline. If, on the other hand, the separated corpuscles are suspended in an isotonic solu- tion of sucrose or dextrose and there subjected to a current of carbon dioxide, no alkalinity results. The most satisfactory explanation of these phenomei;ia is based on the view that the carbon dioxide penetrates the covering of the blood corpuscles, and reacting with some of the corpuscle contents, probably the proteins, gives rise to the carbonate ions HCO3' and CO3". The plasmatic membrane being permeable to anions, an ex- change between these carbonate ions and chlorine ions in the surrounding fluid becomes possible, and leads to the production of sodium carbonate, and consequent alkalinity, in the sodium salt solution. Emphasis has already been laid on the condition that any such exchange of ions across a membrane ^ Hamburger, Zeitsch. Biol., 1891, 28, 405; v. Limbeck, Aroh. eieper. PaiAoZ.,1895, 35, 309; Keppe,P/agrer's^rcA., 1897, 67, 189; Hamburger and VAU Lier, Engelmamn's Arch. Physiol., 1902, 493. ELECTROLYTIC DISSOCIATION 161 must take place in electrically equivalent proportions. If in the case of blood corpuscles the CO3" ion is ex- changing with the or ion, it is obvious that for every carbonate ion that leaves a corpuscle two chlorine ions must enter ; in order to preserve osmotic equilibrium between the corpuscle contents and the surrounding solution, water also must pass in, and the bulk of the corpuscles must increase. No such increase in the volume of the corpuscles is to be expected if the COg" ion is exchanging with the SO/' ion. The correct- ness of this line of argument has been confirmed by experiment in the following w£i,y. Equal quantities of blood corpuscles are suspended in isotonic solutions of (1) sucrose, (2) sodium sulphate, (3) sodium chloride, (4) sodium nitrate, (5), potassium nitrate, and a current of carbon dioxide is passed in each case. The volumes occupied by the corpuscles after centrifuging are equal for cases (1) and (2), equal also for cases (3), (4), and (5), but greater for the second set than for the first. From recent investigations it appears that the cover- ing of red blood corpuscles is permeable not only for anions, but also, in certain cases at least, for cations. According to Hamburger,^ when a small quantity of calcium chloride is added to bullock's blood, the calcium distributes itself between serum and corpuscles, that is, the covering of the corpuscles is permeable to the calcium ion. Such corpuscles, further, into which calcium has thus penetrated, lose the extra amount they have taken up when they are washed with normal serum ; the calcium ion, that is, can pass out as well as in.- Hamburger maintains that the passage of calcium ions into the corpuscles occurs only when an exchange with other cations is possible. 1 Zeit. pKyHkal. Chem., 1909, 69, 663, 162 PHYSICAL CHEMISTEY , If it should turn out on further investigation that the red blood corpuscles are permeable for cations generally, then Overton's generalisation, according to which the permeability relationships of plant and animal cell mem- branes are alike (see p. 80), would have to be modified. Specific Action of Ions. — In the foregoing para- graphs attention has been drawn to a property possessed by only one ion of an electrolyte, the manifestation of which is restricted by the aqtion of electrostatic forces. There are, however, other properties which are specifically characteristic of either the anion or the cation, and the manifestation of which is free from any such limitation. That we should be able to detect the specific activity of any one ion is only natural in view of the generally additive character of the properties of electrolytes, and is further in harmony with the comparative independence of the ions postulated by the electrolytic dissociation theory. The influence of various alkali salts on the contractility of muscle may be taken as an instance of the way in which a specific property is associated with some parti- cular ion or ions. On p. 138 it was stated that if a frog muscle is allowed to lie in isotonic sucrose or dextrose solution long enough to extract all the salts from the fluid which bathes the muscle fibres, the muscle loses its power of transmitting or responding to a stimulus. The contractility, however, is restored on treatment of the muscle with solutions of sodium salts. Any sodium salt serves for this purpose; the character of the anion with which the sodium is associated is practically immaterial.^ This observation in the physio- logical field is closely related to the fact, already dis- cussed, that the chemical reactions of salt solutions are additive in character; the solutions of calcium salts, ^ Overton, PHuger's Archiv., 1904, 105, 176. ELECTEOLYTIC DISSOCIATION 163 for instance, give certain reactions which are the same whether it is the nitrate, the chloride, or the sulphate which is employed; the character of the anion with which the calcium is associated is immaterial. In con- trast to the power of sodium salts to restore the contractility of muscle stands the behaviour of potas- sium salts; none of these is able to neutralise the paralysing effect of treatment with sucrose solution. Further investigation on these lines shows that the sodium salts are in a category by themselves, and that the maintenance of contractility is a specific function of the sodium ion. In this or any other case where some effect is specifi- cally associated with the one ion of an electrolyte as distinct from the other ion and from the undissociated molecule, then the magnitude of the effect ought mani- festly to depend on the degree of the ionisation. This conclusion has been verified to some extent by the work of Paul and Kronig^ on the germicidal effect of various salts. For the purpose of comparison the salt solutions were allowed to act for a given time on approximately equal numbers of anthrax spores, and the number of colonies which developed subsequently was taken as a measure of the germicidal power of the salt solution. Other conditions being kept uniform, it was found that the number of colonies which develop after treatment of the spores with a given salt decreases as the treat- ment is prolonged and as the concentration of the salt solution is increased. For equally concentrated solutions of salts, all containing a cation of marked germicidal power, the number of colonies developed ought to in- crease as the degree of dissociation diminishes. Paul and Kronig tested this contention by comparing the disinfecting power of mercuric chloride, bromide, and '■ ZeU. phydkal. Chem., 1896, 21, 414. 164 PHYSICAL CHEMISTRY cyanide ; it is known that for equal concentrations of these salts the degree of dissociation is greatest in the case of the chloride, and. least in the case of the cyanide. The following table gives the results obtained : — Number of Colonies developed after Disinfecting Solution. Treatment lasting for 20 Minutes, 86 Minutes. HgClg (1 mol. in 64 litres) 7 HgBr^ ( „ „ „ ) 34 Hg(CN)2 ( „ 16 „ ) oo 33 On the assumption that the germicidal effect of the undissociated molecules and of the anions is negligible, these figures are in harmony with the view that the degree of dissociation of the three mercury salts increases from the cyanide to the chloride. So far therefore we may lay down the proposition that the disinfecting power depends not on the total concentration of mercury salt, but on the concentration of the mercuric ion.i But when mercury salts other than the halogen salts are investigated, it appears that the concentration of the mercuric ion is not the only factor which determines the germicidal power. Paul and Kronig found that mercuric nitrate, although dissociated to a much greater extent than mercuric chloride, has .a much weaker germicidal effect. According to Hober, this is due to the fact that of the two salts the chloride alone is soluble in the lipoid substances of which the living cell membrane consists; in virtue of this it is able to get ' Interesting evidence as to the specific action of tlie mercuric ion is supplied by Senter's study of the influence of various substances on the catalytic efficiency of haetnase {Zeit. physiJcal, Chem., 1905, 51, 673). It was found that hydrocyanic acid and mercuric chloride, which are partly dissociated substances, paralyse the activity of haemase much more powerfully than mercuric cyanide, which is practically undis- sociated. ELECTEOLYTIO DISSOCIATION 165 at the protoplasm inside much more rapidly than the nitrate, and its power of penetration more than makes up for its deficiency of mercuric ions. Whether this be so or not, it is evident that the specific character of an ion, as regards germicidal action at least, is liable to be masked by the intervention of other factors. This is what happens in the case of acids regarded as dis- infecting agents. Acids are alike in that when dissolved in water they all yield hydrogen ions to a greater or less extent, and it has been shown by Paul and Kronig that the germicidal effect of an acid is in the first place determined by its degree of dissociation, that in fact the hydrogen ion has a specific toxic action.^ The weaker acids, however, are more toxic than we should expect if there were a complete parallelism between germicidal power and degree of dissociation ; acetic acid, for instance, which from the figures recorded on p. 131,, is seen to be feebly dissociated, is in regard to toxic power not far behind hydrochloric acid, which is highly dissociated. Here, according "to Overton, it is the solu- bility of the undissociated molecules of the organic acids in the plasmatic membrane which accounts for their exceptional toxic power. A case where it is pre-eminently the undissociated molecule of an acid, and not the hydrogen ion, which exerts a specific action is found in connection with artificial parthenogenesis.^ It appears from Loeb's inves- tigations that unfertilised eggs of Sirongylocentrotus pur- 'pwratus, when placed for lJ-2 minutes in a mixture of N 50 cub. cm. sea-water + 3 cub. cm. j^ butyric acid (or other monobasic fatty acid), and then replaced in normal sea-water, develop a typical fertilisation membrane. The 1 Compare Senter, loc. cii. ' Loeb ; see p. 73. 166 PHYSICAL CHEMISTRY minimum concentration of monobasic fatty acid necessary for the production of the membrane diminishes as the number of carbon atoms in the molecule of the acid increases. Further, the strong mineral acids, hydro- chloric, sulphuric, and nitric acids, are much less effective than the monobasic fatty acids; it was found that -so far as inducing the formation of a membrane is con- N . . . N cerned, ^^^ butyric acid is more effective than ^ HOI. All the evidence, in fact, goes to show that it is the undissociated acid molecule which penetrates the egg and brings about the formation of the membrane. Hydrogen and Hydroxyl Ions. — The hydrogen ion has been alluded to as possessing a specific toxic power, but all the characteristic properties of acid solutions are to be regarded as associated specially with this ion. Similarly the hydroxyl ion, present in the solutions of bases, confers on these solutions certain well-marked properties, which are to be regarded as characteristic of this ion. The hydrogen and hydroxyl ions merit more detailed consideration, not only because acids and bases are such important groups of electrolytes, but also because these ions are exceptional in various ways. Reference to the table of ionic conductivities shows that these two ions are far and away more mobile than any others, either cations or anions. This fact, as the argument on p. 157 shows, involves the consequence that in regard to diffusive power acids and bases surpass all salts. Again, the hydrogen and hydroxyl ions are those which by their combination yield a molecule of water, and it has been suggested that this circumstance has something to do with their exceptionally high ionic velocities. The hydrogen ion, it is supposed, travelling under the in- ELECTROLYTIC DISSOCIATION 167 fluence of an electric force through an aqueous solution of an acid, collides with the anion side of a water molecule and displaces the hydrogen from the other side. This new hydrogen ion carries on the charge until it collides with a water molecule, when the process is repeated. In this way, it is supposed, the real distance to be traversed between the two electrodes is shortened, so that the mobility of the hydrogen ion appears to be greater than it really is.' In regard also to their power of acting as catalytic agents the hydrogen and hydroxyl ions occupy an ex- ceptional position. There are numerous reactions, for instance, which take place with appreciable rapidity only in the presence of acids, and it is found that the rate of the reaction is approximately proportional to the concentration of the hydrogen ions. The inversion of sucrose is a case in point, and the parallelism between the velocity of this change under the influence of various acids and the concentration of the hydrogen ions in each case is clearly shown by the following table.^ The figures refer to equivalent quantities of the various acids, and hydrochloric acid is taken as the standard in con- nection both with the velocity and the hydrogen ion concentration. The actual method of measuring the velocity of inversion will be discussed later, but for the present the figures in Column I. may be accepted as representing the relative velocities of inversion under the influence of equivalent quantities of different acids. Instead of the hydrogen ion concentrations there are recorded in Column II. the relative conductivities of the acids in equivalent concentration. A strict measure of the hydrogen ion concentration would be given by 1 Tlimstra, Zeit. phyaihal. C%cm., 1904, 49, 345 ; Danneel, Zeit.fur Eleh trochem., 1905, 11, 249; Dempwolff, Phynhal. Zeit., 1904, 5, 637. ' Ostwald, Jov/rn. praht. Chemie, 1884, 30, 95. 168 PHYSICAL CHEMISTRY a, the degree of dissociation in each case, but a = — , and as the value of \^ does not vary very much from one acid to another, the conductivity of each solution may be taken as an approximate measure of the hydrogen ion concentration. HCl. . . . CHCI2.COOH CH2CI.COOH H.COOH . . CH3.OOOH . I. II. 100 100 27 25 4-8 4-9 1-5 1-7 0-40 0-42 The parallelism between the two sets of figures is unmistakable. There are other reactions, such as the hydrolysis of esters, which are accelerated by acids, and the velocity of which is approximately proportional to the concen- tration of the hydrogen ion. The acceleration of these reactions appears therefore to be a specific property of the hydrogen ion, not of acids as such. If this view is accepted, then a sucrose solution, or a solution of methyl acetate, may be regarded as a reagent for hydrogen ions. The presence of these ions in any fluid may be detected and their amount estimated by studying the influence of this fluid on the inversion of sucrose or the hydrolysis of methyl acetate. The information given by such an investigation is quite different from that given by a titration of the fluid with a standard alkali solution; by this latter operation we ascertain merely the total acid present, both in the dissociated and undissociated conditions. Various reactions are similarly available for the de- tection and estimation of the hydroxyl ion. It is well known that esters are readily saponified or hydrolysed by alkalis, and closer investigation of the problem has hown that the rate of saponification depends, not on ELECTROLYTIC DISSOCIATION 169 the total alkali concentration, but on that of the hydroxyl ions. The equation for the hydrolysis of ethyl acetate by sodium hydroxide in dilute aqueous solution is generally written OH8.OOOC2H5 + NaOH = CHg-COONa h CaH^OH, but since sodium hydroxide and sodium acetate are both dissociated to a large extent under these conditions, the change would, from the point of view of the elec- trolytic dissociation theory, be more correctly repre- sented by OH3.COOO2H5 + Na- + OH' = CH3.OOO' + Na- + C^HgOH. Since Na* occurs on both sides of the equation, it may be simplified to CH3.COOO2H5 + OH' = CH3.COO' + O^HgOH. In harmony with this form of the equation it is found, as already stated, that the velocity of saponification of ethyl acetate or other ester by a base depends on the concentration of the hydroxyl ion in the solution, and is practically independent of the positive radical of the base. By way of illustration the following figures may be quoted. The velocity of saponification of ethyl acetate by jf^ KOH at 24*7° is represented by the number 6-41 ; the corresponding figure for ^ NH^OH at the same temperature is found to be 0"16. Since the degrees of dissociation for ^ KOH and ^ NH^OH are respec- tively 0-97 and 0'027, then on the assumption of an exact proportionality between velocity of saponification and hydroxyl ion concentration we should expect for the velocity of saponification by tq NH^OH, the value 170 PHYSICAL CHEMISTRY Q:g= = 0'18. This figure is in good agreement with the value actually observed. A reaction of a different kind which is accelerated by hydroxyl ions is the change of diacetonalcohol into acetone.i The velocity of this change is found to be proportional to the concentration of the hydroxyl ions, which act purely as catalytic agents, like hydrogen ions in the inversion of sucrose. The change diacetonalcohol -♦•acetone furnishes, therefore, a means of detecting the presence and measuring the concentration of hydroxyl ions as distinct from undissociated bases. It should be noted, however, that in the case of weak bases, such as ammonia, there is not by any means exact proportionality between the velocity of change and the concentration of the hydroxyl ions. The Dissociation of Water.^Reference has already been made to the interest which attaches to the hydrogen and hydroxyl ions on the ground that by their combina- tion they yield water. So far, in fact, as aqueous solutions are concerned, these ions stand in a special relationship to the solvent. The question thus arises : Does water itself contain hydrogen and hydroxyl ions, and if so, what is the extent of the dissociation? It is evident that in any case the proportion of hydrogen and hydroxyl ions in water must be comparatively small, for, according to the view already adopted, an electric current is able to pass through an aqueous solution only in so far as there are ions present. Pure water is a very poor conductor. We may compare, for instance, the specific conductivity of good distilled water,, which is about 7x10"* at 18°, with that of normal sodium chloride solution, which is 7'44xl0"^ at the same temperature. In other terms, distilled water enclosed in a centimetre cube, two opposite • Eoelichen, Zeit. physikal. Chem., 1900, 33, 129. ELECTEOLYTIO DISSOCIATION 171 faces of which act as electrodes, offers a resistance of about 140,000 ohms, while normal sodium chloride solu- tion, under the same conditions, offers a resistance of 13 -4 ohms. The conductivity of ordinary distilled water, moreover, arises chiefly from the impurities which it con- tains, notably carbon dioxide, and may be considerably reduced by simple methods. Kohlrausch has shown that when a current of air carefully freed from carbon dioxide is aspirated for some time through a sample of dis- tilled water the -conductivity of the latter is materially diminished, a result due to the removal of the greater part of the carbon dioxide. This ga2 2-5 2-0 1-7 5-5 2-75 0-73 6-5 1-0 1-0 1 Jau/m. Chem. Soc , 1908, 93, 428. Compare BourdjUon, ibid., 1913, 103, 791. 172 PHYSICAL CHEMISTRY The middle portion of the distillate is the purest, and is that which should be employed in the preparation of solutions for conductivity work (see p. 126). Nothing is to be gained by producing still purer water for ordinary investigations of conductivity, because even a sample for which «X 10* = 0"75 — 1"0 deteriorates during the contact with air which unavoidably occurs in the transference from the storage flask to the conductivity cell. It is, however, an interesting question how far water can be freed from adventitious electrolytic impurities, and whether the residual conductivity then obtained is to be attributed to the dissociation of the water itself. Kohlrausch has pushed the purification of water to its utmost limit, and by distillation of a specially purified sample in vacuo has obtained water for which ic X 10* = 0*04 at 18°. If this figure is taken as representing the con- ductivity of absolutely pure water, then it is possible to calculate the concentration of the hydrogen and hydroxyl ions in this liquid. For this purpose we may regard pure water .as a very dilute solution containing hydrogen and hydroxyl ions, and the equivalent conductivity must, according to Kohlrausch's law, be very nearly equal to fi; =318 + 174 = 492, for the ionic conductivities 11,- H r "OH of the two ions at 18° are respectively 318 and 174. Now «x<^ = X, where ^ is the volume in cub. cm. which contains 1 gram - equivalent of each ion, and ^ = ^=__g?__^=12-3xl0» cub. cm. = 12-3x106 litres. That is to say, the quantity of water which contains 1 gram of hydrogen in the ionic form is over 12 million litres. The significance of this figure is open to criticism, in BO far as Kohlrausch's investigations furnish of them- selves no definite proof that the figure 0-04 x 10~° is the conductivity of absolutely pure water. By three other independent methods, however, a value has been deduced ELECTROLYTIC DISSOCIATION 173 for the dissociation of water which is in good agreement with that calculated from the conductivity. There are therefore reasonable grounds for the view that the residual conductivity observed by Kohlrausch for his purest water is to be attributed to the dissociation of the water itself, and not to any impurities which it still contained. Complex Ions. — In the earlier part of this chapter reference has been made to the additive character of the reactions of salt solutions — ^the fact on which the practice of the analytical chemist is based : the wet reactions so frequently employed are tests for the presence of various ions, not for salts as a whole. In this connection it is noteworthy that a metal which enters into the com- position of a dissolved salt, although it generally forms the cation of the solution, does not do so invariably. Frequently it becomes part of a complex anion, and as each ion has its characteristic reactions, the tests which are employed to recognise the metal in the catipnic con- dition gave no result in this case. A simple illustration is furnished by silver in potassium cyanide solution. If potassium cyanide is added to a solution of silver nitrate a precipitate of silver cyanide is obtained, which, however, dissolves up again when excess of potassium cyanide is added. The solution so prepared does not answer to the ordinary test for silver : sodium chloride may be added without producing any precipitate. The natural con- clusion is that there can be no appreciable quantity of silver ions in the solution, and the question then arises : In what form is the silver present? The answer to this question was furnished long ago by Hittorf, who showed that when a solution of silver cyanide in potassium cyanide is electrolysed the silver migrates from the cathode to the anode, while of course in the case of an ordinary silver salt solution the silver travels as cation from anode 174 PHYSICAL CHEMISTEY to cathode. In the cyanide solution, therefore, the silver must be part of the anion, and when the changes of con- centration occurring at the electrodes during electrolysis are determined, it appears, as Hittorf showed, that the ions are K and A^(GN\. The transport of a metal from cathode to anode as part of a complex anion may be demonstrated directly in those cases where the anion in question possesses a characteristic colour. It is possible, for instance, to detect easUy by an electrolytic experiment the difference be- tween copper in a solution of copper sulphate and copper in Pehling's solution.^ Two thistle funnels are sealed together so that the total length of the tube between the bulbs is about 30 cm. The tube is then bent as shown in Pig. 21. A normal solution of sodium chloride in 12 nm cm — fe-J= Fie. 21. per cent, gelatin is run into the tube from B to D and allowed to set. One of the bulbs. A, is then filled with copper sulphate solution, the other, C, is charged with the deep blue neutral solution which is obtained when cupric tartrate is dissolved in caustic potash, excess of the alkali being avoided. Platinum electrodes are immersed in these two solutions, and are so connected with a source of current, that the electrode which dips in ^ See Masson, Journ. Chem. Soc, 1899, 75, 725. ELBCTEOLYTIO DISSOCIATION 176 the copper sulphate solution acts as anode. The E.M.P. applied to the electrodes ought to be about 30 volts, and the tube containing the jelly is kept in cold water during the experiment. After the current has passed for some time it is observed that the end of the jelly column next A is coloured pale blue; that is, the copper ions are migrating from anode to cathode. The other end of the jelly column, however, is also coloured blue, of a deeper shade, showing that complex ions containing copper are moving from cathode to anode. A similar method has been employed by Donnan and Bassett ^ to show that the blue colour exhibited by cobalt chloride solutions under certain conditions is to be attributed to the presence of a complex anion contain- ing cobalt. Evidence of the formation of a complex salt is fre- quently found in an increase of solubility. As a general rule, the solubility of a salt is diminished in presence of another salt with a common ion; thus, for example, sodium chloride is less soluble in hydrochloric acid than in pure water at the same temperature. There are, however, numerous cases where an increase of solu- bility occurs on adding a salt with a common ion ; thus silver cyanide is soluble in potassium cyanide, and mer- curic chloride is more soluble in sodium chloride solution than in pure water. In both these cases complex salts are formed, and the metal becomes part of the anion, so that the concentrations of Ag' and Hg", even if not quite nil, are exceedingly small. In view of this, it is only natural that, as shown by Paul and Kronig,^ the germicidal power of a solution containing 1 mol. AgN03 + 2 mols. KCN in 4 litres is exceedingly small compared with that of a solution con- » Journ. Ohem. Soc, 1902, 81, 939. ' Zeit. phygikal. Ghem., 1896, 21, 425. 176 PHYSICAL CHEMISTRY taining 1 mol. AgNOj in 4 litres. The silver ion, which is responsible for the toxie effect, is present in the first solution only to a very small extent. Similarly, the germicidal power of mercuric chloride is much reduced when sodium chloride is present in the solution ; the addition of the latter salt involves the disappearance of mercuric ion as such, and its conversion into a com- plex anion of weak toxic power. Another case of the formation of complex ions may be mentioned. It is well known that a solution of copper sulphate to which sucrose has been added fails to answer to the ordinary tests for copper ; potassium hydroxide may be added to the solution without causing any precipitate. In harmony with this it has been found by Kahlenberg,^ that in a solution containing sucrose, copper sulphate, and potassium hydroxide in the pro- portions represented by CijHgjOn + CuSO^ + 3K0H there are practically no copper ions. Further, Kahlenberg and True have shown ^ that while seedlings of Lupinus alhus L. are killed in a solution containing a very minute quantity of copper ion, they are able to grow in a solution containing sucrose, copper sulphate, and potassium hydroxide in the afore-mentioned proportions, even when the amount of copper present is as much as ^j^th of a gram-atom per litre. It makes, in fact, a great deal of difference whether the copper is present as Cu" or as part of a complex ion. 1 Zeit. physikal. Chem., 1895, 17, 612. ' Bot. Gazette, 1896, 22, 81. CHAPTEE IX COLLOIDAL SOLUTIONS Crystalloids and Colloids. — In the preceding chapters dealing with the physical and biological characteristics of aqueous solutions reference has been made almost exclusively to solutions of such substances as sugar, salt, glycerine, acetic acid, and potassium nitrate. These compounds have been classed as electrolytes or non- electrolytes, according to the osmotic activity of their solutions, and their power to conduct the electric current. There is, however, a large class of substances which, on Account of their special characteristics, must be distin- guished both from electrolytes and non-electrolytes, as these terms are ordinarily understood. It was Graham who first made this distinction, and pointed out that substances which crystallised readily from water were characterised by high diffusive power, and by the ability to pass through animal or vegetable membranes; those substances, on the other hand, which cannot easily be obtained in the crystallised condition, amorphous sub- stances in fact, are characterised by low diffusive power and by inability to pass through animal and vegetable membranes. The substances belonging to the first class, such as sucrose or sodium chloride, Graham termed crystalloids; those belonging to the second class, such as starch, gum, albumin, and caramel, he termed colloids. Solutions of these latter substances differ in many respects from those of crystalloids ; they are of great interest and importance on both physical and 177 178 PHYSICAL CHEMISTRY biological grounds, and they merit special consideration from the point of view adopted in this volume. At the outset it ought to be explained that the term ' colloid ' is now employed in a sense somewhat different from that in which Graham used it. It is generally interpreted at the present time as referring, not so much to a certain class of substances, but rather to a condition which a large number of chemical com- pounds may assume more or less readily.^ A ' colloidal solution,' therefore, is not necessarily a solution of a colloid (in Graham's sense); it is to be interpreted as a solution the special characteristics of which are similar to those, say, of a gum, but the dissolved substance may be quite outside the class which Graham termed ' colloids ' ; it may be, for instance, ferric hydroxide, arsenious sulphide, or platinum. These latter sub- stances, it is true, differ from gum, albumin, &c., in that they can be persuaded to form a colloidal solutioij only in an indirect way ; mere contact with water, however prolonged, will not bring ferric hydroxide or arsenious sulphide into solution. The precipitation of these substances, therefore, from their colloidal solu- tions cannot be directly reversed, and they are accord- ingly sometimes termed ' irreversible ' colloids, in contrast to gum, albumin, &c., which belong to the class of ' reversible ' colloids, and are directly soluble in water. There are other points of contrast between a reversible and an irreversible colloid, which will appear later. The substance which forms a colloidal solution is, as Graham showed, characterised by inability to pass through an animal or vegetable membrane, and on this fact is based the use of dialysis as a means of preparing a colloidal solution, free from dissolved crystalloids. A ' See Ostwald, Gnmdriss der aUgemeinen Ohemie (1909), p. 548. COLLOIDAL SOLUTIONS ' 179 piece of parchment or bladder is tied over one end of a wide glass cylinder, and into the receptacle so formed, a ' dialyser,' as it is called, the solution which is to be purified from crystalloids is poured. The lower end of the dialyser is then immersed in water, into which the crystalloids gradually diffuse through the meifibrane closing the dialyser. If the water is frequently re- newed the colloidal solution inside is soon practically free from salts or other crystalloids, although it is very difficult to remove the last traces of these substances. Instead of a dialyser of the kind just described, a simple tube made of parchment paper may be employed. Charged with the colloidal solution, it is hung up by its ends and suspended in a vessel through which pure water is kept flowing. As an example of the use of dialysis, the preparation of a solution of silicic acid may be taken. When a solution of sodium silicate is poured into excess of hydrochloric acid, the silicic acid which is formed remains in solution along with sodium chloride and the extra hydrochloric acid : the mixture is subjected to dialysis, in the course of which the sodium chloride and hydrochloric acid diffuse out through the membrane of the dialyser, leaving behind a colloidal solu- tion of silicic acid. Dialysis may be similarly employed in preparing a colloidal solution of ferric hydroxide, or in freeing a solution of egg albumin from admixed salts. As Graham pointed out, there is a marked difference in the diffusive power of crystalloids and colloids. This appears from the following figures, which represent the relative times required for equal diffusion of two crystal- loids and two colloids, sodium chloride being taken as the standard of comparison : sodium chloride, 1 ; sucrose, 3 ; egg albumin, 21 ; caramel, 42. The diffusion of enzymes has recently ^ been investigated, and it appears that these 1 Herzog, Zeit. Electrochem., 1907, 13, 633. 