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Cornell University Library arV19217 Physical chemistry for physicians and bi 3 1924 031 262 094 olin.anx Cornell University Library The original of tliis book is in tlie Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031262094 PHYSICAL CHEMISTRY FOE PHYSICIANS AND BIOLOGISTS BY DR. ERNST gOHEN Professor of Oenerdi cmd Inorganw Chemistry in tl^e Xfnimerxity of Utrecht AUTHORIZED TRANSLATION FROM THE GERMAN BY MARTIN H. EISCHER, M.D. Instructor in P7i/ysiology in the University of California NEW YORK HENRY HOLT AND COMPANY 1903 3i Copyright, 1903, BY HENKY HOLT & CO. BOBBBT DRUMHOND, PRINTER, KBW YORK To PROF. DR. HECTOR TREUB. NOTE TO THE AMERICAN TEANSLATION. The development of physiology and biology has, during the last years, been so decidedly under the influence of physical chemistry, that those who wish to follow the progress of the former science must be famiUar with the principles of the latter. Prof. Cohen's book not only serves as an introduction to physical chemistry, but also teaches the physician and the biologist how to apply this science to medical and biological problems. This combi- nation gives it a unique place in the literature of physi- cal chemistry, and for this reason, as weU as for the masterly treatment of the subject, I encouraged Dr. Fischer to undertake, with the consent of Prof. Cohen, an English translation of his book. Jacques Loeb. Univbhsity of Caupoknia. TEANSLATOE'S PEEFAOE. That accuracy of expression which is so obvious a char- acteristic of Prof. Cohen's book the translator has en- deavoured to preserve, perhaps at the partial sacrifice sometimes of English idiom. The translation has had the benefit of a revision by Prof. Cohen, who has made numerous corrections and additions. I also acknowledge with much pleasure my in- debtedness to Dr. Herbert N. McCoy of the University of Chicago,- whose careful criticisms and suggestions have much improved the quality of the translation. Mabtin H. Fischer. Berkeley, Caiifohnia, November 29, 1902. AUTHOE'S PEEFAOE. I HAVE prepared the following pages in response to the request of a number of physicians to give in a series of lectures a rfeum^ of those subjects in physical or gen- eral chemistry which are of importance in medicine. The fact that a large number of observations are de- scribed in modem medical literature that are based upon our newer conceptions of physical chemistry renders it imperative that the physician become acquainted with these theories and methods if he does not wish to have such observations and their practical applications remain a sealed book to him. These lectures are in no way a text-book of physical chemistry. I have merely endeavoured to show in them the close relation that exists between this new branch of ■ chemistry and the biological sciences, and also, in response to the wishes of my hearers, to describe in some detail the more important methods of physical chemistry. The book may perhaps serve as an introduction to the study of the excellent text-books now available devoted to physical chemistry. Should the lectures contained in the following pages incite any one to a study of this subject and to its applica- tion to the medical sciences, the purpose of this volume will have been accomplished. viu AUTHOR'S PREFACE In conclusion I wish to express my thanks to my friend Professor Georg Bredig, who very kindly assisted me in correcting the proofs, and to Dr. J. M. Baart de la Faille for many helpful suggestions. Eknst Cohen. Amsterdam, August 1901. mTEODUCTION. I CONSIDER it a happy sign of the times that such a group of medical men as you have evinced the desire to study more closely the acquisitions of general or physical chemistry within the last fifteen years. That the views and methods to which this young branch of our scientific knowledge has led can be of the greatest value to. the physician is evidenced in a most striking way by the fact that these find daily a more far-reaching appli- cation to the problems of physiology, pharmacodjmamics, and biology. May my lectures assist in convincing you of the great value that the study of this beautiful science has for the physician! So far as the subject-matter that is here to be discussed is concerned, I believe that, in view of the limited number of lectures, any definite system may be relegated to the background. The chapters about to be discussed will deal as far as possible with those problems which are of greatest interest to the medical man who devotes himself to experi- mental research; while at the same time his attention will be directed to the results that have already been obtained in this direction. 1 FIRST LECTURE. Reaction Velocity. We take as our starting-point the law of chemical mass action (Guldberg and Waage, 1867), which states that in chemical reactions the chemical action is proportional to the active mass of the reacting substances; the active mass of a substance is the amount of the same in the unit of volume {concentration). If a number of substances capable of reacting chemically with each other are brought together, a reaction ensues which after a certain time comes (practically) to a standstill; we say then that the system is in equilibrium. Both the course of the reaction and the equilibrium which is estab- lished at the end of the reaction are governed by the law of Guldberg and Waage. If we consider the simplest case, one in which only one molecule of a substance undergoes decomposition, we deal with a A. MONOMOLECULAR REACTION If, for example, hydrogen arsenide is heated in a glass tube, the gas is split into arsenic and hydrogen, according to the equation AsH3 = As+3H. 8 4 PHYSICAL CHEMISTRY. We call this decomposition a monomolecular one, since the reaction occurs in the simple molecule AsH,. Since, however, the arseniuretted hydrogen disappears during the reaction (being decomposed into its constituents by heating) according to the law of Guldberg and Waage, the velocity of decomposition cannot remain constant; the decomposition velocity must progressively decrease, since the active mass of hydrogen arsenide progressively de- creases. If we imagine that during each minute a tenth of the arseniuretted hydrogen present at the time is de- composed, we get after 1, 2, 3, etc., minutes the following degrees of decomposition: npTjQg Amount of Substance Amount Decomposed Present. (per Minute). 0-1 1.000 0.1 X 1.000 = 0.100 1-2 (1.000-0.100) =0.900 0.1 X 0.900 = 0.0900 2-3 (0.900 - 0.0900) = 0.810 0.1X0.81 =0.0810 3-4 (0.810 - 0.081) = 0.729 0.1 X 0.729 =0.0729 4-5 (0.729 -0.0729) = 0.656 0.1 X 0.656 =0.0656 etc. etc. etc. At the beginning of the reaction the amount 1.000 was present. According to our assumption, one tenth of this (0.1) is decomposed per minute, so that at the end of the first minute the amount of undecomposed substance still present is 1.000-0.1x1.000=0.900. Of this amount a tenth part is decomposed in the second minute, that is to say, 0.1X0.900 = 0.0900; at the end of the second minute the amount of substance still imdecomposed is therefore 0.900 - 0.0900 = 0.810 ; and so on. If C is the concentration of the hydrogen arsenide at the time t [C is measured in gram-molecules * per litre, that is to say, we call * Instead of the word gram^mokcule, at Ostwald's suggestion the shorter term mol is often used. , REACTION VELOCITY. 5 the concentration of the arseniuretted hydrogen 1 when each litre contains 1 mol ( = 78 g. hydrogen arsenide, since As = 75, Hg^S)] and dC is the slight change that the con- centration of the solution suffers in a very short time dt, then we can express the law, the reaction velocity is pro- portional to the concentration, as follows: dC . . ■ -J- is the reaction velocity, that is, the relation between the quantity decomposed and the time required for this dC decomposition; -5- has a minus sign before it because the concentration of the arseniuretted hydrogen decreases as the time increases, that is, as the value of t becomes greater. The significance of the factor k is found immediately when we substitute in the above "differential equation" C=l ; fc is the reaction velocity when the substance undergoing decomposition has the unit of concentration.- k is called the velocity constant or the reaction constant. The above equation therefore shows us in what way the very slight (infinitely sUght) change in the concentration (dC) in a very short (infinitely short) period of time (di) is connected with the concentration (C) of the substance undergoing decomposition. But it is impossible to perform an experiment that will last only an infinitely short time. Every experiment occupies a definite time, and with nothing further the above equation would, for practical purposes, be useless. But integral calculus teaches us how the infinitely small changes in concentration (dC) in the infinitely]small periods 6 PHYSICAL CHEMISTRY. .^ of time {dt) may be summed up, and how from this the (finite) change in concentration in a certain limited time may be calculated. Through " integration ' ' the equation is rendered appli- cable to the experimental data. This mathematical procedure, "integration," yields the result that between the concentration C and the time t, when the system has this concentration, the following relation always exists: — l-C — kt + constant. (2) In this equation hC represents the natural logarithm of the concentration. If the measured concentration of the substance undergoing decomposition is at the time <46'"*''- The values of the third column, k, are therefore calculated as follows: 7.29 ^ 1 5.82 ,, 1 1 10 ^-40 10 ^^40 * - r^ 7^ 1 _5^ 1 - ^-^^ 10 40 10 40 7.29 1 4.90 ^ 1 1 10 '40 10 ^^40 „™ ^ 10 ^ 40 ^ 10 ^ 40 As the table shows, the mean value of k, as calciilated by this method, is 6.86. What is the significance of this figure, 6.86, from a chem- ical standpoint ? It shows that if ^ normal ethyl acetate is saponified by -J^ nonnal NaOH at 25°, 6.86 mols of the ester are saponified per minute if 1 mol of the ester and 1 mol of the caustic soda are present per litre, and care is taken that the products of the reaction are constantly re- moved, and the decomposed ester and base are as con- stantly renewed. REACTION VELOCITY. 19 The velocity with which different strong bases, as NaOH, KOH, Ca(0H)2, BaCOH)^, SrCOH)^, bring about saponifi- cation is, at the same temperature, the same for all. The explanation of this fact will be given later when the theory of electrolytic dissociation is discussed. It will there be seen that it is the so-called OH (hydroxyl) ion, one of the dissociation products in dilute aqueous solution of the bases under consideration, that brings about the saponifi- cation. From these facts it follows that the determination of the velocity of saponification is a general method for deter- mining whether or not certain substances in solution break up into OH ions. In this way, for example, Wys * has calculated the degree to which water dissociates into its ions, H and OH, and Shields f has investigated the dis- sociation of salts into free bases and acids, — the so-called hydrolysis of salts. To these phenomena we shall retxim later. * Zeitschr. f. physik. Chem. 12, 514 (1893). t Ibid. II, 492 (1893) and 12, 167 (1893). SECOND LECTURE. The Inversion of Cane-sugar and Catalysis in General. Op great interest in the study of chemical djoiamics and also in the discussion of many physiological problems is the change that cane-sugar suffers under the influence of dilute acids. This problem was exhaustively studied in its djmamical relations as early as 1850 by L. Wilhelmy.* If an aqueous solution of sugar is mixed with a dilute acid, a reaction occurs which may be represented by the following equation: C12H22O11+ HjO = CeH,jOg+ C,HyOg. Cane-sugar Water /'<2-glucose\ /' upon p. 29: fti = 0.541. * This cooling does not in reality bring the reaction to a com- plete standstill, but, in consequence of the great lowering of the temperature, the velocity of the inversion is so markedly reduced that in the few minutes necessary to determine the polarisation it cannot noticeably advance. INVERSION OF CANE-SUGAR AND CATALYSIS. 31 For solution No. 2 was found A = 4.422; x^ = 1.135; from which, according to equation (2) upon p. 29, fcjis calculated: k^ = 0.158. Wherefore =^B = -^0.05 = 0.0146. fci 0.541 s -0 ==s - ^B= 0.025 - 0.0146 = 0.0104. '■ = -^ X 0-0104 = 4.16; 0.25 that is to say, in the experiment here described the albumose united with 4.16 per cent of its own weight of hydrochloric acid. In a similar manner it was fomid that at 40° protalbu- mose . unites upon the average, with 4.32 per cent of its weight of hydrochloric acid; deutero-albumose unites at this temperature with 5.48 per cent, while antipeptone unites with 15.87 per cent of its weight.* Bugarszky and Liebermann f have worked upon the same problem, employing, however, an entirely different method, to which we shall return later. These authors express themselves in the following way concerning the experiments of Cohnheim: "The results obtained by Cohnheim with the aid of „the sugar-inversion method employed by him, which show that in an aqueous hydrochloric acid solution the velocity of the inversion is diminished through the presence of albumins, permit indeed of the interpretation * Through the determination of the velocity of saponification of an ester by sodium hydroxide in the presence of various albumins one could determine in an analogous manner how much sodium hydroxide unites with these substances; this is a problem that has been solved by different means by Bugarszky and Liebermann. t Pflilgers Arch. f. d. ges. Physiologie 72, 51 (1898). 32 PHYSICAL CHEMISTRY. that hydrochloric acid unites with albumins, but may, in part at least, have their origin in the fact that, through the presence of the albuminous substances in the solution, a mechanical hindrance is established which interferes with the free movement of the molecules and consequently diminishes the reaction velocity." With this remark, which, as will become evident later, has been proved to be not entirely correct (Bugarszky and Liebermann, though through different channels, yet came to the same conclusions as Cohnheim), we enter into a dis- cussion of the DISTURBANCES IN CHEMICAL REACTIONS. In connection with the remark just cited we ask our- selves first of aU: Do chemical reactions proceed in a gelati- nous medium with the same velocity as in pure water, or does such a medium act as a mechanical hindrance? This question has been thus decided by Reformatsky: * The catalysis of methyl acetate, for example, which under the influence of dilute acids takes place according to the follow ing equation: CH3C00CH,+ H30= CHgCOOH-F CH3OH, (methyl acetate) (acetic acid) (methyl alcohol) proceeds with the same velocity in soUd agar-agar jelly as in pure water. As will become evident later, this result is in fuU accord with the fact that the diffusion of dissolved substances in agar-agar occurs with the same velocity as in aqueous solu- tion, under otherwise similar external conditions. It was therefore to be expected, a priori, that in Cohn- * Zeitschr. f. physik. Qiem. 7, 34 (1891); comp. also Levi, De nuovo Cimento (4) 12, 293 (1900). INVERSION OF CANE-SUGAR AND CATALYSIS. 33 heim's experiments there could be no discussion of a lower- ing of the reaction velocity in consequence of a " mechani- cal hindrance." The results to which Reformatsky's investigations have led are of importance for physiology. Many physiological processes go on in a medium which is not of a purely aqueous nature, but which contains albumin or albuminous sub- stances. Evidently these will have no influence upon the progress of the reaction so long as they do not act chemi- cally upon the reacting substances. The disturbances which make themselves felt in a re- action may come from widely differing sources. So, for example, it has developed that in gas reactions (as, for example, in the decomposition of arseniuretted hydrogen, comp. p. 3) the condition (rough, smooth) of the vessel wall exerts a great influence upon the reaction velocity.* We find ourselve here in a territory which stands in need of more thorough investigation. The medium in which a reaction that takes place in solu- tion occurs also exerts an important influence upon its velocity. Thus Menschutkin f has proved that the ve- locity with which the reaction N(C,H,)3 + C^H,! = N(C3H,),I (triethylamine) (ethyl iodide) (tetraethyl ammonium iodide) takes place at 100° in the following indifferent media is a * van't Hoff-Cohen, Studien zur chemischen Dynamik, Leipzig 1896, p. 33 et seq., where references to the literature may be found; E. Cohen, Zeitschr. f. physik. Chem. 20, 303 (1896); Bodenstein, ibid. 29, 433 (1899); V. Henri, Journal de physiologie et de patho- logic ginerale, Nov. 1900, p. 933. t Zeitschr. f. physik. Chem. 6, 41 (1890). 34 PHYSICAL CHEMISTRY. very different one. (The velocity in Hexane is taken as 1 in the table.) Name of Medium. Velocity. Hexane 1 Benzol 38.2 Brombenzol 150 Acetone 337.7 Benzyl alcohol 742 The reasons which have thus far been given to explain these differences are not without objection. In gas reactions the medium seems to exert nO influence (Cohen). If, for example, arseniuretted hydrogen is de- composed in the presence of either carbon dioxide or hy- drogen, the decomposition proceeds with the same velocity in both instances.* * Zeitschr. f. physik. Chem. 23, 483 (1898). THIRD LECTURE. The Action of Ferments. As is doubtless known to you, ferments are divisible into two groups, the organised ferments, which are active only during their growth and reproduction, and the unorganised or soluble ferments, — at Kiihne's suggestion called enzymes, — which may be extracted from the cells in which they have been formed, and which are able to manifest their characteristic effects outside of the cells also. The catalytic action of ferments has only within the last few years been thoroughly studied from the standpoint of dynamical chemistry. For our present knowledge con- cerning this subject we are especially indebted to the observations of Tammatm,* O'SuUivan and Tompson,t Croft Hill, J Duclaux and V. Henri. § Duclaux in his TraitB de Microbiologie (1899) gives a review of the mate- rial at hand. The inversion of cane-sugar is catalysed (accelerated) not only by weak acids, but also by the enzyme invertin * Zeitechr. f. physik. Chem. 3, 25 (1889); 18, 426. (1895). Zeit- sohr. f. physiol. Chem. 16, 269 (1892). t Jovim. of the Chemical Society 57, 834 (1890) t Ibid. 73, 634 (1898). See also Emmerling, Berichte der deut- schen chemlschen Gesellschaft 34, 600 (1901). C. Oppenheimer, Die Fermente und ihre Wirkungen, Leipzig 1901. Reynolds Green, The Soluble Ferments and Fermentation, Cambridge 1899. § Zeitsehr. fUr physik. Chem. 39, 194 (1902). Journal de physi- ologic et de pathologic generale 3, 875 (1901). 35 36 PHYSICAL CHEMISTRY. {sucrose). From the experiments of O'Sullivan and Tompson, one might think that the laws which govern the inversion of cane-sugar imder the influence of this enzyme are abnost the same as those that govern the in- version in the presence of dilute acids. The course of the reaction could then be represented by the equation t A—x But it will be shown that this equation does not hold imder all conditions. On the contrary, the catalysis under the influence of invertin is governed by entirely different and more complicated laws than those that govern the catalysis under the influence of dilute acids. Only when a large amount of ferment is present and the temperature is not very high is the course of the catalysis in the pres- ence of the ferment for a short time similar to the course of the catalysis in the presence of dilute acids. It has been shown that the results obtained by O'Sullivan and Tompson are attributable to the way in which they accidentally arranged their experiments. But what, now, is the cause of the difference in the in- version process under the influence of the invertin and that of dilute acids? It probably Ues in the fact that the ferment undergoes decomposition rather easily. Not only in solution, but in the dry condition also, the ferment suffers (until then unknown) changes which decrease its activity. Besides this it has been proved that the products formed by the ferment in the catalysed reaction exert an im- portant influence upon the course of the reaction. In THE ACTION OF FERMENTS. 37 passing it may be pointed out that it has not yet been proved whether the reaction products exert an inhibiting influence primarily, or if a secondary effect is to be attrib- uted to them in that they reduce the activity of the cata- lyser, — the ferment; An interesting biological field for investigation is therefore open here for the physical chemist. We shall now direct our attention to a subject that has been closely studied in several directions* As may be known to you, the glucosides, such as amygdaUn, sahcin, heUcin, phloridzin, and arbutin, are hydrolysed by emulsin (synaptase), that is to say, they break up into simpler products upon taking up water. In the case of salicin the reaction occurs according to the following equation: C.3Hi,0,+ H,0 = C,H,0,+ C,H, A- (salicin) (saligenin) (glucose) While in the inversion of cane-sugar the catalytic agent (the acid) remains unchanged, Tammann has shown that the catalyser — ^the emulsin — in this case suffers decompo- sition; this decomposition, into at present entirely un- known decomposition products, proceeds, as experiment has shown, as a monomolecular reaction. The active mass (see p. 3) of the emulsin consequently decreases during the hydrolysis of the salicin, and the reaction velocity of the hydrolytic process in consequence also decreases. Now, in general, if the amount of ferment added is large and the temperature is low, it may happen that the decom- position velocity of the ferment is so slight when com- pared with the velocity with which the sahcin is decom- posed, that the change in the active mass of the ferment may apparently have no influence upon the velocity of the * Tammann, Zeitschr. f. physik. Chem. i8, 426 (1895). 38 PHYSICAL CHEMISTRY. decomposition of the salicin. This was the case in the experiments of O'Sullivan and Tompson, in which the invertin suffered only a slight decomposition. Because of this accidental condition of affairs it seemed as though the reaction which they studied progressed as a monomolecu- lar one. If, further, we remember that the reaction products (d-glucose and d-fructose) have no influence upon the velocity of the inversion of cane-sugar by dilute acids, while they often have a marked effect upon the velocity of inversion when this is accelerated by ferments, it be- comes intelligible why the process of taking up water under the influence of ferments runs a totally different course from that under the influence of dilute acids. How great the inhibiting effect of the reaction products may be is shown by the following experiment: After a cer- tain amount of sahcin had been hydrolysed at 26° by emul- sin, the reaction came to a standstill when 83 per cent of the salicin had been decomposed. However, after one of the reaction products, the saligenin, was removed by shak- ing out with ether, the reaction recommenced, and after twenty-four hours the entire amoimt of salicin originally present was decomposed. The inhibiting influence of the reaction products can also be shown in a somewhat similar way by making two experiments, in the first of which, ceteris paribus, the ferment is mixed with the substance to be decomposed, while in the second a certain amoimt of the reaction products is previously added; it is then seen that in the latter the reaction from the start progresses more slowly than in the first-described instance. In consequence of the inhibiting influence of the reaction products, fermen- THE ACTION OF FERMENTS. 39 tations show a limit; the reaction does not progress en- tirely to an end, but comes to a standstill even though a certain amount of substance which could be decomposed by the ferment is still present. The point at which this limit is reached is dependent upon the amount of ferment added originally, and upon the temperature. That a limit must be reached in the action of ferments which suffer a decomposition in the course of the reaction which they catalyse — that, in other words, even when a large amount of the ferment is present and its action is allowed to go on indefinitely, a certain amount of the substance undergoing decomposition under the influence of the ferment must remain unaltered — may be shown in the following way (Tammann). If A is the amount of ferment originally present, B the amount of substance the decomposition of which is catalysed by the fer- ment, X the amount of the ferment which at the time t becomes in- active, and y the amount of substance which at this time has been decomposed, then, since the reaction velocity at the time t is pro- portional both to the concentration of the substance undergoing decomposition and to the concentration of the ferment (Guldberg and Waage, see p. 3), ^ = k(A- x){B - y) £oIge, 6o, 468 (1897). See also Piotet, Compt. rend, ixs, 814 (iSSS^ TEMPERATURE AND REACTION VELOCITY. 