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http://www.archive.org/details/cu31924003870676
Practical Methods for Deter-
mining Molecular Weights
HENRY BILTZ
Privatdocent at the University in Greifswald
Translated (with the Author's Sanction) by Harry C.
Jones, Associate in Physicai, Chemistry in Johns
• Hopkins University, and Stephen H:
King, M.D., Harvard University
Easton, Pknna..
Che Chemical piiblfebitig Company
1899.
B Sd
i-.:^-
Copyright, 1899. by Edward hUrt.
VICTOR MEYER
IN MEMORIAM
TABLE OF CONTENTS
Page.
DERIVATION OF MOLECULAR WEIGHT FROM VAPOR-
DENSITY I
Theory of vapor-density determination .^ 2
The Gas-dispi,acement Method 6
Description of a simple apparatus for the gas-displacement
method 8
Carrying out a simple vapor-density determination 10
Modifications of the vaporizing vessel 14
Source of heat 18
The substance 22
Determination of volume 24
Filling the vaporizing vessel with an indifferent gas 27
Measuring the temperature of the experiment 32
Other Methods Based upon the Gay Lussac Principi,e. 34
Mercury displacement method 34
Hofmann 's method 35
Method of Dumas 36
Determination of the Densities of Gases 43
Determination of vapor-densities under diminished pres-
sure ■ 44
Procedure of La Coste 45
" " Lunge and Neuberg 45
" " Dyson, and Bott and Macnair 46
" Schall ■ 47
" " Malfatti and Schoop 47
" " Habermann 47
Critical Examination of Results-- 48
Smaller deviations .- 48
Dissociation 49
Difference betvpeen the results of the Dumas, and the gas-
displacement method 58
OSMOTIC METHODS 62
Beckmann's differential thermometer 66
Determination of the Molecular Weight by the '^
Freezing-point Method 73
The simple freezing-point apparatus of Beckmann 79
Carrying out a simple molecular weight determination,
with the Beckmann freezing-point apparatus 83
Mechanical stirring device 93
Procedure when hygroscopic solvents are used 96
VI CONTENTS
Determination of the Molecular Weight of Solids- • • loo
The thermostat 102
The behavior of individual solvents 105 ,
Table of solvents io5
Solvents which cannot be used in certain cases i ■ i
Increase in accuracy in investigating very dilute solutions. 113
Critical Examination of Results > 17
Smaller anomalies inherent in the method 117
Electrolytic dissociation 121
More complex molecules 125
DETERMINATION OF MOLECULAR WEIGHT BY THE
BOILING-POINT METHOD 141
The simple boiling-point apparatus of Beckmann 1 45
Carrying out a simple molecular weight determination,
with the simple boiling-point apparatus of Beckmann . 1 49
The boiling-point apparatus of Jones 1 61
Carrying'out a determination with the Jones apparatus. . . 164
Modifications of the boiling-vessel 1 67
Modifications of the boiling-jacket 1 70
The heating 172
The introduction of the substance 175
The use of the different solvents 1 77
Some solvents which cannot be used in certain cases 181
Effect of atmospheric pressure 184
Critical Examination of Results i85
Smaller deviations inherent in the method 186
Electrolytic dissociation 189
Complex molecules 191
Choice of method 196
Determination op Molecular Weight from the Prin-
ciple OF Lowering of Solubility 197
DETERMINATION OF THE MOLECULAR WEIGHT OF
HOMOGENEOUS SOLIDS OR LIQUIDS 202
Description of the Method of Traube 205
Experimental determination of the molecular volume 206
Calculation of the molecular volume 206
Determination of the molecular weight 211
Modification of the Traube Procedure for Solutions- 219
a. Indifferent solvents 220
i>. Aqueous solutions 221
Determination of the Density of a Liquid 225
Tables 229
AUTHOR'S PREFACE
The methods for determining molecular weights,
have been extended and increased within the last few
years, by a number of pieces of work. These contri-
butions are scattered throughout the literature.
A brief description of the methods can be found in a
number of smaller special works. These books are,
however, considered to be somewhat too elementary
for the use of a chemical laboratory. They show how,
in simple cases, the molecular weight of a substance
can be ascertained, and they suffice as a guide for car-
rying out a determination for practice. The investi-
gations in the chemical laboratorj-, however, iticlude
very often, more complex cases, which can be dealt
with only by a thorough study of the original litera-
ture. The purpose of this book is to furnish infor-
mation in such cases, either directl}-, or by referring
to the existing publications.