180 PHYSICAL CHEMISTRY substances, like others whicli form colloidal solutions, are characterised by low diffusive power. Osmotic Pressure of Colloidal Solutions. — In an earlier chapter it has been suggested that the phenomenon o£ diffusion in solution is closely connected with osmotic pressure. If there is such a connection, it is to be expected that the solution of a colloid, characterised as it is by a low rate of diffusion, will exert at the most only a small osmotic pressure. This conclusion is con- firmed by experimental ^ork, as will appear from the examples quoted below. In some cases indeed colloidal solutions have been found to exhibit no osmotic activity whatsoever; Reid,i for instance, working with carefully purified albumin solutions, came to the conclusion that these exert no osmotic pressure. In any investigation of the osmotic activity of a colloid, the question whether the solution is absolutely free from electrolytes is of the utmost importance ; an electrolyte is highly active material from the osmotic point of view, and a small trace present in a colloidal solution may easily lead to erroneous conclusions. As has been hinted already, it is not easy to remove the last traces of electrolytes from a colloidal solution, and there can be no doubt that the older determinations of the osmotic pressure of colloids, such as those made by Pfeffer on gum arabio, gave too high values, owing to the presence of electrfllytic material. E6cent investigators who have determined the osmotic pressure of colloidal solutions have devoted much more attention to the problem of purification, and the values given by them may be regarded as repre- senting more closely the real osmotic pressure of the colloid. The osmotic pressures of colloidal solutions of ferric 1 Jowrn. Phytiol., 1904, 31, 438. COLLOIDAL SOLUTIONS 181 hydroxide have been determined by Duclaux,i and the values obtained are recorded in the following table. A Per Cent. Fe,(OH),. Pressure in cm. Water. 1-08 0-8 2-04 2-8 3-05 5-6 6-35 12-5 8-86 22-6 glance at the figures will show how small the pressures are even for the 5'35 per cent, and the 8'86 pe/cent. solutions : the pressure developed in the latter case is that which would be given by a solution containing about one-thirtieth of a gram of sucrose in 100 grams of water. The figures recorded in the table show that although the osmotic pressure increases with the con- centration, there is not anything like proportionality between the two variables. More attention has been devoted to the question of the osmotic activity of the serum proteins, egg albumin, and gelatin. In his experiments on the osmotic pres- sure exerted by serum proteins, StarKng^ employed an osmometer, the semi-permeable diaphragm of which con- sisted of peritoneal membrane soaked in gelatin and supported by silver wire gauze. The osmometer was charged with a solution of the serum proteins, the other side of the membrane being bathed by a salt solution which was approximately isotonic with the colloid solution in the osmometer. As the gelatin membrane was freely permeable to salts, the pressure observed in the osmometer was attributed to the colloids ; the conclusion reached was that the osmotic pressure of blood serum containing 7-8 per cent, of proteins amounts to 25-30 mm. of mercury. 1 Compt. rend., 1905, 140, 1544. 2 Joarn. Phyaiol., 1895, 19, 312 ; 1899, 24, 317. 182 PHYSICAL CHEMISTHY Reid,i using a similar osmometer with a formalised gelatin membrane, found that when precipitates or crystals of protein are repeatedly washed with salt solutions, and the osmotic activity of samples of the material is investigated at intervals, the pressure observed for 1 per cent, protein concentration falls off steadily with continued washing ; ultimately, as already indicated, solutions of protein are obtained which give no osmotic pressure. Hsemoglobin, however, was found to give a fairly definite pressure, amounting to 3"51-4'35 mm. of mercury for 1 per cent, concentration of haemoglobin. The former observations would seem to indicate that the osmotic pressure frequently found for protein solutions is due, not to the proteins themselves but to something associated with them which may be gradually removed. It is, however, noteworthy, on the other hand, that the osmotic pressure developed by a colloidal solution is in many cases remarkably steady; this is difficult to explain if the pressure is attributed to crystalloids associated with the colloid, for the membranes employed in studying the osmotic activity of colloids are all readily permeable to crystalloids, so that these could produce at the most only a temporary effect. As an example of the persistence of the osmotic pressure developed by a colloid, an observation made by Moore and Roaf^ may be quoted. These investi- gators have studied in detail the behaviour of gelatin solutions in an osrnometer closed with a parchment membrane. This osmometer consisted of two platinum capsules supported and held in opposition by brass chamberis. The rim of each capsule was provided with a flange, and between the flanges there came-, when the apparatus was put together, a thick platinum grid, ' Loc. (tit. 2 Biochem. Journ. 1 906, 2, 34. COLLOIDAL SOLUTIONS 183 supporting the membrane of parchment paper. Fig. 22 shows the osmometer fitted up and joined to the manometer. In one experiment the osmometer was charged with 10 per cent, gelatin, and a week later the osmotic pres- FiG. 22. sure was found to be 74 mm. of mercury at 31° 0. ; the experiment was continued for two months, during which time the outside of the parchment membrane 184 PHYSICAL CHEMISTRY was constantly tathed with water. At the end of that period the osmotic pressure was found to be 70 mm. of mercury at 26° C. Such a persistence of the pres- sure seems to show that it corresponds to a real equili- brium, and is not merely a passing phenomenon due to slowly diffusing crystalloids. Other interesting observations made by Moore and Eoaf relate to the influence of temperature on the osmotic pressure of a gelatin solution. The osmotic pressure increases with rising temperature, but the increase is more rapid than it would be if the osmotic pressure were strictly proportional to the absolute tempera- ture. Further, if a gelatin solution, after being kept for a short time at 70-80°, is cooled, say, to 25°, the value then observed for the osmotic pressure is considerably higher than it was before the solution was heated. Only after the solution has been kept for some days at the lower temperature is there a return to the former value. The osmotic pressure exhibited by a gelatin solution is therefore to some extent dependent on its previous history. These observations seem to be most satisfactorily interpreted by supposing that the gelatin solution contains large molecular groups or aggregates, which tend to break up as the temperature rises, thus leading to an abnormally great increase of the osmotic pressure. When the solution is cooled the large molecular aggregates corresponding to the lower temperature are, it may be supposed, re-formed only slowly, and until this is complete the osmotic pressure is higher than the true equilibrium value. This phenomenon of ' hysteresis ' in connection with the osmotic activity of substances in colloidal solu- tion indicates that the osmotic pressure in such a case is not completely defined by the two factors concentration and temperature. It is probable, as already suggested, COLLOIDAL SOLUTIONS 185 that the extent of aggregation of the colloid depends to some extent on its previous history; this being so, the number of units or separate aggregates in the solution, and therefore also the osmotic pressure, would not always be the same at a given temperature. Striking evidence that the osmotic activity of a colloid depends on other factors than concentration and tem- perature is furnished by a recent investigation of the influence exerted by electrolytes on the osmotic pressure of colloidal solutions.^ The colloids studied in this investigation were gelatin and egg albumin, and the osmometer used consisted of a flask-shaped vessel of collodion provided with a rubber stopper and vertical glass tube. A membrane of collodion is tough and only slightly extensible ; it is practically impermeable to gelatin and egg albumin, but is readily permeable to all crystalloids. With this apparatus Lillie deter- mined the osmotic pressure exerted by a colloid (1) when in a relatively pure condition, (2) when in the presence of crystalloids. The osmotic effect of the crystalloid in the latter case was eliminated by adding it also to the liquid outside the cell, so that the con- centrations of the crystalloid on the two sides of the membrane were equal. It was then ■ found that the osmotic activity of gelatin and egg albumin, while practically uninfluenced by sucrose and other non-electro- lytes, is markedly affected by electrolytes. In presence of small quantities of either acid or alkali the osmotic pressure of a gelatin solution is notably increased, whilst that of an egg albumin solution is slightly lowered. Salts, on the other hand, bring about a lowering of osmotic activity for both colloids, the magnitude of the effect varying with the concentration and the nature of the salt. This may be illufetrated by the following figures 1 Lillie, Amer. Jaurn. Phyaicl., 1907, 2270, 1. 186 PHYSICAL CHEMISTEY for the osmotic pressure of 1"25 per cent, egg albumin and gelatin solutions : — 1-25 per Cent. Salt Present. Egg Albumin. Osmotic Pressure in mm, Hg. 1'25 per Cent Salt Present. Gelatin. Osmotic Press in mm. Hg. None . . . . 18-0 None . . . . 5-9 gNaOl . . . 6-8 gNaOl . . . 2-8 |kno3. . . 7-3 gNaBr . . . 3-1 gNaCl . . . 3-25 o^Nal . . 96 . 3-4 SKNO3. . . 3-0 ^NaNOa . 96 ^ . 3-0 It is apparent, then, that the osmotic activity of a colloid at a given concentration varies to a very marked extent with the nature and amount of crystalloid present. The lower pressures observed for egg albumin and gelatin in presence of salts can be attributed only to a reduction in the number of colloid units or aggregates in solution ; so that the effect of salts, even in small quantities, is to increase the aggregation of the colloid. This is perhaps only natural, for it must be borne in mind that the addition of large quantities of salt to a protein solution leads frequently to the precipitation of the protein ; the increased aggregation brought about by small quantities of salt may therefore be regarded as the first stage in a process which leads ultimately to precipitation. Lillie's investigation indicates also that the pheno- menon of hysteresis occurs in connection with the change in the aggregation of the protein which accompanies change in the amount of electrolyte present. The state of aggregation induced by a given electrolyte appears to persist to some extent even after the electrolyte has been removed, and it is at least possible that the very low values recorded by Eeid^ for the osmotic pressure of ' Loe. cit. COLLOIDAL SOLUTIONS 187 protein solutions were due to the treatment witli concen- trated salt solutions to which the protein was subjected. The influence of electrolytes on the osmotic behaviour of colloids has been strikingly confirmed by a recent study of Congo red.^ This dye may be regarded as a colloid, inasmuch as it does not diiluse through parch- ment paper: in an electric field it moves towards the anode, and it is precipitated very readily by di- and tri- valent cations. The osmotic activity of congo red, measured in the form of osmometer described by Moore and Eoaf, is very nearly equal to that calculated on the supposition that it dissolves as single molecules, forming a true solution. Bayliss finds, however, that the theoreti- cal osmotic pressure can be obtained only in the complete absence of extraneous electrolytes^; even the carbon dioxide present in ordinary distilled water brings about a notable fall in the osmotic pressure, owing to the aggregation of molecules to particles. Molecular Weight of Colloids. — As has already been pointed out in an earlier part of this volume, the know- ledge of the osmotic pressure of a solution enables us to calculate the molecular weight of the dissolved substance. Such a calculation is based on the assumption that osmotic pressure is proportional to concentration and absolute temperature. As shown, however, in the fore- going paragraphs, concentration and temperature are not the only factors which determine the osmotic pressure of a substance in colloidal solution. It is therefore futile to deduce a value for the mole- cular weight of a colloid from the osmotic pressure of its solution: such a value could not be regarded as a characteristic figure for the colloid in question : it would 1 Bayliss, Proe. Roy. Soc., B, 1907, 81, 269. ' See also Biltz and Vegesaok, Zeit. phyaikal. Ohem., 190P, 68, 357 ; 1910, 73, 481; Donnan and Harris, Jowrn. Chem. Soc, 1911, 99, 1554. 188 PHYSICAL CHEMISTRY have reference only to the particular conditions of the colloid at the time when the osmotic pressure was determined.. Values for the molecular weight of substances in colloidal solution may be deduced also from their effect on the vapour pressure, the boiling point, and the freezing point of water. Such values, however, must be accepted with reserve, on the grounds specified in the foregoing paragraph. There is, further, a special reason why little reliance can be placed on the indirect measurement of osmotic pressure in the case of a colloidal solution. If P is the osmotic pressure of an aqueous solution, and t is the extent to which the freezing point of the solution is lower than that of water, then, as shown on p. 110, P=12'03^ atmospheres. According to this formula, the freezing point of a solution which gives an osmotic pressure of 50 mm. of Hg — an easily measurable quantity — would be only about 0'005° below the freezing point of water. Such a small temperature difference might easily escape detection in ordinary work, and in any case the erperimental error in its determination is relatively large. For the measurement, therefore, of the osmotic pressure of a colloidal solution the direct method is to be preferred. The values frequently quoted for the molecular weight of such colloids as dextrin, glycogen, and silicic acid — values based on the determination of the freezing point — have a very limited significance, partly on account of the deficiencies of the method em- ployed, and partly on account of the variability in the aggregation of a colloid with the conditions. Colloids in an Electric Field. — Nearly twenty years ago Linder and Picton ^ made the interesting observation that when two wires connected with the terminals of 1 Jom-n. Chem. 8oe., 1892, 61, 148. COLLOIDAL SOLUTIONS 189 a battery were placed in a colloidal solution of arsenious sulphide the sulphide was attracted by the positive pole, and was gradually transported thither. Ferric hydroxide in colloidal solution was, on the other hand, attracted by the negative pole. It appears, therefore, that the particles of colloidal arsenious sulphide carry a negative electric charge, while those of colloidal ferric hydroxide carry a positive charge. The behaviour of colloids generally in an electric field has been extensively studied, and it is found that, as a rule, they carry a definite charge. In the following table various common colloids are classified according as they are electro-positive and move to the cathode, or electro-negative and move to the anode : — Electro-positive. Electro-negative. Ferric hydroxide Arsenious sulphide Chromium hydroxide Silicic acid Methylene blue Tannin Bismarck brown Caramel Haemoglobin Starch Platinum Gold Indigo The movement of colloids in an electric field may be demonstrated with the help of the apparatus described on- p. 154. The bottom of the U tube is charged with a solution of caramel, for instance, the upper part of each limb being occupied by distilled water. When platinum wires connected with the terminals of a 200-volt circuit are put in the water of the two limbs, it is obvious after a long time that the column of caramel solution has fallen in one limb and risen in the other. If the wires are subsequently tested, it will be found that the one towards which the caramel advances is connected with the positive terminal of the circuit. A similar experiment might be made with any of the colloids mentioned above. 190 PHYSICAL OHEMISTEY An apparatus of the same kind has been employed * to determine the actual rate at which colloidal metals migrate from cathode to anode under the action of an electric force. As shown by Bredig,^ a colloidal solution of platinum, gold, or silver can be prepared by producing a small electric arc between wires of the metal in question when these are immersed in water. The passing of the discharge between the ends of the wires brings about what is known as the 'electrical pulverisation' of the metal ; a coloured solution is obtained in each case, which can be filtered without change, and which can be purified by dialysis from any electrolytic impurities. The solution contains an appreciable quantity of metal, and is analogous in its properties to colloidal solutions of arsenious sulphide, ferric hydroxide, and many organic substances. If, now, the bend of the U tube of the apparatus referred to in the previous paragraph is filled with a colloidal solution of platinum, gold, or silver, and the upper parts of the two limbs contain water of the same specific conductivity as the colloidal solution, then when wires connected with a battery are put in the two water columns the potential gradient is uniform through- out the tube ; the fall of potential per centimetre is known. Under the action of the electric force the coUoidally dis- solved metal moves towards the anode, and from the distance actually traversed in a given time the velocity of migration may be calculated for the potential gradient prevailing in the tube. In this way Burton has found that for a potential gradient of 1 volt per cm. the velocity of migration of colloidal platinum, gold, and silver is about 0'0002 cm. per second, which is rather more than one-third of the rate at which the silver ion moves under similar conditions. 1 Burton, PhU. Mag., 1906, 11, 425. 2 Zeit. physikal. Ohem., 1899, 31, 258. COLLOIDAL SOLUTIONS 191 One of the most significant facts bearing on the be- haviour of colloids in an electric field is Hardy's observation^ that protein in solution may be either electro-positive or electro-negative, according to circum- stances. Hardy used the slightly opalescent fluid ob- tained when white of egg is mixed with 8-9 times its volume of water, filtered and boiled: this fluid is alkaline in reaction. When it is dialysed against dis- tilled water, coagulation occurs, and the coagulum may be broken up and suspended in distilled water without solution taking place. If, however, a trace of acid is added, the flakes of the coagulum disappear, and an opalescent fluid with acid reaction is produced. If a current is passed through the original alkaline fluid, the protein moves from cathode to anode and a coagulum forms round the anode, while if a current is passed through the acid fluid described in the last sentence, the protein moves from anode to cathode. It appears, there- fore, that in an alkaline medium the protein is electro- negative, but that in an acid medium it is electro-positive. It was found, further, that if the coagulum obtained by prolonged dialysis is thoroughly broken up and suspended in distilled water, no movement of the protein .particles occurs in an electric field. If, however, the coagulum formed at the anode by passing a current through the original alkaline fluid is thoroughly broken up, the particles leave the anode and move towards the cathode ; their electrical character has changed. Such a reversal of the electric charge on a colloidal substance has been observed in other cases. Burton, for instance, working with colloidal solutions of silver and gold,^ has found that the addition of small quantities of aluminium sulphate causes first a 1 Journ. Physiol., 1899, 24, 288. 2 PhU. Mag., 1906, 12, 472. 192 PHYSICAL CHEMISTRY decrease in the charge on the colloidal particles, and ultimately a reversal. Analogy between Colloidal Solutions and Suspen- sions. — ^The behayiour of substances in colloidal solution when exposed to the action of electrical forces is very similar to the behaviour of suspensions in the same circumstances. With the - apparatus already described, it can be shown that when a current is passed through suspensions of quartz powder, gum mastic, or shellac, the suspended particles move towards the anode. A great deal of other evidence is available in support of the view that there is a close relationship between colloidal solutions and ordinary suspensions. When we speak of a ' suspension ' we may think of a fluid, in which distinguishable particles are floating about. There are, however, all grades of suspensions; many of them can be filtered without alteration, and in many cases no individual particles can be detected with the naked eye: the microscope at least is required to render the suspended particles visible. But if all the optical methods available for the recognition of the' non-homo- geneous character of a liquid are applied to colloidal solutions, evidence is obtained that these also contain distinct particles. One of these methods consists in the application of the Tyndall test. It is well known that if a beam of light enters a darkened room in which dust particles are floating its path is rendered evident by the scattering of the light at the surface of the particles; each one of these appears as a bright moving speck. Similarly, when a powerful beam of light passes through a vessel containing a suspension, say, of fine silver chloride particles in water, its path is rendered evident by the scattering of the light which takes place at the surface COLLOIDAL SOLUTIONS 193 of the suspended particles; further, the light which is scattered is partly polarised. If, on the other hand, the beam is passed through a solution which is perfectly- free from all suspended particles, no scattering of the light takes place, and the path of the beam cannot be detected ; such a solution is described as ' optically empty.' Now the Tyndall phenomenon, that is, the appearance of opalescence whidi is observed when a powerful beam of light is passed through a fluid con- taining definite suspended particles, is exhibited also by the majority of colloidal solutions. Picton and Linder,^ for instance, describe a colloidal solution of ferric hydroxide which, examined under a powerful microscope, appeared to be perfectly homogeneous, and which yet betrayed the track of a beam of light very distinctly, the light being completely polarised. A clear solution of haemoglobin, similarly examined, gave a dis- tinct soft luminous beam, the light of which was com-' pletely polarised. A positive result is obtained also with solutions of such substances as dextrin and gum arable in water. The extent of the analogy which thus appears to exist between suspensions and colloidal solutions has been thoroughly tested in recent years with the help of the ultramicroscope, as devised by Zsigmondy and Siedentopf .^ The usefulness of this instrument depends on the Tyndall phenomenon, but whereas the power of any solution to exhibit the Tyndall phenomenon permits merely the conclusion that the solution contains distinct individual particles, the ultramicroscope makes it possible to detect the individual particles themselves, even where the most powerful microscope has failed to reveal any trace of heterogeneity. In the ultra- 1 Journ. Chem. Soc., 1892, 61, 148. * See Zsigmondy's Colloids and the Ultramicroscope, p. 103. 194 PHYSICAL CHEMISTRY microscope provision is made for focussing an intense beam of light in tKe liquid under examination, and in viewing the beam at right angles to its direction by a microscope. Any particles suspended in the liquid are then revealed in the field of the microscope as bright moving discs on a dim background. The power of the ultramicroscope to detect discrete particles is considerably greater than that obtainable in ordinary microscopic methods. Particles of less than 140 X 10"° mm. diameter are as a rule not visible under the microscope (compare the wave-length of red light, which is about 700 x 10"° mm.), but with the ultra- microscope particles in a solution of colloidal gold as small as 4 X 10"' mm. have been detected. One way in which the size of the particles revealed by the ultra- microscope may be estimated has recently been de- scribed by Burton,^ and some figures may be quoted showing the method adopted by this investigator. A solution of colloidal silver containing 6-8 mg. of silver in 100 cub. cm. was diluted with water to 100 times its original volume. "With the help of the ultramicro- scope the number of particles in O'l cub. mm. of the diluted solution was found to be 300. Hence in 1 cub. cm. of the original solution there must have been 3 x 10' particles weighing 6"8xl0"° gram. If it is assumed that the particles are spherical and that their specific gravity is 10'5, then the mean radius is 1-7x10"° cm. From experiments with colloidal platinum-, gold, and silver, Burton found as the average diameter of the particles in these cases 2 x 10"° - 6 X 10"° cm. It is interesting to note that the smallest particle which can be detected in the ultramicroscope under the most favourable conditions (with bright sunshine) is about ten times as great as an 1 Phil. Mag., 1906, 11, i25. For a review of the methods used in determining the size of colloidal particles, 8^e Henri, Zeit. Ohem. Ind. Kolloide, 1913, 12, 246. COLLOIDAL SOLUTIONS 195 average chemical molecule, calculation having shown that the diameter of a chloroform molecule is about 8 x 10"' mm., that of an ethyl alcohol molecule about 0'4xl0~', and that of a hydrogen molecule about 01 X 10"'. The great majority of colloidal solutions, when ex- amined in the ultramicroscope, are found to contain distinct particles. Cases are on record, however, in which the ultramicroscopic examination of colloidal solu- tions showed them to be optically empty. Zsigmondy, for instance, prepared a colloidal solution of gold which could not be shown to contain discrete particles. Such observations warn us that, while there is good ground for regarding suspensions and colloidal solutions as being closely allied, no hard-and-fast line of division can be drawn on the other hand between colloidal and crystalloidal solutions. For while, as already explained colloidal solutions can be prepared which are optically empty, there are solutions of crystalloids, sucrose, for instance, which cannot be obtained in this condition, however carefully they have been freed from suspended matter.^ Strictly speaking, we must from the mole- cular standpoint regard all solutions as being ultimately non-homogeneous, and it is due to the inadequacy of our optical apparatus that we are unable to recognise separate particles in a dilute aqueous solution of ethyl alcohol or sodium chloride. One observation bearing directly on the question of the homogeneity of crystal- loidal solutions has been recorded by van Oalcar and Lobry de Bruyn,^ who found that by rapidly centrifu- galising sucrose solutions differences in concentration could be induced. Similar treatment of a saturated solution, of sodium sulphate led to the crystallisation of some of the salt. ^ Lobry de Brnyn and Wolff, Hee. trav. ehim., 1904, 23, 155. • Bee. trav. Mm., 19D4, 23, 218. 196 PHYSICAL CHEMISTRY The inadvisability of attempting to put suspensions, colloidal solutions, and crystalloidal solutions in three absolutely distinct classes is emphasised by the fact that it is possible to prepare colloidal solutions of one and the same substance of all degrees of heterogeneity. Linder and Picton,i in their study of colloidal solutions of arsenious sulphide, showed that various ' grades ' of solution could be obtained, according to the method of preparation. They describe and distinguish the following : — (a) Contained aggregates which were visible under the microscope. (jS) Was free from microscopically visible particles, but diffusion of the particles did not occur. (7) Contained invisible particles which diffused, but were kept back by filtration through a porous pot. (S) Contained invisible particles which diffused and were capable of passing through a porous pot. The solution, however, scattered and polarised a beam of light. This example shows how far it is possible to vary the extent of aggregation of one and the same sub- stance in colloidal solution. If it was a question of deciding whether a given arsenious sulphide solution was really a colloidal solution or only a suspension, the verdict would depend on the criterion of homogeneity employed: a solution which, according to one test, was a true colloidal solution would, according to another test, be merely a suspension. It is obvious, therefore, that, while there are no doubt broad distinctions to' be drawn between suspensions, colloidal solutions, and crystalloidal solutions, the one class merges gradually into the other. The size of the individual particle ' Loo, eit. COLLOIDAL SOLUTIONS 197 present in a solution increases without any noticeable break from that, say, of an alcohol molecule in water, through that of the carbohydrates and proteins in aqueous solution, to cases where the individual particles are so large that we speak of them as ' suspended.' Brownian Movement. — The invention of the ultra- microscope and the study of the phenomena exhibited by colloidal solutions have directed attention afresh to an observation which was made nearly a century ago by the botanist Robert Brown, and which has since then been^the subject of repeated investigation. With the aid of the microscope Brown observed that fine particles suspended in water, such as gamboge or fat particles from milk, executed a vibratory movement about a mean position. This movement has been shown to be independent of any temporary forces due to slight differences of temperature or concentration; so long as the particles float in the liquid, the movement con- tinues without ceasing. The ultramicroscope has revealed the fact that a colloidal solution containing particles much smaller than Brown was able to observe is the scene of still greater activity. Zsigmondy, describing the movement of the gold particles in a gold hydrosol, compares them to a swarm of dancing gnats. The finer the particles, the more rapid is their movement; with increase in size the movement becomes slower, and it is ultimately imperceptible when the diameter of the particles is about 0*004 mm. Zsigmondy considers that in contra- distinction to the typical Brownian movement about a mean position, the motion of the smallest gold particles in a gold hydrosol is continuous ; an individual particle, after moving about in a zigzag fashion, may suddenly rush across the field like a living thing. The mean 198 PHYSICAL CHEMISTRY free path is therefore considerably greater in the case of the smallest gold particles than it is in the ordinary Brownian movement, but there is no doubt that the phenomenon is essentially the same in the two cases. The problem has recently been attacked by Svedberg,* who has prepared a number of colloidal solutions of platinum in various media and shown that the amplitude of vibration of the particles is nearly inversely pro- portional to the viscosity of the medium. The mean velocity, however, of a platinum particle of given size is, practically constant; for a particle weighing about 2-5 X 10"^^ gram the mean velocity is estimated to be 3x10"' cm. per second at the ordinary temperature. Comparison of these figures with the corresponding ones given by Ramsay^ for larger particles leads to a cal- culation of the velocity with which a platinum molecule would move. It is noteworthy that the value so cal- culated is in agreement with the value based on the assumptions of the kinetic theory. It is therefore probable that the Brownian movement of suspended or colloidal particles is an expression of the molecular movement which is attributed to matter generally. This view has been strengthened by still more recent work, both theoretical and experimental.* Indeed Ostwald* has expressed the opinion that the agreement between the observed and calculated values for the rate of movement of a suspended particle is so close as to amount to an experimental proof of the kinetic nature of heat. Filtration of Colloidal Solutions.