55 reactions. What influence, now, has temperature upon such catalytic activities? A great difference exists between the influence of tem- perature upon purely chemical reactions and those in which ferments play a r61e. While the formula l'k= constant — -=• shows that with a rise in temperature, that is with an in- crease in the value of T, the value oil-k and consequently of k becomes progressively greater,* this is not the case in reactions in which ferments take part. Here also we find a region in which the reaction velocity is increased by an increase in the temperature, yet this increase is not with- out limit. A temperature is finally reached at which the reaction velocity attains a maximum, after which a further increase in temperature diminishes the velocity. If the temperature is raised still higher, the velocity finally falls to zero, that is to say, the reaction comes to a standstilLf This behaviour is represented graphically in Fig. 9, in which the abscissas indicate the temperatures, the ordi- nates the reaction velocities, of the action of indigo enzyme obtained from Indigo f era leptostachya (curve 1), from Polygonium tinctorium (curve 2), from Phajus grandiflorus (curve 3), from Saccharomyces sphcericus (curve 4), and * Conversely, by lowering the temperature, k becomes steadily less. If r = 0, that is at absolute zero (= - 273°), then l-k = — 00 , and the reaction velocity k = 0. t The temperature at which the reaction velocity reaches its maximum is generally called by biologists the optimum temperature of the given reaction, while by the maximum temperature is imder- stood the temperature at which the reaction no longer takes place. 56 PHYSICAL CHEMISTRY. emvlsin (curve 5) from sweet almonds, upon indican, which is thereby broken up into indoxyl and glucose (Beyerinck *). In general, it is found that the curves of all ferments have a similar form. 61°C / \ / s^ \ A y \ \ / r/ \ \ I / y / ^ \ \ \ ^ 5_ ^ ^ \ \ Fig. 9. The temperature for the maximvun velocity of any given ferment is not always the same, but is dependent upon the properties of the medium in which the ferment acts. Why is a maximal velocity reached ? The answer to this question is found in the decomposition which the ferment suffers upon an increase in the temperature. We have already discussed this in the case of emulsin (see p. 37). * Verslagen der Kon. Akad. van Wetenschappen te Amsterdam, 8, 572 (1900). TEMPERATURE AND REACTION VELOCITY. 57 If, for example, a watery solution of salicin and emulsin were heated together^ and the ferment remained constant in its action, the reaction velocity would progressively in- crease with an increase in temperature, just as in the case of the inversion of cane-sugar by dilute acids. The fer- ment, however, suffers decomposition at the same time, and the rapidity of this decomposition increases in a similar way with an increase in temperature. The product of these simultaneously occurring reactions will be repre- sented by a curve which attains a maximum at one point. This experiment shows to be indeed the case. Now, since the two reactions, the joint effects of which yield this curve, have their individual characteristics, which in part depend upon the properties of the medium in which the reaction occurs, it can readily be seen that the maximal velocity may not always be reached at the same temperature even for one and the same ferment. UtiUsable data on the influence of temperature upon fermentation are very scanty.* According to Tammann's f observations the velocity with which emulsin undergoes decomposition above 60° when in aqueous solution may be fairly well represented by the formula of van't Hoff-Arrhe- nius. If, from this equation, the decomposition velocity at 75° is calculated from the velocities observed at 60° (A;=0.80) and 70° (A; = 5.9), it is found that fc = 14.7. Actual experiment yields 15.3 for the value of k at 75°. These figures also show what an enormous influence a rise in temperature has upon this decomposition, for the velocity of the decomposition rises above sevenfold by an increase in temperature of 10°. * Duclaux, Traite de Microbiologie T. H, 174 (1899). t Zeitsohr. f. physik. Chem. i8, 426 (1895). 58 PHYSICAL CHEMISTRY. A continuation and amplification of the experiments of Tammann are greatly to be desired, in order to discover the principles that underlie the action of various ferments. The fermentative action of platinimi in the decomposition of hydrogen peroxide is governed, at not too high tempera- tures, by the same laws that govern simple chemical reac- tions. The influence of temperature may be represented by the van't Hoff-Arrhenius formula. This fact becomes intelUgible when we remember that the progressive decrease in the activity of the colloidal pla- tinum through heat when compared with the great rapidity of the decomposition of the ILfi^ i^ s" slight that the active mass of the platinum may be regarded as constant during the reaction. If the colloidal platinum were as sensitive to an increase in temperature as the ferments, a maximal velocity would be found in the catalysis of hydrogen per- oxide in the presence of this inorganic ferment also. Such a maximum has indeed been proved to exist by C. Ernst * in the case of the decomposition of oxy-hydrogen gas in water in the presence of colloidal platinum. Indeed the investigations of Brcdig and Miiller von Ber- neck have already rendered it probable that if the col- loidal platinum and the hydrogen peroxide solution were togelJier heated more strongly, a temperature at which the reaction velocity shows a maximum would be found here also. Since numerous chemical changes take place in the ani- mal and vegetable body, the question arises: What in- fluence has temperatuure upon these chemical changes and upon the phenomena of development which are closely associated therewith? * Zeitschr. f. physik. Chemie 37, 448 (1901). TEMPERATURE AND REACTION VELOCITY. 59 The changes going on here are naturally of a much more complicated order than those that occur in mtro, and the discovery of the laws that govern them is consequently accompanied by considerable experimental difficulties. Let us consider, first of all, the investigations that aim to illustrate the influence of temperature upon the rapidity of the development of plants.* In the experiments upon plants, in which an increase in the length of certain parts of the plant in the unit of time was chosen as a measure of development, it soon became evident that the rapidity of development when graphically represented as a function of the temperature furnishes a curve which is analogous to that with which we have be- come acquainted in the action of ferments. The rapidity of development at first increases with an increase in temper- ature, passes through a maximum, and falls finally to zero. Here also the temperature of maximal velocity varies, being different for each plant species. There is often given in botanical literature a low tem- perature hmit at which the growth of plants is supposed to cease suddenly. But it is always pointed out in these investigations that death occurs only at a temperature a few degrees below this. From what we know in general of the course of reactions at low temperatures, there seems to me to be no reason for assuming the existence of a temperature limit at which growth ceases suddenly. Much more probably we are dealing with a very slow rate of growth T^hich can be meas- ured only by observations extended over long periods of time. * For references to the literature, see among others A. B. Frank, Die Krankheiten der Pflanzen (Breslau 1895, Trewendt) p. 216. 60 PHYSICAL CHEMISTRY. The quantitative determinations on the influence of tem- perature upon the development of plants as found in the literature are, in general, not sharply defined; the tem- peratures at which the observations have been made show considerable variations. Now, since only a fleeting glance sufiices to show that changes in temperature exert here also a great influence upon the velocity of development, particularly within those temperature limits which are most Uke the conditions under which these plants exist in nature, it will be readily appreciated that the data ob- tained in this way are full of great errors and are not fit for further consideration. Yet in a few cases almost as great an influence of tem- perature as in simple chemical reactions may be proven to exist. Careful experiments have been made by Clausen * to determine the influence of temperature upon the excretion of carbon dioxide by bean-germs, wheat-germs and syringa- buds; variations in temperature did not exceed 0.2° in these experiments. The results of Clausen's experiments are given in the table on the opposite page. The figures in the second, third, and fourth coliunns give the amounts in milligrams of carbon dioxide exhaled by the given plants (100 g.) per hour. We see that even at 0° a not inconsiderable amount of carbon dioxide is given off by all of the plants experimented upon. Indeed respiration must occur even below 0°, " and it can scarcely be doubted that it does not cease until the plant freezes." The table shows that here also the velocity attains a * Landwirtschaftliche Jahrbilcher 19, 893 (1890), where refer- ences to the literature may be found. TEMPERATURE AND REACTION VELOCITY. 61 maximum, after which with a fiirther increase in tempera- ture it again falls. Temperature. Wheat-germs. Bean-germs. Syringa-buds. 0° 7.27 10.14 11.60 6 13.86 18.78 19.93 10 18.11 28.95 30.00 15 34.37 45.10 48.45 20 43.55 61.80 78.85 25 58.76 86.92 93.30 30 85.00 100.76 108.00 35 100.00 108.12 146.76 40 115.90 109.90 176.10 45 104.45 95.76 164.10 50 46.20 63.90 152.80 65 17.70 10.65 44.00 If we consider the increase in the velocity between 0° and 25°, we- find that the amount of carbon dioxide expired increases in all eases about 2.5-fold, with an increase in temperature of 10°. This increase is therefore as great as that in simple chemical reactions (see p. 51). According to Oscar Hertwig,* frog's eggs are much better adapted to experiments on the influence of temperature upon the rate of development of hving organisms than plants or germinating seeds such as are often employed by plant physiologists in such investigations. Hertwig has made an extensive study of the influence of temperature upon the rapidity of the development of the eggs of Rana fusca and Rana esculenta. Even though the temperature was not kept absolutely constant in these experiments, the variations were not very great, so that the data obtained by Hertwig permit of closer quantitative consideration. * Arch, f . ■ mikroskop. Anat. u. Entwickelungsgesch. 51, 319 (1898). 62 PHYSICAL CHEMISTRY. In Fig. 10 is represented graphically the rate of develop- ment of frog's eggs as a function of the temperature. IS ^^ I * — «" /♦• /fl' «• iO' XZ' ih' Fig. 10. Hertwig measured the periods of time in which a given developmental stage was reached at various temperatures. These time intervals are inversely proportional to the rate of development. Upon the ordinates of our curves are given the time intervals (days); upon the abscissas, the temperatures. The observations include the temperatures from 6° to 24°. The curve in Fig. 10 is based upon the following table; Stage I in Development was reached: Velocity of Development. At 6° in 4.75 days 1 " 10 " 3.16 " 1.2 " 15 " 2 " 2.4 " 20 " 1.2 " 3.9 " 24 " 1 " 4.75 If we consider the velocity at 6° as equal to 1, then at 10° it equals |^X 1 = 1.2; at 15° it equals ^X 1=2.4, TEMPERATURE AND REACTION VELOCITY. 63 etc. The figures of the third column were obtained in this way. Stage II in Development was reached; Velocity of Development. At 6° in 7 days 1 "10 "5 " 1.4 " 15 « 3 " 2.3 " 20 " 1.6 " 4.4 " 24 " 1.25 " 5.6 Such tables can be made for each of the different (7) stages investigated. The rate of development at 6° is taken in each instance as equal to 1. In this manner the following table is obtained: Temper- ature. I II III IV V VI VII Aver- age. 6» 1.0 1.0 1.0 1.0 1.0 1.0 1.0 1.0 10 1.2 1.4 1.4 1.5 1.6 1.6 1.8 1.5 15 2.4 2.3 2.25 2.4 2.8 3.0 3.5 2.6 20 3.9 4.4 4.5 4.6 ,5.3 5.5 6.0 (4.9) 24 4.95 5.6 6.0 6.0 7.0 7.0 7.5 (6.3) The curve in Fig. 10 has been constructed from the figures of the last column. The fact that the values ob- tained in the horizontal rows (particularly those below 20°) show no great variations (where these exist they are to be attributed in part to variations in temperature) makes possible the calculation of an average without great error. Here also an increase in temperature of 10° doubles or trebles the velocity; in other words, a temperature effect as great as that in simple chemical reactions exists here too. What Hertwig himself thinks of the continuation of these observations is shown most clearly in his own words: "I intend to examine the questions suggested here more ac- curately in experiments upon the eggs of echinoderms, 64 PHYSICAL CHEMISTRY. which I consider most suitable for such investigations, and shall then try to see in how far the whole subject is capable of strict mathematical treatment." Of prime importance is the answer to the question, What influence has temperature upon the rapidity with which poisons (or medicines) show their effects? The great ex- perimental diSiculties that stand in the way of an exact investigation of this subject have not yet been overcome, for until recently none of the principles of physical chem- istry have been employed. For the first observations in this direction we are in- debted to Alexander von Humboldt,* for this old master of biology found that heat increased the activity of such substances as "oxygenierte Kochsalzsaure " (chlorine), opium, and alcohol, no less than the action of alkali sul- phides. The experiments were in those days made upon the elementary tissues, heart, and motor nerves. Kunde,t Hermann,! and Kronecker § also studied this question, and CI. Bernard |1 found that while even the most intense poisons take effect very slowly upon cooled frogs, they act the more rapidly the higher the tempera- ture. The more recent investigations of Luchsinger,^ Bnmton,** * tfber die gereizte Muskel- und Nervenfaser II, 218 (1797). t Verhandlungen der physik.-medizin. Gesellschaft in Wiirzburg 1857, 175; Virchows Arch. i8, 357 (1860). X Dubois-Reymonds Archiv fiir Anatomie und Physiologie 1867» 64. § Ibid. 1881, 357. II Legons sur les anesth^tiques et sur I'asphyxie, Paris 1875, 132. IT Physiolog. Studien. Thermisch-toxikologische Untersuchun- gen. Leipzig 1882. ** Handbuch der allgem. Therapie und Pharmakologie, Leipzig 1893, 48. TEMPERATURE AND REACTION VELOCITY 65 Stokvis,* and Saint Hilaire.f who worked upon this sub- ject under Richet's direction, have only shown the diffi- culties that he in the way of an answer to this ques- tion. It is difficult to follow quantitatively the influence of temperature upon the velocity with which chemical agents act upon the animal organism because various factors play a r61e in bringing about the final result. Thus the absorption velocity changes with changes in temperature; while the irritability of organisms and tissues is also dependent to a large extent upon the tem- perature. The influence of temperature upon the velocity of in- toxication as determined by our measurements is therefore the sima of the influence of temperature upon various Ufe phenomena which can be analysed into their constituents only with the greatest difficulty. While Richet J is of the opinion that the variations in the reaction velocity at various temperatures between a tissue and a poison are determined solely by the tempera- ture, Stokvis § has proved that the irritabiUty of the tissue also plays a heavy r61e in the process. For if at a low temperature the poison is increased in amount to correspond to the decreased irritability of the tissues brought about by lowering the temperature, the same velocity of intoxication may be attained under these circiunstances as at higher temperatures. Later we shall discuss in greater detail the bactericidal * Feestbundel voor Bonders, Amsterdam 1888, 465. tThSse, Paris 1888. j Bulletin de la Soci^t^ de Biologie, 18. April 1895. §1. c. 66 PHYSICAL CHEMISTRY. powers of various disinfectants, but we will point out here that temperature has a great influence upon the velocity of disinfection also. Heider* in particular has studied this question quantitatively, after observations had been made in the same direction by Koch,t Nocht,t Henle,§ and Pane. 1 1 Heider, for example, found that anthrax spores which had not been destroyed after an exposure for thirty-six days to the action of a 5 per cent carbolic acid solution at room temperature, were killed after three minutes when the temperature was raised to 75°.^ The practical value which a study of the influence of temperature upon the velocity of the action of various therapeutic agents might have manifests itself most clearly when we remember, for example, that the reactions which occur in a feverish organism take place much more rapidly than those in the normal individual, and that the same velocity is to be expected ** only when the increase in tem- perature is taken into consideration and the dose of medi- cine administered to the patient is diminished correspond- ingly. * Arch. f. Hyg. 15, 341 (1892). t ijber Desinfektion, Mitteilungen aus dem Kaiserlichen Gesund- heitsamte I (1881). t Zeitschr. f. Hyg. 7 (1889). § Arch. f. Hyg. 11, 188 (1889). II Atti della R. Accademia medica di Roma (2) 5 (1890). 1[ An especially arranged experiment had shown that a rise in temperature to 75° does not injure the bacteria if kept in pure water. ** In what manner the effect of the drug is associated with this velocity is a question by itself, into a discussion of which we can- not enter here. See E. Juckuff, Versuche zur Auffindung eines Dosierungsgesetzes. Leipzig 1895 TEMPERATURE AND REACTION VELOCITY. 67 An extensive field for investigation is therefore opened here, in which the physico-cheminal principles "discussed above can point the way.* * See Stokvis, Atti dell' XI Congresso medico internazionale, Roma 1894, p. 354. FIFTH LECTURE. Equilibrium. We have already pointed out (p. 3) that two classes of phenomena are governed by the law of mass action: first, reaction velocity; second, equilibrium, which is estab- lished when the reaction has come to an end. In the discussion of the extensive field of the phenomena of equiUbrium, we shall consider in detail especially those which, because of their direct or indirect bearing upon physiological or biological problems, demand our atten- tion most particularly. For a better understanding of the subject, however, it may perhaps be necessary to deal first of all with a few of the more purely physico-chemical phenomena. If a number of substances capable of reacting chemically with each other are brought together, a reaction ensues which after a given tftne comes to a standstill (practically), — the system is in chemical equilibrium. The rapidity with which this state of equilibrium is reached is dependent upon the velocity of the given reaction (consequently upon the temperature, and the medium in whith the reaction occurs). If, for example, we mix, at a definite temperature, equiva- lent amounts of acetic acid and ethyl alcohol, a reaction ensues according to the equation CH3COOH+ C^H^OH = CH3COOC,H5+ H,0. (acetic acid) (ethyl alcohol) (ethyl acetate) (water) 68 EQUILIBRIUM. 69 The reaction takes place in the direction from left to right. Tf , however, we bring equivalent amounts of ethyl ace- tate and water together, ethyl alcohol and acetic acid are formed, — in other words, the above reaction takes place from right to left. Neither in the first nor in the second instance does the reaction become complete; before the given amounts of acetic acid and ethyl alcohol, or ester and water, have undergone complete decomposition the reaction ceases. A condition of equilibrium is established which may be represented, according to van't Hoff, by the following: CH3COOH+ C^HjOH ^ CH,C00C,H3+ H^O. (1) The system found to the left of the t^ sign we shall hereafter designate the f.rst, that to the right the second system. A reaction such as the above, which can take place from left to right, as well as from right to left, is called a reversi- ble reaction. As can further be seen from equation (1), after equilib- rium has been estabUshed, the four substances reacting with one another are present in the reaction mixture. The characteristic feature of such a condition of equilibrium is found in the fact that it is always the same (we always assmne in our considerations that the external conditions governing the reacting system, such as pressure and tem- perature, remain constant) no matter from wliich side it is reached. In other words, it is immaterial whether we mix one mol acetic acid with one mol ethyl alcohol, or one mol ethyl acetate with one mol water, — the condition of equilib- rium reached in either case is entirely the same. 70 PHYSICAL CHEMISTRY. Now this behaviour is in no way an exception to what generally occurs in a reaction between different substances. On the contrary, the statement can be made that nearly all reactions are reversible. We shall see later that under certain conditions equihb- rium may lean particularly toward one side, that is to say, under certain conditions the first or the second system may be so prominent that the presence of the other system can no longer be recognised by the analytical means at our disposal. The given reaction then no longer gives the im- pression of a balanced action,* but seems to have proceeded completely toward one side. If, for example, we bring sulphuric acid (H^SOi) ^"d sodimn hydroxide (NaOH) together, an apparently com- plete transformation into sodium sulphate (Na^SO^) and water (H,0) takes place, and the reverse process in which sodium sulphate is decomposed into sodium hydroxide and sulphuric acid by water seems not to occur. There are, nevertheless, a number of reasons at hand for assuming that the last-named process actually does occur, and that in consequence, at the end of the reaction, sulphuric acid, sodium hydroxide, sodium sulphate, and water are present in the reaction mixture. Only the amounts of sulphuric acid and sodium hydroxide present are so small that they cannot be proven to exist by the analytical means at our disposal. As the delicacy of our analytical reactions in- creases, the number of known balanced actions grows accordingly. A consideration of the fact that the decomposition repre- sented in equation (1) takes place because two reactions * Reactions that proceed to an equilibrium are also known as balanced actions. EQUILIBRIUM. 'J'l occur simultaneously but in opposite directions, points the way for a sharp definition of the condition of equilibrium. We shall choose as an example the formation of ethyl acetate from acetic acid and ethyl alcohol. If we consider the reaction CH3COOH + C2H5OH = CH3COOC2H5 + H2O, (2) it can be said that double decomposition between the acetic acid and the alcohol molecules can occur only where these molecules meet. The number of such collisions between molecules in the unit time is clearly proportional to the concentration of the acid (Caow) and that of the alcohol (Caio.)- The velocity (s,) with which the reaction represented in equation (2) occurs is therefore Si = fciCaofd X Calc, (3) where fci represents the velocity with which the reaction would take place if both of the reacting substances had the unit concen- tration. Simultaneously with reaction (2) the following opposing reaction takes place: CHaCOOCjHs + H2O = CH3COOH + C2H5OH. (4) If the concentration of the ester is Cester, that of the water Cwater, then the velocity of this decomposition (sj) is S2 ^ KzCester X C/waterj (5) wherein ifcj is the velocity with which this reaction (4) would occur if both of the reacting substances had the unit of concentration. When equilibrium has been reached, then Si = Sj; consequently, according to (3) and (4), A'lC^fMjid X Calc ^ /CgC ester X t/ water, rCi Cester X (cwater io\ or ;— = -7j rr7=i ■ (") kz C'aoid X Calo. 72 PHYSICAL CHEMISTRY. The relation (-jr) between the velocity constants of the two opposed reactions is known as the equilibrium constant (K) of the reaction. Therefore 7^ ^ ^ eater X ^' water /y\ "'Z f^ acid XO ale. We see from this equation thai when equilibrium has been estabUshed, a definite relation (K) exists between the product of the concentrations of the reacting substances, ester and water upon the one hand, and acid and alcohol upon the other. If molecular amoimts of the acid and the alcohol are brought together, experiment shows that equilibrium is estabhshed as soon as two thirds of the amoimt of the sub- stances present has undergone decomposition. If we designate the original concentration of the acid by C (the concentration of the alcohol is then also equal to C), then for the example given here From this value of K we can now predict at what point equihbrium will be established when we bring together any given amounts of acid and alcohol, for the relation ex- pressed by equation (8) must always exist,, in the state of equilibrium, between the concentrations of the substances present. For example, let us ask the question: When one molecule of acetic acid is mixed with a molecules of alcohol, how many mole- cules of the acid will have been decomposed when equilibrium has been estabUshed? EQUILIBRIUM. 