The forms of apparatus, used by chemists in deter-
mining molecular weights, are described here, and as
far as appears to be necessary, are shown in drawings.
The manner of carrying out the experiments is de-
scribed with considerable fullness. Details, which
facilitate work, practical devices, which teaching and
my own experience have furnished, are treated at con-
siderable length. Modifications of apparatus, and
manipulation, are treated in special sections. I believe
that the experimenter will not have his individual
initiative interfered with, by such a detailed descrip-
tion of the methods. As soon as he has overcome the
viii author's preface.
difficulties first met with, and in doing so this book
will be helpful, he will introduce changes and improve-
ments, in each particular case, according to his own
judgment. Special stress has been laid upon the thor-
ough study of the results of experiment. A critical
examination of the observations, which i$ sufficiently
thorough, is of the greatest importance for the correct
exploitation of the experiments, and certainly, in many
cases, this is not easy.
While I have treated the subject mainly from the
point of view of practice, nevertheless, I could not re-
sist the temptation to add to certain sections, some in-
troductory remarks, which would give a theoretically
clear, and rational explanation of the methods. These
introductions to the chapters are to be regarded as very-
elementary, and should serve rather as incentive to
further study, than as real instruction.
I have included the interesting method of Traube,
which has been only recently discovered, since it will
undoubtedly be of great value to chemists, in many
cases. The results of this method should be used with
some caution, until it has been thoroughh' worked
out and established.
It was my intention to dedicate this book to my hon-
ored teacher Victor Meyer, the brilliant investigator in
the field of molecular science, as an offering on his
fiftieth birthday. A few weeks before his death, the
proof was submitted to him, and the dedication ac-
cepted by him. Let the work be now dedicated to
his memory. Prof. Dr. Henry Biltz.
Creifswald, August, fSgy.
TRANSLATORS' PREFACE
In the preparation of the English edition of this
work, we have been guided by the belief, that it would
be of service in American and English laboratories,
where molecular weight determinations are made. It
can be fairly claimed that there is no book in English,
and probably not in any other language, which deals
with the problem of molecular weight determinations
as satisfactorily as this recent publication by Biltz.
We believe that the book will not only be useful in
the laboratory, but on account of its method of treat-
ment, will also prove to be of service as a book of ref-
erence to the literature of, molecular weight determina-
tions.
A comparison of the translation with the original,
will show that a number of additions, omissions, and
changes, have been made. These have either been in-
troduced by the author and forwarded to us, or were
made with his approval. We have added an index.
At first we thought of preparing a short chapter on
the. method of determining the molecular weights of
pure liquids, by measuring their surface-tension. We
have, however, concluded that the method as worked
out by Ramsay and Shields (Ztschr. phys. Chem., I2,
433), is too refined for general laboratory use, and
would, therefore, scarcely find a place in the present
volume.
We have tried to avoid a too literal translation. We
have endeavored to ascertain the author's meaning,
and to express this as clearly as possible, in idiomatic
English. Harry C. Jones.
Stephen H. King.
DERIVATION OF MOLECULAR WEIGHT FROM
VAPOR-DENSITY
Avogadro' advanced the hypothesis in 1811 that the
same number of molecules is always contained in equal
volumes of different gases at the same pressure and
temperature. At the same time he pointed out that
a method for the determiiiation of molecular weights
can be founded upon this principle. If equal volumes
of different gases always contain an equal number of
molecules, then the molecular weights are proportional
to the densities of the gases. Since, however, other
investigations have shown that the hydrogen molecule
consists of two^ atoms, its molecular weight being
therefore two, the densities of gases 7'ef erred to hydro-
gen as unity ^ when doubled^ give directly the molecular
weights of the substances in the gaseous state.
Air is 14.367 times as heavy as hydrogen. The
vapor-density referred to hydrogen as unity is obtained
from the vapor-density referred to air as unity by
'A. Avogadro : Ostwald'sKlassikerderexakten Wissenschaften,
No. 8, pages 3 and 4.