— Filtration is the ' Zeit. Elehtrochem., 1906, 12, 853. = Ohem. News, 1892, 65, 90. ' See Svedberg, Zeit. Elehtrochem., 1906, 12, 909 ; Perrin, Oompt. rend., 1908, 146, 967 ; 147, 475, 530 ; also Perrin's Brovmicm Movement and Molecxdar Reality (1910). ' • Grundrias der allgemeinen Chemie (1909), p. 543. COLLOIDAL SOLUTIONS 199 time-honoured method of freeing a liquid from suspended particles, and the remarkable similarity between sus- pensions and colloidal solutions leads us naturally to inquire how far this method is efficient when applied to colloidal solutions. The inquiry really reduces itself to the question whether we can procure filters with sufficiently small pores. The analytical chemist knows that the possibility of filtering a very finely divided precipitate depends on the texture of the filter paper. In the case of colloidal solutions, which pass unchanged through the finest filter paper, the possibility of a mechanical separation of the colloid depends on the discovery of a filter with exceedingly small pores — of a diameter 1 x 10"' — 40x 10"° mm. One such, as suggested by Martin, is obtained by impregnating the pores of a Pasteur-Chamberland candle with gelatin. A filter so prepared is highly permeable to crystalloids such as sodium chloride and butyric acid, but is very slightly permeable to colloids such as ferric hydroxide and soluble starch,^ so that if a colloidal solution of ferric hydroxide is filtered under 100 atmospheres pressure in such an apparatus the filtrate consists of practically pure water. The permeability of such a filter to certain colloids increases as the concentration of the impregnating gelatin solution diminishes. This fact has been utilised in the attempts which have recently been made to differentiate between various colloidal solutions by means of graded filters. These, according to Bechhold's suggestion,^ may be prepared (1) by impregnating filter paper with a solution of collodion in glacial acetic acid and then dipping in water, or (2) by soaking filter paper in gelatin solution and then hardening with formaldehyde. The size of 1 See Craw, Proc. Roy. Soc., B, 1906, 77, 311. ' Zeit. phydkal. Ckm., 1907, 60, 257. 200 PHYSICAL CHEMISTET the pores in such gelatinised filters diminishes as the concentration of collodion or gelatin used in their pre- paration increases. A series of graded filters is thus obtainable which may be used to sort out a number of colloidal solutions according to the size of particles they contain. It is true that the pores in a filter are not all of equal diameter and that the particles in a colloidal solution vary in size, but still it is possible to discover for a given colloidal solution which one of the series of filters is just able to prevent the passage of the colloid. Such experiments obviously lead to a classification of colloidal solutions according to the size of the particles they contain, and the following table given by Bechhold is based on work of this kind : ^ — Suspension! Piussian Blue Colloidal Platinum Colloidal Ferric Hydroxide Casein (in Milk) Colloidal Arsenious Sulphide Colloidal Gold (40X 10-» mm.) 1 per cent. Gelatin 1 per cent. Hsamoglobin Serum Albumin Diphtheria Toxin Protalbumose Colloidal Silicic Acid Deuteroalbumose Litmus Dextrin Crystalloids Although the value of this table is qualified by the fact that the size of the particles in the colloidal solution of a given substance varies with the mode of preparation, yet the order given is_ in general agreement with theoretical considerations and with the results of ultramicroscopic investigation. ' The pressures under which filtration took place in Bechhold's experiments were between 0'2 and 5 atmospheres. CHAPTEE X THE SEPARATION OF COLLOIDS FROM THEIR SOLUTIONS Suspension and Emulsion Colloids. — In the foregoing chapter a good deal of evidence has been brought forward showing that the region of colloidal .solution adjoins that of true solution on the one side and that of suspensions on the other. When now we consider the influences which bring: about a separation of the colloid from its solution, it is found that the substances which form colloidal solutions may be divided into two classes. In relation to precipitating or coagulating agents the one class resembles suspensions, while the other behaves more like crystalloidal substances. The two classes are those which have already been referred to (p. 178) as irreversible and reversible colloids ; they may be distinguished also as ' suspension colloids ' and 'emulsion colloids,' or as 'suspensoids' and 'emul- soids.' ^ A colloid belonging to the suspensoid class gives with water a mixture which is non-viscous and non-gelatinising, but is coagulated on the addition of small quantities of electrolytes. A colloid belonging to the emulsoid class gives with water a mixture which is viscous, gelatinises, and is not readily coagulated by salts. The Coagulation of Suspensoids. — One of the most characteristic features of a colloidal solution of arsenious > von Weimarn, Zeit. Chem. Ind. KoUoide, 1908, 3, 26. 201 202 PHYSICAL CHEMISTRY sulphide or ferric hydroxide is the ease with which these colloids are precipitated on the addition of electrolytes. A similar sensitiveness to small quantities of salts is exhibited by suspensions. Bodlander has shown that the sedimentation of kaolin suspensions is accelerated by the addition of electrolytes, and Hardy has found i that a suspension of gum mastic in water, prepared by adding a dilute alcoholic solution of the gum to distilled water, is precipitated immediately by very small quantities of magnesium sulphate or barium chloride. On the other hand, the stability of a suspension or the solution of a suspensoid is practically unaffected by the addition of a non- electrolyte. In making a comparative study of the influence of various electrolytes in causing • precipitation of suspen- soids, it is necessary to follow a strictly uniform pro- cedure. Experience has shown, firstly^ that an amount of salt which is not capable of causing immediate coagula- tion is nevertheless effective after a certain interval, and secondly, that the total quantity of electrolyte required to bring about complete coagulation of the suspensoid varies according as the electrolyte is added all at once or in several portions successively. We have here an indication of the part which the time factor plays in the behaviour of colloidal solutions (compare p. 184). In order to avoid complications arising from these causes Freundlich has suggested the following procedure : ^-^2 cub. cm. of the electrolytic solution are added to 20 cub. cm. of the suspensoid solution, the latter being well shaken during the addition; the mixture is then allowed to stand for two hours, after which time a few cubic centi- metres are filtered off, and the filtrate is examined, chemically or colorimetrically, for the suspensoid. • ZeU. physikal. Chem., 1900, 33, 385. » Ibid., 1903, 44, 131. THE SEPAEATION OF COLLOIDS 203 The following table records some of the results ob- tained by Preundlioh in his investigation of the in- fluence of electrolytes in precipitating a colloidal solution of arsenious sulphide. The tests were carried out as described in the previous paragraph, and the numbers given in the table represent the minimum concentration for each electrolyte which brought about coagulation in two hours ; the figure given in each case is the concen tration of the electrolyte' after mixing with the arsenious sulphide solution. Electrolyte. ™»1- NaCl 71-2 KNO3 69-8 JK2SO4 91-5 NH4CI 591 HCl 42-9 MgCij ~. '. '. '. '. '. Too MgSO^ 113 Ca(N03)2 0'95 BaClj 0-96 ZnSOi 1-13 AICI3 . '. '. '. '. '. '. 003 A1(N03)3 0-14 iCeg(S0,)3 0-13 Inspection of this table shows, firstly, that exceedingly small quantities of electrolytes suffice to cause the coagu- lation of arsenious sulphide solutions ; secondly, and more particularly, that the coagulating power of an electrolyte in relation to arsenious sulphide is mainly determined by the valency of the cation. The higher the valency of the cation, the smaller is the quantity of electrolyte required to bring about coagulation. Equally striking is the comparative influence of salts in bringing about the coagulation of colloidal ferric hydroxide. This is shown by the following table. 204 PHYSICAL OHEMISTEY the figures in which have the same significance as those quoted in the previous table. It is evident that in relation to colloidal ferric hydroxide the coagulating power of a salt is mainly determined by the valency of the negative ion ; the valency of the ^positive ion is here relatively unimportant. NaCl 9-25 PaClj 9-64 KNO3 11-9 Pa(N03)2 140 K2SO4 0-20 MgSOt 0-22 KjCrjO, 0-19 The contrast in this respect between colloidal arsenious sulphide and colloidal ferric hydroxide becomes still more interesting when it is borne in mind that the colloidal particles of arsenious sulphide are negatively charged, . while those of ferric hydroxide are positively charged. The full significance of this was first appre- ciated by Hardy, ^ who formulated the rule that the ion of an electrolyte which determines the coagulation of a colloidal solution is the one which has a charge opposite in sign to that on the colloidal particles. The validity of this rule is strikingly confirmed by Hardy's experiments on the coagulation of the protein solution described on p. 191. It will be remembered that in a faintly alkaline medium this protein is electro-negative, while in a faintly acid medium it is electro-positive. It is accordingly found that in presence of a trace of alkali aluminium sulphate is much more effective than sodium sulphate in bringing about the coagulation of the protein, while magnesium sulphate occupies an in- ' Zeii. physihal. Ohem., 1900, 33, 385. _ THE SEPARATION OF COLLOIDS 205 termediate position ; when, however, the protein solution contains a trace of acetic acid, the three sulphates are about equally effective in causing coagulation. Similarly it is found that while barium chloride is more effective than sodium sulphate in coagulating the electro-negative protein, the positions of the salts are reversed in relation to the electro-positive protein. All these resuTts, taken in conjunction with the fact that non-electrolytes are ineffective, show that the coagu- lation of suspensoids is essentially a process in which ions are primarily involved. It is therefore not sur- prising to find that when various electrolytes all yield- ing the same cation are used to coagulate arsenious sulphide, the effectiveness increases with the degree of dissociation ; the smaller the extent to which the electrolyte is dissociated, the greater relatively is the quantity of it required to bring about complete coagu- lation. This is shown in a general way by the following table ; >• the figures in the second column give the con- centration necessary in each case to cause coagulation of a colloidal arsenious sulphide solution : — ... Gram-Equivalenta Spec. Conductivity •*-™°' per Litre. at 18° (comparative). HCl 0-0038 14-5 HNO3 0-0038 14-3 H2SO4 0-0043 13-2 H2C2O4 0-009 14-4 H3PO4 0-015 13-9 CH3.COOH 0-70 12-6 It is seen that although very different quantities of the acids must be taken to bring about coagulation, yet each of the coagulating solutions has approximately the same conductivity, that is, approximately the same number of ions. If the coagulation of a suspensoid is the result of a ' Hardy, loo. cit. 206 PHYSICAL CHEMISTEY neutralisation of electric charges, one on the colloid particles and one on the coagulating ion, then the pre- cipitated colloid, the ' coagulum,' or ' hydrogel ' as it may be called, ought to contain either the acidic or basic part of the added electrolyte. This is actually the case ; Linder and Picton ^ found that when a colloidal solution of arsenious sulphide is precipitated by adding barium chloride, the coagulum contains barium. This barium cannot be removed from the precipitate by continued washing with water, but when the precipitate is treated for some time with a solution of another salt, the barium is replaced by the metallic part of this salt. Similar observations have been made by Whitney and Ober,^ who show that when colloidal arsenious sulphide is precipitated by barium chloride, the quantity of barium carried down in the coagulum is independent of the concentration of the solution, but is proportional to the amount of sulphide precipitated. The composition of the coagulum obtained by Whitney and Ober is represented by QOAsjSg + lBa, and in pro- portion as the coagulum retains barium the filtrate becomes acid. Further, when four equal quantities of colloidal arsenious sulphide are precipitated by barium, strontium, calcium, and potassium chloride respectively, the coagula retain equivalent quantities of the four metals. The retention of the precipitating metal by the coagulum appears to be a case of adsorption,^ which will be, discussed later. Some interesting observations are on record dealing with the coagulation of colloidal arsenious sulphide by mixed electrolytes. The coagulating effect of the mixed chlorides of two uni-valent metals is simply the sum of the two separate effects; the effect, however, of a » Journ. Chem. Soc, 1895, 67, 63. " Zeit. physihal. Ohem., 1902, 39, 63. « Freundlich, Zeit. pliysikal. Chem., 1910, 73, 385. THE SEPAEATION OF COLLOIDS 207 mixture containing the chloride of a uni-valent metal and the chloride of a di-valent metal, is less than that calculated on the additive basis. There appears, there- fore, to be a certain antagonism in this respect between uni-valent and di-valent cations, and it is worth noting that a similar antagonism has been observed in some physiological experiments made by J. Loeb.^ This in- vestigator found that freshly fertilised eggs of Fundulus heteroclitus when transferred from sea-water to an iso- tonic solution of pure sodium chloride all die without developing. If, however, there is first added to the pure sodium chloride a small quantity of the chloride of almost any di-valent metal, the resulting mixture is a more or less suitable medium for the development of fertilised Fundulus eggs. The toxic effect of pure sodium chloride is thus inhibited by salts with di-valent cation. In the previous chapter it was suggested (see p. 186) that the increased aggregation of a colloid brought about by small quantities of a salt might be regarded as the first stage in a process which ultimately leads, to precipitation. Now the precipitation of a positive colloid, as we have just seen, is determined chiefly by the negative ion of the added electrolyte, and the precipitation of a negative colloid by the positive ion of the added electrolyte. It might therefore be expected that the addition of an alkali (i.e. of OH' ions) to the solution of a positive suspensoid in quantity insufficient to produce coagulation would lead to an increase in the size of the suspensoid particles, and that a similar result would follow the addition of an acid (i.e. of H* ions) to a negative sus- pensoid in quantity insufficient to produce coagulation. This has been verified by Mayer, SchaefEer, and Terroine,^ who used the ultramicroscope to study the changes of 1 Amer. Journ. Physiol., 1902, 6, 411. Compare Osterhout, Science, 1911,31, 187; 1912,35, 112. " Compt. rend., 1907, 145, 918. 9 208 PHYSICAL CHEMISTRY size exhibited by the colloid particles. They found further that the addition of H" ions in small quantity to a positive colloid led to a decrease in the size of the particles, as did also the addition of OH' ions to a negative colloid. The colour changes exhibited by gold and silver hydrosols on the addition of minute quantities of electro- lytes are similarly to be referred to alterations in the aggregation of the colloid particles. Reciprocal Coagulation of Suspensoids. — The study of the influence of electrolytes on suspensoids has shown clearly that in the process of coagulation the charge on the colloid is neutralised by that on one of the ions of the added electrolyte. If this view of the coagulation pro- cess is correct, then we 'may fairly expect that if we neutralise the charge on the colloid in any other way, a similar result will follow. In the previous chapter evfdence has been recorded showing that some colloid- ally dissolved substances carry a negative charge, while others carry a positive charge. It may therefore be reason- ably expected that if the solution of a positive colloid. is added to the solution of a negative colloid, (1) coagula- tion will result, and (2) the coagulum will contain both colloids, for, as already stated, the coagulum obtained when barium chloride is added to arsenious sulphide solution contains both arsenious sulphide and barium. The experiments carried out by Biltz ^ have verified both predictions. This investigator showed, first, that no coagulation occurs when hydrosols of the same electrical sign are mixed. When, however, a solution of a posi- tively charged colloid is added to that of a negatively charged colloid precipitation occurs in all cases, unless the quantity of the added colloid is relatively either very small or very great. For a certain proportion I ^er. deut. chem. Ges., 1904, 37, 109p. THE SEPARATION OP COLLOIDS 209 of the colloids precipitation of both is complete ; as the quantities deviate from this optimal ratio, precipitation is increasingly incoraplete. It is possible, for instance, to bring about the complete precipitation of arsenious sulphide from its solution by the addition of a suitable quantity of ferric hydroxide hydrosol ; similarly, aniline blue, which forms a negative hydrosol, is precipitated by magdala red, which forms a positive hydrosol. The precipitation of egg albumin by solutions of various complex acids — e.g. molybdic, tungstic, and tannic acids — furnishes an example of the mutual coagu- lation of two colloids.^ Metaphosphoric acid, too, forms a pseudo-solution or hydrosol which precipitates albumin, while the crystalloidal orthophosphoric acid has no such effect. An interesting case in which the reciprocal coagulation of two colloids has been employed for a practical purpose is furnished by a recent investigation of Michaelis and Eona.* They shovv that mastic suspension and a faintly acid solution of protein precipitate each other completely when they are mixed in a certain proportion ; if they are mixed in any other proportion, the precipitation is in- complete. This observation is taken as the basis of a method for the removal of the last traces of proteins from blood serum. The bulk of the protein in the serum is precipitated with alcohol, and the filtrate, containing not more than 1 per cent, of protein and a trace of acetic acid, is treated with excess of mastic suspension. This of itself does not bring about complete precipitation of the protein, but if the excess of mastic is coagulated by the addition of a small quantity of an electrolyte, it carries down all the remaining protein with it. The filtered liquid is then free from both mastic and protein. * See Mylius, Ber. deut. chem. Qes., 1903, 36, 775 ; Biltz, loo. cit. ' £:ochem. Zeit., 1907, 2, 219 ; 5, 365. 210 PHYSICAL CHEMISTRY The Precipitation of Emulsoids. — Emulsoids differ notably from suspensoids in their slight sensitiveness to the presence of neutral alkali salts. Comparatively small quantities of these are able to produce coagulation of arsenious sulphide or ferric hydroxide, while the quantities required to cause precipitation of, say, serum albumin from its solution are very great. The precipita- tion of an emulsoid by a neutral alkali salt is reversible, while the corresponding precipitation of a suspensoid is irreversible. Further, the factors governing the pre- cipitation are quite different in the two cases. All the evidence goes to show that the precipitation of a suspen- soid by an electrolyte is essentially electrical in character ; the precipitation of a reversible colloid by a neutral alkali salt, on the other hand, has much in common with the phenomenon of ' salting out,' familiar especially to the organic chemist. Electrical influences have nothing to do with the precipitation of a reversible colloid, for as Pauli has showii,^ protein from serum can be so purified by dialysis that even in a steep potential gradient it exhibits no tendency to migrate either towards the anode or towards the cathode, yet in this neutral condition the protein can be precipitated by alkali salts ; hence it is clear that the factors which determine precipitation in this case are not electrical. The grounds for regarding the precipitation of emul- soids by neutral alkali salts as allied to the pheno- menon of ' salting out ' rather than to the coagulation of suspensoids are to be found in the relative effects of these salts. The results of many investigations of the influence of salts on the solubility of hydrogen, carbon dioxide, ethyl acetate, and other sparingly soluble sub- stances (compare p. 26), have shown that the effect of any particular salt is the sum of the effects of the ions ; • Beitr. chem. Physiol. Path., 1906, 7, 531. THE SEPAEATION OP COLLOIDS 211 a diminution in the solubility of any of these substances is not due to the cation in one case, to the anion in another, as in the coagulation of suspensoids; each ion is responsible for part of the effect. By comparing the effects of a number of potassium salts in lowering the solubility of, say, hydrogen in water, it is possible to arrange the anions according to the magnitude of their influence; similarly, by comparing the effects of the chlorides of the alkali metals on the solubility of hy- drogen, it is possible to arrange the cations according to the magnitude of their influence. The order of the anions determined in this way, beginning with the one which is most effective in lowering the solubility of hydrogen, &c., is SO/', CI', Br', I', NO3' ; the corresponding order for the cations is Na", K', NH^". Hofmeister and Pauli^ have studied in a similar fashion the influence of various alkali salts in precipitating proteins, and they find that the effect of a given alkali salt is an additive function of the two ions. When the ions are arranged ■according to the magnitude of their effects, the following series are obtained, the first member of each series being the most effective in causing precipitation : SO/', HPO^", CH3.COO', CI', NO3', Br', r, CNS'; Li', Na", K', NH/. Comparison of these with the previous series shows that the order is very nearly the same in the two cases. The precipitation of reversible colloids by neutral alkali salts appears therefore to be closely allied to the process of ' salting out,' and, like the latter, is probably connected with the hydration of the salts. This result emphasises the fact that solutions of reversible colloids approximate more to true solutions that do solutions of suspensoids. When a neutral solution of protein is made slightly acid or slightly alkaline, its properties undergo a marked 1 See Pauli, Beitr. cJiem. Physiol. Path., 1902, 3, 225. Compare Bobertson, /. Biol. Chem., 1911, 9, 303. 212 PHYSICAL CHEMISTRY modification. In a potential gradient the protein now migrates towards the anode or cathode according as the medium is alkaline or acid, and in respect also to the precipitating power of salts its behaviour now resembles that of an ordinary suspensoid.^ The properties of a protein solution containing a trace of alkali or acid have accordingly been discussed in an earlier paragraph of this chapter, where it was shown that in these circumstances it is the valency of the cation or anion which is the predominating factor in determining the precipitation. The modification in the character of protein which results from the addition of small quantities of acid or alkali is demonstrated also by its behaviour towards salts of the heavy metals. These are unable to precipitate carefully dialysed neutral protein, but as soon as the protein has acquired an electro-negative character, it is readily pre- cipitated by small quantities of these salts ; the precipita- tion, further, is irreversible in character, and therefore quite different from the precipitation of neutral protein by alkali salts. The readiness of protein to change its character with the acid or alkaline reaction of the m.edium becomes intelligible on the basis of Hofmeister's theory, that the proteins are produced by the condensation of several amino acids, and that the protein molecule is character- ised by the presence of at least one amino group and one carboxyl group. On this view protein is an ' am- photeric ' electrolyte, that is, an electrolyte which may act either as an acid or as a base — which may split off either hydrogen or hydroxyl ions. According to circumstances, therefore, the protein molecule may assume either an acid or a basic function: it forms salts both with bases and with acids. ' Hardy, Zeit. physikal. Chem., 1900, 33, 385 ; also Pauli, Beitr. chem PhynoU Path., 1906, 7, 531. THE SEPAEATION OF COLLOIDS 213 Protective Action of RcYersible Colloids. — When a reversible colloid is added to the solution of a suspensoid, the precipitation of the latter by electrolytes is more or less inhibited. This is not generally due to an increase in the viscosity of the medium, and consequently increased resistance to sedimentation, for the protective efEect is produced by very small quantities of the reversible colloid, insufficient to cause any appreciable change of viscosity. As an illustration of this phenomenon we may take the influence of various reversible colloids on the stability of a gum mastic suspension. Bechhold has shown ^ that while a mixture of 1 cub. cm. mastic suspension + 1 cub. cm. O'lN MgSO^ made up to 3 cub. cm. with water is completely coagulated in 15 minutes, no coagulation occurs within 24 hours if 2 drops of a 1 per cent, gelatin solution are added before making up to 3 cub. cm. ; the gelatin ' protects ' the mastic. The coagulation of mastic suspension is similarly inhibited by ox blood serum and gum arable. An extreme case of this protective action is furnished by the colloidal silver halides described by Paal and Voss.^ These are obtained by adding sodium halide to silver hydroxide in presence of sodium protalbate or lysalbate, salts which are prepared by the action of sodium hydroxide on egg albumin. The colloidal solutions of silver halide so obtained are opalescent, and yield a slightly coloured solid, containing as much as 90 per cent, of silver halide, and yet dissolving readily in cold water. It is probable that in such cases the emulsoid forms a thin envelope round each suspensoid particle, and so prevents the aggre- gation and consequent flocculation of the particles. Reversible colloids differ appreciably in their power to 1 Zeit. phyaihal. OJiem., 1904, 48, 40i>. * Ber. deut. chem. Oes., 1904, 37, 3862. 214 PHYSICAL OHEMISTEY protect suspensoids from coagulation by electrolytes, and an attempt has been made by Zsigmondy i to differentiate various protein substances on this basis. A red solution of colloidal gold turns blue on the addition of sodium chloride and other salts owing to increase in size of the colloid particles, but this change of colour may be pre- vented by the presence of proteins. A more or less definite amount of each protein is required to secure this result, and the proteins may be classified correspond- ingly. For this purpose Zsigmondy used the ' gold number,' which is defined as the weight in milligrams of the reversible colloid which is just insufficient to pre- vent the change from red to blue in 10 cub. cm. of colloidal gold solution after the addition of 1 cub. cm. of 10 per cent, sodium chloride solution. How far the ' gold number ' varies from one case to another will be seen from the following table : — Gold Number. Gelatin 0-005- 001 Caseinogen O'Ol Globulin 0-02-005 Egg albumin amorpli 0"03-0'06 Egg albumin cryst 2-8 Fresh egg-white 0-08-0-15 It is noteworthy that albumoses are altogether unable to exert a protective action on the red solution of colloidal gold. Colloids in Biology. — In view of the enormously im- portant part played by colloids in the living cell itself and in all physiological fluids, it is obvious that a know- ledge of the peculiar characteristics of these substances is a necessary preliminary to any effort to interpret vital phenomena. In recent years our knowledge of the pro- ' Zeit. anaZyt. Oliem., 1901, 40, 697 ; see also Schulz and Zsigmondy, Beitr. chem. Physiol. Path., 1902, 3, 137. THE SEPAEATION OP COLLOIDS 215 perties of colloids has been growing rapidly, and numerous and noteworthy attempts have been made to use this new knowledge in attacking biological problems of various kinds. In this and the foregoing chapters, in which a brief account of the outstanding characteristics of colloids has been given, reference has been made incidentally to various cases in which the behaviour of colloids seems to have a direct bearing on certain biological phenomena. There are, however, numerous other problems in which colloids are essentially involved, and oh which much new light has been thrown by the colloid investigations of the past ten or fifteen years. In this period much work has been done with the object of elucidating the nature and mode of action of enzymes, toxins, and antitoxins, and as these are all col- loids, it is only natural that attempts have been made to correlate their behaviour with that of less complex bodies of the same class. As a first example of such correlation we may take what is known as the Danysz phenomenon. The toxicity of a mixture of diphtheria toxin and antitoxin depends on the way in which the two are mixed. If the amount of toxin added is such that the mixture is non- toxic, then in a second experiment, in which the same amounts of antitoxin and toxin are taken, in which, however, the toxin is added in instalments, the resulting mixture is toxic. This phenomenon is exactly analogous to what happens in the precipitation of a colloid by an electrolyte, or in the precipitation of one colloid by another; the amount of electrolyte or colloid required for complete precipitation varies -according as it is added all at once or in instalments. The condition of a toxin-antitoxin mixture, therefore, resembles that of colloidal solutions in that it is not completely defined by a statement of its composition; its character depends on its previous history. 216 PHYSICAL .CHBMISTET In connection also with the agglutination of bacteria,' notable attempts have been made to interpret some at least of the phenomena by reference to the known be- haviour of ordinary colloids.