73 If we let X equal this number, then, since origmaUy one molecule of acetic acid was present, in equilibrium the concentration of the acetic acid, Cacid = 1 " " alcohol, Caio =a " " ester, " " water. Then, according to equation (8), K =4: Cester = J', C water *= X* rxr (1 - rt(a - r) Developing this equation and finding the value of ;' gives r = |(o + 1 - Vo" - a + 1). Berthelot and P6an de St. Gilles,* to test the correctness of this equation, mixed one molecule of acetic acid with various amounts (a molecules) of alcohol, and after estab- lishment of equilibrium determined experimentally the value of J-, which was at the same time calculated by the above equation. The following table shows how well the calculated values agree with those determined experimentally: • a T (observed). r (calculated). 0.05 0.05 0.049 0.08 0.078 0.078 0.18 0.171 0.171 0.98 0.226 0.232 1 0.665 0.667 8 0.966 0.945 The table shows that when, for example, one molecule of acetic acid is mixed with 8 (a =8) molecules of alcohol, equiUbrium will be estabhshed when 0.966 molecules of the * Annales de chimie et de physique 65, 385 (1862) ; 66, 5 (1862) ; 68, 225 (1863). See also van't Hoff, Ber. d. deutsoh. chem. Gesell- soh. 10, 669 (1870). 74: PHYSICAL CHEMISTRY. acid, that is 96.6 per cent, have been changed to ethyl acetate. The fact is yet to be emphasised that the rapidity with which equiUbrium is established increases with an increase in temperature. EquiUbrium in this particular case is, however, almost independent of temperature, that is to say, the concentrations of the substances present in the re- action mixture after the estabUshment of equilibrium are independent of the temperature. In the given instance, therefore, where one molecule of acetic acid reacts with 8 molecules of alcohol we cannot, through an increase in temperature, bring about the decomposition of more than 96.6 per cent of the acid.* In the formation of an ester from acid and alcohol we are dealing with an equilibrium in a homogeneous liquid sys- tem. All the substances present, acid, alcohol, ester, and water, are homogeneously mixed. We shall now direct our attention to a system which is also homogeneous, though not hquid, but gaseous. If hydriodic acid (HI) is heated in a closed chamber, it is decomposed into its constituents according to the for- mula 2HI = H,+ I,. (1) Such a process is termed dissociation. The hydriodic acid dissociates into hydrogen and iodine. Such phenom- ena were first studied by Georges Aim6 in 1837, and very thoroughly by Sainte Claire Deville in 1857. If the temperature is kept constant, the pressure does not vary during this operation. Our equation states that * The reason why temperature has no influence upon the state of equilibrium in this particular case will be discussed later. EQUILIBRIUM. 75 two volumes of hydriodic acid yield one volume of hydrogen and one volume of iodine vapor. The total volume con- sequently remains unaltered during the decomposition, and therefore the pressure remains unaltered also. But hydrogen and iodine can also combine, according to the equation H,+ I, = 2HL (2) In accordance with the facts given on p. 68, it can be easily seen that the two simultaneously occurring reac- tions (1) and (2) must lead to the establishment of an equilibrium, which may be represented by the equation What relation now will exist between the concentrations of the reacting substances in the state of equilibrium? The velocity (s,) with which the reaction 2HI = Hj + I^ takes place may be represented, according to Guldberg and Waage, by the equation «i = fciCm X Chi (4) Herein Chi represents the concentration of the hydriodic acid, while ki is the velocity with which the reaction would proceed if ■ the concentration of the hydriodic acid were equal to 1. In a similar manner the velocity with which the reconstruction of the hydriodic acid out of its constituents occurs, that is the velocity of the reaction, Hj + I2 = 2HI, may be represented by the equation S2 = k^Cni X C12 . (5) When equilibrium is established, then 'J'6 PHYSICAL CHEMISTRY. Wherefore kfim X Chi = hC^^ X Cij, or hiC^m = IciCni X C12, "2 _ If _ "hi ^o\ h~^~ Cn^-X Ci,' ^"^ or in words: The equilibrium constant (K), which we shall here call the dissociation constant, is equal to the square of the concentration of the undissociated hydriodio acid, divided by the product of the concentration of the hydrogen and iodine vapour. Equation (6) may be stated in a different form if one remembers that the concentration of a gas (the number of mols per litre) is proportional to the pressure of the gas. For we are able, by increasing the. pressure upon a given weight of gas, for instance doubling it, to bring into the same volume twice the number of molecules of the gas. If we represent the pressure of the hydriodic acid (that is, the partial pressure exerted by the undissociated hydriodic acid in the gas mixture HI+ H2+ 1,) as equal to p h » the partial pressures of hydrogen and iodine vapour as equal to Ph2 and Pi^, equation (6) assumes the following form: ^=;r%-- (7) Ph,XPi. '2 or in words: When equilibrium is established, the square of the partial pressure of the hydriodic acid divided by the product of the partial pressures of the hydrogen and iodine vapour is a constant. By means of this equation the question can now be immediately answered: What will happen if, at constant temperature, the pressure under which the gas mixture (HI+Hj+Ij) exists is increased? EQUILIBRIUM. 77 Will the dissociation of the hydriodic acid increase, de- crease, or remain unaltered? If we compress the gas mixture to the nth part, that is to say, if we decrease its volume n times, then according to the law of Boyle, which states that at constant temperature the pressure of a given weight of gas is inversely propor- tional to the volume, the pressure will be increased n times. Consequently p^ni becomes w^-p'hi. V^2 becomes nf^^, and pij becomes nfi^; and the equiUbrium constant be- comes «Vhi fm npHzXnpi^ PhzXPij =K, which is to say that the state of equilibrium is independent of the pressure exerted upon the system in which the equi- Ubrium is established. This is a sequel to the fact that the volume is not altered by the dissociation, for two volumes of HI yield one volume of H^ and one of I^. Bodensteiu * in particular has exhaustively studied the dissociation of hydriodic acid quantitatively, and has proved the correctness of equation (7). Equally interesting is the question: What will happen when we add to the gas mixture after equiUbrium has been estabUshed any indifferent gas, such as nitrogen, while the volume of the mixture is left unchanged? WiU the dis- sociation change in this case? It is evident from the be- ginning that the dissociation wiU imdergo no change. Ac- cording to the law of Dalton, when different gases are * Zeitschr. f. physik. Chem. 12, 392 (1893); 13, 56 (1894); 22, 1 (1897). See also Lemoine, Etudes sur les Equilibres chimiques, p. 72, Paris 1881. Extrait de rEncyclop#die chimique dirig^e par M. Frimy. 78 PHYSICAL CHEMISTRY. mixed in a container, the partial pressure of each gas is not changed by the presence of the others. If, therefore, we add to the gas mixture of hydriodic acid, hydrogen, and iodine vapour (without changing its volume) any given amount of nitrogen, the partial pres- sures Phi) Pb2! ^^'^ Pi2 remain unaltered, and since equi- librium is dependent upon these values (see equation 7), it, also, will not change. The oase is, however, entirely different if (at constant volume) we add a certain amount of one of the dissociation products (hydrogen or iodine vapour) to the gas mixture. If, for example, we introduce hydrogen into the mixture, the partial pressure p^^ ^^ increased, and since K niust re- main constant, p's.i will increase. The same would be the case if any given amount of iodine vapour were added to the gas mixtures: pi^ would then increase, and also j^^i to a corresponding degree. We can consequently draw the following conclusion: Dissociation is decreased through the addition of the products of dissociation. Of great practical importance is the dissociation which calcium carbonate (CaCOj) suffers in the so-called process of burning. In this case a solid substance (CaCOj) yields upon dis- sociation a different soUd substance, calcium oxide (CaO) and a gas, carbon dioxide (COj). The system resulting from this reaction, which takes place according to the formula CaCO, >>i/>u>>i>>ii/m>uiuiii>uiiiuw^^^^^ Fig. 13. for long periods of time. The temperature is observed at which the last trace of the solid goes into solution. If the flrst method is employed, the apparatus repre- sented in Figs. 13 and 15 can be used for this purpose. In Fig. 13 (apparatus of Noyes *), BBB is a copper stir- rup that can be fastened into the thermostat (Fig. 1 on p. 11) by means of the screws S^ and S^. The shaft aa turns about the points o and a. This shaft can be made to rotate by connecting the cord pulleys fij, e^, and e^ with a hot-air * Zeitsohr. f. physik. Chem. g, 603 (1892). EQUILIBRIUM. 101 motor. The cone pulley c^e^ permits a regulation of the speed of revolution (for example, one revolution per second). To the axle an are soldered six copper rings hhh into which six flasks ///^ sealed with rubber stoppers, may be fastened by means of screws. The finely pulverised soUd and the Uquid are introduced into the flasks, care being taken that a large excess of the former lies at the bottom of the flasks, and is present when saturation has been accomplished. After the bottles are stoppered, the apparatus is set into the thermostat, and the temperature of the same is regulated by using the regulator described upon page 11. With substances the solubiUty of which varies greatly with the temperature, great importance is to be attached to the care with which the temperature is kept constant during the experiment. The shaking is continued from one to three hours. The higher the temperature, the more rapidly will equiUbrium (saturation) be estabhshed, and the time of the experi- ment may be proportionately diminished. In order to be certain that saturation has indeed been reached, two determinations are made, — the first, for ex- ample, after two hours, the second after three hours. If both experiments yield the same result, then two hours of shaldng sufiice in further determinations made at the same temperature. After saturation has been reached, the sedi- ment in the flasks is allowed to settle, the surface of the water in the thermostat is brought just under the necks of the flasks, and, after being carefully dried, the pipette of Landolt (Fig. 14) is dipped into one of the flasks. By means of this pipette, which has been previously dried and 103 PHYSICAL CHEMISTRY. weighed, one can remove, without fear of loss through evaporation, a certain amount of the saturated solution which is to be used for analysis. To do this the ground caps H and A are removed, and the lower part of the pipette is dipped into the saturated solu- tion. Through suction at G the solution enters through CD into the expanded pairt E of the pipette. Since the opening of the tube DC is very narrow at B, solid particles are held back. The glass caps are then replaced and the weight of the filled pipette is determined. After the weight of the saturated solution has been thus determined, it is washed into a flask and ana- lysed. At low temperatures, where loss through evapo- ration is less to be feared, instead of the Landolt pipette a ^-cm. wide straight glass tube may be used, to which by means of a short rubber tube a smaller glass tube is attached. The latter is about 2 cm. long and drawn out in the middle; a cot- ton plug serves as a filter. When through suction the saturated solution has entered the wide tube, the rubber connection is broken and the solution is quickly permitted to flow into a weighing flask which is immedi- ately stoppered and weighed. If only small amounts of the solid are at our disposal, the apparatus pictured in Fig. 15 (van Deventer-Goldschmidt) for determining solubility offers certain advantages. 4 is a glass cyhnder that can be closed at both ends with the perforated caoutchouc stoppers S and B. In this cylinder the solid substance and the liquid are EQUILIBRIUM. 103 mixed. The stirring is accomplished by the centrifugal glass stirrer HAOF of Witt. This consists of a pear- shaped glass body OF perforated by four openings, each pair of which lie diametrically opposite each other. The 104 PHYSICAL CHEMISTRY. handle H of the stirrer passes through the glass tube G fastened into the stopper S, and is made to rotate rapidly by means of a cord pulley K, connected with a hot-air motor. K rests upon the obliquely cut tube G. The tube W passes through the stopper B, and holds at the constriction a cotton plug to serve as a filter. The glass stopper D, to which the glass rod DE is fused, seals W as long as the stirring continues. When saturation is reached D is raised by pulling FD upwards, and suction is appUed at z. The saturated solution, after filtering through W, flows into the previously weighed vial R; as soon as a sufficient amount has collected therein, the entire apparatus is quickly removed from the thermostat, and R is dried and stoppered with a glass stopper. The solution is then weighed and analysed. At higher temperatures, or in case the liquid employed is volatile, the stirrer is fastened into the cylinder A by means of a mercury seal, in such a way that the stirring is not interfered with. The second of the above-mentioned (see p. 100) methods of determining solubility is used especially when we are dealing with temperatures that lie near or above the boiling- point of the solvent. Many solubility determinations have been made accord- ing to the above-described methods. In Fig. 16 the results with several salts (in water) are represented graphically. The ordinates give the parts by weight of the salt in 100 parts by weight of water, while the abscissas indicate the temperatures. Three varieties of solubility can be distinguished in the figure: EQUILIBRIUM. 105 1. The solubility increases with an increase in tempera- ture; this is the case most frequently, for example with KNO3 and NajSO,.10H,O (Glauber's salt). 2. The solubility decreases with an increase in tempera- ture; this is the case with anhydrous Na^SO^ and the ao" calcium salts of many organic acids (calcium succinate, calcium citrate). 3. The solubility does not vary with the temperature; this is approximated by sodium chloride. We will now consider somewhat more closely the curve that the solubiUties of a substance at various temperatures form — ^the so-called solubility curve — remembering that we are dealing with the solubility of a salt in water. 106 PHYSICAL CHEMISTRY. The points a, b, and c upon the curve in Fig. 17 give the composition of the saturated solution at the temperatures ti, t^, and «3, that is to say, these points represent the number Hegion of supersaturated solutions. "y Region of unsaturated solutions. i I Temperature. »■ Fig. 17. of grams of salt that dissolve at these temperatiu-es in 100 g. of water. The points a^, b^, c^ then refer to solutions which at the temperatures ti, t^, t^ contain a greater amoimt of the salt per 100 g. of water than they would contain if they had been saturated at the given temperatures. {Swpersatu- rated solviions.) The points a,,, b,„ c„ give the constitu- tion of solutions which at the temperatures t^, t^, t^ con- tain less salt per 100 g. of water than they would contain if they had been saturated at the given temperatures. {Un- saturated solutions.) The solutions the composition of which is represented by the points on the solubility curve — that is, the satu- rated solutions — exist at the corresponding temperatures in stable equilibrium. This is not the case with the EQUILIBRIUM. 107 supersaturated solutions; these, whenever possible, pre- cipitate their excess of salt and pass into the condition of stable equiUbrium. The state of these supersaturated solutions is designated as metastahle. How now can we prepare a supersaturated solution, such, for example, as corresponds in composition with the point Pi? If we heat salt and water together up to the temperature t, at which the last trace of salt just goes into solution, then we say that the solution is just saturated at t°, and its com- position is then represented by the point P. If now the solution is carefully cooled until the tempera- ture has fallen to t^, care being taken meanwhile that no crystals precipitate out of the solution during the cooling (we are then proceeding along the line PP^ and not along Pel), then after cooling there is found in the solution at the temperature i, as much salt as is represented by the point Pi, that is, therefore, a larger amount than would be in the solution if it had been saturated at this temperature, for the composition of the solution saturated at t^ is repre- sented by the point C. The solution is therefore now supersaturated at the tem- perature tg. The same condition of affairs could also have been brought about if, through evaporation, water had been withdrawn from the solution which at the temperature t^ is saturated, and the composition of which is represented by the point C. If this is done with care and crystaUisa- tion is avoided, the concentration of the solution is in- creased, and we proceed along the Una CPi to the point Pi. If an extremely small crystal of the dissolved substance or of an isomorphic substance (that is a substance which 108 PHYSICAL CHEMISTRY. crystallises in the same crystalline form) is introduced into the supersaturated solution, the metastable condition is broken up through this "germ," and the stable state is estabUshed, — enough sohd salt crystallises out that the concentration of the solution again corresponds to the point c; the solution is again saturated for the tempera- ture ty If the supersaturated solution is cooled much below its temperature of saturation, the condition of super- saturation can be destroyed even without contact with a crystal. In those cases in whidh the supersaturation can be broken up by a "germ" of the dissolved substance, the question arises, What amount suffices to call forth the crystallisation? The answer to this question in the case of supersaturated sodium chlorate solutions (a solution of 107 g. of sodium chlorate in 100 g. of water remains supersaturated at room temperature for an indefinite period) was obtained by Ostwald * in the following way: Drops of the supersaturated sodium chlorate solution were brought in contact with extremely small amounts of ■ solid sodium chlorate, and it was determined what amount of sodium chlorate just sufficed to call forth crystaUisation, and what amount was ineffective. The soUd sodium chlorate was diluted by trituration with powdered quartz, the dilutions being prepared in the manner employed by homoeopathists. 1 g. of the chlorate was, for example, triturated with 9 g. of powdered quartz; 1 g. of this mixture (containing Jj g. of the chlorate, therefore) was further triturated with 9 g. of powdered quartz; a mixture then results * Zeitschr. f. physik. Chem. 22, 289 (1897). EQUILIBRIUM. 109 that contains per gram J^XTV=(tTT)'' = T^Tr g- of the chlo- rate, etc. One gram of the nth mixture accordingly con- tains (xV)" g- of sodium chlorate. Drops of the supersaturated sodium chlorate solution were now brought in contact {inoculated) with these mix- tures. These experiments showed that -^ milligram of the fifth mixture called forth the crystallisation, while yV miUi- gram of the sixth, dilution was ineffective. From this it is seen that 0.0001 X d^)' g. = XTnr5Tnnr "flg. of the sohd sodium chlorate sufiices for the dissolution of the super- saturation. We have thus far considered only the case in which we deal with the equilibrium between one solid substance and one Uquid. The conditions of equilibrium become some- what more compHcated when we deal with two soUds and one hquid, etc. To within fifteen years the explanation of the manifold phenomena in the extensive field of equihb- rium was most unsatisfactory, since guiding principles in experimental investigation were absent. Supported by the so-called phase rule * of Gibbs, Bak- huis Roozeboom,t van't Hoff,t and Bancroft § with their * In illustration of the conception "piase'' it may be pointed out that when, for example, water and water vapour, or ice and water vapour exist side by side, water and vapour or ice and va- pour constitute the phases of the given systems. We therefore deal with three phases in the system, saturated solution and aque- ous vapour, namely, solid salt (which lies upon the bottom), solu- tion, and vapour. Each phase constitutes a homogeneous whole, which by mechanical means may be separated from the remaining phases. t Die Bedeutung der Phasenlehre. Leipzig 1900. Die hete- rogenen Gleichgewichte vom Standpunkte der Phasenlehre. Braun- schweig 1901. t Bildung und Spaltung von Doppelsalzen. Leipzig 1897. § The Phase Rule. Ithaca 1897. 110 PHYSICAL CHEMISTRY. pupils have studied the general conditions that determine equilibrium. THE INVERSION TEMPERATURE. If in the above-described manner we prepare saturated solutions of Glauber's salt (NajSO^-lOHjO) at various temperatures (beginning, for. example, with zero degrees), it is found by analysis that between 0° and 33° the solu- bility of the salt steadily increases with an increase in the temperature. (See curve EF in Fig. 16.) If we increase the temperature above 33° and proceed with our solubility determinations, we find that above this temperature the solubiUty curve FG is not continuous with the curve EF, but that a break occurs at 33°, — ^the change in solubiUty for each degree suddenly assiunes an entirely different value from that which it had before. Thus the solubihty determinations made by Loewel * furnished the following figures which show how many grams Na2S04 per 100 g. of water are present in the satu- rated solution. Saturation with NaaSOi'lOHjO. Saturation with NagSOt. 31.84° 40 32.65° 49.78 32.65 49.78 60 47 Change in solubility per degree. Change in solubility per degree. If now we remove the sediment lying at the bottom of the saturated solution and by analysis determine its com- position, we find that we have to deal no longer with Na^SO^-lOHjO (Glauber's salt), but with another salt, the anhydrous Na^SOi. ♦Annales de chimie et de physique (3) 29, 62 (1850); 37, 157 (1853)5 49,32(1857). EQUILIBRIUM. Ill We can therefore say: Above 33° Glauber's salt cannot exist, it is converted into the anhydride. This salt has a solubility of its own (also a corresponding solubility curve GF) ; the break at 33° has its origin, therefore, in the fact that at this temperature a different sediment comes into existence. If the Glauber's salt has been transformed by heating above 33° iiito the anhydride (with coincident splitting off of the ten molecules of water of crystallisation) and we cool the newly arisen system to below this temperature, the water of crystallisation will again be taken up by the anhy- dride, and the hydride, the Glauber's salt, will be re-formed. This reversible process may be expressed by the following equation: Na2S04 • lOHjO T± Na,S04-|- 10H,O.* While, therefore, above 33° the Glauber's salt is com- pletely converted into the second system, conversely, below this temperature, Glauber's salt is formed until the second system has entirely disappeared. At 33° both systems can exist side by side. This temperature, above which the Glauber's salt is transformed into the anhydride, is desig- nated the inversion temperature of the Glauber's salt. If the second system is put into a vessel and very slowly cooled to below the inversion temperature, care being taken that " germs " of the first system are entirely ex- cluded, the anhydrous condition can also be maintained below this temperature. The anhydride is then, however, * Strictly speaking, the fact should also be brought out in the equation that the anhydride formed forms a saturated solution with the water of crystallisation that is split off. Nevertheless the equation given above represents the general course of the re- action very well. 112 PHYSICAL CHEMISTRY. in the metastable state; an extremely small trace of Glau- ber's salt suffices to bring about the total inversion into NajSOi • lOHjO. This behaviour brings to mind phenom- ena with which we became acquainted earlier (see p. 107) in dealing with supersaturated solutions. We see from Fig. 16 that at the inversion temperature the solubihties of the two systems which can be trans- formed from one into the other are equal; at this point the solubihty curves of the two systems cut each other. If, for example, we cool a solution saturated with Na^SO^ at 35° to below the inversion temperature, if germs of NajSO^ • lOHjO are excluded, the curve GF can be followed, that is to say, a saturated solution of Na2S04 can be produced below the inversion temperature. The point H, for example, indicates the constitution of such a solution at 20°. This solution is supersaturated with regard to Na^SO^-lOH^O (for the composition of the saturated solu- tion of Glauber's salt at 20° is indicated by the point L) ; if a crystal of Glauber's salt be introduced into the solution, the sediment will immediately be converted into Glauber's salt, and this salt will crystallise out until the solution con- tains the amount represented by L. The transformations described here for Glauber's salt are found, in general, in other salts holding water of crys- talhsation. Many another interesting phenomenon con- nected with the existence of an inversion temperature might be described here, yet we shall rather illustrate by simple examples two of the various methods that can be employed in determining the inversion temperature.