^ Avogadro furnished the only proof, up to 1868, that the mole-
cule of hydrogen consists of at least two atoms, and it was an as-
sumption that it did not contain more than two. A. Kundt and E.
Warburg. (Pogg. Ann., 135, 337 and 527 (1868)), showed that the
molecule of riiercury is monatomic, whence it follows that the hy-
drogen molecule is not composed of more than two atoms.
2 MOLECULAR WEIGHTS
multiplying by 14.367, and the molecular weight by
multiplying by 28.73.'
On the other hand, the density of a substance re-
ferred to air as unity is calculated by dividing the
molecular weight, in terms of hydrogen as the unit, by
28.73. If the molecular weight of oxygen is taken
as = 16, as is now generally done in accordance with
the suggestion of Ostwald, the number 28.95 is to be
used instead of 28.73.
It has been the custom for a long time to select air
as the unit for vapor-density determinations. Practi-
cally this is permissible, but theoretically it is to be
rejected, because air is a mechanical mixture and its "
composition therefore varies, if only slightly. It is
desirable to preserve the usual method of calculation,
because it has been applied almost without exception
to the data thus far obtained.
The vapor-density method for determining molec-
ular weights is indispensable for the solution of a
number of questions, especially among inorganic com-
pounds, while it has been replaced in many cases by
osmotic methods to be described later, especially in
the field of organic chemistry. Vapor-density determi-
nations are indeed of interest at elevated, and at very
high temperatures. The most important changes of
apparatus, etc., necessary for working at high tempera-
tures, should therefore be described, if only briefl}-, and
the more important literature given.
Theory of Vapor-density Determination. — By vapor-
density is to be tiitderstood the density of a substance in
' H. Kopp : Compt. rend., 44, 1347 (1857).
VAPOR-DENSITY 3
the gaseous state, compared with air at the same tem-
perature and pressure. The vapor-density is a con-
stant,' independent of the temperature, since from the
law of Gay Lussac, all gases undergo equal changes in
volume for equal changes in temperature.
In order to calculate a vapor-density we must know
the weight of the substance (g), .and that of the air
(G), which, at the same temperature and pressure, oc-
cupies the same volume as "the substance when vapor-
ized. Then the density d is :
cr
The weight of the air G can be ascertained by direct
weighing, as Bunsen^ has done in a series of determi-
nations. It is more convenient to avoid the weighing
and to measure the volume instead. In the latter case,
however, pressure and temperature must be taken into
account. The weight of i cc. of air, under normal
conditions (o° C, 760 mm.), is 0.001293 gram. The
volume V, reduced to normal conditions, is found
from the laws of Gay Lussac and Boyle, from the fol-
lowing equation : If v is the' volume read at t° C. and
' The density of a solid or a liquid is dependent upon the tem-
perature, even if water at the same temperature as the substance is
taken in eyery case for comparison, because the coefficient of ex-
pansion of water is not the same as that of the substance under in-
vestigation. For this reason, water, which is not at the same tem-
perature as the substance, but is at 4° C, is selected for density
determinations. The densities thus obtained give the mass of the
substance contained in unit volume.
' E>«3unsen : Ann. d. Chem. u. Pharm., 141, 273 (1867).
4 MOLECUI,AR WEIGHTS
p mm. pressure, and a is the coefficient of expansion of
air (a = 0.00367),
V = ^ .
760 (i +at)
From which :
^ 0.001293 vp , , 7600(1+ at)
Q = — — y^? — ~ ; and d = .
760(1+ at) 0.001293 vp
For the logarithmic calculation of a vapor-density
determination it is desirable to collect the numerical
factors so that their quotient is in the denominator :
^^ g(i+at) _
0.00000170 1 3 V p
* . . I
The table given in the appendix contains log — —
for the values of t, which most commonly occur. To
these are added the logarithms of the values in the
(^nominator (log 0.0000017^013 = 0.23079 — 6), and
Ijpum is subtracted from log g.
lis is the general formula for calculating the vapor-
densitV- It is modified when certain values cannot be
determined directly ;
a.o
liq^,i^
<
\
"^
—* — -=
A^v&.
i
— it
/20 150
no
XIO XfO no 300 330 J60
Temperature.
Fig. 9.