^ If an animal is inoculated with cultures of typhoid bacteria, a substance, agglutinin, is produced in the serum, and this substance, when added to a suspension of typhoid bacteria, causes the latter to clump together and to sink to the bottom of the liquid in which they are suspended: this phenomenon is de- scribed as ' agglutination,' This process bears a general resemblance to the precipitation of an insoluble salt which frequently follows the addition of one salt solution to another, but to conclude from this that the interaction between typhoid bacteria and agglutinin is purely a chemical reaction would be unjustifiable. For, as we have seen, a colloid may be precipitated by an electrolyte or by another colloid, even in cases where the possibility of chemical interaction in the ordinary sense is excluded. "When different quantities of agglutinin are added to a given quantity of typhoid bacteria, it is found that for one particular quantity of agglutinin the ag- glutination is at a maximum. If either a very small or a very large amount of agglutinin is added to the bacteria, no agglutination whatever occurs. The occur- rence of such maximum effects for particular concentra- tions of the interacting substances is indeed fairly frequent in the field of immunity. It is possible to regard this phenomenon as the analogue of what happens when sodium hydroxide is gradually added to a solution of alum ; the precipitate first formed is dissolved by excess of the reagent, and the amount of precipitate is a maximum for certain definite proportions of alum and sodium hydroxide. But the interaction between agglutinin and 1 Eisenberg and Volk, Zeit. Hygiene, 1902, 40, 155. « Bechhold, Zeit. physihal. Chem., 1904, 48, 385 ; Biltz, ifiioJ., 615. THE SEPARATION OP COLLOIDS 217 bacteria is not thereby proved to be purely a chemical effect, for, as already stated (p. 209), the mutnal pre- cipitation of colloids is characterised by the same features. When one of the colloids is in very large excess no precipitate is formed, and the maximum precipitation for a given quantity of the one colloid is obtained only with a certain proportion of the other colloid. It is noteworthy that a serum containing agglutinin can agglutinate bacteria only in the presence of the salts of the serum; if the serum is dialysed, and so freed from electrolytes, no agglutination takes place. That this should be so is not surprising' when we bear in mind the important part played by electrolytes in relation to colloids. A suspension of agglutinin bacteria — ^that is, bacteria which have been treated with a serum containing agglutinin and thereafter thoroughly washed — resembles a mastic suspension in being completely precipitated by small quantities of salts, and Bechhold (loc. cit.) has shown that the precipitating power of a salt in relation also to agglutinin bacteria is determined mainly by the valency of the cation. A suspension of typhoid bacteria alone, although it moves towards the anode in a potential gradient, is not precipitated by sodium chloride. The bacteria behave like suspended particles which are pro- vided with a coating of reversible colloid, and are so protected from the action of salts of the alkali and alkaline earth metals. Such are a few of the cases in which a comparison of the agglutina,tion of bacteria and the properties of ordinary colloids is highly suggestive. The problem of agglutination, however, is very complex, and it is unlikely that it will be solved merely by correlation with the phenomena of colloidal solutions, or even on the wider basis of an adsorption theory (to be discussed in the following chapter). For the reaction between agglutinin 218 PHYSICAL CHEMISTRY and bacteria is a specific one ; typhoid bacteria are agglutinated pre-eminently by the serum of animals pre- viously treated with cultures of typhoid bacteria, not by the serum of animals inoculated with cultures of other bacteria. Such specific characteristics can be explained only on chemical lines, and a discussion of the agglutina- tion, of bacteria from this point of view is outside the scope of the present volume. There are various other phenomena of physiological interest in which the mutual precipitation of two colloids is a main feature, and in the interpretation of which the conditions governing such a precipitation must be borne in mind. There is, for instance, the observation that if red blood corpuscles from one animal are injected into another animal of a different species, a substance is produced in the serum of this second animal which has the power of agglutinating red corpuscles of the injected variety. In this connection it is worthy of mention that when blood corpuscles are suspended in a sucrose solution, or in a neutral solution of an alkali or alkaline earth salt, they move towards the anode in a potential gradient. Hober ^ attributes this to the protein and lecithin present in the plasmatic membrane ; these substances generally exhibit anodic convection. Like these also, the blood cor- puscles reverse their migration when a little acid, copper, silver, iron, or aluminium salt is added to the medium in which they are suspended. A suspension of red blood coi-puscles is agglutinated not only by serum obtained from an animal which has been inoculated with these corpuscles, but also by numerous colloids, positive as well as negative — stannic acid, ferric hydroxide, mastic, andi various dyes. 1 Pfiiiger's Arch., VMi, 101, 607 ; 102, 196. CHAPTER XI ADSORPTION Surface Development in Colloids. — It is not pro- posed to discuss in detail in this* volume the various theories which have been brought forward dealing with the stability of colloidal solutions and with the separa- tion of colloids from their solutions.i Two factors, however, which must obviously enter into any inter- pretation of the relation between a colloid and its medium may be noted here. There is, firstly, the existence in a great many cases at least of a potential difference between the colloid particles and the surround- ing medium, and secondly, the relatively enormous surface of contact between the colloid and its environment. The importance of the electrical factor will have become plain to the reader from the facts described in the two pre- ceding chapters. A little consideration wUl show that the other factor, which we may call the surface factor, is equally important in the interpretation of the pheno- mena exhibited by colloids. All the facts go to show that a colloidal solution is essentially non-homogeneous; it is what is known as a two-phase system, built up of a fluid medium containing definite and distinct sus- pended particles in an extreme state of subdivision. With the help of the ultramicroscope it is possible in 1 See, for instance, lla,TAj,Zeit. physikal. Chem., 1900, 33, 385; Bredig, Anorgan. Fermente, Leipzig, 1901 ; Billitzer, Zeit. physikal. Chem., 1904, 45,327; 1905,51,129; Michaells, in Korany i and Bichter's PAj'***"'**'''''^ Chemie und Medizin, Leipzig, 1908. 219 220 PHYSICAL CHEMISTEY a great many cases to detect these particles and to follow their movements. Now, when a given quantity of matter is divided up more and more finely, its sur- face area is immensely increased. Suppose, for instance, that a compact sphere of any material with a diameter of 1 mm., and therefore a surface area of 0-0314 sq. cm., were divided up into a number of small spheres each with a diameter of 0"01 mm. The number of spheres would now be 10^ and the total area of their surfaces would be 3'14 sq, cm. If the division were carried farther until each small sphere had a diameter of 0*0001 mm., and would therefore be hardly visible under the microscope, their number would be 10^^, and the total area of their surfaces would be 314 sq. cm. To bring about such a subdivision requires the application of energy, which is stored up in the finely divided spheres in the form of surface energy; this is defined as the product - surface area x surface tension. In two- phase systems, therefore, where the surface of the one phase is developed to a relatively high degree, as it is in colloidal solutions, the surface energy becomes an important factor in determining the behaviour of the system.^ Especially is this the case where a change in the aggregation of colloid particles is concerned ; this means a change in the surface area, and this again involves a change of the surface energy. It has been stated above that in the relationship between a colloid and its environment electrical energy also is involved. The parts played by electrical and surface energy respectively in the phenomena of colloidal solutions are not however independent of each other : there is a' close connection between the two. It is ' It is an interesting question whether this argument cannot be extended to cover the case of orystalloidal solutions, regarded as two- phase BjatejDS. See Wo. Ostwald, Gnmdriss der KoUoidchemie, p. 126. ADSORPTION 221 well known that the surface tension of mercury in con- tact with a sulphuric acid solution is affected by altera- tions in the potential • difference between metal and solution. Obviously, in view of the fact that electrical charges of the same sign repel each other, the existence of a charge at the surface of the mercury tends to increase the surface, and is therefore opposed to the surface tension, which tends to diminish the surface. A reduction in the electrical charge at the surface means an increase in the surface tension. This example shows that in the case of colloidal solutions the connection between the electrical and surface factors must be very close. Instead of following out the influence of these factors in determining the properties of colloids, as has been attempted by Hardy, Bredig, Billitzer, and others, we shall consider the phenomena exhibited by colloids from a wider point of view which has been very generally adopted in recent years. We may regard the interaction of colloids with each other and with various solid and dissolved substances as being essentially a process of ' adsorption.' This term is used to describe a phenomenon which is frequently observed when a foreign substance is introduced into a two-phase system. When opportunity is afforded this foreign substance to distribute itself throughout the system, it is often found to be locally concentrated at the surface of one of the phases. This concentration, as will appear from the cases discussed below, is not generally to be regarded as a chemical process ; the phenomenon is physical in character, and is especially striking when the surface of the adsorbing phase is highly developed. It is in regard to this local concentration on the surface that adsorption differs from absorption ; when we speak of a gas as being absorbed by a liquid, we picture the gas as distributed uniformly throughout the mass of the liquid. Perhaps, however, we can best 222 PHYSICAL CHEMISTRY appreciate what is involved in the term ' adsorption ' by studying, first, the distribution of a substance in a two-phase system where no surface concentration occurs. Distribution of a Substance between Two Immiscible Liquids. — When a substance is shaken up with two immis- cible liquids, some of it is found to be dissolved in the one layer, some of it in the other layer ; it is said to be ' dis- tributed ' between the two phases. The absolute amount of the substance found in each liquid layer after equilibrium has been established will naturally depend on the volume of each liquid taken, but if we eliminate this by comparing the coticentrations (i.e. weights per unit volume) of the substance in the two layers, we get a definite measure of the distribution. If c^ is the concentration of the substance in the first liquid, and Cj its concentration in the second liquid, then the ratio - is known as the 'partition coefficient' or the 'distribution ratio.' Ex- periment has shown that if the molecular condition of the dissolved substance is the same in each of the two liquids, then the partition coefficient is independent of the absolute values of Cj and Cg, independent, in other words, of the concentration. This is illustrated by the figures in the following table relating to the distribution of iodine between water and carbon tetrachloride ; ^ the figures in the first colomn (cj) are the concentrations of iodine in the aqueous layers, those in the second column are the concentrations of iodine in the corre- sponding carbon tetrachloride layers : — «1- "2- 0-2913 25-61 87-9 0'1934 16-54 85-5 0'1276 10-88 85-3 0*0818 6-966 85-1 0-0516 4-41.2 85-8 I Jakowkin, Zeit. pliysik(^. Chem., 1895, 18, 585, ADSORPTION 223 The rule, of whicli the foregoing figures are an illustration, namely, that the ratio of the concentrations of a substance distributed in two immiscible liquids is independent of the concentration, is really the same as Henry's law dealing with the absorption of a gas by a liquid under varying pressures. In an earlier part of this volume (p. 20) it was stated that accord- ing to Henry's law the quantity of gas dissolved by a given quantity of a liquid at a given temperature is proportional to the pressure. Suppose that a given quantity of water is shaken up with hydrogen (1) at 1 atmosphere pressure, (2) at 3 atmospheres pressure, until saturation is complete in each case, that is, until equilibrium is established between the gas phase and the liquid phase. According to Henry's law, the quantity of gas dissolved in the liquid in the second case is three times as great as it is in the first case, that is, its concentration in the liquid phase is three times as great. But the hydrogen in the second case is under 3 atmospheres pressure as compared with 1 atmosphere in the first case, and the concentration in the gas phase will have increased in the same pro- portion. The ratio, therefore, of the concentrations of hydrogen in the gas phase and in the water is the same under 3 atmospheres as under 1 atmosphere ; or, putting it generally, the ratio of the concentrations of the gas in the gas phase and in the liquid phase, when equilibrium has been established, is independent of the pressure. Expressed in this form, Henry's law is seen to be practically identical with the rule relating to the distribution of a substance between two immiscible liquids. Such a distribution is a physical process; it can be regarded as chemical only in so far as we regard the process of solution of, say, sucrose in water as due to 224 PHYSICAL CHEMISTRY the action of chemical forces. It ought to be noted also that when a gas is dissolved in a liquid, or when a substance is distributed between two immiscible liquids, the equilibrium which is established is reversible, that is, it can be reached from both sides. Suppose, for instance, that 100 cub. cm. of water are shaken with 20 cub. cm. of a solution of iodine in carbon tetrachloride ; equilibrium is rapidly established, when it will be found that some of the iodine has gone into the water. Suppose that, in a second experiment, 100 cub. cm. of water are shaken with 10 cub. cm. of an iodine solution of double the concentration of the first one. When equilibrium is reached the 100 cub. cm. of water will be found to contain more iodine than in the first case. If, however, another 10 cub. cm. of carbon tetrachloride are added and the mixture is shaken, the extra iodine is taken out of the water, and the equilibrium finally reached is the same as in the first case. If the molecular condition of the dissolved substance is different in the two liquids, then the value of the ratio — is not independent of the concentration. This statement is borne out by the following figures relating to the partition of acetic acid between benzene and water :^ — c^ is the concentration of the acid in the benzene layer, Cj the concentration in the aqueous layer. «1- Ca- 3. 3. 0-043 0-245 5-7 1-40 0-071 0-314 4-4 1-39 0-094 0-375 4-0 1-49 0-149 0-500 3-4 1-67 It is obvious that the partition coefficient varies with the concentration, and this is to be attributed to the fact 1 Nernst, Zeit. physihal. Chem., 1891, 8, 110. ADSOEPTION 225 that the molecular condition of acetic acid is not the same in benzene as it is in water. From the depression of the freezing point produced by acetic acid in these two solvents, it is known that the acid in benzene solution consists almost entirely of double molecules (although the proportion of simple molecules increases with dilution), whereas acetic acid in water, apart from the slight electrolytic dissociation, exists in the form of simple molecules. Now, on theoretical grounds it follows that if the molecular weight of the dissolved substance in the first liquid is n times the molecular n weight in the second liquid, then the ratio _£ ought to have a constant value independent of the concen- tration. From what has been said, it is evident that for the partition of acetic acid between benzene and water n = 2, and we should therefore expect the value of I? J. to be independent of the concentration.^ This is "i approximately the case, as shown by the figures in the last column of the foregoing table, and such varia- tion as the figures show is probably due to the fact that the proportion of simple molecules in a benzene solution of acetic acid increases somewhat on dilution. If, conversely, the distribution of a substance between two liquids at various concentrations has been found n to be such that 5l is independent of the concentration, the conclusion may be drawn that the molecular weight of the substance in the first liquid is n times that in the second liquid. Equilibrium between a Gas and a Solid. — As an example of a case where surface effects become pro- minent, we may take, first, the distribution of a gas ^ Nernst, loe. nt. 226 PHYSICAL CHEMISTRY between a gas phase and a solid phase ; that is, we shall consider the way in which the amount of a gas taken up by a solid varies with the pressure of the gas. In view of the results obtained in connection with the distribution of a substance between two non- miscible liquids, it might be expected that a study of the equilibrium between a gas and a solid would lead to a knowledge of the molecular condition of the gas which is taken up by the solid. This expectation, however, is not fulfilled, for the taking up of a gas by a solid is found to be determined mainly by surface effects. The facts can best be explained by reference to the case of carbon dioxide and carbon, studied by Travers.^ This investigator determined the concentration (a;) of carbon dioxide in the carbon at various pressures (P), sufficient time of course being allowed for the gas and solid to come into equilibrium with each other. The results obtained at 0° 0. are recorded in the first two columns of the following table: — Pmm. X. X Up 4-1 0-38 0-24 25-1 0-77 0-26 137-4 1-45 0-26 416-4 2-02 0-27 858-6 2-48 0-26 From a consideration of these it is seen that the amount of carbon dioxide taken up by the carbon increases much more slowly than the pressure. Travers found, however, that x increases proportionally to the cube root of P, as is shown by the constancy of the figures in the third column of the table, and the question arises : What interpretation is to be given of this relationship between Proc. Soy. Soc., A, 1906, 78, 9. Compare Homfray, HM., 1910, 84,99. ADSOEPTION 227 P and xf How is it that a similar relationship, ex- pressed by the equation ^ = const, is found for carbon dioxide and carbon at other temperatures, as well as for hydrogen and carbon? If we suppose that the gas is uniformly distributed throughout the carbon, forming a solid solution, and reason by analogy from Nernst's experiments on the partition of acetic acid between water and benzene, we should reach the con- clusion that the molecular weight of carbon dioxide in carbon is one-third of its molecular weight in the gaseous condition. It is obvious that on chemical grounds this conclusion must be rejected, and it appears therefore that to regard the carbon dioxide as uniformly dis- tributed through the carbon, and so forming a homo- geneous solid solution, is not permissible. There are various indications, in this and similar cases, that the surface of the solid is mainly, if not exclusively, con- cerned ia taking up the gas, and the phenomenon is accordingly described as 'adsorption' rather than 'ab- sorption.' Adsorption by a Solid from a Solution. — Very similar to the phenomena just discussed is the power of carbon to adsorb various substances from, their solutions. Numerous cases of this adsorption have recently been investigated with the object of discovering the nature of the equilibrium between the carbon and the solution, and of finding how the quantity of sub- stance adsorbed by the carbon varies with its concen- tration in the solution. It is noteworthy that the adsorption equilibria between carbon and an aqueous solution are reversible — that is, they can be reached from either side. An illustration of this important point may be quoted.^ One gram of » Freundlich, Zeit. phyiikal. Chem., 1906, 57, 385. 228 PHYSICAL CHEMISTEY carbon was shaken for 20'5 hours with 100 cub. cm. of a 0'0688N solution of acetic acid; by this time equilibrium was established, and it was found that the acid solution was now 0'0608N. In another experiment one gram of the same carbon was shaken for 21 hours with 50 cub. cm. of a 01376N( = 0-0688x2) solution of acetic acid; 50 cub. cm. of water were then added, and the mixture was shaken for an hour, at the end of which time it was found that the acid solution was 0'0606N. This is practically the same value as in the first case, which shows that the same equilibrium is reached when the carbon is charged directly with the acid as when a slightly overcharged carbon is deprived of part of its adsorbed acid. In the experiments which have just been described the carbon was shaken with the acid for about 20 hours in order to secure the establishment of equilibrium. In reality, however, the time required is remarkably short. It has been found that when a solution of acetic acid is added to carbon, once shaken with the hand, and then allowed to stand for 20 minutes, the concentration of the solution has fallen very nearly to its equilibrium value. This observation supports the view that the taking up of acetic acid from its solutions by carbon is a process in which the surface, of the carbon is mainly concerned, for the penetration or diffusion of the acid into the interior of the carbon granules could only be a comparatively slow process. The relation between the concentration of acetic acid in the carbon and that in the solution when equilibrium has been reached is brought out by the figures in the following table.^ Those in the first column (cj) repre- sent the equilibrium concentrations of the acetic acid ' Freundlioh, loc. ott. ADSOEPTION 229 in the solutions, and are given in millimolecules per cub. cm. ; the figures in the second column (Cj observed) represent the equilibrium concentrations of the acetic acid in the carbon, and are given in millimolecules per 1 gram of carbon. A glance at the table shows that the amount of acetic acid taken up by the carbon increases much more slowly than its concentration in the solution. In this respect the adsorption of dissolved acetic acid by carbon and the adsorption of carbon dioxide by the same substance are closely similar. Adsorption of Acetic Acid by Carbon. /3= 2-606. J) =2- 35. «(. e, observed. c, calculated, 0-0181 0-467 0-474 00309 0-624 0-596 0-0616 0-801 0-798 0-1259 1-11 1-08 0-2677 1-55 1-49 0-4711 2-04 1'89 0-8817 2-48 2-47 2-785 3-76 4-01 The parallelism, however, goes further, for the relation- ship between the concentrations of acetic acid in the solu- tion and in the carbon can be represented by a formula of the same general type as 1^= const. This general adsorption formula is c, = ^.C;J', in which ^ and p are constants for a given temperature and a given dissolved substance, while 'c, and c, represent, as already stated, the concentration of the dissolved substance in the solid and liquid phase respectively.' The applicability of this formula to the adsorption of acetic acid by carbon may be tested by assuming that the formula Cs=/3 .c,p is valid in this case, and then using the experimental figures of the first two columns to evaluate P and p. The mean values so • For other formulae see Arrhenius, Medd. K, Vetensk. NohelvniU, 1911, 2, No. 7, 1. 230 PHYSICAL CHEMISTEY obtained are /3= 2-606 and ^ = 2-35. When these figures are put in the general formula, we get Cj = 2-&08ci^5 , so that from the ascertained value of c,, given in the first column, we can calculate what the value of c, ought to be. Agree- ment between the value of c, so calculated and the ex- perimental value of c, furnishes a proo£,of the applicability of the original exponential formula. The numbers in the third column of the foregoing table are the calculated values of c, for each solution, and it will be seen that they agree remarkably well with the observed values. 1 The empirical exponential formula, then, c, = iS.c5, may be taken as representing the adsorption equilibrium between carbon and aqueous acetic acid. Freundlich has further shown that the same general formula is applicable to the adsorption of many other substances by carbon, not only from their aqueous solutions, but also from their solutions in alcohol, benzene, and ether. The "value of p varies from one case to another, but only within somewhat narrow limits ; it appears, therefore, to be to a large extent independent of the solvent and the dissolved substance. Thus for benzoic acid in w;ater^ = 2'96 ; bromine in water, p = 3'44; picric acid in water, ^ = 4'17; benzoic acid in ether, ^ = 2*2. The similarity between the adsorption of two such different substances as benzoic acid and bromine, evidenced by the comparatively slight difference in the values of p, is particularly striking,^ and may be taken as showing that the process of adsorption is not generally a chemical phenomenon in the ordinary sense, as has been maintained in some quarters. Further, when a solution of a substance is shaken up with a solid with which it may react chemically, the equilibrium reached is essentially different from the » See Freundlich, Zeit. Chem. Ind. Koll., 1908, 8, 212, ADSOEPTION 231 adsorption equilibrium between, say, carbon and aqueous acetic acid. The difference is well brought out in an investigation by Walker and Appleyard^ of the equili- brium between solid diphenylamine and an aqueous solution of picric acid. Diphenylamine unites with picric acid to form a compound, diphenylammonium picrate, and both the amine itself and the compound are practically insoluble in water. The compound is capable of dissociating into its constituents, for when it is treated with water some of the picric acid dissolves, and an equivalent quantity of diphenylamine remains behind; if the treatment with water is continued long enough, all the picric acid is extracted from the com- pound. In their experiments Walker and Appleyard shook three lots of 50 cub. cm. of saturated picric acid solution ( = 16'8 mg. acid per gram of water at 40 -G") with 2 grams, 1 gram, and 0*5 gram of diphenylamine for 4^ hours, and then, equilibrium having been reached, determined the concentrations of the picric acid in the water and in the diphenylamine. The results for the three experiments are shown in the adjoining table: — Milligrams of Picric Acid. In 1 gram Water. In 1 gram Diphenylamine. 13-8 7-5 13-7 15-5 13-8 300 It is obvious that the equilibrium concentration of the picric acid in the diphenylamine has risen steadily, while that in the solution has remained constant. These results are quite distinct from the adsorption phenomena already discussed, and show how the distri- bution of a substance between a liquid and a solid phase is affected by the intervention of chemical affinity. This is an important point, and it may be well to ' Jowrn. Ohem. Soo., 1806, 69, 1334. 232 PHYSICAL CHEMISTRY indicate graphically the distinction between adsorption and chemical combination ; this may be done by tracing in each case the curve which represents the corre- sponding variations of c, and Cj. Suppose, in the first place, that we have a case of pure adsorption, to which the exponential formula is applicable. Such a case is represented by the continuous curve 1, which is concave to the Cj axis. Its course is obviously in harmony with the observation which is made in all cases of adsorp- tion, namely, that c, increases much more slowly than Fig. 23. C( ; for very small values of Cj the adsorption is relatively complete. In a case of chemical combination, on the other hand, none of the dissolved substance is taken up by the solid until its concentration in the solution reaches a certain value (13*8 mg. picric acid per gram of water in the case studied by Walker and Appleyard) ; up to this point, that is, Cj increases steadily, while c, remains equal to zero. When the critical value is reached, however, any attempt to increase c, further results merely in an increase of Cj, while Cj remains constant. This continues until the formation of the ADSORPTION 233 compound is complete', when Cj may increase again. The curve 2, therefore, representing the variation of c, and Ci in the case where the solid forms a compound with the dissolved substance, is simply a broken line, the vertical part of which corresponds with the interval over which formation of the compound is proceeding. In view of the distinction which has just been drawn, it is .fairly clear that the fixation of, say, acetic acid by carbon is not due to any chemical interaction in the ordinary sense. The suggestion that acetic acid forms a solid solution in carbon must also be rejected, for in this case we should have to conclude from the observed recorded data that the molecular weight of acetic acid dissolved in carbon is less than half its molecular weight in water. This is not in the least credible. At the same time it must be allowed that in certain other cases there is evidence for the formation of a solid solution in addition to surface adsorption. Thus Davis has shown,^ in a study of the equilibrium between carbon and a solution of iodine in' various organic solvents, that when the carbon is brought into contact with an iodine solution there is, first, a surface condensation, which is complete in a few hours, followed by a slow diffusion into the mass of the carbon; this latter process goes on for weeks or months. In ex- periments carried on for only a short time, the same equilibrium point is reached from both sides, but the amount of iodine contained in the carbon under such equilibrium conditions is much less than the amount which it takes up after prolonged contact with the iodine solution. In the cases of adsorption which have been cited so far, there can be no doubt that surface condensation 1 Jmi/rn. Chem. Soe., 1907, 91, 1666. See also McBain, Zeii. physihU. Ohem., 1909, 68, 471. 234 PHYSICAL CHEMISTRY plays the main part, and indeed it appears that on thermodynamical grounds the most stable condition of any solution, when surface tension considerations only are taken into account, is the one characterised by a minimum surface tension. Hence if the solute lowers the surface tension of the solvent, it will accumulate in the surface layer of the solution. Such spontaneous accumulations in surface layers are well known. Eams- den has shown ^ that solid or highly viscous coatings are formed on the free surfaces of protein solutions, of other colloidal solutions, of fine and coarse suspensions, and of a few apparently crystalloidal solutions. A similar inter- pretation can be offered of the local concentration which occurs at the common surface of adsorbing, solid and solution. Noteworthy in this connection are the views of Macallum,* who contends that surface tension is a prime factor in such vital phenomena as muscular contraction, secretion and excretion, and cell division, and traces differences in the surface tension of living matter by a microchemical study of the distribution of inorganic salts. Adsorption of Arsenious Acid by Ferric Hydroxide. — We may now proceed to consider cases of adsorption which are complicated by the irreversibility of the equili- brium or the intervention of chemical affinity. One interesting case where chemical affinity may be a factor, is the use of freshly precipitated ferric hydroxide as an antidote in cases of arsenical poisoning. The power of ferric hydroxide to remove arsenious acid from its solutions has generally been attributed to the formation of a basic ferric arsenite, but Biltz has found* that it is a typical case of adsorption. 1 Proc. Roy. Soo., A, 1903, 72, 156. 2 Brit. Assoc. Report, 1910, 740 ; Proo. Roy. Soc., B, 1913, 86, 627. ° £er. deut. chem. Qes., 1904, 37, 3138. ADSOEPTION 235 When the hydroxide is shaken with a solution of arsenious acid, the equilibrium which is established is reversible, for it can be reached from both sides. Experiments in which a definite quantity of freshly precipitated ferric hydroxide was shaken with a definite volume of solution containing different amounts of arsenious acid showed that if x is 'the equilibrium concentration of arsenious acid in the solution, and y the corresponding concentration in the hydroxide, then the observations are in harmony with the formula I y = Kx^ . That is, the distribution of arsenious acid between water and precipitated ferric hydroxide is essentially the same as the distribution of acetic acid between water and carbon; in both cases the removal of the dissolved substance from the solution is relatively complete in very dilute solution. This analogy makes it very unlikely that the removal of arsenious acid from solution by ferric hydroxide is due to the forma- tion of a compound, and the fact that arsenious acid in aqueous solution has a normal molecular weight makes it impossible to regard the process as due to the formation of a solid solution. Eegarding it, on the other hand, as a case of surface condensation, we can understand why the efficiency of ferric hydroxide in removing arsenious acid from solution depends on its physical condition. Adsorption of Dyes. — The adsorbed substances so far considered have been crystalloids. Many of the most interesting cases of adsorption, however, are furnished by organic dyes, some of which in aqueous solution are crystalloid in character, while others are colloidal. Walker and Appleyard^ were able to show that when silk is dyed with picric acid a real equilibrium is attained 1 Journ. Chem. Soc., 1896, 69, 1334. 