* * See Reicher, Zeitschr. f. Krystallographie 8, 593 (1884). E. Cohen, Zeitschr. f. physik. Chemie 14, 53 and 535 (1894) ; 16, 453 EQUILIBRIUM. 113 Mercuric iodide, Hgl^, belongs to the group of polymor- phous {cdlotropic) substances, that is substances which can crystallise in various crystalline forms. Two modifica- tions of the mercuric iodide are known — a red which is tetragonal and a yellow which is rhombic. If the red iodide is heated, it is transformed into the yellow form when the inversion temperature is exceeded. If the yellow form is simply cooled to below the inversion temperature, the red modification is re-formed. We can represent this process by the equation HgI,(red)<=>HgI,(yeUow). Since in this instance the two systems can be clearly dis- tinguished from each other by the differences in their colours, to determine the inversion temperature one need only observe" the red iodide in a test-tube while slowly increasing the temperature, and determine at what tem- perature the change in colour takes place. The investigations of Rodwell * and Schwarz f have shown that this takes place at 126°. Above 126° the red iodide is transformed into the yellow, below 126° the yellow is converted into the red. If, however, the yellow iodide is cooled very carefully to below 126° (with exclusion of crystals of the red form), it continues to exist below this temperature, is then, however, in the metastable condition. The addition of a trace of the (1895); 25, 300 (1898); 30, 623 (1899); 30, 601 (1899); 31, 164 (1899). van't Hoff, Bildung und Spaltung von Doppelsalzen, p. 33. • * Philosophical Transactions 173, 1141 (1882). t Preisschrift GOttingen 1892, p. IS, where references to the lit- erature may also be found. 114 PHYSICAL CHEMISTRY. red iodide calls forth an immediate conversion into the red form. Only at 126° can the two forms exist indefinitely- side by side,— rthat is to say, be in equilibrium. The second method for determining the inversion tem- perature that is here to be described is the so-called dUato- metrical. The principle underlying it is that in most in- versions the specific volumes (that is, the volume of a gram of the given substance) of the substances present at the beginning and at the end of the inversion are different — that the inversion is accompanied by a change in volxune. As an example we will consider more closely the allotropic modifications of tin which have been studied in this direc- tion by Cohen and van Eijk.* Casual observation in coimtries where very low tempera- tures prevail in winter, as also specially prepared prelimi- nary experiments, had shown that when the imiversally known white tin is cooled to low temperatiires, it is changed into another form having a greyish colour; the latter upon heating can be reconverted into the white form. That the conversion of the white into the grey form is accompanied by considerable expansion is shown by the simple experi- ment that the white metal becomes covered with inniuner- able greyish, wartUke swellings (see Fig. 18) when cooled. The specific volume of the grey tin is therefore greater than that of the white. f *Zeitschr. f. physik. Chem. 30, 601 (1899); 33, 57 (1900); 35 588 (1900); 36, 513 (1901), where references to the literature may also be found. t Since the specific volume is equal to the reciprocal vahie of the specific gravity, the specific gravity of the grey tin is there- fore less than that of the white. In harmony with this, prelim- inary experiments thus far performed have shown that at 16° the specific gravity of the white tin = 7.3, of the grey =5.8. EQUILIBRIUM. 115 3 116 PHYSICAL CHEMISTRY. If, now, we wish to determine the inversion temperature of grey tin ^ white tin, we make use of the dilatometer represented in Fig. 19. The inside of the glass tube A is filled up with a mixture of grey P and white tin by pouring the mix- ture through the funnel C. The funnel is then cut off at B and the small glass capillary BC is fused thereto. The vessel A and a part of the capillary are now filled with any indifferent fluid (such as oil or petroleum). For this purpose the pipette HPH, containing this fluid, is connected with the capillary at C by means of a thick-walled rubber tube, and the air is exhausted from ABCHP by connecting H (where the arrow is shown in the figure) with the hydraulic air-piunp. By ^ this means the air-bubbles escape through the liquid into P; when the air has been exhausted the connec- tion with the hydraulic air-pump is broken, and the liquid is permitted to pass into A (by holding HPH vertical). This procedure is repeated until AB is entirely, and the capillary BC partially, fiUed with the liquid. If by acci- dent this stands somewhat too high in the capillary, the excess is removed by introducing (at C) a veiy fine capil- lary connected with the air-pump. Behind the capillary BC is put a paper (miUimetre-paper) \7 / B \ \J / A Fig. 19. EQUILIBRIUM. 117 or porcelain millimetre-scale which permits one to read off the height of the liquid in the same. The dilatometer is now immersed in a thermostat the -temperature of which, for example, is 5°. After fifteen minutes the apparatus has assumed this temperature. If this hes below the inversion temperature, the meniscus of the liquid will rise in the capillary; for under these condi- tions grey tin is formed at the expense of the white, and this change necessitates an increase in volmne, which must betray itself by a rise of the liquid in the capillary. If we increase the temperature above the inversion tem- perature, the grey tin will be converted into the white -form, and so bring about a fall of the liquid in the capillary. Through interpolation of the values obtained we can determine the temperature at which the thermostat must be kept in order that the colimin of liquid in the capillary may show no variations. This temperature is the tempera- ture of inversion, for at this temperature both modifica- tions can exist side by side, without one being converted into the other, that is without the occurrence of a change in volume. Thus in one experiment the findings were as follows : Rise of the Temperature. Time in Hours. Fluid in the Capillsiry. Rise per Hour. -5° 25 100 4 15 37.5 2.5 5 12 6 0.5 10 17 0.85 0.05 17 15 0.60 0.04 20 24 -0.96 -0.04 While, therefore, at 17° the rise per hour amounted to 118 PHYSICAL CHEMISTRY. 0.04 mm., at 20° it equalled —0.04 mm. By a simple interpolation we get for the inversion temperature 18.5" According to this, below 18.5° the grey form of tin is the stable one, while the long-known white form is then meta- stable. We come, therefore, to the surprising conclusion that all tin objects, such as we are acquainted with in daily life, exist in a state of metastable equiUbrium. Only on warm days, when the temperature lies above 18.5°, is their condition a stable one. Just as we can compel a metastable solution of sodimn sulphate, which is supersaturated in respect to Glauber's salt (see H in Fig. 16), to assiune the condition of stable equiUbrium for the given temperature through "inocula- tion" with a crystal of Glauber's salt, white tin, which below its inversion temperature also exists in metastable equilibrium, can also be made to pass over into the stable grey form, by bringing it in contact (inoculating it) with a crystal of the grey form.* The nodules upon the tin block pictured in Fig. 18 arose in this manner; if the block is kept at a temperature below 18.5°, they become pro- gressively larger. Since the conversion finally leads to total disintegration of the metal, this phenomenon has re- ceived the name of "tin pest." SOLUTIONS OF SOLIDS IN SOLIDS. The so-called solid solutions (van't Hoff f) have up to the present time been studied but sUghtly. Various substances which have the same crystalline form (isomorphic sub- stances) can under various conditions crystallise together, * We cannot here go into greater details; for these see the ref' erences given on p. 113. t Zeitschr. f. physik. Chem. s, 322 (1890). EQUILIBRIUM. 119 and so form, as mixed crystals, a solid solution. In the con- sideration of the phenomena of diffusion we shall become acquainted with a few other examples of this sort* THE INFLUENCE OF TEMPERATURE UPON EQUILIBRIUM. The general law governing the influence of temperature upon equilibriima was deduced by van't Hoff in 1884 from thermodynamical considerations.! {The principle of tnobile equilibrium.) In words this may be stated as follows: Every equilib- rium between two different conditions of matter (systems) is, at constant volume, displaced by lowering the tempera- ture towards that system the formation of which evolves heat. The following statements which may be deduced from the above principle include all possible cases: 1. When the transformation of the first system into the second takes place with the production of heat,t an in- crease in temperature will be followed by a displacement of the equihbrium towards the side of the first system. 2. When the transformation of the first system into the second takes place with an absorption of heat, an in- * References to the literature may be found in Bodlander, Neues Jahrbuch fur Mineralogie, Geologie und PalSontologie; Beilage 12, 52 (1898). t Etudes de Dynamique chimique, Amsterdam 1884. See van't Hofif-Cohen, Studies in Chemical Dynamics, Leipzig and London 1896, translated by Dr. Thos. Ewan. X Chemical actions that take place with heat production, those, therefore, in which heat is set free, are termed exothermic; those which occur with heat absorption, in which, therefore, heat is ab- sorbed, are termed endothemic. 120 PHYSICAL CHEMISTRY. crease in temperature will be followed by a displacement of the equilibrium towards the side of the second system. 3. When the transformation of the first system into the second occurs without caloric effect, then an increase in temperature will be followed by no displacement of the equiUbrium. To illustrate the use of these statements we shall apply them to a few of the subjects before discussed. If we consider the decomposition CaC03?^CaO+COj, and ask toward which side the equilibrium will be displaced if the temperature is increased, we must first answer the question, Does the transformation of . the first system (CaCOj) into the second (CaO+CO^) occur with heat pro- duction or heat absorption? Now calorimetrical measure- ments have shown that the dissociation of calcium carbon- ate into calcium oxide and carbon dioxide is an endo- thermical process. We can therefore, by making use of the law of mobile equihbrium, at once say that through an increase of temperature the eqtiilibritmi between CaCOj, CaO, and COj will be displaced towards the side of the second system, which is to say, therefore, that through an increase in temperature more calciimi oxide and carbon dioxide will be formed. An interesting example of the application of the above propositions is furnished by the equihbriimi between solids and Uquids, — ^for example, by the solution equilib- rium between a salt and water. We have seen that the solubility of salts can increase, decrease, or remain constant with an increase in temperature. EQUILIBRIUM. 121 We deal here with an equiUbrium that can be repre- sented by the equation Salt+ water ?± saturated solution. If we wish to know how the solubility of a given salt varies with the temperature, that is to say, whether the same increases, decreases, or remains constant with an in- crease in temperature, we have to ask: Does heat produc- tion accompany the transition of the first system (salt-|- water) into the second (saturated solution), or does the change take place with heat absorption, or is no caloric effect demonstrable? If heat is produced, that is to say, if the heat of solution * of the salt has a positive value, then with an increase in the temperature the equiUbrium will be displaced towards the side of the first system (salt+ water), and salt will be precipitated from the solution: the solubility decreases with an increase in temperature. This happens, for example, in the case of NajSO^ (anhy- drous) and the calcium salts of many organic acids (see p. 105). If the transition of the first system (salt+ water) into the second (saturated solution) is accompanied by an absorp- tion of heat, then the solubility of the given salt will in- crease with an increase in temperature, as is the case with * We deal here with the heat of solution produced when a mol of salt dissolves in a solution which at the temperature of the experiment is almost saturated, that is to say, with the heat pro- duction, which is designated the theoretical heat of solution to dis- tinguish it from that which is produced when a mol of salt is dis- solved in pure water. The latter is called the heat of solution of the salt. 122 PHYSICAL CHEMISTRY. the largest number of salts, for example Glauber's salt, potassium nitrate, etc. The solubility undergoes no change with an increase in temperature when the production of heat in the transition equals zero. The latter is approxi- mated in the case of sodium chloride. That the equilibrium CH3COOH+ CjHjOH T± CH3COOC,H5+ H,0, as was said before (see p. 74), midergoes no change when the temperature is increased, is explained by the fact that the production of heat in this transformation equals zero. EIGHTH LECTURE. The Friction of Liquids. Since this property of liquids is of importance to the physiologist also, as recent investigations have demon- strated anew, I wish to deal for a moment with the phe- nomena that come under this heading. If the form of a liquid is altered, or the liquid particles change their relative positions, energy is required, since the particles of a Uquid stick to each other in a peculiar way, and this force (internal friction, viscosity, tenacity, transpiration) has to be overcome in order that the change in form, or the movement, may occur. The laws that govern the movement of liquids in tubes were first exhaustively studied for practical purposes by the engineer Hagen* (1839) and the physician Poi- . seuille.f The latter sought to become more closely ac- quainted with the flow of blood in the animal body (hsemo- dynamics). Just as in the days of iatrochemistry, when physico-chemical investigations were made almost entirely in conjunction with medicine, we see here another illustra- tion of the reciprocity that exists between the practical things of life and science. The empirically established laws of Hagen and Poi- * Poggendorffs Annalen 46, 437 (1839). , t Annates de Chimie et de Physique (3) 7, 50 (1843); (3) 21, 76 (1847). 133 124 PHYSICAL CHEMISTRY. seuille were later deduced from theoretical considerations and confirmed by Stokes.* It was found that when a liquid flows through a long, small-caUbred cylindrical tube, the wall of which it wets, the volume (7) of the Uquid that escapes in the unit of time may be expressed by the following: Herein ;r= 3.1415 . . . , D is the pressure under which the liquid escapes, r the radius of the tube, I the length of the same, and rj a constant for the given Uquid dependent upon the temperature and designated the coefficient of internal friction (viscosity coefficient). This coefficient is equal to the work required to move in one second two fiquid surfaces of 1 sq. cm. surface parallelly over each other, the same distance as the distance between the two surfaces. If we determine the value of ij in (1), we find TvDr* The greater the value of rj, the more viscid we say is the given liquid, — ^the greater is its tenacity. If we wish to determine t) by the above equation, the fiquid is permitted to flow, under a definite pressure (D), through a tube the radius (r) and the length (I) of which have been very accu- rately determined, and the amount of fiquid (V) escaping per second is measured. Such determinations have actually been made. Since * Cambridge PhUosophical Transactions (3) 8, 304 (1847) FRICTION OF LIQUIDS. 125 d the exact determination of the radius of the tube is by no means an easy task, and since the friction coefficient is proportional to the fourth power of the radius of the tube, a slight error in the determination of r will effect a consider- able error in the value of >j. In many cases, therefore, we are content to determine only the so-called relative viscosity, that is to say, the rela- tion between the friction coefficient of the given Uquid and that of water at the same temperature. The use of the simple viscosimeter of Ostwald (Fig. 20) furnishes a convenient means of attaining this end. The capillary db through which the Uquid flows is connected with the bulbs k and e. A definite volume of water (2 to 3 c.c), measured by means of a small pipette, is introduced into the bulb e and suction is appUed at a, so that k is filled and the water rises to above the Une c marked on the glass. The liquid is then permitted to flow out through db; by means of a stop- watch (divided into -^ seconds) the times are noted at which the surface of the water passes the marks c and d. During the experiment the entire apparatus is immersed in a ther- mostat, since the viscosity varies with the temperature, decreasing about 2 per cent with each degree of temperature increase. The experiment is then repeated with the Uquid the viscosity of which is to be determined. It is to be noted that the water (or the liquid) does not flow out under constant pressure; the pressure progres- sively diminishes during the outflow, yet this can be taken into account in the calculation. Fig. 20. 126 PHYSICAL CHEMISTRY. The calculation, into which we cannot enter more closely here, yields the following. If we represent the time occupied by the water in falling from c to d by t„, and if s„ is the specific gravity of the water at the tem- perature of the experiment, ijo the friction coefficient of the water at this temperature, and the corresponding values of the liquid the viscosity of which we wish to determine are equal to t, s, and ij, then Tj : rjD = St : s^„, St or V = V<>TT- If we take the friction coefficient of the water at the tempera- ture of the experiment as equal to unity (we can do this since we only wish to determine how many times the viscosity of the liquid is greater than that of water at the same temperature), then St ' "IT- In the calculation of t) we have to determine, besides the times required for the outflow of the Uquids, the specific gravity of the water and that of the hquid under investiga- tion at the temperature of the experiment. The apparatus illustrated herewith (Fig. 21), a somewhat modified pyknometer of Sprengel-Ostwald,* can be used for this purpose. The part b holds 5-20 c.c. The capillary tubes a and e have everywhere the same diameter, a is dipped into the Uquid the specific gravity of which is to be determined, and suction is apphed at e. When the apparatus has been filled, it is hung into a thermostat, and after the tempera- ture has become uniform the position of the liquid in a and * I am indebted to my coUeague, Prof. HoUeman of Groningen, for calling my attention to this modification which originated with J. F. Eijkman (Recueil des Travaux chimiques des Pays-Bas 13, 24 (1894)). See also HoUeman, Recueil 19, 85 (1900). FRICTION OF LIQUIDS. 127 e is read off upon the scale, which is graduated into half- millimetres. If now the volume ^ of one centimetre of the divi- sions has been determined once and for all by weighing with water, then the volume of any- liquid in the pyknometer is known; * when further, through weighing, the weight of the same has been determined, the specific gravity can be calculated in the customary way. The following table gives an idea of the viscosity of sev- eral pure substances. If we consider the viscosity of water as equal to one, then at the same temperature that of Methyl alcohol = . 63 Ethyl alcohol =1.19 Ethyl acetate =0.55 Acetic acid = 1 . 28 Even though the extensive investigations that have been made in this direction since the work of Hagen and Poi- seuille have led to only a few generalisations, yet several simple relations between the amount of indifferent sub- stances contained in dilute solutions and the relative * With volatile substances this contrivance possesses the great advantage that the vaporisation occurs slowly, if care is taken that the liquid does not come too closely to the ends of the capil- laries. 138 PHYSICAL CHEMISTRY. friction coefficients of the same have been found by Arrhenius.* Thereby the strange fact has come to light that nearly all aqueous solutions of the substances examined have a higher friction coefficient than the water itself, while many of the dissolved substances in the pure state have a lower friction coefficient than water. So, for example, an aque- ous solution of the mobile sulphuric ether has a greater viscosity than the much less mobile water. Even though the studies of Poiseuille, as has already been said, were intended originally for the solution of phys- iological problems, investigations upon the internal friction of animal fluids were resumed only much later by Haro,t Ewald,! and Lewy.§ These measurements were, how- ever, all made upon defibrinated blood and so do not justify a conclusion regarding the viscosity of unaltered living blood. Hiirthle and Opitz || have recently conducted very care- ful experiments upon the viscosity of the blood of various animals. The determinations were made at 37°. The authors believed that the ordinary methods could not be employed, since blood, very soon (several minutes) after being shed, suffers certain changes that exert an impor- tant influence upon its viscosity. To overcome the difficulties hence arising, they *Zeitschr. f. physik. Chem. i, 285 (1887); Reyher, ibid. 2, 744 (1888); Wagner, ibid, s, 31 (1890); Kanitz, ibid. 22, 336 (1897); Euler, ibid. 25, 536 (1898). t Compt. rend. 83, 696 (1876). % Dubois-Reymonds Archiv, Physiol. Abt. 1877, 208 and 1878, 536. § Pflugers Archiv 65, 447 (1896). II Ibid. 82, 415 (1900). FRICTION OF LIQUIDS. 139 brought the outflow capillary in direct connection with the carotid of the animal experimented upon, and used the pulsating blood pressure as the pressure imder which the outflow took place. PreUminary experiments had shown that the formula of Poiseuille holds also under these condi- tions. The very complicated apparatus constructed by them for this purpose we shall not describe more closely at this point. A few months ago Hirsch and Beck * suc- ceeded in handling the same problem experimentally by using a somewhat modified form of the Ostwald viscosime- ter. By this the entire operation has been greatly simpli- fied, and the universal employment of this viscosimeter as a cUnical instrument does not seem impossible, once the relations between the viscosity of the blood (or other ani- mal fluids) and other properties of the same have been studied more closely. Hirsch and Beck experimented with Uving human blood at 38°, — ^that is, therefore, in the proximity of the normal body temperature. The apparatus (Fig. 22) consists of the hand-bellows A, the calcium chloride tube B, the pressure-bottle C, the open manometer D, the thermostat E, and the viscosimeter F. The pressure-bottle is covered with felt to guard against heat radiation, and the manome- ter, in order to render it more delicate, is filled with benzol distinctly coloured with some organic dye. As a thermo- stat the apparatus illustrated in Fig. 1 (p. 11) may be used. The somewhat modified Ostwald viscosinieter is illustrated in Fig. 23. Since blood coagulates very rapidly, the vis- cosimeter must be filled quickly. For this reason the * Deutsches Archiv fur klin. Medizin 69, 503 (1901), where ref- erences to the older literature upon hsemodynamics may be found. 130 PHYSICAL CHEMISTRY. occlusion-tube V is ground into S. The capacity of the U^haped part as compared with that of the upper expanded part G is such that a sufficient amount of blood for the ex- periment is present when its surface is on a hne with the Fig. 22. beginning of the bulb-shaped expansion at M. The capac- ity of the tube G is about \ c.c; the diameter of various capillaries ranges between 0.25 and 0.35 mm. Care should be taken that the apparatus is set up perpendicularly. The experiment is made in the following way: After the FRICTION OF LIQUIDS. 131 Fig. 23. 