Vapor-density of acetic acid as determined by the Dumas method.
V. Meyer' on the one hand, and Crafts and F. Meyer^
on the other, obtained similar results with iodine.
The density 8.8 to 8.7 was found from 200° to 600°,
from which the formula 12^=8.77 is derived. A
decrease in the density was manifested above 600°.
With increasing temperature the density further
V. Meyer : Ber. d. chetn. Ges., 13, 394, loio (iS
' J. M. Crafts and Fr. Meyer : Compt. rend., 92, 39 (1881).
THE RESULTS 51
decreased, and from^ about 1400° the vapor-density
was again constant, being, however, only about one-
half of the above value, 4.5. The gas-displacement
method was used in this investigation.
The anomalies first mentioned are due to the same
cause. This is clearly seen from the last example.
The molecule of iodine even up to 600", evidently
consists of two atoms. These molecules cannot exist
at a higher temperature. They decompose into part
molecules I^. At first only a small number of the
molecules, I^, are decomposed. This number increases
as the temperature rises, and from 1400° up, all the
molecules of I, are decomposed to I^.
Deville' has introduced the term ''dissociation" for
this decomposition of complex molecules. He observed
this phenomenon in other investigations. It was a
peculiar fate that Deville was indeed the most violent
opponent of the application of the dissociation theory
for the explanation of anomalous vapor-densities. It
was Cannizzaro,^ Kopp,^ and Kekul^,* who recognized
almost simultaneously, that abnormal vapor-densities
can be explained by means of this theory.
The experimental proof of a dissociation of the
vaporized substance can be very clearly furnished for
at least some substances. Among these is phosphorus
pentachloride, PCI , which gives values for the vapor-
density considerably lower than 7.20 which corre-
' H. St. Claire Deville : Compt. rend., 45. 857 (1857).
^ S. Cannizzaro: Nuovo Cimento, 6, 428 (1857).
^ H. Kopp : Am. Chem. und Pharm., 105, 390 (1858).
•* A. Kekule : Ibid... 106, 143 ; Amnk., 1858.
52 MOLECULAR WEIGHTS
spends to the formula PCK A. Neumann,' using the
Dumas method, obtained the value 5.08 at 182°, at
higher temperatures lower values, and from 290° up,
the constant value 3. 7 was found. That a dissociation
had, in fact, taken place according to the equation,
PC1,= PC1,+ 2CI,
giving the double number of molecules, which would
explain the half-value for the vapor-density, was shown
by the color of the vapor. This, according to the
investigations of Deville,' had the yellow color of
chlorine ; being an especially striking example of the
phenomenon of dissociation.
Pebal,3 in a beautiful diffusion experiment in which
a diaphragm was used, succeeded in separating the pro-
ducts of dissociation of ammonium chloride, — hydro-
chloric acid and ammonia. The important diffusion
experiments of Wanklyn and Robinson^ show, perhaps,
in a more striking way, the dissociation of certain
vapors. They vaporized the substance to be tested, in
a flask. The more rapidh' diffusing products of disso-
ciation were carried away in larger amounts than the
more slowh- diffusing, by the air-current which was
allowed to pass over the neck of the flask. When the
experiment was interrupted after a time, analysis
showed that, as a matter of fact, a larger quantity of
■ A. Neumann: Ann. Chem. und Phann., Suppl., 5,349 (1867).
'' H. St. Claire Deville: Compt. rend., 62, 1157 (1866); Ann.
Chem. und Phann. 140, 168 (1866).
' L. V. Pebal : Ann. Chem. und Pharm., 123, 199 (1862).
* J. A. Wanklyn and J. Robinson : Compt. rend., 52, 547 ( 1861) ;
J. prakt. Chem., 88, 490 (1863).
THE RESULTS 53
the more slowly diffusing products of dissociation was
contained in the flask. In the case of phosphorus
pentachloride, more chlorine than phosphorus tri-
chloride was carried away, so that when the experi-
ment was interrupted a mixture remained behind
which was richer in phosphorus and poorer in
chlorine.
The tendency to dissociate was especially manifested
by those compounds which are easily formed by
bringing together the products of their dissociation ;
e.g.^ the ammonium salts and organic ammonium
compounds, chloral hydrate, chloral alcoholate, sul-
phuric acid, nitric acid, sulphuryl chloride, and some
alcohols which, through a splitting off of water, form
unsaturated hydrocarbons.