236 PHYSICAL OHEMISTEY which is independent of the original distribution; that is, the equilibrium is reversible. They showed also that, if s represents the equilibrium concentration of picric acid in the silk, and w the corresponding con- centration in the water, the experimental results are satisfactorily reproduced by the formula s = Kwp^ the usual adsorption formula. More recently it has been found ' that the same general formula represents the adsorption of crystal violet and patent blue by carbon, of crystal violet and patent blue by wool, of new magenta and patent blue by silk, and of crystal violet and new magenta by cotton. In all these cases the adsorption equilibrium is re- versible, and it is remarkable that the values of p (exclusive of the cases in which crystal violet was used) all lie between 4 and 7 "7. So far, then, as these experiments go, they give support to the view that the process of dyeing is essentially an adsorption phenomenon, not depending on any chemical affinity between the dye and the fibre, or consisting in the formation of a solid solution in the fibre. There are, however, a number of observations which indicate that other factors besides adsorption have to be taken into account in interpreting the relation of a dye to the fibre. The very fact that it is possible to get a fast colour in certain cases proves that the equilibrium between dye and fibre is not always reversible. In such cases one might be inclined to regard the process as a chemical interaction resulting in the production of an insoluble compound of the nature of a salt. The view of dyeing as a chemical reaction appears to be supported also by the observation that when a basic colouring matter (that is, an organic base + an inorganic acid, for example, 1 Freundlich and Losev, Zeit. phygikal. Ckem., 1907, 59, 284. ADSOEPTION 237 magenta or crystal violet) is employed to dye wool, the base alone is taken up by the fibre, while the acid is left in the solution. In spite of this, the colour of the dyed fibre is that of the salts of the base. All this is very suggestive of chemical action, but the curious thing is that a. similar splitting up of the colouring matter into base + acid occurs when carbon or pure cellulose is used in place of wool. In these cases the suggestion of salt- formation cannot be accepted. Altogether the problem is a vdty complicated one, and cannot be fully discussed here. It appears very probable that the splitting up of the basic dyes which has just been mentioned is an electrical phenomenon, and that the adsorption pure and simple is masked to some extent.^ The non-reversible character of the equilibrium between dye and fibre in some cases may be attributed to the transformation of the free base deposited on the fibre into a tautomeric modification. 2 That both adsorption and chemical action may be concerned in a dyeing process is shown by an observa- tion recorded by Bayliss.* If well-washed aluminium hydroxide is added to a dilute solution of the blue colloidal free acid derived from congo red, the dye is taken up by the suspended hydroxide, which is coloured blue. If this blue product is suspended in water and warmed, chemical union takes place, and the aluminium salt of Congo red is formed, which has the usual red colour of the salts. Attention has already been drawn to the interesting fact that when a basic colouring matter is employed to dye wool the free base alone is taken up by the fibre, 1 See Michaelis in Koranyi and Bichter's Physikalisohe Ohemie und Medium, vol. ii. p. 350. ' See Frevmdlich and Losev, loe. cit., p. 301. ' Zeit. Chem. Ind. Koll., 1908, 3, 224. 238 PHYSICTAL CHEMISTEY while the acid remains in solution. The fibre, in fact, decomposes the dye-salt into acid and base. Other cases where colloids have this effect are known. In the fore- going chapter it was pointed out that when a colloidal solution of arseniouB sulphide is coagulated by the addition of barium chloride some of the salt is decom- posed; the coagulum is found to contain barium, while the solution contains an equivalent quantity of hydro- chloric acid. In both these cases, as in many others, the electrical charge on the solid phase is the main factor in determining the surface equilibrium. Proteins and Adsorption. — The previous pages will have shown how very common is the phenomenon of adsorption. To sum up: The equilibrium between a solid phase and a solution in which it is immersed is frequently characterised by a local concentration of the dissolved substance at the surface of the solid phase, and in the majority of cases it is impossible to interpret this phenomenon by assuming the formation of a solid solution or the occurrence of a chemical reaction between solid and dissolved substance. The equilibrium is therefore described as an adsorption equilibrium, and one of its most prominent characteristics is the fact that the amount of dissolved substance taken up by the solid increases much more slowly than the concentration of the solution ; the removal of the dissolved substance is there- fore relatively most complete in dilute solution. These facts find a definite expression in the adsorption formula : c,=P . CiV where ^ > 1. The magnitude of the adsorption effect will of course depend on the surface development of the adsorbing solid. Hence it is that carbon in the form of charcoal has been so largely used in the study of adsorption. But in any case where the surface area of a solid is relatively great ADSOEPTION 239 for its volume, the conditions are favourable for the phenomenon of surface condensation. Whether such a solid immersed in a solution will exhibit the phenomenon will naturally depend to some extent on the nature of the dissolved substance, and especially on its electrical character. Since surface development is a preliminary condition for the manifestation of adsorption, and since that condition, according to the argument at the be- ginning of this chapter, is satisfied by colloidally dis- solved substances, it is not surprising that the behaviour of colloids is capable in many cases of being referred to the occurrence of adsorption phenomena. The opinion has rapidly gained ground that where mixtures of colloids and ions are involved, as in the living cell, the equili- brium between these partakes largely of the nature of an adsorption equilibrium. In such a complex case it is, of course, impossible to say exactly what part is played by the chemical and physical factors respec- tively, but the study of proteins is showing that these substances, which are so essentially associated with the living cell, are peculiarly liable to exhibit adsorption phenomena. Not only are proteins readily adsorbed by charcoal, mastic suspension, kaolin suspension, and freshly precipitated ferric hydroxide, but they themselves appear to adsorb electrolytes from solution. There are many grounds for the conclusion that the experimental behaviour of proteins is best interpreted in terms of adsorption. One of the lines of investigation which lead up to this view may be briefly sketched here. The temperature of heat coagulation of protein, as recently shown by Pauli,^ is markedly affected by traces of salts. The protein solution used by this investigator was obtained by long-continued dialysis of ox-blood serum, and exhibited no migration in an electric field; 1 Zeit. Chem. Ind. KolU, 1908, 8, 2. Q 240 PHYSICAL CHEMISTEY the protein was therefore electrically neutral. When neutral salts of the alkali or alkaline earth metals are added in very small quantity to such a protein solution, so that the concentration of the salt in the mixture is not above 0"05N, the temperature of heat coagulation of the protein is raised in all cases. The lower the concentration of the salt solution, the greater relatively is the extent, to which the coagulation is inhibited. If ^0 is the temperature of heat coagulation for the protein solution alone, t that for the solution of protein 4- salt, and c is the concentration of the added salt, then it can be shown that the experimental data are in harmony with the formula t — tQ = K(f, m Zeit. Hygiene, 1902, 40, 155. 242 PHYSICAL CHEMISTRY be characteristic of adsorption, viz. the more dilute the solution, the more completely is the dissolved sub- stance taken up by the solid phase. More than that, the relation betwen B and S is satisfactorily represented by the formula B=KS^, where ^=24-7 for the whole series. The figures given in the last column of the table have been obtained by taking the numerical value of B in each case, and calculating >S' by means of the formula. The errors of observation are considerable, and it is stated that it is impossible to determine values of S below 1. In these circumstances the agreement be- tween the observed and calculated values of S is satis- factory, and permits the conclusion that the equilibrium between bacteria and agglutinin may fairly be repre- sented by a formula of the ordinary adsorption type.^ The applicability of the foregoing formula to the dis- tribution of agglutinin between typhoid bacteria and agglutinin solution was first demonstrated by Arrhenius, who however rejects the adsorption theory, and main- tains that the agglutination is not to be attributed to a special surface action. He believes that the bacterial cell contains a substance which is a good solvent for the agglutinin, and draws the conclusion that the mole- cular weight of the agglutinin in this solvent is two- thirds of the molecular weight of the agglutinin in the surrounding fluid.^ It is doubtful whether it is permissible to regard the applicability of the empirical adsorption formula as definitely establishing the nature of the equilibrium between bacteria and agglutinin. The substances in- volved are complex, and there are one or two facts which suggest caution. There is, firstly, the specificity of the agglutinins; that is, the agglutinin produced by 1 See Craw, Joum. Hygiene, 1905, 5, 113. ^ See Immunoehemistry, p. 148. ADSORPTION 243 injecting an animal with, typhoid bacteria is capable of agglutinating typhoid bacteria in a pre-eminent degree. Such a fact suggests that agglutination may be something more than a purely physical phenomenon. Secondly, there is evidence that the serum of an animal which has been inoculated with typhoid bacteria contains not one, but several agglutinins of different degrees of activity. In view of these facts, any argument as to the nature of agglutination based on the applicability of the adsorption formula appears to be open to criticism. CHAPTER XII CHEMICAL EQUILIBRIUM AND THE LAW OP MASS ACTION Keversible Reactions, — The chemical reactions employed for the purposes of analytical chemistry may be de- scribed as ' complete ' reactions, for they are such that they proceed until one or other of the reacting com- pounds has entirely disappeared. Suppose, looking at things from the standpoint of the analytical chemist, we take the change on which the ordinary method of detecting and estimating silver or chloride in solution depends. This change is represented by the equation AgN03+NaCl = AgCl + NaN03, and it is well known that the reaction proceeds until either the silver nitrate or the sodium chloride is completely removed; short of that there is no halt in the reaction. Similarly, the reaction between hydrochloric acid and sodium hydroxide in aqueous solution proceeds until either one or the other disappears; they cannot exist together in the same solution. It is noteworthy that such complete reactions are, indeed must be, non-reversible. It is impossible, for instance, to regenerate silver nitrate and sodium chloride from a suspension of silver chloride in sodium nitrate solution, certainly not to an extent which can be detected by ordinary analytical methods. There are, however, numerous reactions which may be described as ' incomplete ' : they do not proceed until one or other of the reacting substances has completely disappeared. The reaction stops short at an equilibrium 244 CHEMICAL EQUILIBEIUM 245 point at which the products of the change, and the original substances as well, are all represented in the reaction mixture. Such reactions, too, are ' reversible ' ; that is, the substances represented on the right-hand side of the equation will, if brought together, react to produce the substances represented on the left-hand side of the equation; further, an equilibrium point is reached which, provided that equivalent quantities of the reagents have been taken in both cases, is the same point as is attained by starting with the substances on the left side of the equation. An illustration of such reversibility is furnished by the reaction between hydrogen and iodine. If a small quantity of iodine is introduced into a glass bulb, and the bulb is then filled with hydrogen, sealed off and exposed to a temperature of, say, 440°, the two elements begin to combine. After an hour or two, however, the reaction stops, and if the bulb is cooled and opened, it is found to contain hydrogen iodide, hydrogen, and iodine. If, on the other hand, the bulb were filled with pure hydrogen iodide and kept at 440° until no further change took place, it would be found that the bulb, when cooled and opened, contained hydrogen iodide, hydrogen, and iodine, as in the other case. The reaction therefore is reversible, and this fact may be indicated by substituting oppositely directed arrows for the usual sign of equality in the equation representing the change, thus: H,-hl2^2HI. Another standard case of reversibility is the reaction between ethyl alcohol and acetic acid. When 1 gram- mol. of ethyl alcohol is mixed with 1 gram-mol. of acetic acid, a reaction takes place resulting in the formation of ethyl acetate and water; the reaction, however, is incomplete, and stops at an equilibrium point at which the reaction mixture contains J gram- 246 PHYSICAL CHEMISTEY mol. alcohol, J gram-mol. acid, f gram-mol. ethyl acetate, and f gram-mol. water. If, on the other hand, 1 gram-mol. of ethyl acetate is mixed with 1 gram-mol. of water, a reaction sets in resulting in the formation of ethyl alcohol and acetic acid. This change likewise stops at an equilibrium point at which the composition of the reaction mixture is the same as that already stated. Since the reaction is thus reversible, it may be written C2H5OH-I- OHg.COOH^OHg.OOOOaHg-l- H^O. Law of Mass Action Applied to Reversible Reac- tions. — The law of mass action states that the velocity of a chemical reaction is proportional to the molecular concentration of each of the reacting substances. The line of proof of this law may be traced by considering a reaction which takes place between two gases A and B, and by looking at matters from the molecular-kinetic standpoint. In such a case the reaction can take place only in so far as the molecules of A come into contact with the molecules of B. The velocity of the reaction, therefore — that is, the rate at which A and B disappear — will be proportional to the frequency of the collisions between a molecule of A and a molecule of B, even al- though only a certain proportion of the collisions is fol- lowed by chemical interaction. But, on kinetic grounds, the frequency of the collisions between a molecule of A and a molecule of B is proportional to the product of their molecular concentrations, hence it follows that the velocity of reaction between A and B is proportional to the product of their molecular concentrations (or their 'active masses,' as it is sometimes put). A similar line of argument may be followed in the case where A and B are dissolved substances. Suppose, now, that we are dealing with a reversible reaction, represented by A+B^C+I), and suppose that the four substances are mixed together so that in the CHEMICAL EQUILIBEIUM 247 mixture their (molecular) concentrations are a^, h^, Cg, and dg respectively. If these are not the proportions corre- sponding to the equilibrium point a reaction will take place, from left to right or vice versd according to the circumstances, and will continue until equilibrium is established. The velocity of the reaction may obviously be resolved into two component opposing velocities, firstly V^, the rate at which ,^4 and £ are reacting to form C and D, and secondly V^, the rate at which G and D are reacting to form A and B. The difference between Vi and Fj is the observed velocity of the reaction. Now, at the moment of mixing, according to the law of mass action, Vj^ = kja^hf, and 'F2 = /l;2^o^o> where ^^ and k^ are proportionality factors, so that the observed velocity immediately after mixing is F^ — Fg = h-^a^h^ — \Cf^df^. After the reaction has proceeded for some time, and has consequently approached the equilibrium position, the values of the concentrations will be difEerent, say, a, b, c, and d. The velocity of the reaction will therefore now be Ic-^db — h^cd. If the reaction has proceeded long enough to reach the equilibrium point, at which we may suppose the concentrations are a^, i„ c„ d^, then the velocity of the reaction is zero, and k^ajj^ = Ic^c^^. This may be written y^ = ^ or Z'=^, where ^ is a constant independent of the concentrations of the reacting substances, depending only on the nature of the reaction and the temperature. K is known as the equilibrium constant, and the signifi- cance of the equilibrium formula may be stated in the following terms: For any reversible reaction at a given temperature, the product of the equilibrium concentra- tions of the substances on the right-hand side of the equation stands in a constant ratio to the corresponding product for the substances on the left-hand side. The extent to which this application of the law of 248 PHYSICAL OHEMISTEY mass action to reversible reactions is verified. by experi- ment is best appreciated by a more detailed consideration of the reaction between ethyl alcohol and acetic acid: O2H5OH + OH3COOH Z CH3.COOC2HJ + HgO. It has been stated g^lready that the equilibrium system reached after mixing 1 gram-mol. of alcohol and 1 gram-mol. of acid contains J gram-mol. of alcohol, J gram-mol. of acid, f gram-mol. of ester, and"§ gram-mol. of water. If V is the volume of the system at the point of equilibrium, then the molecular concentrations of the four substances i.l are i, *. 5 and * respectively. Hence Z'=— ,'=^=4. V' v' V « ^ •' 0,6, I . § V V If, now, the law of mass action is strictly applicable to this reversible reaction, then we ought to find the same value of K even when the initial proportions of alcohol and acid are quite different. Suppose, for instance, that 1 gram- molecule of acetic acid is mixed with m gram-molecules of alcohol, and that the reaction is allowed to proceed to the equilibrium point. . If a; is the fraction of a gram- molecule of ester which is present in the equilibrium mix- ture, then the corresponding quantities of acid, alcohol, and water are 1-x, m—x, and x respectively ; further, if v is the volume of the equilibrium mixture, the concentrations of acid, alcohol, ester, and water are — -, —^, — , and- respectively. Applying the equilibrium formula we ob- tain ^=irf7^= (i_^^(^r ^y The value of x is ob- tained by determining the amount of free acetic acid in the equilibrium mixture ; this is permissible, since the velocity of the reaction becomes appreciable only at high temperatures ; at the ordinary temperature the free acid may be removed by neutralisation without the back re- action setting in to any appreciable extent. From the CHEMICAL EQUILIBRIUM 249 known values of m and x it is th6n possible to calculate K, and if the law of mass action is valid, the value so calculated ought to be the same as that obtained with equivalent quantities of the reacting substances. There is, however, another way in which the applicability of the law may be tested, namely, by taking IC=4t, the figure already recorded, and calculating for each value of m what the value of x ought to be on the basis of the equilibrium formula. The comparison of the values of x so calculated and those directly observed is made in the following table : — m. x: (found). X (calc). 0-08 0-078 0-078 0-28 0-226 0-232 0-50 0-414 0-423 0-67 0-519 0-528 1-6 0-819 0-785 2-24 0-876 0-864 8-0 0-966 0-945 The excellent agreement of the figures in the second and third columns demonstrates the applicability of the law of mass action to the reversible reaction between ethyl alcohol and acetic acid. A glance at the table further shows that, although by treating acetic acid with the equivalent quantity of alcohol it is possible to convert only 66-6 per cent, of the acid into ester, yet by using a large excess of alcohol practically the whole of the acid can be converted into ester. Similarly, the first line of figures in the table shows that when the acid is in large excess, practically the whole of the alcohol is converted into ester. The same features characterise every reversible reaction. For each such there is a formula with a characteristic constant which defines the relationship between the re- acting substances at the point of equilibrium. 250 PHYSICAL CHEMISTRY Application of the Law of Mass Action to Electro- lytes. Ostwald's Dilution Law. — On the groiind of evidence submitted in earlier chapters the view has been adopted that an electrolyte AB, dissolved in water, is to a greater or less extent dissociated into its ions A' and B', and that the degree of dissociation increases with dilution of the solution. The equilibrium, therefore, between an undissociated electrolyte and its ions may be shifted in one direction or the other by simply diluting or concentrating the solution. The process of dissociation is, in fact, a reversible action, and may be represented as AB'^A' -^-B' . As Ostwald pointed out, the law of mass action ought to be applicable in such a case. Suppose that in volume V of the solution there is altogether 1 gram-equivalent of electrolyte, and that the degree of dissociation is a ; then the quantity of the undissociated electrolyte, stated as fraction of a gram-equivalent, is 1 - a, and the quantity of each ion, similarly expressed, is Q,; the concentrations are -yr- and y respectively. Y y The equilibrium formula in this case is K— j_^ — , _^^rp- -y- ^ "■' which means that, accordttig to the law of mass action, the degree of dissociation must so vary with the dilution that . ° -„ is a constant for the particular electrolyte chosen. The equation K= ,^_ .„ is the algebraic ex- pression of what is known as Ostwald's Dilution Law, As an example of a case where the validity of Ostwald's Dilution Law is amply verified, we may take acetic acid. The value of a, which is required for the calculation of K, is most easily ascertained by deter- mining the conductivity as described in Chapter VII. The values of a so deduced for a number of acetic acid CHEMICAL EQUILIBEIUM 251 solutions containing 1 gram-equivalent of the acid in V litres are recorded in the following table; the corre- sponding values of K are entered in the last column : — F. ». £^xlO» 0-994 0-004 1-62 2-02 0-00614 1-88 15-9 0-0166 1-76 18-1 0-0178 1-78 1500 0-147 1-69 3010 0-205 1-76 The values of K are satisfactorily constant, for it must be observed that, owing to the very character of the equilibrium formula, the value of K is very sensitive to experimental error. Thus, for example, if a for the first solution had been found to be 0-0041 instead of 0-0040, the value of ZxlO^ would have been 1-70 instead of 1'62. The figure usually taken as the value of K for acetic acid — the ' dissociation constant ' — is 1-8 X 10~^ at 25°. The dissociation constant of all weak (that is, slightly dissociated) acids and weak bases may be determined in a similar fashion, but it is remark- able that for strong acids, such as hydrochloric acid, for strong bases, such as sodium hydroxide, and for neutral salts, such as potassium nitrate, the value of 2 . ^ .y varies regularly with dilution. The fact that the behaviour of strong acids, strong bases, and neutral salts is not in harmony with Ostwald's dilution law has not yet been satisfactorily explained, and indicates one direction in which the electrolytic dissociation theory requires to be supplemented. It is instructive to compare the values of K obtained for different organic acids. A few typical cases are given below. It is noteworthy how the introduction of chlorine into the acetic acid molecule increases the 252 PHYSICAL CHEMISTEY Acid. K. Acetic O'OOOOIS Monochloracetic . . . 0'00155 Dichloracetic .... 0*0514 Formic 0-000214 Benzoic 0-00006 Salicylic 0-00102 value of the dissociation constant; the much greater value of K for salicylic acid as compared with benzoic acid is also interesting. The Strength of Acids. — The occurrence of such notable changes in the value of K from one acid to another raises the question of the significance of the dissociation constant. As already stated, j5r= ,._^ .y , so that if we, are considering two acids which are feebly dissociated, for which therefore 1— a is practically 1, and if we compare the two acids at the same con- centration, we have ^j= ' and Kj = ^. From this it appears that the value of K for an acid is an expres- sion of its inherent ability to dissociate into its ions. If, now, we remember that all acids are alike in splitting ofE the hydrogen ion, and that with this ion are associated all those properties which are characteristic of acids as a class, it follows that the dissociation constant of an acid is a measure of its ability to exhibit those charac- teristic properties. The value of JT, in other words, is a measure of the stjength of the acid. If this is so, then the order of the acids arranged according to their values of K ought also to be the order of their strength deduced on other grounds. This turns out to be the case, as shown by the investigations of Ostwald and others. ITie strength of two acids may be compared by allowing them to compete for an insufficient quantity of a base, and then to determine, from the volume CHEMICAL EQUILIBRIUM 253 changes which occur, what proportion of the base has been appropriated by each acid. Or the effect of each acid in promoting the inversion of cane sugar may be determined (see pp. 167, 277) ; the rate of this change is approximately proportional to the concentration of the hydrogen ions present, and may be employed to com- pare the degrees of dissociation of two acids in equi- valent concentration. That a base is shared by two acids in proportions depending on their relative strength is an important fact, which is demonstrated by the following experi- ment. A dilute solution of the sodium salt of p-nitro- phenol is prepared, and equal portions of the solution are put in three test glasses. The solution, it should be noted, has an intense yellow colour, whereas the p-nitrophenol itself, when dissolved in distilled water, gives a very pale yellow solution. Accordingly, when standard hydrochloric acid, say „, is gradually added to one of the portions, a point is reached at which the colour is almost completely discharged ; this is the point at which enough hydrochloric acid (say x cub. cm.) has been added to turn out practically all the p-nitrophenol from its combination with the soda; in competition with such a weak acid as p-nitrophenol, hydrochloric aeid is able to appropriate practically the whole of the base. If, however, x cub. cm. of -^ monochloracetic acid are added to the second portion of the salt solution, the colour is not discharged ; it remains distinctly yellow, showing that in competition with monochloracetic acid, which is much weaker than hydro- chloric acid, p-nitrophenol is able to retain some of the ' soda. If to the third portion of the sodium salt solution X cub. cm. 5" acetic acid are added, the colour of the 254 PHYSICAL CHEMISTRY mixture is markedly more intense than in the second case, for now, since acetic acid is comparatively weak, the p-nitrophenol retains an appreciable fraction of the available soda. If the relative strength of two acids has been deter- mined by studying their influence in equivalent con- centration on the rate of inversion of cane sugar, the figure obtained is valid only for the concentration in question. That this must be so is evident if we take the particular case of hydrochloric and acetic acids. From conductivity data it follows that the dissociation of acetic acid, although small, increases much more rapidly with dilution than that of hydrochloric acid, so that the disparity between the two acids in regard to their content of hydrogen ions diminishes with in- creasing dilution.- Since the rate of inversion of cane sugar is approximately proportional to the concentration of hydrogen ions, it is only to be expected that the strength of j^q acetic acid (measured in terms of the effect of :r^ hydrochloric acid on the rate of sugar inversion) is greater than the strength of y acetic acid (measured in terms of the corresponding effect of y hydrochloric acid). This point is illustrated by the following figures for the relative influence of hydro- chloric and monochloracetic acids on the rate of inver- sion of sucrose; the figure for hydrochloric acid is in each case taken as 100 : — f Acid. i Acid. HCl 100 100 OHoCLCOOH 5 14 If this argument is followed out, it is obvious that at infinite dilution all acids would be equally strong. CHEMICAL EQUILIBEIUM 255 Strength of an Acid as Affected by its Salts. — The equilibrium between the undissociated molecule of a weak acid and its ions is, as we have seen, a reversible one, and it is possible therefore to shift the equilibrium in either direction according to the conditions. The evidence submitted in connection with the reversible reaction between ethyl alcohol and acetic acid showed that the greater the concentration of alcohol in the equilibrium mixture the smaller was the correspond- ing concentration of acetic acid. This is an illustra- tion of a general principle, which, if applied to the equilibrium between, say, acetic acid and its ions, CHg.COOH^l^CHj.COO' + H-, shows that by increasing the concentration of acetate ions the concentration of hydrogen ions would be diminished. It is easy to increase the concentration of the acetate ions by add- ing sodium acetate, solutions of which are shown by conductivity data to be highly dissociated. We should therefore expect that an acetic acid solution to which sodium acetate has been added would contain fewer hydrogen ions than an equally concentrated solution of acetic acid to which no sodium acetate has been added ; the acid effect would be weakened by the pre- sence of a neutral salt of the acid. This conclusion is strikingly verified by the figures given in the follow- ing table.^ V represents the rate of inversion of sucrose under the influence of -jCHgCOOH in presence of gradually increasing quantities of sodium acetate : the actual method by which Fis determined will be described later, and for the present it may simply be taken as a measure of the concentration of hydrogen ions in the acetic acid solution. The numbers in the column * Arrhenius, Zeit. physiJcal. Chem,, 1890, 5, 1. R 256 PHYSICAL CHEMISTRY headed V obs. show that, in accordance with the argu-, ment outlined above, the concentration of hydrogen N ions in -jOHgOOOH diminishes steadily as the con- centration of 'sodium acetate in the same acetic acid solution is increased. More than that, it is possible, on the basis of the equilibrium formula, to calculate the concentration of hydrogen ions in each solution, and therefrom to calculate the velocity of inversion under the influence of that solution ; the values so obtained are tabulated under V calo. Inverting Solution. robs. rcalc. ^CHgOOOH 0-75 ... 91 + ^0H3COONa 0-122 0-129 It ^i n 0-070 0-070 If ^20 n 0-040 0-038 » 4 n 0-019 0-017 » -! 11 00105 0-0100 The agreement between the observed and calculated values is striking evidence in favour of the electrolytic dissociation theory, which is involved in the calculation. It must, however, be pointed out that such a calculation cannot be successfully made for the influence of neutral salts on the inverting efficiency of strong acids. In one sense this is not strange, since, as already indicated, Ostwald's dilution law is not valid for these. But the influence of, say, sodium chloride on the activity of hydrochloric acid is not even qualitatively in agreement with what we should expect on the basis of the electro- lytic dissociation equilibrium. The rate at which sucrose is inverted by hydrochloric acid is increased by the addition CHEMICAL EQUILIBEIUM 257 of a neutral chloride, an effect that is generally referred to as ' neutral salt action.' The magnitude of the effect is considerable, for Arrhenius has shown that the rate of inversion of a 10 per cent, sucrose solution by 0"05NHC1 is increased by about 25 per cent, when the solution is also 0"4N in relation to sodium chloride. Other neutral chlorides exert a like accelerating influence. Neutral salt action has not yet been satisfactorily ex- plained, although numerous attempts have been made ; ^ Arrhenius, for instance, suggests that neutral salts increase the osmotic pressure of the sucrose, while Caldwell^ regards neutral salt action as a concentrat- ing effect brought about by the hydration of the salt. In any case, some factor is involved in neutral salt action of which the electrolytic dissociation theory, in its original form at least, takes no cognisance. Reactions between Ions. — The influence of sodium acetate or any other neutral acetate in repressing the dissociation of acetic acid is one example of the ionic reactions which occur when solutions of electrolytes are mixed, and of which only indirect evidence can be ob- tained. If a little concentrated sodium acetate solution is added to a solution of hydrochloric acid nothing obvious happens, but indirect evidence can be obtained showing that a reaction does indeed take place, which results in the almost complete removal of the hydrogen ions from the solution. If, for instance, sulphuretted hydrogen water is added to a solution of ferrous sulphate which has been acidified with hydrochloric acid, no precipitate is produced ; on the further addition, however, of a little concentrated sodium acetate solution, a black precipitate of ferrous sulphide is thrown down immediately. The 1 See Senter, Journ. diem. Soo., 1907, 91, 462. 