132 PHYSICAL CHEMISTRY. rubber tube connection has been broken at P and the arm leading to the T tube has been closed with a pinch-cock, any desired pressure, such as about 400 mm. of water = 452 mm. of benzol (specific gravity 0.88) is estabhshed. The thermostat is then set at the temperature of 38°. The viscosimeter connected with the stand and the suc- tion-tube Z is kept in an air-bath of the same temperature. The occlusion-tube is removed, its ground end lightly vaselined, and laid aside ready for use. Through a small cut in the skin a vein is laid bare in the forearm, and a glass capillary of the form shown on p. 133 (Fig. 24) is introduced into the vein for the removal of blood. After the first few drops have been thrown aside, the blood is permitted to flow into the U-shaped part of the apparatus to the point indicated above, the occlusion-tube is put into place, and the apparatus is set into the thermo- stat. The blood is now sucked to a point above the mark X, the suction-tube is connected with the tube leading to the pressure-bottle, and the pinch-cock is opened with one hand, while with the other the stem of a -^second stop- watch is pressed as soon as the surface of the blood passes the mark X. When the lower mark X^ is passed, the stem of the watch is again pressed, while the pinch-cock is at the same time allowed to close; the time is noted, it is quickly determined whether the pressure has remained constant, and suction is again made for another measure- ment. With the same specimen of blood two to six deter- minations may be made in this way. The apparatus is cleaned by rinsing with dilute caustic soda or sodium car- bonate followed by distilled water, and dried in a drying- oven. In order to calculate the relative viscosity of the blood FRICTION OF LIQUIDS. 133 ()j) compared with that of water at 38°, the specific gravity of the blood (s), as also that of water at 38°, and the time of outflQw of the latter at this temperature, would have to be determined (see p. 126). To overcome the difficulties that would accompany the determination of the specific gravity of the blood used in each experiment Hirsch and Beck, when very great accu- racy is not required, determine once and for all the time of outflow (io) at 38° of a Uquid the specific gravity («„) of which is about equal to that of the blood. They use anilin. If the relative viscosity of the anilin at this, temperature compared with water at 38° has been determined in the Ostwald viscosimeter and has been found to equal jjj, then (since s = Sg) t where t is the time of outfiow of the blood in their appara- tus. From this )j can at once be calculated. As an average value for human blood (specific gravity 1.045 to 1.055) it was found that r]= 5.1 at 38°, when the viscosity of water at this temperature is taken as unity. For dog blood was found, at the same tem- perature, 4.7, for cat blood 4.2 (Hiirthle and Opitz). Too great value is, however, not to be attached to these figures, since it was found that not only individual differ- ences exist, but that the nature of the food also has a distinct effect in animals. Haro and Ewald found that the viscosity of the (defibrinated) blood decreases with an increase in temperature, while Lewy states that it remains almost constant from 27-45° and then rapidly diminishes. ^F^ 134 PHYSICAL CHEMISTRY. The investigations of Opitz showed that between 15° and 40° the viscosity decreases with an increase in tem- perature (as is also the case with simple liquids), but that the decrease per degree of difference in temperature is almost constant. Now such a regular increase is not found in the case of water or aqueous salt solutions; with these the viscosity- diminishes more rapidly at higher temperatures than at lower. Since serum in this respect behaves like water, the regular decrease in the viscosity of the blood must be attrib- uted to the presence in the blood of the soUd substances, which with an increase in temperature suffer certain (as yet unknown) changes that compensate in part for the rapid decrease in the viscosity of the serum. The procedure described above makes the solution of many an important problem, such as the determination of the relationship existing between the viscosity of the blood and the secretion from the kidneys, accessible to experiment.* * Jacoby, Lecture to the Mediz. Gesellsch. zu GOttingen, Jan. 10, 1901. Abstract in Deutsche med. Wochenschr. 27 (1901), Ver- einsbeilage, p. 63. NINTH LECTURE. Osmotic Pressure. If a salt solution * is put into a vessel and pure water is carefully poured upon it, after the whole has been left en- tirely undisturbed for some time it is found that the salt has distributed itself through the entire solution; the movement of the dissolved substance (here the salt) does not cease until it has distributed itself uniformly through- out the solution. The phenomenon described here, the movement of the particles of dissolved substance from places of higher con- centration in the liquid to places of lower concentration, is called the diffusion of the substance. We shall later discuss this phenomenon more fully. Here we ask first of all, What is the cause of the diffusion; how is it brought about? If we wish to render apparent the movement of the dis- solved substance in the liquid, we can accomplish this by separating the place of higher concentration from that of lower concentration by a wall which will give passage to the liquid but hot to the dissolved substance. Such a wall is termed semir-permeable. The dissolved substance in its movement through the liquid will now be stopped by this wall, and in consequence * When we here and in what is to follow, for the sake of brev- ity, speak of salt and water (salt solution), we generally. mean thereby any substance that is dissolved in the given liquid. 135 136 PHYSICAL CHEMISTRY. will exert a pressure upon it. This pressure we term the osmotic (from wdeoo = to drive through) pressure of the solution. The first jabservations upon this subject date from NoUet* (1754), who used a bladder as a semi-permeable wall. NoUet filled a glass, the bottom of which was made of a bladder, with spirits of wine, and found that water passed through the bladder into the alcohol as soon as he dipped the glass into pure water. If the glass was closed above, the bladder burst after some time because of the pressure produced within the glass. The significance of this diffusion in the animal organism was also recognised by NoUet, yet his experiments, as also those of the physiologists who studied this phenomenon up to the middle of the nineteenth century, led to no general conclusions.! Practical methods of producing semi-permeable walls were brought forward by the celebrated wine merchant and chemist, Moritz Traube, in his "Experimente zur Theorie der Zellenbildung und Endosmose " J (1867), yet the first quantitative osijnotic measurements were de- scribed by Pfeffer in his " Osmotische Untersuchungen " § (1877). Pfeffer succeeded in fiirmly supporting the readily broken semi-permeable walls of Traube, the so- * Le5ons de physique experimentale, Amsterdam 1754. t For the old literature concerning this subject see Vierordt, Archiv fiir physiologische Heilkunde von Roser und Wunderlich S, 479 (1846). Also Jagielsky, Programm des Gymnasiums Trze- meszno, 1859. {Archiv f. Anatomie und Physiologie 87, 1867. See also: Ge- sammelte Abhandlungen von Moritz Traube, Berlin 1899. 200- 206; 213-217. § Leipzig 1877. OSMOTIC PRESSURE. 137 called precipitation membranes, in the pores of unglazed vessels of earthenware. Such a membrane maybe made in the following way: A Pasteur-Chamberland filter is sawed in half with a scroll- saw. The resulting small clay cyhnder is closed with a perforated rubber stopper through which is passed a glass tube. The cyUnder is dipped into dilute hydrochloric acid, which is sucked through the waU of the cyUnder by a hydrauUc air-pump, in order to remove any caohn dust that might choke up its pores. In a similar way the cylin- der is then rinsed with water. A beaker is now filled with a solution of potassium ferrocyanide (139 g. per litre), the cylinder is dipped into it, and the solution is sucked through its wall. After the cyhnder has been again rinsed in water it is dipped into a second beaker containing a copper sul- phate solution (249 g. of the salt per htre), the inside of the cylinder being also filled with the solution. A layer of copper ferrocyanide is now deposited within the wall. of the cylinder 2CuS0,+ K,Fe(CN),=Cii3i^e(CN)e-F 2K2SO4; this precipitate of copper ferrocyanide constitutes the semi-permeable precipitation membrane which is permeable for water but impermeable for salts. — ^Yet we must at once point out the fact that the latter statement is not strictly true. A certain amount of most substances always migrates through this wall,* and only for the "membranogenous" *See Walden, Zeitschr. f. physik. Chem. 10, 699 (1892), where references to the literature may be found. See also Naccari, Ren- diconti deUa Accademia dei Lincei 6, 25 (1897). Ponsot, Bulletin de la Soci6t6 chimique de Paris (3) 6p, 9 (1895). Flusin, Compt. rend. 131, 1308 (1900); 132, 1110 (1901). Morse and Horn, Jour- nal Amer. Chem. Society 26, 80 (1901). 138 PHYSICAL CHEMISTRY. in this instance, therefore, the potassium ferro- cyanide and the copper sulphate, is the membrane truly impermeable. Other solutions can be used in making such membranes, such as potassium ferrocyanide, with a zinc salt. The semi-permeable wall then consists of zinc ferrocyanide. Membranes of Prussian blue or calcium phosphate have also been used by Pfeffer; yet the best results are obtained with copper ferrocyanide. If we introduce a sugar solution into a cell C (Fig. 25) prepared in this manner, and close it with the stopper S which is perforated by the tube AB, then, when C is dipped into pure water, the sugar endeavours to pass from the place of higher concentration (the solution) to that of lower concentra- tion (the water without the ceU). But this movement is opposed by the semi-permeable membrane, and in consequence the sugar exerts a pressure upon the membrane. Since this wall, however, is imyielding, and so resists the pressure, a pull is exerted upon the water by the solution, which tends to dilute the latter. This comes to pass if the solution enters the tube, and the water from G streams through the membrane into the cell and dilutes the solution. This process goes on Fig. 25. until the hydrostatic pressure resulting in AB prevents the further entrance of water. When Bngar solu- tion. OSMOTIC PRESSURE. 139 equilibrium has been established, this hydrostatic pressure is equal to the osmotic pressure of the solution. Conversely, however, the latter may be measured by ascertaining the hydrostatic pressure which "exists when eq\iihbrium is established. Pfeffer measured the osmotic pressure of sugar solutions of various concentrations with a mercury manometer, and obtained with such an osmometer the following results: Temperature about 14°. Grama sugar per Osmotic pressure in 100 g. water. mm. of mercury. 1.0 535 2.0 1016 2.74 1518 4.0 ....2082 6.0 3075 Pfeffer studied the influence of temperature upon the osmotic pressure of a one per cent sugar solution. Osmotic pressure in Temperature. mm. of mercury. 14.2 510 132.0 : 544 6.8 505 13.7 525 22.0 548 15.5 520 36.0 567 The values contained in brackets were always obtained with the same osmometer. v- We therefore deal here with very considerable pressures.* The data collected by Pfeffer solely for the purposes of plant physiology lay unused for about eight years, when * See Errera, Sur la M3rriotome, Bulletins de rAcad6mie Royale de Belgique No. 3, 1901. Cited from reprint. 140 PHYSICAL CHEMISTRY. they were brought to Ught again by van't Hoff in the presentation of his theory of osmotic pressure. This was communicated to the Swedish Academy of Sciences in Stockholm* in an essay entitled "Lois de I'Equihbre chimique dans I'Etat dilu6, gazeux ou dissous," later pub- lished in a somewhat different form under the title " Die Rolle des osmotischen Druckes in der Analogie zwischen Losungen und Gasen," in the Zeitschrift fiir physikalische Chemie.f In these essays van't Hoff deduces from thermodynami- cal considerations the following law: At constant temperature the osmotic pressure of dilute solutions is proportional to the concentration of the dis- solved substance. (Law of Boyle-van't Hoff.) This law is the analogue of Boyle's law for dilute gases, which states that at constant temperature the (gas) pressure of a gas is proportional to its concentration. J In order to test the correctness of this law van't Hoff used the measurements of Pfeffer. It must be remem- bered, however, that the temperatures at which Pfeffer piade his observations were not kept absolutely constant, feiit varied between 13.2 and 16.1. The following table shows in how far the measurements coincide with the law stated above: * Kongl. Svensk. Veteriskaps-Akademiens Handlingar 21, 17 (1886). In the German by G. Bredig. Ostwalds Klassiker d. exakten Wissenschaften No. 110, Leipzig 1900. t Zeitschr. f. physik. Chem. i, 481 (1887). Studies in Chemi- cal Dynamics. Revised and enlarged by Ernst Cohen. Trans, by Thoinas Ewan Easton. Amsterdam and Londoii 1896. , t It will be noted that the concentration is inversely proportional to the volume. OSMOTIC PRESSURE. 141 C p Concentration of Osmotic pressure in 5 ^ mnai-nnt the solution. mm. of mercury. C '=°'>'"'°'- 1.0% 535 535 2.0 1016 508 2.74 1518 554 4.0 2082 521 6.0 3075 513 P The relation -;^, which according to theory should have a constant value, does indeed approach the same. This means, for example, that doubling the concentration doubles the osmotic pressure. Such a distinct analogy between the osmotic pressure of a dilute solution and the gas pressure of dilute gases having here been found, it lay at hand to ask whether an analogue of the law of Gay-Lussac also existed. For dilute gases this law may be stated as follows: At constant volume the pressure of a given weight of gas in- creases as the absolute temperature. If we make the expansion coefficient of gases (™s) equal to a, then at t°, according to Gay-Lussac, Pi = Po(l + at), (1) wherein Pt and Pq represent the pressures of the gas at the tem- peratures i° and 0°. If we calculate the temperatures according to the absolute tem- perature scale— consequently from —273° as zero — then the abso- lute temperature T which corresponds with i° is' T ^ t + 273, t=T - 273, l + at = l + l-^iT- - 273), l + ^^-Jg. 142 PHYSICAL CHEMISTRY. Equation (1) then assumes the following form: T The law of Gay-Lussac may consequently also be thus expressed: At constant volume the pressure of a gas is proportional to the absolute temperature. This form of the law is also often used. Van't Hoff indeed found that such an analogous law could be deduced for dilute solutions, and found it sup- ported, as we shall see, by Pfeffer's measurements. The law for dilute solutions is as follows: At constant volume the osmotic pressure of dilute solutions increases as the temperature, or also: The osmotic pressure of dilute solu- tions is proportional to the absolute temperature. (Law of Gay-Lussac-van't Hoff.) If now the osmotic pressure P^ has been determined at 0°, then it can be calculated for t° by the equation The following table contains a few of Pfeffer's measure- ments and the calculations of van't Hoff corresponding thereto: Pressure Fressiire. in mm. of "4-^?!"- tTe ^h- Calou- mercury. ™™- ^^^- served. lated. Sodium tartrate 1564 36.6° 13.3° 1432 1443 983 37.3 13.3 908 907 Cane-sugar 544 32.0 14.15 610 512 567 36.0 15.5 521 529 The law of Avogadro for dilute gases is: Under equal pressure and at the same temperature equal volumes of all gases contain the same number of molecules. This may also be applied to dilute solutions, when it assumes the following form; OSMOTIC PRESSURE, 143 At the same osmotic pressure and the same temperature equal volumes of all dilute solutions contain the same nmn- ber of molecules. (Law of Avogadro-van't Hoff.) But besides this it can be proved that this number of molecules is equal to that contained in the same volume of a gas under the same pressure and at the same tempera- ture. The law thus expanded may now be stated in the follow- ing form: The osmotic pressure of a given weight of dis- solved substance is equal to the gas pressure that the sub- stance would exert were it in the gaseous state, and con- tained in the same volume as that occupied by its solution. Van't Hoff tested this law also by Pfeffer's measure- ments. The following table contains the data bearing upon this question. Under P„ are given the osmotic pressure (in atmos- pheres) observed in a one per cent sugar solution, under Pg the gaseous pressures which the same amount of sugar (1 g.) would exert at the corresponding temperature if it were contained in a volume equal to that of the solution. It must be remembered that 1 g. of sugar + 100 g. of water forms a solution which at 0° has a volume of 100.6 c.c. Temperature. Po. Pg- 6.8° 0.664 0.667 13.7 691 683 14.2 671 685 15.5 684 688 22.0 721 703 32.0 716 727 36.0 746 736 While, therefore, at 6.8°, for example, the osmotic pres- sure of a one per cent sugar solution amounts to 0.664 at- mosphere in the Pfeffer osmometer, calculation yields the 144 PHYSICAL CHEMISTRY. result that the same amount of sugar (1 g.) in the volume in which it is contained in the solution (100.6 c.c.) would theoretically exert in the gaseous state a pressure of 0.667 atmosphere. The agreement is a very satisfactory one when it is remembered how difficult it is to produce absolutely semi-permeable menibranes (see p. 137). How now was the pressure, 0.667 atmosphere, given above, cal- culated? We deal here with the answer to the question, What pressure would 1 g. of sugar exert in the gaseous state if it could be vapourised at 6.8°, and if the volume of the resulting gas amounts to 100.6 c.c? It must be pointed out, first of all, that a mol of any gas at 0° and 760 mm. pressure occupies a volume of 22.4 litres; this value is obtained by remembering that 1 litre of hydrogen at 0° and 760 mm. pressure weighs 0.09 g., and that a mol of this gas (= 2.016 g.) under the same conditions consequently occupies a volume of TpTjH- = 22.4 Htres. Since, according to Avogadro, at the same temperature and at the same pressure the same number of mole- cules are found in the same volume, a mol of any gas (at 0° and 760 mm.) will occupy this volume. Consequently 342 g. of sugar (the molecular weight of sugar CijHj^Oii = 342) in the gaseous state at 0° and 760 mm. pressure would also occupy a volume of 22.4 litres. 1 g. of sugar at 0° and 760 mm. would consequently fill a space of 22 4 22400 -3^htres=-3^c.c. = 65.5c.c. If we calculate this volume upon the basis of 100.6 c.c, then the corresponding pressure (X) at 0°, according to the law of Boyle, may be calculated from the following proportion: 100.6 :65.5 = 1 : X. The gaseous pressure of the sugar, if it existed as a gas at t°, would consequently be 0.651(1 + at) atm., where a is the expansion coefficient of gases, = ^=^. OSMOTIC PRESSURE. 145 If now we put t = 6.8, this pressure is found to rise to 0.667 atm., the value given in the table. We have already pointed out the fact that the mem- branes of the Pfeffer osmometers are always more or less permeable for the dissolved substance; for accurate measurements of osmotic pressure these can therefore not be employed; to this is to be added that precipitation membranes cannot bear high pressures, but are ruptured relatively easily. The methods employed for exact measurements are for these reasons all indirect ones. First of all we shall consider a few physiological methods of (indirectly) measuring osmotic pressures. a. The Determination of Osmotic Pressure by Plasmolysis.* Solutions which at the same temperature have the same osmotic pressure are termed isosmotic or isotonic solutions. In the method of plasmolysis described by Hugo de Vries,t the endeavour is made to find a solution having a concentration which has the same osmotic pressure as the cell-sap of certain plant-cells, — ^in other words one that is isotonic with this cell-sap. If now, while using the same plant-tissues, this concen- tration is determined for solutions of various substances, we know that the concentrations found are also isotonic when compared with each other, and the results will be * See Fr. von Rysselberghe: Reaction osmotique des cellules vegetales. BruxeUes 1899, — where references to the literature may be found. t Pringsheims Jahrbiicher fiir Wissenschaftliche Botanik 14, 27 (1884); there two othef methods are described into which, how- ever, we cannot enter more fully here. Zeitschr. f. physik. Chem. 2, 415 (1888); 3, 103(1889). 146 PHYSICAL CHEMISTRY. independent of any accidental characteristics of the plant- cells employed. Tradescantia discolor has cells that are especially well adapted to these purposes. The cuticle of the middle vein upon the under side of the leaf is employed. Tangential sections are made of this, each of which con- tains several hundred Uving cells. If these cells are placed in strong salt solutions, the pro- toplasmic contents shrink. Since the cell-wall does not alter its shape, the cell contents contract into a spherical mass, which usually remains connected with the cell-wall by a few strands, while the spaces intervening between the granular and at times pigmented protoplasm and the cell- wall are filled by the colourless, transparent, extravasated solution. (C in Fig. 26.) Since the protoplasm is sur- rounded by a membrane that is permeable for water, but Fig. 26. which prevents the passage of substances dissolved in the water, in case the salt solution into which the planMissue is dipped has a greater osmotic pressure than the proto- OSMOTIC PRESSURE. 147 plasmic contents, the latter will lose water and shrink. If the solution is less concentrated, then the shrinkage is cor- resRpndingly less, and the protoplasm then separates from the cell-wall only in the comers. (B in Fig. 26.) If the osmotic pressure of the solution is less than that of the cell- sap, or equal to it, then the protoplasm will not separate from the cell-wall. (A in Fig. 26.) Now by finding the concentration of a solution in which plasmolysis occurs, and another, differing from it but slightly, in which plasmolysis does not occur, two limits are determined between which lies the concentration that is isotonic with that of the cell-sap. If we fin'd that plasrnolysis occurs in a 1.01 per cent solution of potassiixm nitrate, and also in a 0.58 per cent solution of sodiimi chloride, while in a 1 per cent solution of potassium nitrate or a 0.57 per cent sodium chloride solu- tion this does not occur, then the two first-named solutions are isotonic with the cell-sap, and consequently also with each other. De Vries has employed the method of plasmolysis, amongst others, for determining the molecular weight of raflBnose, concerning which various ideas were prevalent at the time. The molecular weight was given as: C12H22O11+ 3H3O (= 396) by Berthelot and Ritthausen. CigHjjOig-l- 5H2O (= 594) by Loiseau and Scheibler. CjeHeAz+lOHjO ( = 1188) by Tollens and Rischbiet. By using cells from Tradescantia discolor de Vries deter- mined the concentration of a raffinose solution that is isotonic with a cane-sugar solution containing y*^ mol (=-j»jX342 g. =3.42 per cent) per Utre. 148 PHYSICAL CHEMISTRY. Experiment showed that a 5.96 per cent solution of rafiinose has, at the same temperature, the same osmotic pressure as a 3.42 per cent solution of cane-sugar. Since, according to the law of Avogadro-van't Hoff, the same number of molecules is present in solutions which at the same temperature have the same osmotic pressure, when X is the molecular weight of the raffinose sought, we can say: Number of molecules of | ( Number of molecules of raflSnose ) I cane-sugar. 3.42^5.96 342 ~ Z ' or Z=596. This figure proves that the formula for rafiinose origi- nating with Loiseau and Scheibler, Ci8H320ib+ 5HjO, is the correct one. b. The Determination of Osmotic Pressure by the Red-blood- corpuscle Method. This method, which originated with Hamburger,* is based upon the following experiment: 20 c.c. of a 1.1 per cent potassium nitrate solution is put into a test-tube, and five drops of defibrinated beef-blood are added. The tube is then shaken, and the blood-corpuscles are allowed to settle. After some time one sees a clear, almost colourless layer form above the blood-corpuscles which is entirely free from red blood-corpuscles or hsemoglobin. Into a second test-tube are put 20 c.c. of a less concen- trated potassium nitrate solution, — for example, one con- * Dubois-Reymonds Archiv, Physiologische Abt. 1886, 476; 1887, 31. Zeitschr. f. physik. Chem. 6, 319 (1890); Zeitschr. f. Biologie 26, 414 (1889). See also W. L5b, Zeitschr. f. physik. Chem. 14, 424 (1894). Willarding, Dissertation. Giessen 1897. OSMOTIC PRESSURE. 149 taining 1.0 per cent of the salt; to this are also added five drops of the same blood. The blood-corpuscles settle here also, only the supernatant fluid is no longer colourless, but is tinged with red, — the blood-corpuscles have lost some of their colouring matter. If now two Umits of concentration, not only for saltpetre but also for other substances and for sugar, are sought, one in which the blood-corpuscles sink and leave behind a colourless solution, and a second in which the liquid left behind shows a red colour, we find that the solutions the concentrations of which are represented by the average between these two concentration hmits are isotonic. The following table contains a summary of the results obtained. The accuracy that can be attained is greater than is appar- ent from the table; for a potassium nitrate solution con- taining 0.97 per cent of the salt can be clearly distinguished from one containing 0.96 per cent. If now we know that a certain solution, at a certain temperature, is isotonic with a sugar solution of a known concentration, then we know the osmotic pressure of the solution, for the osmotic pressure of the sugar solution can be calculated from the law of Avogadro-van't Hoff. Concentration of Concentration of the solution in the solution in Name of substance. which the blood- which the blood- Average oorpusoles do not corpuscles begin concentration. lose their colour- to lose their ing matter. colouring matter. Potassium nitrate . . . 1.04% 0.96% . 1.00% Sodium chloride 0.60 0.56 0.58 6.29 5.63 5.13 Potassium iodide 1.71 1.57 1.64 Sodium iodide 1.54 1.47 1.55 Potassium bromide. . 1.22 1.13 1.17 Sodium bromide 1.06 0.98 1.02 150 PHYSICAL CHEMISTRY. In the last column of this table are given the concentra^ tions of the solutions of the various substances in which the blood-corpuscles do not lose their colouring matter. These solutions are therefore isotonic with each other. According to the law of Avogadro-van't Hoff, since these solu- tions are isotonic, they should contain an equal number of dissolved molecules at the same temperature — that is, they should be equi- molecular. The following summary shows that this is indeed the case: One litre of the KNO3 solution contains 10.00 g- - KNO 1, per litre, therefore 10 = ^ mol. One litre of the NaCl solution contains 5.85 g. NaCl per litre, therefore S^«^ 58.5 1 ~ 10 mol. One litre of the KI solution contains 16.4 g. KI per litre, ^-i. r 16.4 theretore .,„- loo 1 ~ 10 mol. One Utre of the KBr solution contains 11.7 g.KBr per litre, therefore -j^ = j^ mol. Equimolecular solutions of different substances conse- quently show the same behaviour toward red blood-cor- puscles, just as is the case, according to the experiments of de Vries (see p. 145), in their effect upon plant-cells. If in using the red blood-corpviscles of cattle it is found that two solutions are isotonic, then this isotonicity is also found to exist when the blood-corpuscles of other animals are used. Yet it must be remembered that the concentra- tions of the solutions at which the haemoglobin is first ex- truded may vary greatly with the different kinds of blood- corpuscles. Thus the colouring matter of the corpuscles of the frog is extruded in a sodiiun chloride solution when the concentration of the salt amounts to 0.21 per cent; from the blood-corpuscles of man the hsemoglobin is ex- OSMOTIC PRESSURE. 151 truded at a concentration of 0:47 per cent; from those of the chicken at 0.44 per cent. Solutions in which the colouring matter is extruded do not have the same osmotic pressure as the blood-corpuscle contents, but a lower one, for otherwise the red blood-cor- puscles would not have increased in volume in them. Be- cause of this increase they finally burst and allow a part of their colouring matter to dissolve in the solution. The concentrations of the solutions that are isotonic with the blood-corpuscle contents could be f oimd by deter- mining the concentrations of the solutions in which no change in the volume of the corpuscles occurs. I would here like to speak briefly of the expression "physiological salt solution," an expression which, though in daily use, has given rise to much confusion, as Ham- burger * and Koppe f have pointed out. Very often we find this name applied to a 0.6 per cent sodium chloride solution, yet we find very diverse reasons given for this fact. - This name has arisen from the idea that such a solution conducts itself entirely indifferently toward animal tissues. This, now, is by no means the case, and holds good, and then but approximately, only for the blood-cor- puscles of the frog. The blood-corpuscles of men, horses, and cattle increase in volume very considerably in such a solution, while in a 0.9 per cent sodium chloride solution no change in volume occurs. This name niight then be ap- plied in the above sense much more properly to the latter solution. Still this name has no general significance, for * La Flandre mSdicale 1894; cited from a reprint. Maahdblad voor Natuxirwetenschappen 19, 102 (1895). See also Jacques Loeb, Pfliigers Arohiv 69, IS (1898). t Pflugers Arohiv 63, 492 (1897). 153 PHYSICAL CHEMISTRY. this concentration would again have to be altered in deal- ing with other animal tissues. For this reason it is more in harmony with our modem ideas when we indicate in each case the osmotic pressure of the salt solution which causes no change in the given tissue, and so entirely do away with the expression "physiological salt solution." According to Hamburger's experiments the serum of many animals is isotonic with a 0.9 per cent sodiimi chloride solu- tion; solutions the osmotic pressure of which (at the same temperature) is higher than that of this sodium chloride solution we shall with Hamburger term hyperisotonic, those the osmotic pressure of which is lower hypisotonic. c. The Determination of Osmotic Pressure by the Hwmatocrit. At the suggestion of C. Eijkman a method for deter- mining isosmotic concentrations was worked out by Grijns,* and shortly thereafter by Hedin,! which was later em- ployed also by Koppe J in the study of many important problems. The apparatus has retained the name given it by Hedin, hcematocrit. This method depends upon the fact that red blood-cor- puscles change their volume when they are brought into a * Verslagen Kon. Akad. v. Wetenschappen te Amsterdam, Feb- ruari 1894; Geneeskundig Tijdschrift voor Ned. Indie 35, Afl. 4; Jaarverslag van het Laboratorium voor pathologische Anatomie en Bakteriologie te Weltevreden 1894; Pfliigers Archiv 63, 86 (1896). t Skandinavisches Archiv fiir Physiologie 2, 134 and 360; ibid. S, 207, 238, 277; Zeitschr. f. physik. C!hem. 17, 164 (1895). Pflugers Archiv 60, 360 (1895). t Dubois-Reymonds Archiv, Physiol. Abt. 1894, 154. Zeitschr. f. physik. Chem. 16, 261 (1895); Miinchener mediz. Wochenschrift 1893, 24. OSMOTIC PRESSURE. 153 solution the osmotic pressure of which differs from that of their contents. In solutions the osmotic pressure of which is greater than that of the cell contents, the volume of the cells is dimin- ished in that water is extracted from them. The converse also holds. Solutions in which the blood-corpuscles undergo no change in voliune must according to this be isotonic with each other. If we remember that the change in volume is determined by the difference between the osmotic pressure of the given solution and that of the blood-corpuscle con- tents, then we can also say that two solutions in which the change in the volume of the blood-corpuscle is the same are isotonic. Now these changes in the volume of the Fig. 27. blood-corpuscles in different solutions can be measured by the hsematocrit. The form given the apparatus by Koppe is illustrated in Fig. 27. 154 PHYSICAL CHEMISTRY. a is a pipette 7 cm. long, made of thermometer tubing and graduated into 100 parts; b and c are two metal plates that serve as seals which can be clamped against the open- ings of the pipette by means of the bent rods dd. In order to make the closure of the openings perfect, the plates are covered with rubber, while the lower plate in addition carries a cork disc. When the pipette is to be used, it is connected with a Pravaz syringe. From a drop of blood obtained by pricking the tip of the finger, blood is drawn into the pipette to any definite mark by sUghtly raising the plunger. The point of the pipette is cleansed of adhering blood, and the given salt solution is immediately sucked in after the blood. The two mix in the funnel-shaped part of the apparatus. The left hand now presses the lower of the two seals against the point of the pipette, while the right hand removes the sjninge, mixes the blood and salt solution with a clean needle, and seals the pipette. After enclosing in a small wooden shell, the pipette is fastened into a centrifuge and centrifuged. The blood- corpuscles collect at the periphery and form a red column in the tube, which at first diminishes uniformly in size, but finally becomes constant. The centrifuging must be kept up until this point is reached. From the length of the column of blood drawn in and the length of the column of blood-corpuscles it can be determined what per cent of the entire volume is occupied by the blood-corpuscles. If, for example, the blood has been drawn into the pipette to the nth mark, and the blood-corpuscle column stands at the mth mark, then the voliune of the latter is 100 — m per cent. n OSMOTIC PRESSURE. 155 We will illustrate the use of the hsematocrit by giving an example. Suppose we wish to determine the concentration of a potassium nitrate solution which is (at the same tempera- ture) isotonic with a sugar solution containing 0.2 mol sugar per litre. We first of all centrifuge the blood with the given sugar solution in. the manner described, and determine the vol- ume of the blood-corpuscle column. Sugar solution 0.2 mol per litre: Blood column 100 Blood-corpuscle column 58.5 Volume of corpuscles in per cent 58.5 We then examine several potassium nitrate solutions having different concentrations in the same manner: KNO3 solution 0.125 mol per litre: Blood column 99 Blood-corpuscle column 53.5 Volume of corpuscles in per cent 54.0 KNO3 solution 0.1 mol per litre: Blood column 100 Blood-corpuscle column 60.0 Volimie of corpuscles in per cent 60.0 While, therefore, a potassium nitrate solution containing 0.125 mol per Utre gives the figure 54 in the hsematocrit, one that contains 0.1 mol yields the figure 60.0, while the sugar solution gives 58.5. There is now to be determined what potassium nitrate solution will give the figure 58.5, for such a solution is isotonic with the sugar solution. Since 6 divisions (60—54) in the pipette scale correspond to the change in concentration from 0.125 to 0.100, 4.5 156 PHYSICAL CHEMISTRY. divisions (58.5 — 54) on the scale will correspond with one 4 5 of -^ . 025 = . 0197. The concentration of the saltpetre solution sought, which is isotonic with the sugar solution, will consequently be 0.125-0.019 = 0.106 mol KNO, per litre.* If the temperature at which the measurement has been made is known, we can calculate the osmotic pressure of the sugar solution (containing 0.2 mol per litre) used, by the law of Avogadro-van't Hoff, and so know also the os- motic pressure of the potassium nitrate solution in &,tmos- pheres. d. The Determination of Osmotic Pressure by Other Physio- logical Methods. I would also like to direct your attention to the investi- gations of Massart.f This observer, by means of a glass capillary, introduced some potassium carbonate solution into a drop of bouillon in which bacteria had been grown. The potassium carbonate serves to attract the bacteria; the bacteria enter the capillary tube, and after twenty to thirty minutes this is entirely filled with them. If, how- ever, increasing amounts of a salt (for example, sodium chloride) are added to the carbonate solution, it is found that the bacteria enter only into the weakest solutions, while they are repelled by the stronger ones. Now it is possible to find a solution the use of which causes the bac- * We shall later explain why a sugar solution containing 0.2 mol sugar per litre is not isotonic with a potassium nitrate solution containing 0.2 mol KNO3 per litre. t Archives de Biologie Beiges 9, 15 (1889), where references to the literature may be found. OSMOTIC PRESSURE. 157 teria to collect at the entrance of the capillary without entering it. In Massart's experiments it was found th&t Spirillum undvla and Bacillics megatherium enter the solutions of very- different salts when the concentration of these salts is equal to 0.04 mol per Utre (or less) ; if the concentration is 0.05 mol per litre, they remain at the entrance of the capillary. One receives the impression that the organisms, as soon as the loss of water which they suffer in the stronger solutions makes itself felt, leave the place that threatens their exist- ence. Here also equimolecular solutions produce similar effects. Massart's studies into the sensitiveness of the eye toward salt solutions of various concentrations are also interes'ting. As is known to you, the introduction of pure water into the eye calls forth an unpleasant sensation. This is also the case when a concentrated salt solution is brought under the eyeUds. Between these two concentrations it is possible to find one which, like the tears, is non-irritable. It was found that such a solution is isotonic with the tears. In this way, therefore, use can be made of the sensitive- ness of the eye to establish the isotonicity of different solutions. Massart found that a sodium chloride solution containing 1.39 per cent * of the salt is isotonic with the tears. According to the chemical analysis of Beaimis,t * As Tve shall see later, the albuminoids dissolved in the tears cannot influence the osmotic properties of this fluid, because of their high molecular weight, and may therefore be neglected here. t Besides NaCl only very slight amounts of other salts are dis- solved in the tears. 158 PHYSICAL CHEMISTRY. 1.3 per cent NaCl is present in the tears, which harmonises well with Massart's findings. Finally, the observations of Wladimiroff * must be men- tioned, who estabhshed the isotonicity of different solu- tions by determining the concentrations at which certain bacteria cease their movements in them. DIFFUSION. It has already been pointed out (p. 135) that when the concentration of the dissolved substance is not the same at all points in a solution, the substance moves from places of higher concentration to those of lower, and that this move- ment is termed diffusion. With gases similar phenomena occur. If, for example, we introduce bromine into a vessel filled with a gas, such as air, we see that the brownish-red bromine vapour gradually spreads through the entire mass of gas, and that this move- ment does not cease imtil the bromine has distributed itself uniformly throughout the entire space. Here also an equalisation of the concentration is brought about through diffusion (gas diffusion). If the pressure of the bromine at a certain place is P, while at another place it is lower, p, then the cause of the diffusion is to be attributed to the existence of the differ- ence in pressure P—f, and the velocity with which the bromine particles migrate is proportional to this difference in pressure. In an entirely analogous way diffusion in liquids is deter- mined by the osmotic pressure of the dissolved substance. If at two places in a solution the concentrations of the * Archiv f. Hygiene lo, 81 (1891); Zeitschr. f. physik. Chem 7, 521 (1891). OSMOTIC PRESSURE. 159 dissolved substance are different, then this difference in concentration, as we have seen above, corresponds to a difference in osmotic pressure between the given points, and a movement of the dissolved substance must therefore occur from the place of higher osmotic pressure to that of lower osmotic pressure. The driving force is here the differ- ence between the two osmotic pressures, and the diffusion velocity will be proportional to this difference in pressure. The first thorough investigations of diffusion in Uquids date from Graham * (1851), yet not until 1855 was a law formulated by Fick f embracing the phenomena of diffu- sion. This can now, since the osmotic pressure of the dis- solved substance has been recognised by Nemst t to be the cause of the diffusion, be stated as follows: The amount of the dissolved substance that in the unit of time diffuses through a given cross-section of a Uquid is proportional to the difference in the osmotic pressure which exists between two cross-sections that lie very (infinitely) near each other. To form a conception of the idea diffusion coefficient, let us imagine a cylindrical mass of a solution (Fig. 28). The cyhnder has a length of 1 cm. and a cross-section of 1 sq.cm. Between the concentration of the solution in the area A and that in B exists the difference in concentration 1, and care is taken that this difference exists always. The dissolved substance will now move (in the direction * Annalen der Chemie und Pharmacie 77, 56 and 129 (1851) ; 80, 197 (1851); 121, 1 (1862). Marignac, Annates de Chimie et de Physique (5) 2, 546 (1874). Liebermann and Bugarszky, Zeitschr. f. physik. Chem. 12, 188 (1893) Hober, Pflugers Archiv 74, 225 (1899). t Poggendorffs Annalen 94, 59 (1855). j Zeitschr. f physik. Chem. 2, 613 (1888). 160 PHYSICAL CHEMISTRY. of the arrow) toward the side of lowest concentration (B). Now the amount of dissolved substance which, when con- stant conditions are estabUshed in the cyUnder, diffuses through the cy Under in the unit of time, is termed the diffvr B IcM. Fig. 28, si(m coefficient of the dissolved substance at the tempera- ture at which the determination is made. The day is chosen as the unit of time, since diffusion takes place so slowly that if a smaller unit of time were chosen the amount of substance that would diffuse would be very small. When we say that the diffusion coefficient of urea at 7.5° is 0.810, we mean that at the given temperature 0.810 g. of urea diffuse per day from a one per cent urea solution through a cylinder 1 cm. long and 1 sq. cm. in diameter. How now can we determine this diffusion coefficient experimentally? Scheffer * proceeded as follows: A bottle E (Fig. 29) holding about 90 c.c. and cylindri- cal at its lower end (4 cm. wide, 6.5 cm. high) is closed with a ground stopper B. The neck of the bottle is about 1.5 cm. in diameter. Through the stopper passes a narrow tube (11 cm. long, 0.5 mm. in diameter) carrying * Ber. d. deutsch. chem. Gesellsch. is, 788 (1882); i6, 1903 (1883) Zeitschr. f. physik. Chem. 2, 390 (1888). OSMOTIC PRESSURE. 161' ■Sz k)^ ^ the stop-cock F and the globe D. The latter holds about 16 c.c. between the marks S^ and Sy The tube ends just above the bottom of the bottle. The slightly- bent tube C is fused to the stopper B. If, for example, the diffusion coefHcient of urea is to be determined, water is introduced into the bottle (three times the volimie of the pipette D) and the pipette, filled with the given urea solu- tion, is set into place. The whole ap- paratus is then put into a room the temperature of which is kept as nearly constant as possible. For since the diffusion coefficient is a function of the / temperature, and increases about 2 per cent for each degree of temperature in- crease, this point is of great importance. But besides this, through, local varia- tions in temperature, currents might be produced which would disturb the process of diffusion. It is for these reasons and because of the difficulty of entirely avoiding vibrations of the ap- paratus during the experiment, that diffusion measurements belong among the most difficult determinations made in the field of physical chemistry. When a constant temperature has been established, the stop-cock F is opened and, to avoid mixing with the water in E, the solution is permitted to flow very slowly into the bottle. When the solution has flowed out to the mark S the stop-cock is closed. Fig. 29. 163 PHYSICAL CHEMISTRY. When the experiment is to be ended in order to determine the amount of dissolved substance that has diffused, the pipette is again filled with urea solution. This is permitted to flow into the bottle by opening the stop-cock, until the liquid in E has reached the tube C. The pipette is then again filled and emptied into E, while the liquid flowing from C is received into a flask and set aside for analysis. Tbfige, manipulations are repeated in such a way that the contents of the bottle are obtained in four different por- tions, which are analysed separately. By this means are determined the amounts of dissolved substance that have diffused after a definite time into the various layers of the liquid. We cannot here enter into a discussion of the somewhat complicated calculation of the diffusion coefficients from the data derived from the analyses. The following figures are given as examples: Diffusing substance. Temperature. Diffusion coefficient. Urea 7.5° 0.81 Chloral hydrate 9.0 0.55 Mannite 10.0 0.38 We have already discussed the meaning of the values given in the last column. So far as the diffusion of the strong acids, bases, and salts is concerned, we can here only say that with the help of the diffusion theory of Nernst, which is based upon the theory of osmotic pressure, it is possible to calculate in advance the diffusion coefficients of these substances. In how far this theory harmonises with the results ob- tained by experiment is shown in the following table, in which k represents the diffusion coefficient of the given substance at 9°. OSMOTIC PRESSURE. 163 In judging of this agreement we must remember what has been said above: diffusion determinations are to be counted among the most difficult problems of experi- mental physical chemistry. Name of substance. ft (observed), k (calculated). Hydrochloric acid 2.30 2.35 Potassium hydroxide 1 .85 2. 13 Sodium chloride 1 . 11 1 . 19 Sodium nitrate 1 .03 1 .15 Sodium acetate 0.78 0.86 ' While gases diffuse with great rapidity,— one has but to remember the great rapidity with which odorous sub- stances spread to great distances, — ^the diffusion velocity of dissolved substances is, as the above figures indicate, exceedingly low. This is to be attributed to the fact that a dissolved sub- stance in its movement through a Uquid has to overcome an enormous friction. An analogue is to be found in the great slowness with which fine powders suspended in a liquid settle to the bottom, even though they have a . greater specific gravity than the liquid in which they are found. By means of Nernst's theory of diffusion, the force neces- sary to move one mol of cane-sugar (342 g.) through water with a velocity of one centimetre per second is calculated to be 6700 miUion kilograms; this force is a measure of the enormous resistance that the sugar molecules have to over- come in diffusion. • We have up to this point described the phenomena of diffusion only in their simplest form, that is to say, when diffusion occurs without an intervening membrane. From a physiological point of view, the latter case is of great 164 PHYSICAL CHEMISTRY. importance; for in plants and animals diffusion often takes place between solutions that are separated by membranes which permit the dissolved substances to pass through only in part. The influence which such membranes exert upon the phenomena of diffusion (or the velocity of absorption in the animal body) has recently been the subject of extensive investigation, yet a discussion of this question must be omitted here, since the subject has not yet been definitely settled.* Of great importance to the physiologist is the fact estab- Ushed by Graham f and Voigtlander J that the diffusion velocity of dissolved substances is not altered when gelati- nous substances, such as glue, agar-agar, etc., are added to the liquid in which the diffusion takes place; even the addition of 4 per cent agar-agar to an aqueous solution does not alter the diffusion velocity. This fact is also of importance in the study of the phe- nomena of diffusion, for the errors which so easily creep into diffusion determinations in consequence of the slightest vibration of the apparatus can be entirely done away with through the addition of agar-agar to the solution. We have already pointed out (see p. 32) that reaction velocity is not influenced by the presence of gelatinous * Hamburger, Dubois-Reymonds Archiv, Physiol. Abt. 1896, 302 and 438. Cohnheim, Zeitschr. f. Biol. i8, 129 (1898). Hober, Pflugers Archiv 74, 225 and 246 (1899), where references to the literature may be found. Hedin, ibid. 78, 205 (1899) Kovesi, Physiol. Centralblatt 11, 595. Eckardt, tjber die Diffusion und ihre Beziehung zur Giftwirkung. Dissertation. Leipzig 1898." Overton, Zeitschr. f. physik. Chem. 22, 189 (1897). t Liebigs Annalen der Chemie und Pharmacie 121, 1 (1862). t Zeitschr. f. physik. Chem. 3, 316 (1889). See also Arrhenius, ibid. 10, 51 (1892). OSMOTIC PRESSURE. 165 substances. The catalysis of methyl acetate, as we have already seen, proceeds with the same velocity in an agar- agar jelly as in water. This fact harmonises with what has just been said concerning diffusion velocity in such media. For in order that a reaction may ensue between the molecules of different substances the molecules must move through the medium in which they are dissolved. If this medium has no influence upon the velocity of their movement, then it can also have no influence upon their meeting in the solution. I would also like to return for a moment to the so-called solid solutions which were briefly mentioned above (see p. 118), for there are a number of facts in the fleld of diffu- sion which prove the existence of such solutions.* If, at ordinary temperature, a lead cyUnder is set upon a cyUnder of gold, and the two are pressed against each other by means of screws, the gold diffuses into the lead. This fact can be tested by cutting thin sections from the lead cyUnder from time to time, and examining them for the amount of gold they contain. Roberts- Austen used for such experiments cylinders 0.28 cm. in diameter and 25 cm. high. After four years the lead and gold cyhnders were entirely fused together. A lead disc was cut out of the cylinder at a height of 0.75 mm., and several others at a height of 0.23 mm. In the four lower discs the presence of gold was clearly demonstrable, in the succeeding sec- tions only in traces. When the influence of temperature upon these phenom- * Spring, Zeitschr. f. physik. Chem. 2, 536 (1888); ibid 15, 65 (1894). Roberts- Austen, Philosophical Transactions of the Royal Society 187, 383 (1896). Also, Proceedings of the Royal Society 67, 101 (1900). 