2 Proc. Roy. SqO., A, 1906, 78, 272. 258 PHYSICAL CHEMISTRY sodium acetate impairs the acid effect of the hydrochloric acid, and a consideration of the phenomenon from the point of view of electrolytic dissociation leads to an intelligible explanation. When hydrochloric acid and sodium acetate, both highly dissociated electrolytes, are mixed in aqueous solution, opportunity is given for the formation of two other electrolytes, namely, sodium chloride and acetic acid, the first of which is highly, the second feebly, dissociated. As we have seen already, the dissociation constant of acetic acid is low, which means that acetate ions and hydrogen ions can exist alongside each other only to a certain small extent, de- fined by the said dissociation constant. Hence when hydrochloric acid and sodium acetate are mixed, the acetate ions and hydrogen ions unite almost completely to form undissociated acetic acid, and the concentration of free hydrogen ions is still further diminished if excess of sodium acetate is added to the hydrochloric acid. If we make the assumption, which is not very far from the truth, that hydrochloric acid, sodium acetate, and sodium chloride are almost completely dissociated, while acetic acid is dissociated to a negligible extent, the main course of the ionic reaction in question is expressed by the equation H- + Cl'+Na-+CH3.0OO'=CH3.COOH+Cl'+Na-. The addition of sodium acetate to hydrochloric acid thus effects a removal of the hydrogen ions, and so amounts practically to a neutralisation of the great bulk of the hydrochloric acid. The sodium salt of any weak acid would do quite as well as sodium acetate ; if, for instance, a strong solution of borax is added to a solution con- taining ferrous sulphate, sulphuretted hydrogen water, and a little free hydrochloric acid, a black precipitate CHEMICAL EQUILIBEIUM ' 259 is produced immediately. The explanation of this effect is the same as that given in the case of sodium acetate. Another ionic reaction which occurs on mixing two electroljrtes which have no common ion is the union of the hydrogen and hydroxyl ions. These ions cannot exist alongside each other except in the minutest quan- tities (see p. 170),' so that the process of neutralisation of hydrochloric acid (or any other strong acid) by sodium hydroxide (or any other strong base) may be represented by the equation: H' + Cl'4-Na-+OH' = F20+Cl'+Na'. The similarity between this neutralisation and the resiilt of adding sodium acetate to hydrochloric acid is apparent. Just as the equilibrium between acetate ions, hydrogen ions, and undissociated acetic acid is defined by the dissociation constant for acetic acid, so the extent to which hydrogen and hydroxyl ions can exist alongside each other in water is similarly fixed. If we apply the law of mass action to the equilibrium HgO^H' +OH'we obtain ■8'= n °° » where Ch, Ooh, and Choo are the concentra- tions of the hydrogen ion, the hydroxyl ion, and water respectively. Since the concentrations of the ions are extremely small, that of the water may be taken as in- dependent of their variations, so th^it Ch.Ooh = ^) another constant. This means that the product oi the concen- trations of the hydrogen and hydroxyl ions in any aqueous solution. must be a constant. Several lines of evidence lead to the figure l"2xl0"" being taken as the value of k at 25° (compare pp. 172 and 317). If water contains both hydrogen and hydroxyl ions in equivalent quantities, it may be regarded as a very weak acid or as a very weak base, so that when a neutral salt AB is dissolved in the water — a salt which 260 PHYSICAL CHEMISTRY is largely dissociated into its ions A' and B' — there is the possibility of ionic reactions taking place which result in the formation of two new undissociated com- pounds, HA and BOH. The extent to which this takes place will depend on the strengths of the acid and the base. If they are both very strong, as would be the case if AB stood for NaCl, the quantities of HA and BOH formed will be very small, and approximately equal quantities of hydrogen and hydroxyl ions will be removed for the purpose. This removal of hydrogen and hydroxyl ions is made good by the dissociation of a small quantity of water, in order to maintain the condition Ch.Coh = 1'2x 10"". Suppose, however, that HA is a weak acid, while BOH ia a strong base — as would be the case if AB stood for borax — then from the ions A', B', H', and OH' more undissociated HA will be formed than undissociated BOH, and there will no longer be equivalent quantities of hydrogen and hydroxyl ions. Although to maintain the condition Ch-Coh=1'2x 10"" a little water will dissociate, this cannot get rid of the excess of hydroxyl ions; the solution will therefore have an alkaline reaction. In harmony with this it is found that borax, however carefully it is purified, always gives an alkaline reaction when dissolved in water. Other salts which behave in a similar way, since they are derived from a strong base and a weak acid, are potassium cyanide and sodium carbonate. If the salt AB, on the other hand, is such that HA is a strong acid, while BOH is a weak bp^se, the solution of the salt must have an acid reaction. The argument which leads to this conplusion is parallel to that already given. The case where a salt, however carefully purified, gives an acid reaction when dissolved in water is illustrated by aniline hydrochloride. The phenomenon of a neutral salt reacting with CHEMICAL EQUILIBEIUM 261 water gft as to give either an acid or an alkaline reaction is known as 'hydrolytic dissociation.' If we wish to determine the extent of hydrolytic dissocia- tion in any given ease, we observe the influence of the salt on the rate of inversion of sucrose or on the rate of saponification of ethyl acetate (see p. 283). The first of these methods is employed when the salt in question is derived from a strong acid and a weak base, the second when it is derived from a strong base and . . . N a weak acid. In this way it has been found that in j^ solution at 25° sodium carbonate is hydrolytically dis- sociated to the extent of 3'17 per cent., potassium cyanide 1"12 per cent., borax 0'05 per cent., aniline hydrochloride 1'5 per cent. Amphoteric Electrolytes. — Water has been described above as an electrolyte which yields at the same time hydrogen and hydroxyl ions. There is an interesting class of substances which in this respect resemble water, and are, further, of considerable importance in connection with the behaviour of proteins. The class referred to is that of the amino-carboxylic acids, substances which contain at least one NHg-group and one COOH-group, and are therefore capable of acting as bases or as acids according to circumstances; in view of this double character they are termed ' amphoteric ' electrolytes. Such an electrolyte will have two dissociation constants, one corresponding to its acid function, the other to its basic function. It is further capable of forming two series of salts, one series by combining with acids, the other series by combining with bases. Just as ammonia, when dissolved in water, exists, to some extent at least, in the form of the compound NH4OH, so it is supposed that glycine, which may be taken as an example of an amino-acid, forms in water 262 PHYSICAL CHEMISTEY CH2.NIL.OH the compound | . The ions produced by the OOOH dissociation of this compound are CH2.NH3- OH2.NH3.OH, CH2.NH3- OH'.H-, I ,1 and I ; COOH COO' COO' the last mentioned results from the simultaneous splitting off of hydrogen and hydroxyl ions, and corresponds really to an intramolecular salt. The concentrations of all these ions are exceedingly small in an ordinary aqueous solution of glycine ; the acid and basic groups present in the molecule are antagonistic, and the result is that glycine, whether regarded as acid or base, is very weak. A similar statement applies to all amino-carboxylic acids. This being so, it is clear that the salts of such an amphoteric electrolyte, both with a strong acid and a strong base, will be liable to hydrolytic dissociation. Suppose that HROH represents the formula of an amino-carboxylic acid, and that the sodium salt NaROH and the chloride HRCl have been prepared ; this is possible, since the amino-carboxylic acid acts as an acid towards sodium hydroxide and as a base towards hydro- chloric acid. The salt NaROH, being derived from a strong base and a weak acid, will be hydrolytically dissociated in aqueous solution, an effect which may be regarded as brought about by an interaction between water and the negative ion of the salt, thus : E0H'+H20:;iHE0H-)-0H'. The hydrolytic dissociation results, therefore, in the negative ion EOH' being replaced to some extent by the OH' ion. The ionic conductivity of the hydroxyl ion is much greater than that of any other anion, hence one result of the hydrolytic dissociation of NaEOH is that the conductivity of the solution is exceptionally high. A determination of the conductivity may in fact be used CHEMICAL EQUIlilBEIUM 263 to calculate the extent of the hydrolytic dissociation. This may be ascertained also by studying the influence of the salt NaEOH on the rate of saponification of ethyl acetate, which, as already stated, is a measure of the hydroxyl ion concentration. The extent of hydrolysis of the salt NaROH having been ascertained by one or other of these methods, it is possible to calculate the acidic dissociation constant h^, of HROH ; the way in which this is done cannot be discussed here. Similarly, by determining the conductivity of the salt HRCl, or by studying its influence on the rate of inversion of sucrose, the extent of hydrolytic dissociation in this case can be ascertained, and the basic dissociation constant hi, deduced therefrom. For amino-carboxylic acids it is found generally that \ is greater than Ic^ ; that is, the acidic character of these compounds is more strongly developed than their basic character. The following figures may be quoted in support of this statement : * — kttJt^°) kb (25°), Glycine 1-8 xlO-"> 2-7 xlO-" Sarcosine 1-2 x lO"" 1-7 x 10"" Alanine 19 x 10-»» 5-1 x 10-12 Leucine 1-8 x lO"'* 2-3 xlO"" /3-Asparagine . . . l-35xlO-s 1-53x10-" The values for h^ recorded in the table are about the same as ka for phenol, so that the acidic character of all these amino-carboxylic compounds is exceedingly feeble. Their basic character is still less marked ; the values of A;^ in the table are roughly about one-hundredth of the corresponding figure for aniline. In the case of a sparingly soluble amphoteric electro- lyte, its peculiar character is clearly indicated by the influence of acids and alkalis on its solubility. A spar- ingly soluble base, aniline for instance, is more soluble 1 See Lundeu, ZeU. phynkcd. Chem., 1906, 54, 561. 264 PHYSICAL CHEMISTRY in dilute hydrochloric acid, but not more soluhle in dilute sodium hydroxide, than it is in water. A spar- ingly soluble acid, salicylic acid for instance, is con- versely more soluble in dilute sodium hydroxide, but hot more soluble in dilute hydrochloric acid, than it is in water. We should expect therefore that the solu- bility of a sparingly soluble amphoteric electrolyte, which functions both as acid and as base, would be increased by adding either acid or alkali. This turns out to be the case, as has been shown, for instance, in the case of theobromine. Paul found ^ that one part of theobromine required for its solution 3282 parts of water at 18°, 2125 parts of ^HCl, or 22-93 parts of N .... ■jNaOH. The solubility of theobromine m acid is little greater than its solubility in water, which means that the hydrochloride is hydrolytically dissociated to a very large extent, and that the basic character of theobromine is therefore feebly .developed. As is evident from the comparative solubility in sodium hydroxide, the acidic character of theobromine is well marked ; k^ in this case is 1"33 X 10"^ There is every reason to believe that the polypeptide group forms an essential part of the protein molecule,^ and as polypeptides are built up by the condensation of amiiio-carboxylic acids, there is good ground for regard- ing the proteins as amphoteric electrolytes. In many respects their behaviour is in harmony with this con- ception of their character. There is, for instance; the observation, due originally to Hardy and confirmed by Pauli,^ that neutral protein acquires electro-positive char- acteristics on the addition of acids, as shown by its > Arch. Pharm., 1901, 239, 48. " See Schryver, The General Characlera of the Proteini. ' Hofmehter's Beitr., 1906, 7, 531. CHEMICAL EQUILIBEIUM 265 migration towards the cathode in an electric field, while it acquires electro-negative characteristics on the addition of alkali. Further support for the view that protein is an am- photeric substance is furnished by the work of Bugarszky and Liebermann,^ who studied the effect of adding egg albumin to 0"05N solutions of hydrochloric acid, sodium hydroxide, and sodium chloride. The effect was measured by determining the freezing points of the electrolyte solutions (1) without any albumin, (2) after the addition of various quantities of albuhiin. Some of the results obtained are incorporated in the following table, the first column giving the weight (^g) of albumin added to 100 cub. cm. of the electrolyte solution, while the three succeeding columns give the observed depressions (A) of the freezing point : — 9- AforO-OSNHCl. AforO-OSITNaOH. AforO-OSNNaCl. 0186° 0-181° 0-183° 0-8 0-172° 0-162° 0-191° 1-6 0-146° 0151° 0-194° 3-2 0-107° 0116° 0-199° 6-4 0-087° 0-097° 0-203° The depression of the freezing point in the case of sodium chloride is increased by the addition of albumin, and the amount of the increase is practically equal to the depression which the albumin produces by itself; thus a solution containing 6-4 grams of egg albumin in 100 grams of water had a freezing point 0-022° below that of water. The effect of egg albumin on the freezing points of 0-05N hydrochloric acid and sodium hydroxide is obviously quite a different phenomenon. The de- pression of the freezing point produced by the given quantity of acid or alkali diminishes markedly as the. quantity of added albumin increases. This shows clearly 1 PjlUger'a Areh., 1898, 72, 51. 266 PHYSICAL CHEMISTRY that the number of molecules originally present in the acid or alkali solution has decreased, and this must be due to the ability of both acid and alkali to form complex molecules with the albumin. Dissociation Equilibrium in a Saturated Solution of an Electrolyte. — ^The systems to which we have hitherto applied the law of mass action have been homogeneous — mainly solutions of electrolytes. It will be interesting now to see in what way the law works out when applied to a non-homogeneous system, con- sisting, say, of a saturated solution of an electrolyte in contact with excess of the solid substance. Suppose we take the case, of benzoic acid, an electrolyte to which Ostwald's dilution law is applicable. In a saturated solution of this acid we have equilibrium between the undissooiated molecules and the ions, as represented by the following: CeH6.C00H ^ G^B^-GOO'+B.-. There is however this peculiarity, that we cannot alter the concentration of the undissooiated molecules so long as the temperature, remains constant, for by sup- position the solution is saturated with benzoic acid, and is in contact with solid benzoic acid. Thus if any- thing happened to increase the concentration of the undissociated molecules, this would simply lead to an equivalent removal of acid from solution. If anything happened to diminish the concentration of the undis- sociated molecules, fresh acid would dissolve until the said concentration was brought up to its saturation value. That is to say, the concentration or active mass of the undissociated benzoic acid molecules in the above dissociation equilibrium is constant, so long as there is excess of benzoic acid present and the tempera- ture remains constant. The application, of the law of CHEMICAL EQUILIBRIUM 267 mass action to the equilibrium between benzoic acid and its ions leads to ^=^, where q and c^ are the concentrations of the ions, and c is that of the un- dissociated molecules. As has just been explained, c is constant under the specified conditions, so that CjC2 = const. Naturally, so long as the solution contains nothing but benzoic acid, 0^ = 62, but if the equilibrium between benzoic acid and its ions is displaced by the introduction of other electrolytes, Cj will be different from c^; even then, however, the law of mass action requires the condition 0^02 = const, to be fulfilled. This means that for any solution which is kept saturated with benzoic acid at a given temperature the product of the concentrations of the ions remains constant, how- ever their individual values may vary. This product of the ionic concentrations in a saturated solution is generally known as the ' solubility product.' In considering the conditions which define the equi- librium in a saturated solution of a sparingly soluble electrolyte we have taken a special case. This case, however, serves to bring out two general principles involved in a non-homogeneous equilibrium; these may be stated as follows: (1) The active mass or concen- tration of any solid concerned in a non-homogeneous equilibrium is constant for a given temperature ; (2) for any dissociation equilibrium in a saturated solution the product of the concentrations of the dissociated parts is a constant for a given temperature.' One or two consequences of the application of these principles to saturated solutions of electrolytes are worth noting. If the product of the ionic concentrations c.^C2 is to remain constant, anything which leads to an increase of C2 must mean a diminution of Cj. Now, as pointed out in the previous part of this chapter, » See, however, Kendall, Proc. Soy. Soc., A, 1911, 85, 200. 268 , PHYSICAL CHEMISTRY it is possible to increase the concentration of one of the ions involved in an electrolytic dissociation equi- librium by adding another electrolyte with a common ion. The result of this is to repress the dissociation of the first electrolyte, that is, to increase the concen- tration of the undisBociated molecules. If, now, the solution is abeady saturated with this first electrolyte, it cannot contain any more of the undissociated mole- cules; the consequence is that some of the electrolyte separates out in solid form. The law of mass action, then, applied to the dissociation equilibrium in the saturated solution of an electrolyte AB, leads us to expect that the addition of another electrolyte which yields either A' or B* as one of its ions, will throw some of the compound AB out of solution; in other words, will lower the solubility of AS. This conclusion is amply verified by experiment. If to a saturated solution of barium nitrate we add a little concentrated nitric acid, solid barium nitrate is pre- cipitated ; the addition of a little concentrated solution of either silver nitrate or sodium acetate to a saturated solution of silver acetate throws down some of the latter salt. The following figures give a more definite shape to the results of experiment : i they represent the extent to which the solubility of thallous chloride at 25° is affected by the presence of an electrolyte with a common ion, namely, either thallous nitrate or hydro- chloric acid; all figures are given in gram-mols. per litre: — Solubility of Thallous Chloride. Concentration of the In Presence of In Presence ol added Electrolyte. TING,. HCl. 0-0 00161 00161 0-0283 0-0083 0-0083B 0-0560 0-00571 0-00565 0-1468 0-00332 0-00316 The diminution in the solubility brought about by ' See Noyes, Zeit. physikal. Chem., 1893, 6, 249. CHEMICAL EQUILIBRIUM 269 increasing quantities of an electrolyte with a common ion is very marked, and a comparison of the figures in the last two columns shows that the effect is pretty much the same whether the common ion is anion or cation, provided the added electrolytes are dissociated to about the same extent. On these lines also we get an in- telligible explanation of the practice, common in analytical operations, of adding a slight excess of a precipitating reagent; any slight solubility which the precipitate may have is thereby reduced. What, it may be asked, would be the result of adding to a saturated solution of an electrolyte another electro- lyte which has no ion common with the first? The principles already laid down enable us to deal with this case. For the addition of an electrolyte with no common ion makes possible the formation of two new undissociated substances, and in proportion as these are formed the concentrations of the ions of the original electrolyte are reduced. In order to maintain the con- dition G^c^ = const, some of the undissociated mole- cules of the original electrolyte dissociate, thereby making room for the passage of fresh solid into solution. The solubility, therefore, of a sparingly soluble electro- lyte must be increased in presence of another which has no ion common with the first. This conclusion also is in harmony with observation.^ Benzoic acid, for instance, is more soluble in sodium acetate solutions than it is in water, a fact which is brought out by the figures quoted in the following table: — Concentration of Sodium Acetate. Solubility of Benzoic Acid. 0-00 0-0289 0-0099 0-0370 00198 0-0446 00493 0-0643 • See Noyes and Chappin, Journ. Artier. Ohem. Soc, 1898, 20, 751; Philip, Journ. Chem.- Soo., 1905, 87, 987 ; 1909, 95, 1466. 270 PHYSICAL CHEMISTRY The numbers given represent in all cases gram-mole- cules per litre of solution. When sodium acetate is added to a saturated solution of benzoic acid, the two new compounds which may .be formed by reactions between the ions are sodium benzoate and acetic acid. The first of these compounds is highly dissociated, like all salts of this type, so that its formation is respon- sible for the removal of only a small quantity of the OgHg.COO' ions. Acetic acid, on the other hand, is a feebly dissociated compound, and its formation means a relatively complete removal of the hydrogen ions. This leads to a big disturbance of the equilibrium between benzoic acid and its ions, to the dissociation of the benzoic acid molecules, and to the replacement of these by fresh solid passing into solution. If sodium chloride were added instead of sodium acetate, the effect on the solubility of benzoic acid would be very slight indeed, because hydrochloric acid is highly dis- sociated compared with acetic acid. On similar lines intelligible explanations can be given of such facts as that silver acetate is soluble in nitric acid, and that magnesium hydroxide is more soluble in solutions of ammonium chloride (or the chloride of any weak base) than in pure water. The Law of Mass Action in Immunochemistry.i — Within recent years the nature of the relationship between toxins and antitoxins has attracted much attention. The work of Ehrlich and others has shown that the addition of an antitoxin to the corresponding toxin resembles generally the neutralisation of an acid by an alkali, but the fact has emerged also that the amount of toxin neutralised is not proportional to the ' See Arrhenius, Immvmoohemistry ; also Michaelis in Koranyi and Eiohter's Phynkalische Chemie und Medizin, vol. ii. . CHEMICAL EQUILIBRIUM 271 amount of antitoxin added. The process is therefore not strictly analogous to the neutralisation of a strong acid by a strong base, but rather to that of a weak, acid by a weak base. In the latter case the hydrolytic dissociation of the salt interferes with the normal course of neutralisation, and in a mixture containing equivalent quantities of a weak acid and a weak base there is still free acid and free base. These are in reversible equilibrium with the salt, thus: AB+HgOi^HA+BOH, To such a reversible equilibrium the law of mass action may be applied, and it follows that by adding excess of the acid the concentration of the free base is diminished, but only gradually. The fact that in a solution containing equivalent quantities of a weak base and a weak acid there is free base and free acid is brought out by a study of the neutralisation of ammonia by boric aoid.^ Free ammonia is a hemolytic agent, that is, acts on red blood corpuscles so as to bring about the escape of the hsemoglobin; boric acid, on the other hand, exerts no appreciable hasmolytic action. The gradual neutralisa- tion of ammonia by boric acid is therefore marked by decreasing hsemolytic activity, and the toxicity (in relation to red blood corpuscles) of a solution containing both ammonia and boric acid may in fact be taken as a measure of the free ammonia which it contains. Since the addition of an exactly equivalent quantity of hydro- chloric acid to sodium hydroxide solution completely removes the hsemolytic effect of the latter, it might perhaps be expected that the addition of an equivalent quantity of boric acid to ammonia would give a^ mixture which is non-toxic in regard to red blood corpuscles. This, however, is not the case, as appears from the ' See Arrhenins and Madsen, Zeit. physikal. Chem., 1903, 44, 7. 5 272 PHYSICAL CHEMISTRY data recorded in the accompanying table. The figures n. Toxicity. 100 0-17 85 0-33 69 0-67 43 10 25 1-33 20 1-67 13 2-0 10 in the second column represent the toxicity (deduced from the haemolytic power) of solutions of 1 equivalent of ammonia, to which n equivalents of boric acid have been added. It is evident that a solution in which there are equivalent quantities of ammonia and boric acid still contains free ammonia, and that addition of excess of boric acid only gradually reduces the con- centration of the free base. , There is a considerable amount of evidence available which shows that in a neutral mixture of a toxin and its antitoxin a certain proportion of each exists in the free state. There is, for instance, the work done by Crawl on the lysin obtained from cultures of Bacillus megatherium. This lysin passes through a gelatin filter, whereas the corresponding antilysin is kept back. Making use of this difference between the two bodies, Craw was able to show that both neutral mixtures^ and those with excess of antilysin contain free lysin, also that both neutral mixtures and those with excess of lysin contain free antilysin. Neiitral mixtures, there- fore, of lysin and antilysin contain both substances to some extent in the free state, and the question arises whether they are in reversible equilibrium with some compound formed by the union of lysin and antilysin. » Proo. Roy. Soc, B, 1905, 76, 179. " Mixtures, that is, which did not hsemolyse in the standard time. CHEMICAL BQUILIBEIUM 273 On the question of the reversibility of the toxin- antitoxin reaction the evidence is somewhat conflicting. Craw finds that the reaction between megatherium lysin and antilysin is reversible when excess of antilysin is present, but, on the other hand, the Danysz pheno- menon may be quoted (see p. 215).^ Danysz found that the toxic properties of a mixture of diphtheria toxin and antitoxin depend on the manner in which they are mixed. Suppose A and T are quantities of antitoxin and toxin such that when A is added to T all at once the mixture is innocuous ; then it is found that if A is added to T at intervals, a portion at a time, the resulting mixture is toxic. This observation is difficult to reconcile with the view that there is a true reversible equilibrium between toxin and anti- toxin.2 Further arguments against the view that the toxin-antitoxin reaction is strictly reversible have been brought forward by Nernst and others.* Considerable difference of opinion exists also on the question how far toxins and antitoxins are in a state of true solution. Some regard them purely as colloids, even suspension colloids, and consider that the relation between them is one of adsorption equilibrium. The treatment of the toxin-antitoxin relationship from this point of view has been already illustrated at the close of the previous chapter in reference to the phenomenon of agglutination. Arrhenius, on the other hand, has found that diphtheria toxin and antitoxin, tetanolysin and antitetanolysin, have a definite power of diffusion, and may be regarded as in a state of true solution. He considers that the equi- librium between a toxin and its antitoxin is reversible ' See Journ. Hygiene, 1907, 7, 601. ' See, however, Arrhenius, Journ. Hygiene, 1908, 8, 1, ' ^eit. EleUrochem., 1904, 10, 377, 7-83. 274 PHYSICAL CHEMISTRY in the ordinary sense, and that therefore the law of mass action may be applied. In various cases the neutralisation of a toxin by its antitoxin has been in- vestigated from this point of view, and the course of neutralisation is found to be in harmony with an equi- librium formula similar to that which represents the neutralisation of ammonia by boric acid. In the case, for instance, of tetanolysin, the following formula was found to apply : Cj^Cg = Kc^, where c^, Cg, and c are the quantities of free lysin, free antilysin, and bound lysin respectively, and Jf=0"115 at 20°. The quantity of free lysin in any mixture was deduced from its hemolytic power. How far the experimental figures are in harmony with the foregoing formula will be seen from the follow- ing table, in which n is the added quantity of antilysin : — n. c, found. c, calc. 100 100 0-05 82 82 0-1 70 66 0-15 52 52 0-2 36 38 0-3 22 23 0-4 14-2 13-9 05 101 10-4 0-7 6-1 6-3 1-0 4-0 4-0 1-3 2-7 2-9 1-6 2'0 2-5 2-0 1-8 1-9 There can be no doubt that there is remarkable agree- ment between the observed and calculated values for the quantity of free lysin, and the formula c^^ = K(? evidently represents the actual numerical relationship between the quantities involved. On this ground Arrhenius draws the conclusion that the reaction between toxin and antitoxin is to be i-epresented as 1 mol. tox^n-fl mol. CHEMICAL EQUILIBRIUM 275 antitoxin ^2 mols. toxin-antitoxin compound. In view, howeyer, of the doubts which exist as to the legitimacy of applying the law of mass action to the toxin-antitoxin reaction, the foregoing conclusion must be accepted with reserve.