166 PHYSICAL CHEMISTRY. ena of diffusion was investigated it was found that the amount of gold which diffuses at 18° into solid lead would be the same after 1000 years as that which diffuses into molten lead (272° C.) in one day. In conclusion I wish to say a few words concerning colloids * and crystalloids. Graham already in his fundamental pubUcations f pointed out that there are a number of substances which, in contrast to the strong mineral acids, bases, and salts, diffuse very slowly. The rapidly diffusing substances are mostly crystalline, while the slowly diffusing ones are amor- phous. The latter he called colloids (because glue belongs to this group), the former crystalloids. In the light of the theory of osmotic pressure this be- haviour of the colloids becomes at once intelligible. The slow diffusion corresponds to a low osmotic pressure, and it is indeed found that this pressure is exceedingly low in the case of the substances named, since they have a high molecular weight. So, for example, from Pfeffer's measurements of the osmotic pressure of solutions of glue, its molecular weight is calculated to be about 5000; from Linebarger's measurements the molecular weight of the colloidal tungstic acid is calculated to be about 1700. While crystalloids diffuse uninterruptedly through coUoidal membranes, such as agar-agar, animal bladders, etc., colloidal solutions cannot pass through them. Upon these phenomena rests the familiar fact that crystalloids * See references to the literature in A. Lottermoser, Die anorga^ nischen Kolloide, Stuttgart 1901. t See foot-note p. 164. OSMOTIC PRESSURE. 167 can be separated from colloids by using animal membranes or parchment paper (dialysis). No sharp border-Une, however, exists between colloids and crystalloids; this is evidenced by the fact that the diffusion of many crystalloids is also hindered by colloidal membranes.* * The communication of C. Eijkman, which has just appeared (Centralbl. f. Bacteriologie, Parasitenkunde und Infektionskranli- heiten 29, 841, 1901), according to which a solution of glue poured upon an agar-agar plate diffuses into the agar-agar in a short time, if only care be taken to maintain a suitable temperature so that the solution does not coagulate, is very worthy of note. Eijkman believes to have proved hereby that colloids can also diffuse into colloids. Further investigations in this direction might prove fruitful. TENTH LECTURE. The Determination of the Molecular Weight of Dis- solved Substances. a. The Depression of the Freezing-point. We have already shown (see p. 147) how the indirect measurement of the osmotic pressure by the method of plasmolysis may be used to determine the molecular weight of a dissolved substance. A direct measurement would be preferable to this, yet we possess, as has been said, up to this time no method which permits of a direct measurement of osmotic pressure with exactness. We shall now direct our attention to two methods which again indirectly, with greater accuracy however than by biological means, enable us to determine the molecular weight of dissolved, non-volatile substances. The Enghsh miUtary surgeon Blagden * observed as early as 1788 that the freezing-point of a solution is lower than that of the pure solvent. Since in ascertaining the depression of the freezing-point (cryoscojyy) of dilute solutions we deal mostly with the determination of slight differences in temperature, special contrivances for such measurements are in use. The apparutus of Beckmann f is often used for such * Philosophical Transactions of the Royal Society 78, 277 (1788). Ostwalds Klassiker der exakten Wissenschaften No. 56 (1894). t Zeitschr. f. physik. Chem. 2, 638 (1888); 7, 323 (1891); 21, 239 (1896). The method of determining the depression of the freezing- 168 MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. 169 purposes. This is illustrated in Fig. 30. C is a battery-jar carrying a metal cover. Through ^ an opening in the cover is pushed the glass tube B, into which is fixed a perforated cork. Through the perforation passes the freez- ing-vessel A, carrying a side tube to facilitate the introduction of the substance to be examined. The' space between A and B serves as an air-jacket; this air- jacket allows any solution intro- duced into A to assume only gradually the temperature of its surroundings (in C). The freez- ing-vessel is closed with a cork, through which pass a thermome- ter D and a stirrer of platinum wire. The thermometer is grad- uated into hundredths of a de- gree,; the thousandth part x>i a degree can be estimated. If with such an apparatus the depression of the freezing-point of a sugar solution is to be deter- mind, we proceed as follows: Into A is introduced a weigiied amount of distilled water,* and the thermometer, the bulb of which is entirely submerged, is put into place. point is, among other things, fully described in H. Biltz, Die Praxis, der Molekelgewichtsbestimmiing. Berlin 1898. * The state of purity demanded by this water will be set forth Fig. 30. I'J'O PHYSICAL CHEMISTRY. The cylinder C is filled with a freezing-mixture of a con- stant temperature, lying a few tenths of a degree below the probable freezing-point of the solution. We shall return later to this freezing-mixture. The freezing-tube is next cooled by thrusting it into the freezing-mixture. When the temperature of the water in A has approached the freezing temperature, A is set into B, and B into C. The temperature of the water now slowly drops, even to below the freezing-point (undercooling). When an undercooling of several tenths of a degree has been reached, the water is vigorously stirred with the stirrer. Usually the water freezes at once; should this not happen, a very small crystal of ice is introduced into the tube A. The thermometer now suddenly rises, since in freezing the latent heat of fusion of the water is Uberated. Finally the temperature reaches a maximum, which lasts for several minutes. This temperature is read from the thermometer and noted as the freezing temperature of the water. The tube A is then held in the hand in order to melt the ice that has formed, and a weighed amount of sugar is introduced into the water through the side tubu- lation. It is very convenient to let the substance to be dissolved slide through the side neck into the freezing- vessel in the form of a pastiUe. These pastilles can be pre- pared in a small press especially arranged for this purpose. After the solution has been thoroughly mixed by stirriilg, the manipulations which have just been described for pure water are repeated, and the freezing-point of the given solution found in this way. By subtraction is obtained the depression which the in greater detail later, in considering the conductivity of dissolved electrolytes. MOLECULAR WEIGHT OF DISSOLVED SUBSTAkCES. 171 freezing-point of the water has suffered by dissolving the sugar in it. A few remarks concerning the conditions under which a freezing-point determination must be made may not be out of place. Of great importance is the regulation of the temperature of the freezing-mixture. Up to a few years ago, the major- ity of such determinations were made with great undercool- ing, that is to say, the freezing-mixture used had a tem- perature which lay many degrees below that of the freezing temperature of the solution. The observations of Nemst and Abegg,* into which we cannot enter here, have shown, however, that through the use of such great imdercooUng important errors creep into the determination of the freez- ing-points of the solutions. Care is therefore to be taken to select a freezing-mixture the temperature of which lies not more than a few tenths of a degree below the freezing- point of the solution. These constant temperatures can be obtained by making use of the so-called cryohydrates.^ For this purpose a *Zeitschr. f. physik. Chem. 15, 681 (1894). See also Raoult, ibid. 27, 617 (1898), where references to the hterature may be found; Battelli and Stefanini, Nuovo Cimento (4) 9, 1899. Cited from a reprint. t To illustrate the term " cryohydrate," the following may be said : If a salt solution is cooled, pure ice begins to form, when the freezing-point of the solution is reached. The concentration of the solution is in consequence increased; if the remaining solution is still further cooled, a temperature is finally reached at which the solution is saturated. Upon further lowering the temperature a mechanical mixture of ice and salt separates out, in which the two exist in the same proportion as in the saturated solution. At this temperature the mixture of ice and salt, called a cryohydrate, melts at ah absolutely constant temperature. As long as the entire mass has not become liquid the temperature remains constant during the process of melting. See E. Schrader, Programm des Real- gymnasiums zu Insterburg (1889), where references to the litera- 173 PHYSICAL CHEMISTRY. mixture of a finely powdered salt and ice or salt and snow is introduced into the cylinder C, care being taken that an excess of salt is always present. In the following short table are given the constant temperatures that may be obtained by using the salts indicated: Name of salt. Temperature. Potassium alum —0.4° Glauber's salt —0.7 Potassium bichromate —1 Potassium sulphate . . —1.5 Copper sulphate —2 Name of salt. Temperature. Potassium nitrate —3° Zinc sulphate —5 Strontium nitrate —6 Barium chloride —7 Instead of these cryohydrates, for the maintenance of constant temperatures, the cold bath may be used with advantage, the temperature of which is kept constant through the evaporation of sulphuric ether or carbon bi- sulphide. The apparatus used for this purpose (Fig. 31) is that employed by Claude and Balthazard* for determin- ing the freezing-point of urine, and is modelled after that of Raoult.f The results obtained with this instrument are very satisfactory, for which reason it might recommend itself as a cUnical instrument, a is the freezing-vessel, b an outer vessel to protect a, which is similar to that found in the Beckmann apparatus. Into the cyhnder A is put ether (three-fourths full), into b alcohol to serve as a con- ductor between the ether and the liquid in the freezing- glass. The surface of the alcohol in b is always to be below that of the hquid in a. ture are to be found. Also, Pfaundler, Bericht. d. d. Chem. Ges. 10, 2223 (1877). Offer, Wiener Akad. Berichte (2) 8i, 1058 (1880). Roloff, Zeitschr. f. physik. Chem. 17, 325 (1895). de Coppet, ibid. 22, 239 (1897). * La Cryoscopie des Urines, Paris 1901. t Zeitschr. f. physik. Chem. 27, 617 (1898). MOLECULAR WEIGHT OP DISSOLVED SUBSTANCES. 173 Tie tube c is connected with an hydraulic air-pump; when this is in operation, air passes by way of the bottle B, in which is contained some sulphuric acid for drying pur- poses, through a number of holes into the ether and causes Fig. 31. this to evaporate rapidly. The temperature can be regu- lated or kept constant in a most convenient way by regu- lating the current of air. Further than this the determina- tions are to be made as with the Beckmann apparatus. If the freezing-points of solutions of various substances 174 PHYSICAL CHEMISTRY. are determined in the manner described, it is found, as Blagden had already observed, that the depression of the freezing-point is proportional to the concentration of the dissolved substance. The foUowing table shows this for aqueous solutions of sugar. Under m is given the number of mols of sugar per 100 g. of water, under t the depression of the freezing-point observed. Further than this the value — has been calcu- m lated, that is, therefore, the (theoretical) depression of the freezing-point that a solution would show in case one mol of the dissolved substance were present in each 100 g. of the same. The latter figure (K) is designated the molecw- lar depression of the freezing-poirk. m t K 0.01305 0.2450 18.8 0.00688 0.3247 18.1 0.003534 0.0634 17.9 0.00178 0.0337 18.8 If, in a similar manner, we determine for other sub- stances, such as urea, ethyl alcohol, etc., the depression of the freezing-point which they would cause in case one mol of the same were dissolved in 100 g. of water, the same value is found for K. So, for example, for an aqueous solution of ethyl alcohol there was found: m t K 0.01324 0.2432 ISA 0.00705 0.1307 18.5 0.00364 0.0685 18.8 As an average of many determinations made with the aqueous solutions of very different substances, K has been foimd to equal 18.6. This figure indicates that in case Acetic acid. Benzene. 39.0° 49.0° 16.7 5.4 MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. 175 one mol of any substance * is dissolved in 100 g. of water, the freezing-point of this solution is depressed 18.6°, that is to say, it freezes at — 18.6° instead of at 0° (the freezing- point of the water). Now, for every solvent, a definite value may in this way be found for the molecular depres- sion (K) of the freezing-point. The following table gives this value for several solvents, as also their freezing-points (melting-points): Water. Molecular depression of the freez- ing-point X 18.6° Freezing-point If now the molecular weight of a substance soluble in any given hquid is unknown, but the value of K for this solvent is known, it is possible, by determining the depres- sion of the freezing-point of a solution containing a known amount of the substance, to determine the molecular weight of this substance. If J represents the experimentally determined depression of the freezing-point which 100 g. of the solvent suffers through the addition of p grams of substance, K the molecular depression of the solvent, and M- the molecular weight of the substance to be n determined, then, since in 100 g. of the solvent ^ mols of dis- solved substance are present, and one mol of dissolved substance in 100 g. of solvent produces a depression of the freezing-point of K degrees: 4 : K = ^ : 1, wheieioTe M = -^. (1) The following experiments are given as examples: a. The depression of the freezing-point of a cane-sugar solution * We shall return later to the exceptions to this rule in the dis- cussion of electrolytic dissociation. 176 PHYSICAL CHEMISTRY. containing 4.4631 g. of sugar in 100 g. of water was determined in a Beckmann apparatus. The freezing-point was found to be 0.2450°- According to this the molecular weight of the cane- sugar is _ 18.6X4.4631 _ ^ 0450 ^^^■^• The formula CijHjjOu gives 342. 6. The depression of the freezing-point 4 oi a, solution contain- ing 4.47 g. of acetic acid in 100 g. benzene was found to be 1.790°. K for benzene equals 49°. If these known values are substituted for the unknown in equation (1), we find _ 49X4.47 _ ^~ 1.790 "^^^■ Now upon chemical grounds the formula of acetic acid has been found to be CH3COOH; this formula gives 60 for the molecular weight. Since upon cryoscopic grounds we have found 123, this is a proof for the assumption that in the benzene the molecules of acetic acid unite into double molecules — association takes place. If the molecular weight [M) of a dissolved substance is known, and the freezing-point (J) of a solution containing p grams of sub- stance in 100 g. of the solvent has been determined, then the molecular depression of the solvent can be calculated from equation (1); for it is V Until now we have considered the molecular depression {K) as a value to be determined experimentally for each solvent. The extensive investigations of Raoult * at first showed such to be indeed the case. Most important, however, is the fact that these constants, as van't Hoff f lias shown, can be calculated from other values. * Annales de chimie et de physique (5) 28, 137 (1883); (6) 2 66 (1884). ' ' t Zeitschr. f. physik. Chem. i, 481 (1887) and Ostwalds Klassi- ker der exakten Wissenschaften No. 110, p. 69. MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. 177 van't Hoff showed that the following relation exists: 0.01991 T^ K=- W Herein K is the molecular depression of the given sol- vent, T the absolute freezing temperature of the same, and W its latent heat of fusion, that is, the number of calories required to convert one gram of the frozen solvent at the temperature of the freezing-point into the liquid of the same temperature. By means of this equation the molecular depression of the freezing-point of any solvent can therefore be calcu- lated, if the freezing-point and the heat of fusion are known. If, for example, we wish to calculate the molecular depression of water by means of this equation, we put T = 273, TF = 80 calories,' - „ 0.01991 X 273' ,„_ K gg 18.5, while experiment has given 18.6 for the value of K. The following table gives a summary of the molecular depressions of the freezing-point of various solvents calculated in this way, and the values that experiment (by using equation (1) on p. 175) has yielded. Name of solvent. Freezing- point. Latent heat of fusion in calories. K 0.019917" W P Water Acetic acid . . Benzene Benzophenon , Diphenylamin, 0° 16.7 5.4 48 54 80 43.2 30 21.5 24 18.5 38.8 51 96 88.8 18.6 39 49 95 88 It is further to be noted that by means of the equation 0.0199ir' K = W from the known molecular depression (K) of a solvent and its known melting-point (T), the unknown latent heat of fusion {W) can be calculated. 178 PHYSICAL CHEMISTRY. From the standpoint of the biologist, the great impor- tance of freezing-point deteiminations lies in the fact that they enable him to ascertain the number of molecules dis- solved in a given volume of any body fluid. We shall later become acquainted with individual exam- ples of this nature, when we have considered the so-called electrolytic dissociation of dissolved substances. Since frequently, in deaUng with the determination of the freezing-point of fluids of physiological importance, only very small amounts of the given liquid are at hand, we shall describe an apparatus which in such cases (for ex- ample, in the examination of blood) has certain advan- tages over those already described. The so-called depres- simeter of J. F. Eijkman* is illustrated in Fig. 32. It consists of a flask of about 10 c.c. capacity that has a small thermometer, graduated into tenths or hundredths of a degree, ground into its neck. In dealing with aqueous solutions, the . instrument is used in the same way as was de- scribed above for the Beckmann apparatus. The separate air-jacket is, however, absent. If we wish to calculate the osmotic pressure of a solution from the observed depression of the freezing- point (J) of the same, the following considerations will peld the result sought. From our equation (1) upon page 175, M- The depression of the freezing-point of a cane-sugar solution containing 1 g. of sugar in 100 g. of water is therefore 18.6 X 1 /\ 342 = 0.054°. * Zeitschr. f. physik. Chem. 2, 964 (1888). MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. 179 We know, upon the other hand, that at 0° the osmotic pressure of this solution amounts to 0.651 atmosphere (see p. 144), where- fore at its freezing-point (— 'o.064°) it is 0.651 (1 —0.054a) = 0.650 atmosphere. A depression of the freezing-point of one thou- sandth of a degree consequently corresponds to an osmotic pressure of ?:|^ = 0.0120 atmosphere.* • We shall now consider how 6. The Elevation of the Boiling-point which dissolved, non-volatile substances impart to a sol- vent may be used to determine the molecular weight of such substances (ehullioscopy). When water boils, the temperature of the hquid is, as is known to you, 100°,' if the barometer stands at 760 mm. If a non-volatile solid, soluble in water, is added to the boiUng water, the boiling-point (when the barometer stands at the same height) rises. For determining this increase the apparatus devised by Beckmann f and illustrated in Fig. 33 is much used. This apparatus consists of an ebuUition-tube A, with two side tubulations t^ and t^; through t^ the weighed substance is introduced into A, while t^ serves for the introduction of a condenser K. The ebullition-tube passes through a prop- erly fitted aperture in the asbestos board L, and rests upon the wire gauze K lying below it. Beneath the stopper r the boiling-tube is held in place by the clamp N. The wire gauze and the asbestos paper rest upon a ring. As an air-mantel to protect against external cooling, the glass cylinder G is used which can be cut from a lamp-chimney, * See foot-note on p. 139. t Zeitschr. f. physik. Chem. 4, 532 (1889) ; 2X, 239(1896). See also the publication of H. Biltz given in the second foot-note on p. 168. 180 PHYSICAL CHEMISTRY. Fig. 33 MOLECULAR WEIGHT OF DISSOLVED SUBSTANCES. 181 and which is closed above by a thin mica plate, or a plate of some other material (glass, asbestos paper). The dotted prolongation of the vessel A and the side tube that is to say, -ggTQ = 0.0001506 mol are present in each litre. Since the degree of dissociation is 0.095 (see above), the concen- tration (Ci and C2 respectively) of the CsHgNiOa ions and of the H ions is equal to 0.095 X 0.0001506 = 0.0000143, and the con- centration of the undissociated part of the acid (Cm) is equal to 0.0001506 - 0.0000143 = 0.0001363. If we write these values into equation (1), we find 0.00000151 X 0.0001363 = 0.0000143 X 0.0000143. 2.05 X 10-'" = 2.06 X 10-'", a very satisfactory agreement, therefore. We shall now answer the question, What wiU be the value of Cj when we add to one litre of the saturated (at 18°) solution of uric acid 36.5 g. hydrochloric acid? If we determine the value of Cj in equation (2) on p. 250, we find, since C^ = Cj, that Ci' + C,r - KCu = 0. C, = -l±M^' +KCu, 2 and it becomes our object to determine the numerical values of /• and KCu in this equation. Now we already know the value of KCu) this value amounts to 2.05 X 10-" = 0.000000000205. In order to find the value of 7-, the concentration of the hydrogen ions in a solution in which are dissolved 36.5 g. (1 mol) hydrochloric acid, we determine Ay and A^ of this hydrochloric acid solution at 18°, from which we then get the degree of dissociation, a = -p . If the determination is made according to Kohlrausch's method, it is found that Av=ZQ\ ; 301 jIoo =384, wherefore <^=5o; = 0.78. This means that in an aque- ous hydrochloric acid solution containing 36.5 g. HCl per litre, 78% of the hydrochloric acid is dissociated into hydrogen and chlorine ions. The concentration y of these ions therefore amounts to 0.78. If we substitute these figures in equation (3), then C^ (^~\ ± I (^\ ' + 0.000000000205. 354 PHYSICAL CHEMISTRY. While, therefore, C^ originally had the value 0.0000143, this value was very greatly reduced by the addition of the hydrochloric acid. In other words, by the addition of hydrochloric acid the dissociation of uric acid is enormously diminished. We have already seen that this decrease in dissociation leads to a decrease in the solubility of the uric acid. Since the concentration of the dissociated uric acid ia 9.5 per cent of the total acid that has gone into solution (see p. 252), the solubility of the acid is diminished by this amount. If the solubility in pure water (at 18°) is 1 : 39480, it therefore f aUs to 1 : 43260 in a solution that contains 36.5 g. HCl per litre (normal hydrochloric acid solution). We have already said that His and Paul, experimentally, found the solubility to be 1 : 42430, which agrees favourably with the above. Similar considerations lead to the conclusion that the solubility of sodium urate in the blood is diminished by the sodium chloride (which has an ion in common with sodium urate) present in it. So, for example, the solubility of sodium urate is decreased by one half in a sodium chloride solution containing -^ mol ( = 0.046%) NaCl per Htre. In general, every sodium salt will bring about this result, for, as we know from what has been said before, the de- crease in solubiUty is due to the presence of the common ion. The addition of sodium bicarbonate will therefore also diminish the solubiUty of the sodium urate. This fact is of great practical importance. Stokvis, for example, in his Lectures on Pharmacology* writes: " The property of rendering soluble the crystalUsed precipitates and concretions of uric acid and the urates is also at- tributed to the bicarbonate of sodium. But the ques- tion as to whether this salt is indeed capable of doing this is still open in spite of the investigations of Pfeiffer,t * Logons de PharmacothSrapie 2, 117, Paris 1898. t Verhandlungen des Kongresses fiir innere Medizin 1886, 44. Ibid. 1888, 327. APPLICATIONS. 255 Posner and Goldenberg." * And further, "that concre- tions, renal calculi, existing in the kidneys or the urinary passages can be dissolved by the internal use of sodium bi- carbonate is highly improbable, if not impossible." But the question can be answered a prim-v by utilising the principles of physical chemistry. If it were possible to increase the amount of sodium bicarbonate in the blood, gouty deposits would in consequence be dissolved not more readily, but more difficultly. Just as wrong is the idea that potassium or lithium salts are able to convert the difficultly soluble urates into more readily soluble compounds and so act as litholytics or litho- tryptics.'f If in spite of this fact, as many authors believe, mineral waters containing alkalies or lithium have a beneficial effect in pathological conditions brought about by a deposition of uric-acid-like concretions, this does not contradict the teachings of the ionic theory; it only means that another explanation must be sought for these curative effects than has thus far been given. Stokvis, for example, attributes the litholytic power of many mineral waters to the increased diuresis and the diminished acidity of the urine which result from the use of these waters. This increased diuresis prevents the depo- sition of uric acid and urates, "but an actual solution of calculi or of tophi that have formed in the joints does not occur, "according to my mind." What has been said of potassium and lithium salts is true also, according to His and Paul, of piperazin and similar preparations the medicinal effects of which are attributed * Zeitschr. f. kUn. Med. 13, 580. t See Paul, Pharmazeutische Zeitung 1900. 256 PHYSICAL CHEMISTRY. to the formation of readily soluble salts of uric acid. The compounds which piperazin forms with uric acid in aqueous solution behave Uke urates. About ten years ago Riidel * beUeved that he had found in urea a substance capable of dissolving uric acid and urates. His pubUcations have excited great attention and have led to the treatment of gouty conditions with large amounts of urea. His and Paul have repeated the measurements of Riidel, atid have f oimd that urea has no effect whatsoever upon the solubility of uric acid or urates, so that a scientific founda- tion for the urea therapy, based upon the results obtained by Rudel and followed by many, is now lacking. Physico-chemical methods will probably play no insig- nificant r61e in the future, when we wish to judge of the pharmacological (or therapeutic) value of spring (mineral) waters; yet it must be borne in mind that these physico- chemical measurements attain a certain importance only when employed in conjunction with a chemical analysis of these waters. For example, as the observations of Roth and Strauss,t of Pfeiffer and Sommer,| and of Strauss § show, the effect of various mineral waters upon absorption and secretion in the stomach is closely related to the osmotic pressure exerted by the salts dissolved in these waters. By determining the depression of the freezing-point, it is possible to ascertain the number of molecules plus ions that are present in a given volume of a water, and this quantity * Archiv f. experiment. Path. u. Pharm. 30, 469 (1892). t Zeitschr. f. klin. Med. 37, 144 (1900). % Archiv f. experiment. Path. u. Pharmakol. 43, 93 (1899-1900). § Therapeutische Monatshefte 13, 583 (1899). APPLICATIONS. 257 is a measure of the osmotic pressure of the solution (for we can regard every mineral water as a solution). Furthermore, by determining the conductivity we have a method of ascertaining the number of free ions, from which, after first determining the depression of the freezing- point, we can discover the number of dissociated molecules. Later, in deaUng with an example taken from the field of physiology, we shall discuss this process of osmotic analysis * in greater detail. Before we leave the field of pharmacology I wish to call your attention very briefly to a few points that are of im- portance in posology (dosology).t In the pharmacopceia of the German government J is found a so-called table of maximal doses in which are stated the largest doses of medicinal substances that may be given to adults. "The apothecary may dispense for in- ternal use a medicine containing one of the following named substances, in larger amounts than here indicated only when the larger amount is emphasised by an exclamation-point (!) * On the analysis of mineral waters see : Koppe, Bedeutung der Salze als Nahrungsmittel, Giessen 1896; Archiv f. Balneotherapie und Hydrotherapie 1898; Deutsche mediz. Wochenschr. 1898, 624; ibid. 1900, No. 32; Therapeutische Monatshefte 14, 1900; Balneologische Centralzeitung, Jan. 21, 1901. Lehnert, Disserta- tion, Erlangen 1897; Scherk, Archiv f. Balneotherapie und Hydro- therapie 1897; Die freien lonen und die ungelosten Salzverbin- dungen in ihrer Wirkung bei Gebrauch von natiirlichen Mineral- wassertrinkkuren, Halle 1898. R. Frenkel, Gazette des Eaux 1899, No. 2083; Duhourcau, Annales de la Soci^t^ d'hydrologie midicale de Paris 1899; Buchbock, Balneologische Zeitung, Au- gust 1899; Kostkewicz, Therapeutische Monatshefte 13, 577 (1899) ; Brasch, Zeitschr. f. diat. und physik. Therapie, 1900, III, Heft 8. P. Th. Miiller, Compt. rend. 132, 1046 (1901). ■f See Stokvis, Nederlandsch Tijdschrift voor Geneeskunde 1896, 105. t Editio IV, 431 (1900). 258 PHYSICAL CHEMISTRY. made by the physician. This holds also in dispensing one of these substances in the form of an injection or a sup- pository." One of the principles upon which this table is based is that the therapeutic action of the substances named therein is proportional to their weight. This assumption is in itself certainly incorrect,* and we know, moreover, that the action of a dissolved substance depends to a great ex- tent upon the mediimi in which it is dissolved (see p. 243). Thus Binnendijk f found that an aqueous solution of carbohc acid has from one half to one fifth its original effect upon dogs and rabbits, whether employed internally or externally, when 20-30 per cent glycerine is added to it. Hallopeau | made the same observation on the action of tartaric acid. The fact (see p. 243) that the addition of sodiimi chloride to an aqueous phenol solution greatly increases its germicidal power, while such an addition decreases the activity of subUmate solutions under certain conditions, also shows very forcibly the great importance of the medium in which a drug is dissolved. In all these illustrations the mere statement of a maximal dose has therefore no value whatsoever, and in the pharmacopoeial table under discussion the medium in which the various substances are dissolved is not considered at all. Extensive reforms based upon physical chemistry are therefore to be hoped for in this field also. * See Juckuff, Versuche zur AufBndung eines Dosierungsgesetzes, Leipzig 1895. T SixiSme Congrfts international des Sciences m^dicales, Amster- dam n, 370. t Nouv. remed. 1893, 91. FOURTEENTH LECTURE. Applications (Continued). C. TO THE FIELD OF PHYSIOLOGY. The very important question, from a physiological stand- point, as to how far proteids such as albiunose and anti- peptone combine with hydrochloric acid, sodium hydrox- ide, or sodium chloride has been exhaustively studied not only by 0. Cohnheim,* but also by Bugarszky and Lieber- mann,t who used among other methods that of determin- ing the freezing-point. If hydrochloric acid is dissolved in water, the freezing- point of this solution is lower than that of the pure water. If albumose is added to the solution, the freezing-point will change but little if the hydrochloric acid continues to exist as such in the presence of the albumose. The number of molecules dissolved in a definite volume of the solution will of course rise upon the addition of the albumose, but since the molecular weight of the proteids is exceedingly high, an addition of several grams of albumose will correspond to only a very slight increase in the number of molecules in the solution, and consequently will lower the freezing- point of the solution but httle. If, however, the hydrochloric acid unites with the albu- mose either wholly or in part, the addition of this proteid will diminish the number of hydrochloric acid molecules * See p. 28. f Pflugers Archiv 72, 51 (1898). 259 260 PHYSICAL CHEMISTRY. (or ions), and will raise the freezing-point of the original hydrochloric acid solution to a corresponding degree; for after the addition of the albumose fewer molecules (or ions) are present in a definite volume of the solution than before. We have a means of answering this question by deter- mining the freezing-point of the solution, with the Beck- mann apparatus, before and after the addition of the albu- mose. Bugarszky and Liebermann determined first of all the freezing-point of proteid solutions containing various amounts of albumose. The following table gives the re- sults of these measurements. Under g is given the number of grams of albumose dissolved in 100 g. of water; under a, the depression of the freezing-point of these solutions.* Albumose in Water. g 0.25 0.60 1. 2. 4. 8. a 0.004 0.008 0.013 0.020 0.033 0.060 The depression of the freezing-point of a 0.05 N. aqueous hydrochloric acid solution (which therefore contained 0.05X36.5 g. HC1=1.825 g. HCl per Utre) to which were 9,dded gradually increasing amounts of albumose, was then measured. In the following table the number of grams of albmnose present in each 100 g. water is given under g, under J the depression of the freezing-point observed; under D is indicated the depression of the freezing-point * Since albumose is a non-electrolyte, it would be expected that its solutions would, from an osmotic standpoint, conduct them- selves as cane-sugar solutions; that is to say, the depression of the freezing-point should be proportional to the concentration of the dissolved albumose. That this is not the case, as the table shows, is to be attributed to the fact that it is very difficult to free albu- mose of aU the dissolved salts. The salts give rise to the observed variations from the calculated freezing-points. APPLICATIONS. 261 which the given solution would show if the number of molecules and ions originally present therein had been in- creased in amount by the number of molecules of albumose added. D is therefore equal to the depression of the freez- ing-point of the pure hydrochloric acid solution (0.186°)+ the depression of the freezing-point (a) of the albumose solution added to it, as given in the foregoing table. Albumose + 0.05 Normal HCl. " ^ 0.186+a 0. 0.186 0.186 0.25 0.184 0.190 0.50 0.178 0.194 1.00 0.167 0.199 2.00 0.148 0.206 4.00 0.116 0.219 8.00 0.156 0.246 We see from this table that with an increase in the amount of albumose added, the freezing-point of the hydrochloric acid solution progressively rises. Molecules (ions) there- fore disappear from the solution; that is to say, complex molecules are formed from the hydrochloric acid and the albumose. As soon as 4 g. of albumose have been added to the hy- drochloric acid, any further addition causes a lowering of the freezing-point, and this in proportion to the amount of albumose added. According to the first table 4 g. albu- mose give a depression of the freezing-point of 0.033°, while from the second table it is seen that 4 g. albumose lowers the freezing-point of the solution (which already contains 4 g. albumose) by (0.156-0.116 = ) 0.040°, a de- pression, therefore, which, within the limits of experimen- tal error, is proportional to the number of albumose mole- cules added 362 PHYSICAL CHEMISTRY. We are consequently led to the same conclusion by the freezing-point method as (see p. 28) by the inversion method, — hydrochloric acid combines with albUmose. Bugarszky and Liebermann have extended their experi- ments to the combining power of albumose with sodium hydroxide and sodium chloride. Albumin and pepsin be- have like albumose in every respect. That sodium chlo- ride does not combine with albumin is shown in the follow- ing tables: Albumin in Water. 9 .... 0.2 0.4 0,8 1.6 3.2 6.4 a .... 0.002 0.004 0.006 0.009 0.015 0.022 Albumin + 0.05 Normal NaCl 1. ff A D = 0.186+O 0. 0.183 0.183 0.4 0.186 0.187 0.8 0.191 0.189 1.6 0.194 0.192 3.2 0.199 0.198 6.4 0.203 0.205 As can be seen from this table, the observed depression of the freezing-point (^A) is always (within the limits of experimental error) equal to the depression of the freezing- point (D), which the solutions should show if the NaCl molecules (+ions) remained unchanged beside the albumin molecxiles added to them. In a similar way it was found that NaOH combines with these proteids. THE TASTE OF DILUTE SOLUTIONS. This is a subject that within the last -few years has been studied from a physico-chemical standpoint. Since we here deal with a subject most difficult of investigation and one of which we know as yet but little, I wish to direct APPLICATIONS. 263 your attention to it. Here, more than anywhere else, the cooperation of the physical chemist and the physiologist is to be desired. As early as 1887 Bailey * observed that equimolecular solutions of acetic acid and hydrochloric acid are not equally sour, but that the hydrochloric acid solution makes a more intense impression upon the tongue than the acetic acid solution. Later Kahlenberg f studied the question, In how far is the taste of dilute solutions dependent upon the electro- lytic dissociation of the dissolved substances? If we consider the question in the light of this theory, then the properties of a very dilute solution of an electro- lyte must be determined by the sum of the properties of the ions contained in it, for in such a solution the dissolved substance is totally dissociated into its ions. If we compare, for example, very dilute solutions of sodium chloride and hydrochloric acid, which contain equiv- alent amounts of NaCl and HCl, then, since the dissolved electrolytes are completely dissociated, the concentration of the chlorine ions is the same in both solutions; the dif- ferences between the two solutions lie in the fact that the one contains sodium ions, while the other contains hydro- gen ions. The differences in taste (in general, the differ- ences in the properties) of the two solutions are therefore to be attributed to the differences between the properties of the sodium and the hydrogen ions. Now a hydrochloric acid solution still has a distinctly sour taste at a concentration at which a sodium chloride * Proceedings, Kansas Academy of Sciences ii, 10 (1887). ■f Bulletin of the University of Wisconsin No. 25, Science Series Vol. 2, No. 1, 1 (1898). 264 PHYSICAL CHEMISTRY. solution containing an eqmvalent amount of sodiiun chlo- ride is entirely tasteless. It follows from this that the taste of such a dilute hydrochloric acid solution is to be attributed to the hydrogen ions contained in it. Since the dilute hydrochloric acid has a sour taste, we must conclude that hydrogen ions have a sour taste. Thus Kahlenberg found that hydrochloric acid solutions having a concentration of ^^ normal, -^^^ normal, or even ^•^ normal have a sour taste, while upon further dilution the sour taste disappears. Sodium chloride solutions at a concentration of -j^ normal are entirely tasteless. If solutions are used that are not entirely dissociated, the additional question as to how far the undissociated mole- cules contribute to the taste of the solution has to be con- sidered. From Kahlenberg's experiments the general conclusion may be drawn that aqueous solutions of hydrochloric, sulphuric, hydriodic, and nitric acids can be just distin- guished from pure distilled water in -j^ normal solutions. This fact is readily intelhgible in the Ught of the dissocia- tion theory, when we remember that these solutions con- tain the same niunber of hydrogen ions (which determine the sour taste) in equal volumes of the solutions, for they are equally strongly dissociated. In the case of acetic acid, both Kahlenberg * and Rich- ards t observed several facts that cannot be as readily explained as the above. Thus it was found that a ^-^ normal solution of this acid has a just perceptible sour taste. Now such a solution is dissociated about 6 per cent, *L. c. t American Chemical Journal 20, 121 (1898); see also Kastle,.. ibid. 466. APPLICATIONS. 365 wherefore the concentration of the hydrogen ions in it is 0.06 X^^ nonaal^Y olbd normal. But we have seen above that hydrogen ions give a sour taste only in concentrations of -j^ normal, from which it would be concluded that an acetic acid solution having a concentration of hydrogen ions of only ^-^jn^ normal ought to be tasteless. In the course of an investigation into the relation be- tween the taste of acid salts and their degree of dissociation, these measurements were corroborated by Kahlenberg.* To explain these facts various hypotheses have been suggested by Richards,t Ostwald,J and Noyes,§ the sub- stantiation of which by more extensive experiments is, however, still lacking. That many as yet unknown factors play a r61e in the action of solutions or pure substances upon the sense of taste is shown by the fact that many of the observations of Kahlenberg are at variance with those of Hober and Kie- sow,|| who, in part at least, studied the same substances. Since all of these authors conclude, from their experiments with salt solutions, that the taste of every salt is made up of the sum of the tastes of its ions, it seems questionable whether further results are obtainable in this direction without utilising the doctrine of psychic inhibition, that is, the general fact that a sensation suffers in intensity through the simultaneous introduction of another sensation, and * Journal of Physical Chemistry 4, 33 and 533 (1900). t Ibid. 207. j Zeitschr. f. physik. Chem. 28, 174 (1899). § Journal of the American Chemical Society (Review of Ameri- can Chemical Research) 22, 73 (1900). II Zeitschr. f. physik. Chem. 27, 601 (1898). 266 PHYSICAL CHEMISTRY. is therefore either weakened or entirely crowded out of the realm of consciousness.* THE OSMOTIC PRESSURE OF ANIMAL FLUIDS. We are all acquainted with the great importance of osmotic phenomena in the metabolism of animals (and plants). The teachings of physical chemistry with which we have become acquainted in the preceding lectures were early employed to explain many of the life-processes that go on in the organism. We stand here at the begiiming of a new epoch in physiology, one which already records many noteworthy contributions. From the exceedingly rich material at hand permit me to bring a few of the most important facts to your atten- tion. It has already been pointed out that the actions of various substances upon each other are comparable only when the number of mols that enter into the reaction are taken into consideration. This naturally holds true also when we deal with the processes that go on in the living organism. To give the concentration of the reacting substances in per cents, as is often done in physiology even to-day, can therefore never yield comparable results. We have already had various illustrations of the truth of this fact. I need but to remind you of the investigations of Hamburger, Massart, Dreser, Paul, and Kronig. To these I add Limbeck,t who determined what concentra- tions of various salts are necessary to produce diuresis, * For specific instances of psychic inhibition, see Heyman's Un- tersuchungen iiber psychische Hemmung, Zeitschr. f. Psychologie u. Physiologie der Sinnesorgane 21, 321 (1899). t Archiv f. experiment. Path. u. Pharm. 25, 69 (1889). APPLICATIONS. 267 and in whose experiments it was found that the different solutions employed were isotonic. This observation strongly supports the idea that the cells which secrete the urine are stimulated by a change in the osmotic pressure of the blood, and that isotonic salt solutions give rise to stimuh of equal intensity. While chemical analysis can tell us much concerning the composition of physiological fluids, it cannot yield us any- thing definite concerning the osmotic behaviour of such solutions. This becomes inteUigible when we remember that the osmotic pressure of a solution is dependent upon the number of molecules (+ions) it contains, and that this cannot be determined by chemical analysis. For when the organic substances present in physiological fluids are incinerated, well-known inorganic acids and salts are formed therefrom by oxidation which, when dissolved in water equal in volume to that of the liquid originally sub- jected to analysis, produce an osmotic pressure entirely different from that of the substances from which they were formed. So, for example, the proteids originally present, which because of their high molecular weight exert an exceedingly low osmotic pressure, yield certain inorganic substances after incineration which, in consequence of their electrolytic dissociation in aqueous solution show a con-, siderable osmotic pressure. If, therefore, we wish to become acquainted with the osmotic behaviour of such animal fluids, we must measure their osmotic pressures by methods which leave them en- tirely unaltered. . . By determining the lowering of the freezing-point we have a direct means of accomplishing our end. This method has been employed by many physiologists in the 268 PHYSICAL CHEMISTRY. study of osmotic equilibrium and its influence upon the metabolism of the animal organism. A general summary of the freezing-point depressions of several important animal fluids, which serve as a measure of their osmotic pressure, is given in the table on p. 269. To this table must be added the fact that, according to Hamburger's * experiments, the freezing-point of defibri- • nated blood is the same as that of serum. In other words, the presence of the blood-corpuscles has no effect upon the freezing-point. This result is inteUigible when we remem- ber that proteids, because of their high molecular weight, have an exceedingly low osmotic pressure, and therefore (practically) do not add to the depression of the freezing- point of the blood. Of importance, too, is the fact, as Hamburger has shown, that the freezing-point of the blood does not change during hemorrhage.! While Koppe states that the depression of the freezing- point of the serum of coagulated and defibrinated blood is equal to 0.570, he finds that the depression of the freezing- point of the red blood-corpuscle pulp is equal to 0.535. The very careful measurements of Kronig and Fueth,| how- ever, have shown that this difference does not really exist, and that the freezing-point of the blood-plasma, or of the blood-serum and blood-corpuscle pulp, is the same. This fact is readily understood when we remember that in the intimate mixture of the blood-corpuscles with the serum * Centralbl. f. Physiol, ii, 217 (1897) t Ibid. 1895, Heft 6. Cited from a reprint. i Monatschr. f. Geburtsh. u. Gynak. 13, 1-35 (1901). Cited from a reprint. APPLICATIONS. 269 ODCOb- _ 4.2 fim NT com ? u3tO = n . y Bottazzi [Arc they live. In live. 189S). era Medizin i8, iicale 1900, 142 fig larine animals b e water in which m in which they 897); ibid. 34, K 1 Centralbl. f . inn IT La semaine mi Ibi BJ Brt ^■^■■s^ blood o that of the me in33, 1 1 1 ra of the equal to f that of in. Medi5 w»0 g.2°a N « ^bfi S^ U ^ Ss ■m the osmotic it this pres rely indepe 394); Zeitsc at IS 15 s 1 ills mu it 1^ § .as fel O »H 270 PHYSICAL CHEMISTRY. an equalisation of the osmotic pressure in the two liquids is to be expected: The osmotic pressure of many other animal fluids has been examined. The table on p. 271 contains a few data concerning the same. The figures given in this table have only a relative value, as fluids from different individuals were examined, and in such cases no inconsiderable variations are always found. For this reason we give a series of observations made upon the body fluids of a single individual; these show that osmotic equilibrium exists between the various body fluids (with the exception of the urine). Depression of the Freezing-point. Of cow's milk 0.570 Of the serum of the same cow 0.570 Of the amniotic fluid . 575 The considerable differences that exist between the ob- servations of various authors' (see, for example, the table on p. 269) are probably attributable to errors in experi- mental technique or differences in the instruments used; we shall return to these later, yet it may be said in passing that greater attention should be paid to such mistakes than has thus far been the case in physiology, for these differ- ences in the data obtained imperil, the conclusions drawn therefrom. The great importance in diagnosis of a study of the osmotic behaviour of the blood and of the urine has been shown most clearly by v. Kor^nyi. Kordnyi's work has been followed by that of many other observers. By de- termining the freezing-point of the blood and of the urine it is possible to discover a lessened permeability of the APPLICATIONS, 271 I g So a^ a^ ^5 o i B m 1^ H O I Pi 13 o d lo feo so feo 5 ,i a I 5 J, «6-t: ■ mo CO a •-^ tH IN rH Cji IN N IN i>ffii I ooo I MOOrH M 1-1 O i-l "H ■ffl WoDPqopq = ft= > 1 ii* a p, a, number of positive me- tallic ions will go into solution in the first differential of time; the solution will in consequence assume a positive charge; at the same time the metal will assume a negative 322 PHYSICAL CHEMISTRY. charge. The negative electricity at the surface of the metal wiU attract the positive ions of the solution, and in consequence at the area of contact between the metal and the solution a so-called electrical double layer will be formed. Now since the metal is negatively charged while the solu- tion is positively charged, a double layer will tend to drive the metalUc ions out of the solution to the metal, where they give up their electrical charges and go over into the neutral metallic state; the double layer therefore opposes the solution tension of the metal. EquiUbrium will be estabhshed between these two opposing forces as soon as both are of the same magnitude. The action of these two forces brings about a difference in potential (electromotive force) between the metal and the solution. If P>p, that is, if the solution is positive as compared with the metal, the resulting electromotive force causes an electrical current that moves from the metal to the solution. If P