^ > 1 The discussion of Ehrlich's views and the exposition of his side chain theory lie beyond the scope of this volume. CHAPTEK XIII THE VELOCITY OF CHEMICAL REACTION General. — In the foregoing chapter the velocity with which a reversible reaction A-{-B :^ G-\-D proceeds to its condition of equilibrium has been conceived as the resultant of two component velocities, one the velocity with which A and B react to form G and D, the other the velocity with which and D react to form A and B. At the point of equilibrium these velocities are equal, the amount of change resulting from the forward re- action per unit of time exactly balancing the amount of change which results from the back reaction. If the reaction is such that the equilibrium position is almost at one extreme, say, at that represented by the right-hand side of the equation A-'rB'Z.G+D, then the back reaction is negligible in comparison with the forward reaction except when the equilibrium is nearly reached; that is, the velocity of the reaction for the greater part of its course is simply the velocity with which A and B react to form G and D. On the basis of the law of mass action, therefore, the velocity of the reaction at any moment, supposing that it takes place in a homogeneous system, is proportional to the product of the molecular concentrations of A and B at that moment. If a and h represent the molecular quantities of A and B which were mixed initially, and if after an interval of time t the molecular quantity of G and D formed is x, then the velocity V of; the reaction at this interval from the start will be given by 276 VELOCITY OF CHEMICAL EEACTION 277 F= \(a, -x)(h- x). But the velocity of the reaction may be defined as the rate at which x is increasing with the time, — tt, as it is put in the language of the differential calculus. The formula therefore which, on the basis of the law of mass action, ought to represent the rate of the change -4+5^ 0-\-D, when the change proceeds until either A or £ has practically disappeared, is ^ = ki{a -x)(b -x). Inversion of Sucrose : a Unimolecular Reaction. — A common example of a reaction of the type ^+-S ^ G-\-D, one too which fulfils the condition that the reaction shall proceed until either A or £ has practically disappeared, is the inversion of sucrose. The change which occurs in the inversion of sucrose may be represented as Cl2Br220ii + HgO = 2C6Hj208, for although the change takes place with appreciable velocity only in the presence of a catalytic agent, such as hydrochloric acid, yet the latter is found unaltered when the reaction is over. Since the inversion is carried out in aqueous solution the formula -^ = /i;i(a-a;)(6 -a;) may be simplified, for in this case the water which actually disappears in the reaction is a very small fraction of the total water present ; * x may therefore be neglected in comparison with b, and we have ^ = ki(a - x)b = k{a -x), where k = kj). Integration of the equation ^ = k(a - x) leads to the formula A; =rlogj —-—, in which, as already indicated, a is the quantity of sucrose originally present, and a-x 1 Suppose, for instance, that a solution containing 171 grams of sucrose per litre is considered. In 1 litre of this solution there is 877 grams of water, whereas the quantity of water combining with the 171 grams of sucrose during inversion is only 9 grams 278 PHYSICAL CHEMISTRY is the quantity still to be inverted after an interval t from the start. Any method which permits a relatively rapid determination of th6 quantity of sucrose in the inverting solution at a given time enables us to test the applicability of this formula, but the only method practically employed in studying the rate of inversion of sucrose is that wMch depends on the use of the polari- meter. It is well inown that a solution of sucrose has a + rotation, whereas the completely inverted solution has a - rotation ; further, the change in rotation from the initial angle ao to the final angle a„, observed after inversion is complete, is a measure of the total quantity of sucrose undergoing change. Similarly, if a is the angle of rotation observed for the solution after an interval t from' the start, the difference between a and a„ is a measure .of the sucrose which has still to be inverted after time t. If, then, Uf, - a„ is taken as a measure of a, a - a„ is a measure of a - a; in the same units ; hence = — — -' The velocity formula may therefore be altered to read k = -: log. "" °'° . The inversion may be allowed to take t ° a-a„ place in the tube of the polarimeter itself, provided that a constant temperature is maintained by a water-jacket. It is a matter of common experience that the temperature coefficient of a chemical reaction is high, hence in any experimental study of the applicability of the velocity formula care must be taken to ensure a constant tem- perature. When a solution of sugar containing acid is kept in a suitably jacketed polarimeter tube, the knowledge of the angle of rotation determined at definite intervals enables us to follow the course of the change and to evaluate k for each point: The data in the following table show how far the actual course of inversion corresponds with the velocity formula : — VELOCITY OP CHEMICAL EEACTION 279 Inversion of Sucrose at 25° by 0-6N HCl. ■Hn minutes. ^^,^°l ,=llog^„^Z^. +25-16° 56 16-95° 0-00218 116 10-38° 0-00218 176 5-46° 000219 236 1-85° 000219 371 -3-28° 0-00221 00 -8-38° It ought to be noted that the expression which has been evaluated in the last column is r losTm °°~°'" , t o^" a-a„ instead of r loge °°~'^'° . But, obviously, if the values of the former expression are constant, the values of the latter must be so also. The figures in the last column are very satisfactorily constant, and the mean value 0-00219 may be taken as a measure of the velocity of inversion of sucrose under the conditions specified, viz. at 25° and in presence of 0-5N HCl. The variation in the velocity coefficient with temperature and with the concentration of the acid will be dis- cussed later. Eeactions, such as the inversion of sucrose, in which i the concentration of one substance only is undergoing change, are known as unimolecular reactions. The course of all changes of this description is expressed by the formula le = i log -^ . All hydrolytic changes which take place in aqueous solution belong to this category, as, for instance, the reaction CH3.COOCH3+H20;iCH3.COOH + CH30H ; under the influence of an. acid this change goes com- pletely from left to right, and the course of the change is represented by the foregoing formula. The rate of hydrolysis of methyl acetate, like the 280 PHYSICAL CHEMISTEY rate of sugar inversion, is within certain limits pro- portional to the concentration of the hydrogen ions present. A determination, therefore, of the rate of hydrolysis of methyl acetate as influenced (1) by any feebly acid fluid, (2) by dilute hydrochloric acid con- taining a known quantity of hydrogen ions, permits the calculation of the hydrogen ion concentration in the said fluid. In this way information can be gained which a mere titration cannot give, for by the latter operation we determine only the total acidity of the fluid, and obtain ,no indication of the ratio of ionised acid to total acid. By a study, however, of the in- fluence of the fluid in question on the velocity of hydrolysis of methyl acetate the extent of the ionisa- tion is ascertained. This method has been employed, for instance, in the investigation of the acidity of the contents of the stomach.^ Further Discussion of the Formula for a Unimolecular Reaction. — The formula 7(; = r log^ -^— , which represents the course of a unimolecular reaction, has in the fore- going pages been reached by purely mathematical operations. Although this is in one sense absolutely satisfactory, it is worth while to consider a little more in detail what is involved in the formula, and to en- deavour to translate the mathematical expressions into terms which may be more capable of direct interpre- tation. Por this purpose it will be convenient to refer specially . to the inversion of sucrose ; any conclusions established for this typical unimolecular reaction may be extended to cover other reactions which belong to the same type. The fundamental formula for the inversion of sucrose 1 See Moore, Proc. Roy. Soc, B, 1905, 76, 138. VELOCITY OF CHEMICAL REACTION 28] is, as already quoted, ^ = k(a - x), where dx is the amount of change in the interval of time dt, a—x is the amount of unchanged sugar at the moment, and A; is a constant. If the formula is written ■ — = Icdt, a — x it is evident that for a given interval of time the amount of change must be a constant fraction of the un- changed sugar present. Experimental work on the rate of inversion of sucrose confirms this conclusion, as appears from consideration of the data in the follow- ing table.i A sucrose solution containing 17"1 grams Time. a +21-55'' 15 20-40° 120 13-75° 135 12-95° 225 8-62° 240 8-02° 00 -7-18° of sugar per 100 cub. cm. was inverted at 20° under the influence of hydrochloric acid, and the progress of the change was followed by determining the rotation (a) of the solution from time to time. The decrease in rotation during the first 15 minutes, namely, 1*15°, is a measure of the amount of change which has taken place during that interval. The average rotation of the solution for the same interval of 15 , , T. . 1 21-55 + 20-40 on nn j minutes may be taken as ^ = ^U-97, and a measure of the mean amount of unchanged sucrose pre- sent during this interval is given by 20-97 + 7-18 = 28-15. The ratio of the amount of change in the first 15 minutes to the unchanged sucrose present may there- 1-15 fore be taken as ^^rr^z = 0-041. If, now, the interval ' Armstrong and Caldwell, Proc. Roy. Soc., A, 1905, 74, 199. 282 PHYSICAL CHEMISTEY between 120 and 135 minutes is considered, the amount of change measured by the decrease of rotation which is found for that interval is 0'80. The average rotation of the solution during these 15 minutes may be taken „ 13-75 + 12-95 -looc J t j-i, as = 13'35, and a measure ol the mean amount of unchanged sucrose present is given by 13-35 + 7-18 = 20-53. The ratio of the amount of change in those 15 minutes to the unchanged sucrose present is therefore 5^:^- = 0-039, practically the same value as for the first 15 minutes of the inversion. Again, if the data for a still later interval (225-240 minutes) are considered, the ratio of the amount of change to the unchanged sucrose present works out to 0-039. The experimental data, therefore, are in harmony with the statement that in a unimolecular reaction the amount of change* in a given short interval is a constant fraction of the unchanged material present. Another result which can be read out of the formula for the inversion of sucrose becomes clear when it is written in the form /<; = ^ lege — j =j log^ j— , i/repre- a senting the fraction of the sucrose which has undergone change up to time t. Since k is a constant for this reaction at a given temperature, it follows that for any selected value of t, y must have a definite value; the fractional amount therefore of the sucrose inverted in a given' time is independent of a, i.e. independent of the amount of sucrose initially present. The validity of this conclusion may be tested by comparing the values of the velocity coefficient obtained in experiments carried out with varying quantities of sucrose : the theory requires that the velocity coefficients so obtained should be equal. How far this is the case will appear ft.. K 560 504 622 510 698 513 770 521 VELOCITY OF CHEMICAL EEACTION 283 from the figures in the following table.^ The numbers Gram-mols, ol Sucrose. - 0-25 0-5 0-75 1-0 in the first column represent the quantity of sugar taken, and the numbers under Ic^ in the second column are the mean values of the velocity coefficient for each experiment, the sugar solution containing hydrochloric acid in each case to the extent of 1 gram-molecule per litre. Instead of being constant, as the theory requires, the values of Ajj increase markedly as the sucrose concentration increases. It has, however, been pointed out that as the sucrose concentration increases, the amount of water present in 1 litre of sucrose solution diminishes to a considerable extent; the concentration of the hydrochloric acid, therefore, which acts as the catalytic agent, is not constant throughout, and hence the values for \ cannot fairly be compared. If the proportion of acid to water is kept constant, that is, if the sucrose and the gram-molecule of hydrogen chloride are in each case dissolved in 1000 grams of water,^ then the values recorded under k^ are obtained for the velocity coefficient. The extent to which these values vary with increasing quantity of sucrose is com- paratively slight, and they may therefore be regarded as confirming the statement that the fractional amount of sucrose inverted in a given time is independent of the amount of sucrose originally present. Saponification of an Ester by an Alkali. A Bi- molecular Reaction. — When sodium hydroxide is added > Caldwell, Proe. Roy. Soc, A, 1906,.78, 287. ' For this method of preparing solutions, see p. 48. 284 PHYSICAL OHEMISTEY to a solution of ethyl acetate, the ester is gradually decomposed into sodium acetate and' ethyl alcohol. The progress of the decomposition is marked by the decreasing alkalinity of the solution, and therefore by extracting a measured portion from time to time, and titrating with standard acid, the velocity of the reaction can be quantitatively studied. The saponification of the ester may be represented by the equation OH3.COOC2H5+NaOH = OH3.COONa+C2H50H, from which it will be seen that in this case the con- centrations of two substances undergo change during the reaction. The law of mass action applied to -this case leads to the formula ^ = /<;(« -x)(b - x), where a and 6 are the initial quantities of ester and alkali, and X is the quantity of sodium acetate produced after an interval t from the start. If this equation is inte- grated, we find the velocity constant h = ., _,. log^ 4^— ^. The mathematical expression which represents the course of the reaction becomes simpler if the ester and alkali are taken in equivalent quantities, i.e. ii a = b. In this case ^ = k{a - xf, the integration of which gives 1 a; the formula h — ,- —, r. How far the facts are in t a{a — x) harmony with this formula may be seen from the figures in the following table.^ The solution used was — ■ in relation both to ester and sodium hydroxide, and during the reaction the mixture was kept at 24' 7°. The figures recorded under a—x are the volumes of a standard "hydrochloric acid required to neutralise exactly 10 cub. cm. of the reaction mixture. ' Arrhenius, Zeit. physihd. Chem., 1887, 1, 110. VELOCITY OP CHEMICAL REACTION 285 ((min.). a-a. 8-04 1 X 4 5-30 0-129 6 4-58 0126 8 3-91 0132 10 3-51 0-129 12 3-12 0-131 15 2-74 0-129 20 2-22 0-131 The numbers given in the last column for ka are very satisfactorily constant, and confirm the application of the law of mass action to a bimolecular reaction. As indicated on p. 168, the rate of inversion of sucrose and the rate of saponification of an ester may be utilised in ascertaining the concentration of hydrogen or hydroxyl ions respectively in any solution. It must, however, be borne in mind that there is an essential difference between the two reactions. In the saponification of an ester by an alkali, the alkalinity of the reaction mixture diminishes as the reaction proceeds, i.e. the hydroxyl ions disappear. In the inversion of sucrose, on the other hand, the acid present does not enter into the products of the reaction, and the quantity of the acid or, in other words, the concentration of the hydrogen ions remains the same throughout the course of the change. The influence of acids in promoting the inversion of sucrose is an example of catalytic action, the general characteristics of which must be considered in some detail. Catalysis. — It is a well-known fact that a chemical change which of itself proceeds with extreme slowness may be greatly accelerated in presence of some apparently foreign substance, the other conditions being unaltered. The amount of this foreign substance may be extremely small, it may not take any obvious part in the chemical change, it 'may be quantitatively recoverable at the end 286 PHYSICAL CHEMISTRY of the change, and yet the rate of the chemical reaction may be markedly altered. This phenomenon has been known for a long time, and is familiar to the chemist as ' catalysis.' It is of the greatest importance in relation ~ to the chemical changes which take place in the living organism, for there we find reactions occurring easily and smoothly, which, apart from the organism, are ex- ceedingly sluggish and diflScult to bring about. The ' catalytic agents ' or ' catalysts ' which promote the pro- cesses of metabolism in the living organism belong to the class of enaymes, and it will presently appear that from the quantitative as well as the qualitative point of view there is a close analogy between enzymes and inorganic catalysts. A quantitative study of catalysis is possible only on the basis of the law of mass action. In the velocity coefficient, as already explained for the inversion of sucrose, we have a quantitative expression for the rate of a chemical change under given conditions. For a given reaction, therefore, which is catalytically accelerated, the value of the velocity coeflElcient at a given temperature is a measure of the efficiency of the catalyst, and by comparing the values obtained for the velocity coefficient in difEerent experiments one can ascertain how the efficiency of the catalyst varies with the conditions under which it works, and how the efficiency of one catalyst compares with that of another working under the same conditions. Characteristics of Inorganic Catalysts. — One of the most striking features about a catalyst is that its quantity may be so minute compared with the quantities of the main reacting substances. An illustration of this is furnished by the influence of molybdic acid on the rate of the reaction between hydrogen peroxide and hydriodic acid. Erode ^ has shown that the velocity of interaction 1 Zeit. pkysikal. Cheta-, 1901, 37, 257, VELOCITY OF CHEMICAL REACTION 287 between these substances in ^7^ solution is more than doubled by the addition of molybdic acid, even in the proportion of 1 molecule molybdic acid to 1 million litres of solution. Another point which has been established by the quantitative study of inorganic catalysts is that, as a rule, the activity of the catalyst at the end of the re- action which it has accelerated is unimpaired. In this connection reference may be made again to the fact that the acid used to effect the inversion of sucrose does not appear in the products of the reaction, and is present in undiminished quantity when the inversion is complete. Another illustration of the same principle is furnished by the behaviour of colloidal platinum in promoting the union of hydrogen and oxygen. In the course of some experiments made by Bredig,^ it was found that when electrolytic gas is shaken with a colloidal solution of platinum at the ordinary temperature, there is a fairly rapid decrease in volume owing to the union of hydrogen and oxygen. In one case where 2'5 cub. cm. of a colloidal platinum solution (containing 0*17 milligram platinum) was shaken with electrolytic gas, the results recorded in the following table were obtained : — Time in Decrease in the Kate o{ Decrease in Minutes. Volume of Gas. cub. cm. per Min. 10 17-8 cub. cm. 1-78 20 35-8 „ 1-80 30 54-8 „ 1-90 40 72-4 „ 1-76 50 90-2 „ 1'78 The average of the figures in the last column is a measure of the catalytic efficiency of the colloidal platinum in the early stages of its activity. The same colloidal platinum was shaken intermittently during fourteen days with electrolytic gas, about 10 litres of which disappeared ' Zeit. physihal. Chem., 1899, 31, 258 ; see also Ernst, ibid., 1901, 37, 448. T 288 PHYSICAL CHEMISTRY in this time under the influence of the catalyst. The actual rate of disappearance of the gas at the end of the fourteen days was then definitely measured, with the following results : — Time in Minutes. 10 Decrease in the Volume of Gas. 20'2 cub. cm. Kate of Decrease in cub. cm. per Min. 2-02 20 30 38-9 „ 58-4 „ 1-87 1-95 40 50 78'1 „ 98-2 „ 1-97 2-01 The average of the figures in the last column is a measure of the catalytic efiiciency of the colloidal platinum after it has exerted its activity for a considerable period. It is obvious that the efficiency is unimpaired ; the aver- age rate of decrease in the volume of the electrolytic gas is even slightly greater at the end than at the beginning. So far, we have conceived a catalyst as a substance which merely accelerates a chemical reaction, and does not appear in the products of the reaction. If this is so, the final state of the reactive system must be independent of the catalyst; the state of equilibrium finally reached between the reacting substances must be the same whether the catalyst has been present or not. In other words, the catalyst influences only the rate at which the condition of equilibrium is reached, not the position of equilibrium itself. The validity of this con- clusion can be tested more suitably in connection with a reversible reaction, for in such a case the position of equilibrium is defined by the value of the equilibrium constant. As already shown, the equilibrium constant for a reversible reaction is equal to the ratio yi, where h-, is the velocity coefficient of the forward reaction, and k^ is that of the back reaction. If, then, the position of equilibrium is not affected by the presence of a catalyst, VELOCITY OF CHEMICAL EBACTION 289 it follows that the forward and the back reactions must be accelerated in the same proportion. This has been shown to be actually the case in connection with the catalytic action of acids on the velocities of esterification and hydrolysis of an ester. That the position of equilibrium for a reversible reaction is independent of the nature and amount of catalyst which has been used to accelerate the estab- lishment of equilibrium is shown clearly by Turbaba's study ^ of the relationship between aldehyde — CHg.CHO — and paraldehyde — (CH3.CHO)3. The equilibrium mixture of these two substances at 50'5° contains 33-9 per cent, aldehyde and 66"1 per cent, paraldehyde. The conversion of paraldehyde into the equilibrium mixture is accom- panied by an expansion, and the course of the change may therefore be followed in a dilatometer. Various substances in varying amount may be employed to accelerate the change, but the difference between the initial and the equilibrium volumes, as shown by the figures below, is the same in all cases ; that is, the position of equilibrium is independent of the nature and amount of the catalyst : — r<~4^»i„.i^ P^f Cent. Feruentage Increase ^***'y"- Catalyst.. ol Volume. Sulphur dioxide . . . 0-08 8-20 „ ... 0-07 8-34 „ ... 0-002 8-19 Zinc sulphate . . , . 2'7 8-13 Hydrochloric acid . . . 0-13 8-13 Oxalic acid 0-52 8-27 Phosphoric acid . . . 0'54 8"10 Another point of great interest is the relationship between the value of the velocity coefficient for a given reaction at a given temperature and the concentration of the catalyst. In a great many cases the relation- 1 See Zeit. physikal. Chem., 1901, 38, 505. 290 PHYSICAL OHBMISTEY ship is a linear one, that is, the velocity coefficient is directly proportional to the concentration of the catalyst. The rate of inversion of sucrose by acids, for instance, is proportional to the concentration of the hydrogen ions, provided that this concentration is low, and on the basis of this proportionality it is possible to calculate the velocity of inversion by dilute acetic acid from the velocity observed with dilute hydrochloric acid. Again, the acceleration of the reaction between hydriodic acid and hydrogen peroxide by molybdic acid is propor- tional to the concentration of the latter.^ In other cases the relationship between reaction velocity and concentration of catalyst is not a linear one.- The influence of colloidal platinum in promoting the decomposition of hydrogen peroxide is a case in point.^ The course of this reaction, it may be explained, is easily followed by extracting a definite volume of the reaction mixture from time to time and titrating with a dilute solution of potassium permanganate. The volume of permanganate required for each extract is a measure of the undecomposed hydrogen peroxide present in the reaction mixture at the time of the extraction. For a given temperature and a given concentration of colloidal platinum the course of the decomposition is represented by the formula for a unimolecular reaction ; this appears from the figures in the accompanying table, tmin. a-x. &. 22-3 10 13-6 0-022 20 8-05 0'022 30 4-6 0023 35 2-8 0-022 where the numbers under a-x represent cub. cm. of permanganate required for a given volume of reaction ' Erode, loo. cit. « See Bredig and von Berneck, Zeit. physikal. Okem., 1899, 31, 258. VELOCITY OF CHEMICAL REACTION 291 mixture, and those under k are the vahies of the velocity coefficient calculated for a unimolecular reaction. The mean value obtained for h in different experiments varies with the concentration of the platinum in the manner shown by the following figures. -Prom these Flatiniim j^ Concentration. 21 X 10-« 0-072 10-5xlO-» 0-024 5-2xl0-« 0-0084 2-6xl0-« 0-0027 it appears that when the concentration of the catalyst is doubled, the velocity of decomposition is trebled. Enzymes as Catalysts.^ — In many respects enzymes resemble inorganic catalysts. To begin with, there is the same striking contrast between the small quantity of the enzyme and the extent of the chemical change which it brings about. O'SuUivan and Tompson ^ refer to a sample of invertase which had induced the inversion of one hundred thousand times its own weight of sucrose and was still active. Senter, in the course of experiments on haemase,^ an enzyme present in the blood, found that when 100 cub. cm. of a solution of blood (obtained by adding 1 cub. cm. of blood to 1000 cub. cm. of water) are mixed with 100 cub. cm. of a hundredth molar solution of hydrogen peroxide, the whole of the latter is de- composed in 5 minutes, although the solution without any enzyme exhibits no appreciable decomposition in 1 2 hours. Enzymes resemble inorganic catalysts also in that, where the reaction involved is a reversible one, they ^ For a detailed dlsonssion of this subject see The Nature of Enzyme Action, by W. M. Bayliss. 2 J(ywrn. Ohem. Soc., 1890, 57, 834. ' Zeit. physihal. Chem., 1903, 44, 2S7. 292 PHYSICAL CHEMISTRY promote both the direct and the reverse changes. An instance of this is furnished by the action of lipase on the esters of the lower fatty acids. If this enzyme is allowed to act on ethyl butyrate in presence of water, partial hydrolysis into butyric acid and ethyl alcohol takes place ; while if it is allowed to act on an aqueous mixture of butyric acid and ethyl alcohol, a certain quantity of the ester is formed.^ The action of an enzyme, however, on the products of a reaction may not be strictly the reverse of its effect on the forward reaction, for it has been found ^ that maltase, the enzyme which hydrolyses maltose into dextrose, exerts a synthetic action on dextrose, producing not maltose, but *so-maltose. In certain cases the course of a reaction induced by an enzyme is in harmony with the law of mass action. The decomposition of hydrogen peroxide under the influence of hsemase* may be taken as an example of this. The course of the decomposition is followed in the same way as already described for the catalysis of hydrogen peroxide by colloidal platinum ; that is, a definite volume of the reaction' mixture is taken out from time to time and titrated with dilute potassium permanganate solution. That the course of the change is in harmony with the law of mass action is shown by the following table, the figures under a-x re- t (min.). a-x. k. 11-0 5i 8-7 0-0194 10 7-4 0-0172 20 4-8 0-0180 30 3-0 0-0188 50 1-3 0-0185 1 Kastle and Loevenhart, Amer. Chem. Journ., 1900, 24, 491. ■' Croft Hill, Journ. Chem. Soo., 1898, 73, 634 ; 1903, 83, 578 ; Emmer- ling, Ser., 1901, 34, 600, 2206, 3810 ; Armstrong, Proo. Boy. Soc, B, 1905, 76, 592. ' Senter, loo. cit. VELOCITY OP CHEMICAL REACTION 293 presenting the volume of dilute permanganate solution required for 25 cub. cm. of the reaction mixture, and those under k being the values of the velocity coefficient calculated for a unimolecular reaction. The initial con- centration of the hydrogen peroxide was in this case -j^th molar, and the experiments were carried out at 0° C. The constancy of the numbers in the last column shows that the catalysis of hsemase follows the course of a unimolecular reaction. Further, it was found by Senter that, for hydrogen peroxide solutions between ■g^th and ^innrth molar concentration, the value of the velocity coefficient is independent of the initial concentration of the hydrogen peroxide; this also sup- ports tjie view that the action of hsemase on hydrogen peroxide is in harmony with the law of mass action (see p. 282). It appears too that, at least in very dilute solutions of hydrogen peroxide, the velocity of decom- position is proportional to the concentration of the enzyme. In many respects there is a close parallelism between the decomposition of hydrogen peroxide by colloidal platinum and the decomposition of the same substance under the influence of haemase. This parallelism ex- tends also to the effect of certain ' poisons ' in paralys- ing the activity of the two catalysts,^ so much so that Bredig has described colloidal platinum as an 'inor- ganic ferment.' The catalysis of hydrogen peroxide by h^mase has been referred to as a case in which enzyme action conforms to the law of mass action, and in which the enzyme behaves very similarly to an inorganic catalyst. The close study, however, of many other cases has shown that very frequently, owing to the operation of ^ Biedig and von Berneok, Zeit. physikal. Chem., 1899, 31, 258; Senter, loo. eit., and Proe. Roy. Soc, 1905, 74, 201. 294 PHYSICAL CHEMISTRY various factors, the course of a reaction which takes place under the influence of an enzyme deviates con- siderably from what we should expect on the basis of the law of mass action. A brief discussion of some of these factors may be found useful. Some Peculiarities of Enzyme Action. — As an in- stance of an enzyme reaction deviating from the course marked out by the law of mass action, the inversion of sucrose by invertase may be quoted. This change has been studied quantitatively by A. J. Brown .^ and the following table embodies the results of one of his ex- periments. In this particular case 25 cub. cm. of in- vertase solution were added to 500 cub. cm. of a 9'48 per cent, sucrose solution, and the mixture was kept at 30°. Portions were extracted from time to time, and from the observed rotation for each sample the extent to which inversion had proceeded at the time of extraction was deduced ; the figures under x repre- sent the fraction of the total sucrose which had under- gone inversion by time t. The numbers iu the last column, instead of being constant, as they ought to be if the inversion proceeds in conformity with the law of mass action, exhibit a marked and regular increase. (min. sc. ^-r^ 3d 0-265 000445 64 0-609 0-00483 120 0-794 0-00571, 180 0-945 0-00698 240 0-983 0-00737 The departure from the law of mass action becomes still clearer when experiments are made in which a 1 Journ. Chem. Soc., 1902, 81, 378. See also Henri, Zeit. phyaikal. . Chem., 1901, 39, 194. VELOCITY OF CHEMICAL EEACTION 295 constant amount of invertase is allowed to act for a given time on varying amounts of sucrose ~ in a constant volume of solution. According to the law of mass action, the fraction of the sucrose inverted in the given time ought to be the same in all cases, independent, that is, of the initial quantity of sucrose present. How far this requirement of the law of. mass action is fulfilled will be seen from the accompanying table : — Grams Sncrose per 100 cub. cm. Grams Sucrose Inverted in 60 min. Fraction of Sucrose Inverted in 60 min. 4-89 1-230 0-252 9-85 1-355 0-138 19-91 1-355 0068 29-96 ■ 1-235 0-041 It is clear that the enzyme, instead of inverting a constant fraction, has inverted an approximately con- stant weight of sucrose in the given time. On the other hand, if the quantity of sucrose is relatively much smaller than in the cases recorded in the foregoing table the law of mass action is fulfilled, in that the weight of sucrose inverted in a given time is always the same fraction of the weight taken initially. This appears from the following figures : — Grams Sucrose per 100 cub. cm. Grams Sucrose Inverted in 60 min. 1-0 0-249 0-5 0-129 0-25 0-060 Other casea in which it has been found that the amount of change induced by an enzyme is, for at least a portion of the change, a linear function of the time, are the hydrolysis of starch by diastase,^ and the hydrolysis of milk sugar by lactase.* * H. T. Brown and Glendinning, Joum. Ohem. Soc., 1902, 81, 388. ' E. ¥ Armstrong, Proo. Boy. Soo., 1904, 73, 500. 296 PHYSICAL CHEMISTRY In connection with the former of these cases it has been shown that it is only the earlier portion of the time-curve which is linear, the later portjpn being logarithmic in character. This is proved by calculat- ing the velocity coefficient Jo=rlog ^zr (■'•) ^°^ ®^°^ ^ observation from the start of the reaction, (2) for each observation after the linear portion has been passed, a new starting point being chosen. A com- parison of two sets of values of k obtained in this manner is given in the following table, which refers to the hydrolysis of a 3 per cent, starch solution by malt extract at 51°-52° : — Time (miD.)- k. Time in min. from new Starting Point. *. 10 0-00498 20 0-00553 30 0-00590 40 0-00620 ■ •• 50 0-00650 10 0-00842 60 0-00690 20 000831 70 0-00706 30 0-00821 80 0-00728 40 0-00837 90 0-00730 50 0-00818 100 0-00732 60 0-00807 110 000749 70 0-00822 120 0-00762 80 0-00840 130 000779 90 0-00855 It will be seen that the values of h in the second column are far from constant, and yet if the first portion of the change is left out of account, practically constant values for the velocity coefficient are obtained. It is permis- sible to draw the conclusion that the later portion of the change conforms to the law of mass action. From the foregoing it appears that it is only when the VELOCITY OF CHEMICAL EBACTION 297 amount of enzyme is relatively small compared with the amount of carbohydrate that a linear relationship between the time and the amount of change is observed. To regard the occurrence of this linear relationship, however, as something peculiar to enzymes is scarcely correct, for it has subsequently been found that a similar feature, if less distinct, characterises the hydrolysis of sucrose by very dilute acid.^ When sucrose solutions contain- ing 171 and 342 grams per litre are inverted at 40° by ^^ HCl, the values calculated for the velocity coeflScient increase during the first portion of the change and then remain constant. In this respect, therefore, there is a close parallelism between acid and enzyme action : in both cases, when the proportion of catalyst is relatively small, the amount of change is to begin with approximately a linear function, and subsequently a logarithmic function, of the time. Another peculiarity about enzyme action which has been observed frequently, is that the activity of the enzyme does not remain constant throughout the whole course of the change which it induces. Tammann,^ for instance, found that in the hydrolysis of amygdalin by emulsin the change is incomplete. The failure of the enzyme to effect complete hydrolysis might be attributed to the really reversible character of the process, but this view is untenable, for if more emulsin is added to a mixture in which hydrolysis has come to a standstill, the reaction proceeds further. This shows clearly that the equilibrium reached when emulsin acts on amygdalin is not one which is independent of the enzyme, as would be the case if the emulsin behaved like an inorganic catalyst. The natural conclusion is that the emulsin 1 Armstrong and Caldwell, Proc. Roy. Sob., 1905, 74, 195. « Zeit. phyml. Ohem., 1892, 16, 271. 298 PHYSICAL CHEMISTRY must be put out of action in some way by the pro- ducts of hydrolysis — a view which finds support in the fact that the action of emulsin on amygdalin is inhibited by the initial addition of benzaldehyde or hydrocyanic acid. This check to the activity of the enzyme cannot, however, be due to its destruction, for when the products of hydrolysis present in an equili- brium mixture are removed, the splitting up of the amygdalin sets in again. The influence of the products of change on the activity of the enzyme lyhich induces the change is apparent also in the values which are found for the velocity coefficient in the hydrolysis of milk sugar by lactase.^ In the accompanying table t gives the time in hours from t. ■X. h. 1 13-7 0-0640 2 22-1 0-0543 3 27-2 0-0460 5 300 0-0310 24 51-0 0-0129 the start, x is the percentage of sugar hydrolysed up to time t, and Ic is the velocity coefficient calculated by the formula for a unimolecular reaction ; the solution contained initially 5 grams milk sugar in 100 cub. cm. In contrast to the case of the inversion of sucrose by invertase (see p. 294)", the values of k in this case decrease as the hydrolysis proceeds, a result that is attributed to the increasing concentration of the pro- ducts of hydrolysis. It can indeed be shown that the initial addition of galactose materially reduces the rate of hydrolysis of milk sugar by lactase, while glucose and fructose are practically without effect. This appears from the following table, the figures in which, apart from the first column, represent the percentages of ' Armstrong, Proc. Roy. Soo., 1904, 73, 500. VELOCITY OF CHEMICAL EEACTION 299 milk sugar hydrolysed; the concentration of milk sugar was in each case 5 grams per 100 cub. cm. : — Time in Hours. Milk Sugar alone. Milk Sugar +6 grams iCructose. Milk Sugar +5 grams Galactose. Milk Sugar +6 grams Glucose. 4 18-0 18-0 16-0 17-6 22 59-2 59-6 47-4 59-6 28 65-6 65-4 52-0 65-4 69 81-4 80-2 61-6 78-4 The retarding influence of the products of change is therefore a specific influence, depending on some special relationship between the enzyme and the particular hexose which exerts the retarding efEect. Further, the activity of the enzyme, according to the investigations of Fischer and others,^ is determined by the degree of similarity in the configuration of enzyme and substrate (that is, the substance undergoing change under the influence of the enzyme). It is interesting to note, on the other hand, that the hydrolysis of milk sugar by hydrochloric acid is accelerated by the addition of glucose or galactose; the products of change exert no specific influence in this case : indeed, the addition of the equivalent quantity of a neutral salt brings about a similar acceleration. The fermentation of glucose by yeast juice supplies another instance of the more complicated character of enzyme actions as compared with changes which are accelerated by inorganic catalysts. It has been found that the ferment in yeast juice is of itself unable to bring about the alcoholic fermentation of glucose ; another body, the 'co-ferment,' as it is called, which is present in yeast juice, is essential to the activity of the ferment.^ A separation of the ferment and co-ferment is effected 1 See Armstrong, Proc. Boy. Soc, 1904, 73, 520. 2 See Harden and Young, Proe. Roy. Soc, B, 1906, 77, 405 ; 78, 369. 300 PHYSICAL OHEMISTEY by dialysis; the residue, containing the ferment, and the dialysate, containing the co-ferment, are separately inactive, but when united give rise to fermentation. The inactive residue obtained on dialysis can be rendered active also by the addition of boiled and filtered yeast juice ; it follows, therefore, that the co-ferment is not destroyed by boiling. During the process of fermen- tation the co-ferment disappears, as has been shown by experiments in which a fairly large quantity of the inactive residue from dialysis and a small quantity of boiled yeast juice have been added to a glucose solution. In this case the evolution of carbon dioxide soon comes to an end, but on the addition of a further quantity of boiled juice fermentation is set up again. The Mechanism of Catalysis. — The phenomena of catalysis generally, and more particularly those of enzyme action, give rise to the question : How does the catalyst exert its influence ? In the present state of our know- ledge it is impossible to give a complete and satisfactory answer to this question, but it is desirable to indicate some of the main facts which have a bearing on the problem, and some of the suggestions which have been contributed towards its solution. It will be convenient to start from the suggestion, which has been very generally accepted, that a catalyst is effective because it forms some sort of combination with the substrate. This intermediate compound, it is supposed, then breaks up into the final products Tof change, the catalyst being liberated. Obviously, if this account of the catalytic change is to give an adequate interpretation of the phenomena, it is necessary to sup- pose that the formation and decomposition of the inter- mediate compound together require a much shorter time for their occurrence than the direct change itself. VELOCITY OF CHEMICAL REACTION 301 In favour of the view that combination of some kind takes place between catalyst and substrate there is a considerable amount of evidence. As found by 'Sullivan and Tompson,! invertase in the presence of sucrose stands without injury exposure to a temperature 25° higher than it does in the absence of sucrose. Similarly, pro- teins exert a protective influence over trypsin.^ More direct evidence of the formation of intermediate com- pounds has been brought forward by Erode ^ in his study of the accelerating influence of molybdic acid on the reaction between hydrogen peroxide and hydrogen iodide. In this case it can be proved that combination takes place between the molybdic acid and the hydrogen peroxide, with the result that the former is practically converted into permolybdic acid. It is then supposed that the reduction of this substance by hydriodic acid takes place much more rapidly than the reduction of hydrogen peroxide. Other facts in favour of the view that catalysts act by forming intermediate compounds are the occurrence of a linear portion in the time curve for the hydrolysis of sugars by relatively smalj'quantities of the appropriate enzymes (see p. 295), and also the specificity of enzymes. But although we may with some confidence assume the formation of intermediate com- pounds in enzyme action and catalysis generally, it is quite impossible in the majority of cases to specify the nature of these compounds. In this connection it must be borne in mind that many catalytic reactions are to be described as non- homogeneous reactions, as, for instance, the union of hydrogen and oxygen under the influence of platinum black. Here the catalyst is solid, whilst the reacting » J ^ value which is in good agreement with the experimentally determined figure. Just as for silver concentration cells, so also for the case of other univalent metals, .^ = '058 logj,, J. It is easily seen that if the electromotive force of a concen- tration cell of this type has been determined, and if the ion concentration round one electrode is known, the ion concentration round the other electrode can be calculated. This principle has found useful application in the de- termination of very small ion concentrations, and has been employed, for instance, in finding the solubility of sparingly soluble salts. As an illustration of the ap- plication of the principle, the problem of finding the solubility of silver iodide may be taken. For this ELECTROMOTIVE FORCE 313 Ag Ag is set up, the potassium nitrate purpose a concentration cell represented by the scheme KNO3' KNO3 being added in order to diminish the resistance of the cell, and to eliminate the liquid potential, as already de- scribed. The solution round one electrode is j^AgNOg, and, as this is very dilute, the silver ion concentration -^^ Fig. 24. in this solution may be taken as '001, the electrolytic dissociation being practically complete. The other elec- trode is bathed by a saturated solution of silver iodide — a solution in which plainly the silver ion concentration is exceedingly small. Experiment shows that the E.M.F. of the concentration cell just described is 0-22 volt, so that we have 0*22 = '058 log^^ — , where Cg is the con- centration of the silver ions in the saturated solution of silver iodide. This equation gives C2=l'6xl0-8 equiva- lents per litre, and since the dissociation of the silver 314 PHYSICAL CHEMISTRY iodide may be taken as complete at such a great dilution, the figure I'GxlO"* represents also the concentration of silver iodide in its saturated solution, and that is simply the soluMlity of the salt. In setting up concentration cells and in the deter- mination of electrode potentials generally, it is con- venient to use separate electrode vessels, which can each be charged with their own particular solutions and then connected by means of an intermediate vessel. The foregoing Fig. 24 shows two electrode vessels which are in liquid connection with the contents of an intermediate beaker ; the latter contains a strong solution of potas- sium nitrate or potassium chloride, in order to eliminate the potential difference between the electrode solutions, as already described. The Hydrogen Electrode and its Applications. — In the foregoing discussion of concentration cells, it has been implied that the electrodes are invariably of metal and are the scene of a reversible equilibrium between a metal and its ions in the surrounding solution. This conception, however, must be extended to cover cases where the electrode substance is really a gas, this being in contact with a solution containing the same substance in the ionised condition. Since hydrogen is the gas which has chief significance in this connection, it is de- sirable to refer to it more especially, and, first of all, to describe the hydrogen electrode. The vessel which is to serve in the construction of a hydrogen electrode is similar to one of those depicted in Fig. 24, but must be modified so as to permit a current of hydrogen gas to be bubbled through the solution : the modification consists in sealing on a narrow tube at the bottom of the electrode vessel. The electrode itself is a piece of platinum foil coated with platinum black (see ELECTROMOTIVE FORCE 315 p. 125), or a thin film of platinum on glass, in either case saturated with hydrogen gas and half immersed in an acid solution, i.e. a solution containing hydrogen ions. When BuflBcient time has been allowed for the solution and the platinum to become completely saturated with the gas, this "hydrogen electrode" has a perfectly definite and steady potential, the numerical value of which is defined by the pressure of the hydrogen gas and the osmotic pressure of the. hydrogen ions in the surrounding solution. In like manner one may construct a chlorine electrode or an oxygen electrode. In the latter case the platinum foil or film, saturated with oxygen, is immersed in an alkali solution, which may be regarded as containing oxygen ions, derived from the hydroxyl ions which are mainly present, thus: 20H';^0"+H20. Reverting to the hydrogen electrode, it is easily seen that, on the basis of the parallelism between this electrode and the metal electrodes already described, concentration cells may be constructed, the E.M.F. of which will be determined solely by the relative concentration of the hydrogen ion round the two electrodes. That is, if Cj and Cj ^re the concentrations of the hydrogen ion in the stronger and weaker acid solutions at the electrodes of a hydrogen concentration cell, the electromotive force of the cell at 17° C. is given by the formula E= '058 logjg ^, supposing that the potential at the common surface of the two solutions has been eliminated. This formula not only allows the calculation of the electromotive force of a hydrogen concentration cell from the concentrations of the hydrogen ion in the two electrode solutions— a calculation that is verified experimentally — but permits the evaluation of the hydrogen ion concentration in the one electrode solution, provided the electromotive force 316 PHYSICAL CHEMISTRY of the cell and the hydrogen ion concentration in the other electrode solution are known. In order, therefore, to find the hydrogen ion concentration in any given liquid, the latter is made one of the electrode solutions in a hydrogen concentration cell, while dilute hydro- chloric acid of known strength is taken for the other electrode solution. This method" is particularly suited for determining very small hydrogen ion concentrations, for, the greater the difference between c^ and Cj, the higher is the electromotive force of the concentration cell. As a first example of the application of this method of finding the hydrogen ion concentration in aqueous solutions, we may take the problem of determining the ionisation of water.^ It has been already explained (p. 259) that the application of the law of mass action to the equilibrium between water and its ions leads to the result that if Oh and Oqh represent the concentra- tions of the hydrogen and the hydroxyl ions respectively in any aqueous solution, then CH.OoH=const. Now, one method of getting the value of this "ionic product" for water depends on the measurement of the B.M.F. of the hydrogen concentration cell represented by the scheme : Hg I i^HCl I j^NaOl I j^N'aOH I H^. In this arrangement I N IN Hg To?)-^^^ ^^^ -^2 loo^^^'^ represent the hydrogen electrodes, the two electrode solutions being connected through an intermediate solution of sodium chloride. The latter is introduced in order to avoid the trouble- some calculation of the potential difference which would arise if the jg^HCl and jg^NaOH were directly in contact. The potentials at the junctions of yqqHCI with j^NaOl, ' See LBwenherz, Zeit. phyiikal. Chem., 1896, 20, 284. ELECTROMOTIVE FORCE 317 and of ]^Na01 with j^NaOH on the other hand, can be calculated easily with the help of the Nernst-Planck formula,! and at 25° are respectively -0307 volt and -0152 volt. In the hydrogen concentration cell under consider- ation, the positive current flows inside the cell from the alkali solution to the acid solution, and the total E.M.F. of the cell, determined by actual measurement, is 0"5378 volt at 25°. The two liquid potentials referred to are both opposed in direction to the electrode potentials, so that if E represents the E.M.F. compounded of the electrode potentials alone, ^= 0-5378 + 0'0307+ 0-0152 = 0-5837 volt. But at 25° 2 ^"=-059 logj^ "j, where c^ is the concentration of hydrogen ion in ^^HCl, and Cg is • • • N the concentration of hydrogen ion in Y7^f^NaOH ; and since conductivity measurements show that hydrochloric acid in ^^ solution is electrolytically dissociated to the extent of 97-6 per cent., Ci=0-01 x 0-976 = -00976. Hence we have 0-5837= -059 logi„ , from which it follows "2 that C2=l-257xl0~^^. The degree of dissociation of 100 N sodium hydroxide in :r^ solution is 0-935, so that the concentration of the hydroxyl ions in jjr-NaOH is -00935. Values have now been obtained for the concentrations of both hydrogen and hydroxyl ions in j^NaOH, and the ionic product for this solution= Ch.Coh= 1'257 X 10"'^ X -00935 = 1-2 X 10~". According to the law of mass 1 Ann. Physih, 1890, 40, 561. ' The higher temperature involves an increase in the coefficient of logjj — ' 'lis value -058 having been deduced for 17° 0. 318 PHYSICAL CHEMISTRY action, the value of the product Ch.Ooh at a given tem- perature is the same in water as in any aqueous solution, and, since in pure water Oh=Coh. it follows that the concentration of hydrogen ion in pure water and the con- centration of hydroxyl ion in pure water are each given by Vl-2 X 10-", that is, 1-1 x 10"'. The example just discussed in detail shows clearly the utility of the hydrogen concentration cell in the deter- mination of minute concentrations of hydrogen ion. For this purpose the electrometric method has the advantage over other methods (see, for example, pp. 167-8), which are adapted rather to the measurement of larger concen- trations of the ion in question. The extent of hydrolytic dissociation of a salt, for instance, is a quantity that can readily be ascertained by the electrometric method. Suppose it were desired to find the extent of hydrolysis— r in other words, the concentration of the hydroxyl ion — in jTTT^ sodium acetate solution. This can be done by set- 1000 •' ting up the concentration cell represented by the scheme : H^ I iSo HCl I mo N-Ol I ^CH3C00Na I H„ deter- mining the E.M.F. of this cell, and then calculating the hydrogen ion concentration m the j^ OHjOOONa as already described. When the hydrogen ion concentra- tion has thus been ascertained, that of the hydroxyl ion can easily be calculated, for, as shown in the last para- graph, the product of the two concentrations. Oh X Oqh) has a constant value, which at 25° is 1'2=10-^*. The first instance of the application of the foregoing electrometric method in connection with more definitely physiological problems is furnished by Bugarszky and Liebermann's work ^ on the relation between protein and * PfiUger'a Arch., 1898, 72; 51. ELECTROMOTIVE FORCE 319 electrolytes. The acid-alkali concentration cell described on p. 316 was employed in this investigation, and the effect of adding protein either to the acid or the alkali was studied quantitatively. In this way definite infor- mation was obtained as to the influence of protein on the concentration of hydrogen ion in a given acid solution and on the concentration of hydroxyl ion in a given alkali solution. The results showed that albumin has the power of combining both with acid and with alkali.^ Concentration of Hydrogen Ions in Physiological Fluids. — The determination of the exact degree of acidity or alkalinity of a physiological fluid by the ordinary titration methods is not an easy matter. In these circumstances the measurement of the hydrogen ion concentration by the eiectrometric method furnishes valuable information. Blood has frequently been ex- amined in this way,^ and by the determination of the I N E.M.P. of such concentration cells as H, tttt; II01 + ■^ I 100 o NaCl -K NaCl Blood H„, it has been shown that the o I o 1 1 concentration of hydrogen ion in fresh defibrinated mam- malian blood is 0'3x 10"'' — 0'7xl0~' at ordinary tem- perature. Since the concentration of hydrogen ion in water at ordinary temperature is 0"8 X 10~', it appears that defibrinated mammalian blood is practically a neutral liquid. It is worth noting, however, that if in the measurement of the E.M.P. of the gas cell, a current of hydrogen is passed through the blood, with the result that the carbon dioxide normally present in this fluid is removed, then a distinctly lower value, viz., O'Ol x 10~' — 0'03 X 10"', is obtained for the hydrogen ion concentra- • See p. 265, and cp. Robertson, /. Physical Chem., 1910, 14, 528. " Hober, Pjfilger's Arch., 1900, 81, 522 ; 1903, 99, 572 ; Michaelis and Eona, Biochem. Zeit., 1909, 17, 317 ; Hasselbalch, iiic?., 1910, 30, 7. X 320 PHYSICAL CHEMISTEY tion. This figure corresponds with a feebly alkaline re- action. Eise of temperature also appears to favour alkalinitj, for eleotrometric measurements, similar to the a,bove but carried out at 37-38°, indicate that at body temperature the concentration of hydroxyl ions in the blood is somewhat greater than at ordinary temperature. The examination of other body fluids on the same lines as those described for blood has confirmed the earlier conclusion that in the case of the higher animals these fiuids are generally neutral. Those which exhibit a notable departure from neutrality are gastric juice, pan- creatic juice, intestinal juice, and urine. Hydrogen cell measurements have shown that in the case of gastric juice Oh (concentration of hydrogen ion) has the value 3 X 10"^ — 9 X 10~^, whilst in the pancreatic juice and the intestinal juice Ch=7x 10-"-ll x IQ-i". The acidity of the urine, even for a single individual, varies within wide limits, and the value of Ch may be put down as lxlO-'-lxlO-«. Reference has already been made to the diflScnlty of ascertaining the acidity or alkalinity of a physiological fiuid by the ordinary titration methods. These methods involve the use of indicators, and it is a well-known fact that many indicators undergo change of colour before the point of absolute neutrality {i.e. Ch=Ooh) is reached. Thus, for instance, the turning point lies at Ch=10~^"*— 10-2-6 for tropaolin 00, at Oh=10-3-1-10-«-* for methyl orange, at Oh=10~^'**— lO"'-" for ^-nitrophenol, and at Oh== 10-8-3- 10-" for phenolphthalein.1 Provided, how- ever, that the turning point, in terms of hydrogen ion concentration, is known for each of a large number of indicators, then with the help of such a " set " of indi- cators the degree of acidity or alkalinity of a liquid not far from the point of neutrality could be ascertained with 1 See Sorensen, Biochem. Zeit., 1909, 21, 131 ; 22, 352 ; 1910, 24, 881. ELECTROMOTIVE FORCE 321 fair accuracy. For the establishment of such a scale of indicators it is necessary to have invariable and repro- ducible standards of acidity and alkalinity, covering more especially the range from Oh=1 X 10~* to Coh = 1 X 10~^- For this purpose the solutions obtained by mixing sodium hydroxide and phosphoric acid in different proportions are of great importance,^ the exact degree of acidity or alkalinity of each such solution being determined and controlled electrometrically. In this way it has been found that for ^NaH^PO^ the value of Ch is 1-2 x 10"*, while for ^NaaHPO^ the value of Ch is 1-4 x 10-9. With a suitable " set " of indicators available, it be- comes possible to ascertain the degree of acidity or alkalinity of a liquid, and Sorensen {loc. cit.) has investi- gated a number of physiological fluids by this colori- metric method. The method, however, must be used with caution, inasmuch as some indicators behave abnormally in presence of proteins or neutral salts. It is, after all, on physico-chemical measurements that one depends for accurate and trustworthy determinations of the concentration of the hydrogen ion in physiological fluids. ' See Prideaux, Biochem. Joiim., 1911, 6, 122. SUBJECT INDEX Abnormal depression of freezing point, 115 Absolute temperature, 4 Absorption and adsorption, 221 Absorption coefficient, 21, 22 Absorption of gases, 20 by blood, 26 Acid-alkali cell, 316 Accommodation in living cells, 66, 67 Acids, Btrength of, 252 Additive properties of salt solutions, 139 Adsorption, 219 and proteins. 238 formula. 229 tlieory of dyeing, 236 Agglutination and adsorption, 240 of bacteria, 216 of blood corpuscles. 218 Air-bladder of flRhes. 26 Amphoteric electrolytes, 261 Antagonism between ions, 207 Aquatic plants, gas exchange in, 24 Artificial parthenogenesis, 165 Association in solution, 115 Bacteria, accommodation shown by, 64, 66 agglutination of. 216 Barley grains, covering of, 37 Bimolecular reactions, 283 Blood, alkalinity of, 319 conductivity of. 136 corpuscles.and isotonic solutions, 68 corpuscles, permeability of, 161 free7ing point of. 111 gases in, 26 osmotic strength of, 70, 72 serum, osmotic pressure of. 181 Boiling point and molecular weight, 95 and osmotic pressure. 93 of solutions. 03 Brownian movement, 197 Carbon dioxide, solubility of, 21 static diffusion of, 16 Catalysis. 285 mechanism of, 300 Catalysts, inorganic, 286 Catalytic action of enzymes, 291, 294 Cell membranes, nature of. 82 surface tension of, 856 Coagulation -of suspension colloids, 201. 208 Colloidal solutions and suspensions, 192 filtration of, 1S8 Colloids. 177 and ions. 203. 211 in an electric field, 188 in biology, 214 Colour of salt solutions, 142 Complete reactions, 244 Complex ions, 173 Concentration cells. 310 Concentration changes during elec- trolysis, 146 Conductivity and fluidity. 156 equivalent, 126 ionic, 150 measurement of, 123 . of physiological fluids, 136 of water, 170 specific. 125 Contractility of muscle, 1C2 Copper, toxic action of, 1 76 Crystalloids, 177 Daniell cell, 309 . Degree of dissociation. 118. 130 Density and molecular weight, 9 Dextrose solutions, osmotic pressure of. 48, 51 Dialysis, 178 Diffusion and osmotic pressure. 33 as factor in catalysis, 302 of colloids. 179 of electrolytes, 156 of gases, 13. 16 Diffusion of gas through liquid film, 22 through multiperforate diaphragm, 18 Dilute solutions, 44 Dilution law, 260 Dissociation constant, 251 degree of. 118. 130 hydrolytic, 260 in solution. 117 of water. 170. 259. 316 Distribution ratio, 222 Dyes, adsorption of. 235 EppusiON of gases, 15 Electric charge on protein, IDl SUBJECT INDEX 323 Eleotrolytlo conduction, 119 dusociation hypothesis, 117, 133 solution tension, 307 Electro-motive force, 807' Electia-negiitive colloids, 189 Electro-positlre colloids, 189 Emulsion colloids, 201, 210 Enzymes as catalysts, 291, 294 Edulllbilum, chemical, 247 constant, 247 Eauivalent conductlyity, 126 relative lowering of solubility, 30 E3:change of ions across a membrane, 160 FEHLiira's solution, 174 Eermentatlon of glucose, 299 Filtration of colloidal solutions, IDS Freezing point and molecular weight, 106 and osmotic pressure, 104 of blood. Ill Gas electrodes, 314 Gaseous diffusion, 13, 16 osmosis, 24, 78 Gas eauation, 10 Gases, absorption of, 20 Gases, kinetic theory of, 6 Gas laws, 1 Gastric juice, acidity of, 320 Gelatin filter. 199 Gelatin solutions, osmotic pressure of, 183 Germicidal effect of electrolytes, 163 Gold number, 214 Grades of colloidal solution, 196 Gram-molecule, 10 HaaiATOOBiT, 71 Hsemoglobin, osmotic activity of, 182 Heat coagulation of protein, 239 Henry's law, 20, 223 Hydration of dissolved substances, 28, 32, 53, 134 Of ions, 135, 155 Hydrogen electrode, 314 ion, 153, 165, 166, 280. 285 Hydrolysis of esters, 168. 279 Hydrolytio dissociation, 260. 318 Hydroxyl ion. 153. 166. 168. 285 Hypertonic solutions, 59, 73 Hypothesis, Avogadro's, 7; 114 of electrolytic dissociation, 117, 133 Hypotonic solutions, 69 Hysteresis In colloidal solution, 184. 186 IMMUHOOHZHISTBY. 270 Incomplete reactions. 244 Inorganic catalysts. 286 Intermediate compounds in catalysis, 301 Inversion of sucrose, 277, 294, 295 Ionic conductivity. 143. 150 dissociation. 117 mobility, 145 reactions, 141, 257 lonisation of water, 816 Ions, 117 Ions and colloids, 203 migration of, 144, 152 specific action of, 162 Isotonic coefficients, 60, 132 solutions, 56 Kinetic theory of gases, 6 Lakisq of blood corpuscles, 68 Law, Boyle's, 2 dilution, 250 Gay-Lussac's, 3 Henry's, 20. 223 of independent migration of the ions. 144 of mass action, 246 of volumes, 6 Laws of gases. 1 Leaf as diffusion apparatus, 16, 18 Lipoid theory. 82 Lowering of gas solubility. 26, 31 Lungs, gas exchange in, 25 Mass action, 246 in immunochemlstry, 270 Mechanism of catalysis, 300 Mercury salts, germicidal effect of, 1C4 Migration of ions. 144 Molecular depression of freezing point. 107 elevation of boiling point, 97 weight of colloids, 187 weight of dissolved substances, 45. 90. 95. 106 weight of gasei and vapours. 10 Molecules and atoms. 7. 8 Neutralisation as ionic reaction. 269 Neutral salt action. 257 Normal temperature and pressure, 9 Oftiuum temperature, 304 Osmometers tor colloids, 181, 183, 185 Osmosis, gaseous, 24. 78 Osmotic pressure. 33 and boiling point. 93 and concentration. 41, 47. 52 and freezing pohit. 104 and gas pressure. 44. 49 and temperature, 41, 48 and vapour pressure, 87 in plant cells, 62, 66 of blood, 70, 72, 181 of colloids, 180 of dextrose solutions, 48, 51 of sucrose solutions, 41. 49. 51. 53 Oxygen electrode, 316 solubility in water, 22 Pabthenoqenesis, artificial. 73, 166 Partition coefficient, 222 Permeability and surface tension. 65a of membranes, 63. 64, 67, 75, 159 Physiological fluids, conductivity of, 136 Physiological salt solution, 72 324 PHYSICAL CHEMISTRY Plants, gas exchange of, 16, 24 Plasmolys^, 58, 80 Potential diifferences in tissues. 158. 159 Precipitation of colloids. 201, 208, 210 Protective action of colloids, 213 Protein and electrolytes, 212 Protein as amphoteric electrolyte, 264 ^ degradation, 138 Proteins and adsorption. 238 Pure water, 170 Reactions between ions, 141, 257 reversible, 244 Beaction velocity, 276 temperature coefficient of. 302 Besistance and conductivity, 125 cell, 124 Salt solutions, 114 additive properties of, 139 colour of, 142 solubility of gases in, 26 Saponiflcation of esters, 169. 283 Semi-permeable membranes, 34. 37, 75 £ilver iodide, solubility of, 313 Size of colloidal particles, 194, 200 Solubility of gases, 20. 26 Solubility product. 267 Specific action of ions. 162 Specific conductivity. 125 Static di^u&ion, 16 Strength of acids. 252. 255 Sucrose, inversion of, 167, 277, 294 osmotic activity of, 41, 49, 51, b» Surface energy of colloids, 219 Surface tension and permeability, 85a tension in vital phenomena, 234 Suspension colloids, 201 Suspensions and colloidal solutions. 192 Temperature coefficient of reaction velocity, 302 Thermometer, Beckmann's, 101 Toxin-antitoxin reaction, 215, 270, 274 Transport number, 148, 149 Tyndall phenomenon, 192 Ultbamioroscope, 193 tTnimolecular reactions, 279 Urine, acidity of, 320 freezing point of, 112 Vapour pressure of solutions, 86, 87, 90 Velocity of ionic migration, 152 of reaction. 276 Volume-normal solutions, 48 Water, conductivity of, 170 dissociation of, 170. 259, 316 Weight-normal solutions, 43 AUTHOR INDEX Abeoo, 303 Ernst. 287. 305 Amagat, 2 Bscombe. 16 Appleyard, 281, 235 Exner. 28 Armstrong, 281, 292. 295. 297. 298. 299 Arrhenius, 116, 212, 255, 257. 270. 271. Faraday. 115 271. 281 Flndlay. 16 Avogadro, 7, 13 Fischer. A.. 61 Fischer, E., 299 Babqek, 92 Flusin, 77 Bassett, 175 Frazer, 16 Bayliss. 138, 187, 237, 29) .301 Freundllch, 202, 206, 227, 230. 236 Eechhold. 213, 216, 217 Fiihner, 856 JBeckmann, 98, 101, 108 Berkeley, Lord, 50, 90 Gat-Ldssao. 3, 5 Bemeck. 290. 293, 303 Geffcken, 29 Billitzer, 219 Getman, 32 Biltz, 95, 187, 208, 209, 216, 231 Glendinnlng. 295 Blackinan, 16 Goebel. 26 BodlSnder, 202 Graham. 15, 177 Bogdan. Ill Guye, 111 Bohi. 25, 26 Bouchard, 112 Haububoeb, 69, 160, 161 Bousfield, 135 Harden, 299 Boyle, 2 Hardy, 191, 202, 201, 205. 212. 219, 264 Bredig. 190, 219. 287, 290 293. 303 Hartley. E.. 50, 90 Brode. 286, 290, 301 Hartley. H.. 171 Brown, A. J.. 37. 291 Hasselbalch. 319 Brown. C. 78 Hedln. 71 Brown. H. T., 16, 295 Henri. 191, 291 Brown, E., 197 Henry. 20. 12. 223 Brunner, 302 Herzog. 305 Eruyn. Lobry de, 195 HiU. C. 292 Bugarazky, 265, 318 Hill. T. G.. 66 Bunsen, 15 Hittorf, 148. 173 Burton. 190. 191. 191 Hober. 164. 218, 319 Hoff. van't. 42. 11. 132 Caidweix, 257, 281, 283. 297 •Callendar. 32. 53 JAKOwmif, 222 Craw. 199. 212. 272. 278 Jones. 32 Czapek, 83, 85a Kahienberq. 111. 176 Bakin. 113 Eastle. 292 Danneel, 167 Koelichen. 170 Danysz, 215, 278 EoUrausch. 113. Ill, 151, 172 DaTis, 233 Koppe, 160 Dempwolfl. 167 Kronig, 163, 175 Deyaux, 24 TJonnan. 159. 175. 187 Lahdsbbrger, 102 Drabble. 65 Iiarmor, 44 Duclaux. 181 Lesaing. ISS Iilebermasn, 29b, 318 JEISEHBEBO. 216. 211 Llllle. 185 ^mmerling. 292 Limbeck. 160 326 PHYSICAL CHEMISTRY Linder, 188, 193, 196, 206 Iioeb, 73, 166, 207 Loevenhart, 292 Lowenherz, 316 Losev, 236 Lowry, 135 Lucas, 306 liUmsden, 102 Lund&, 263 Macaixhm, 23i McBain. 233 Madsen, 271 Maltby. 143 Martin, 199 Masson, 174 Matthaei, 305 Mayenburg. 67 Mayer, 207 Meyer, 11 Michaelis, 209. 219, 237, 270. 319 Mollsch, 23 Moore, 84, 182, 280 Morley, 5 Morae. 46 Mylius, 209 Nebnst, 153, 224, 273. 802. 311, 317 Neubauer, 85I> Noyes, 268, 269 Obeb. 206 Osterhout, 68, 83, 207 Ostwald, W., 142, 167. 198, 260, 262 Ostwald, Wo.. 220 O'SuIlivan. 291. 301 Overton, 79, 85, 162, 165 Piil, 213 Pantanelll, 65 Paul, 163, 175, 264 Pauli. 210, 211, 212, 239, 264 Perrin, 198 Pfefler, 88 Philip, 82, 269 Picton, 188, 193, 196, 206 Planck, 311, 317 Prideaux, 321 Bahsay. 78, 198 Bamsden, 234 Eaoult, 76, 110 Bayleigh, 2 Begnault, 10 Eeicher, 132 Beid, 180, 182 Bitzel, 31 Boaf. 84, 182 Bobertson; 83, 211, 319 Bona, 209, 319 Bothmund, 32 Rubland, 83 SOKUIFFEB, 207 Schryver, 139, 264 Scott, 6 Senter, 164, 257. 291, 304 giedentopf, 193 Sorensen, 320 Starling, 181. 301 Steinbrinck. 23 Syedberg. 198 Tahmahh. 36. 66. 76. 297, 301 Terroine. 207 Tijmstra. 167 Tompson, 291, 301 Traube. 75, 866- Traverg. 226 True. 176 Turbaba. 289 Turner, 103 Tyndall, 192 Vegesack, 187 Veley. 306 Volk, 216, 241 Voss, 213 Vrles, de, 68. 60. 61. 62 WALKER. 89. 102. 231. 235 Waller, 305 Weimam. 201 ■Whitney, 206 Wiesner, 23 youKa, 299 ZSIGMONDT, 93, 197. 214 Printed by Ballanttne, IIanson &' Co. 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