The values of the densities found for all of these
substances near their boiling-point, lie between the
values calculated from the formula and those calcu-
lated from the sum of the dissocia:tion-products. At
higher temperatures values are obtained which indicate
complete dissociation, and these remain constant at
still higher temperatures.
The vapor-density values which are higher than
would be expected from the formula of the substance,
can be explained in a strictly analogous manner; e.g.^
the vapor-densities found for acetic and formic acids
near their boiling-points. It has long been assumed
cooh) ^^^^ (c'ooh)
exist here. Only very recently have the different
methods for determining molecular weights shown
54 MOLECULAR WEIGHTS
that this assumption is correct, as will be pointed out
in discussing the results of the freezing-point and
boiling-point methods. This anomaly disappears in
the case of the fatty acids of higher molecular weight,
butyric acid, etc., both in the vapor-density determi-
nation and in the investigation in solution. The
same relations obtain with nitrogen dioxide as with
the simple fatty acids. It gives higher values for the
vapor-density at lower temperatures. The existence
of double molecules has also been shown here with
the freezing-point method.'
The more complex molecules have, in some cases, a
greater stability, so that concordant values are obtained
for their vapor-densities within a wider range of tem-
perature. The density of the vapor of iodine between
250° and 600° points constantly to the formula I^, that
of the anhydride of arsenious acid,^ from 520° to 770°,
to the formula As O^.
A constant density would undoubtedly be obtained
again for iodine above 1600°, which would correspond
to the second molecular weight I^. But the simple
experiment bearing upon this point has, however, not
yet been made.
It is interesting to note that the dissociation does
not extend to all of the molecules, at one temperature ;
e.g., the vapor-densit)' of arsenious acid at 770°
corresponding to the formula As O^;, might be found
at a little higher temperature (say 800°), to correspond
to the formula As^O^. Experiment has shown, indeed,
' W. Ramsay : Ztschr. phys. Chem., 3, 66 (1889).
■' H. Biltz: hid., 19, 417 (1896).
THE RESULTS 55
ttiat a rise in temperature of over 1000° is necessary
to complete the dissociation, a vapor-density corre-
sponding to the formula As^O not being obtained until
a temperature of 1800° was reached.
The kinetic theory of gases furnishes an explana-
tion of this phenomenon, which at first appears so
remarkable. According to this theory the temperature
of a gas is the expression of the mean velocity of its
molecules. Some molecules, indeed, have this velocity,
others move with greater, while others again with
smaller velocity. The velocity of the different mole-
cules is continually changing and has a different
value at each moment. Only the mean velocity of
all the molecules remains constant — equality of
temperature being assumed. A definite amount of
internal energy is necessary to decompose a molecule.
Only a limited number of all the molecules present
possess this amount at low temperatures. A larger
proportion of the molecules obtains the amount of
internal energy sufficient for their dissociation with
rise in temperature, and the consequent increase in
the total velocity of all the molecules. Therefore, the
amount of dissociation increases. A constantly in-
creasing number of molecules obtains the energy
necessary for their decomposition as the temperature
rises, until finally all of the molecules have reached this
condition and the dissociation is complete.
If we designate the temperature at which an isolated
molecule would be decomposed by dissociation, as the
dissociation temperature, it follows that the dissocia-
tion temperature is not the temperature at which all
56 MOLECULAR WEIGHTS
the molecules of a gas are really decomposed, but the
temperature at which exactly half of the molecules is
decomposed. Only in this case do the dissociation
temperature and the mean gas temperature coincide.
This point would be in the neighborhood of 1400*^ for
arsenious acid.
The "degree of dissociation" is an expression for
the extent to which the dissociation has progressed —
how large a fraction of the molecules originally
present in the undecomposed condition, is decomposed
by dissociation. Let d be the density which corre-
sponds to the undecomposed substance, d' the density
found at a definite temperature (smaller than d), n the
number of part molecules into which each original
molecule decomposes (^ 2 for arsenious acid), and 7
the degree of dissociation, then
__ d— d'
'''^(n— I) d''
It follows from what has been said that we must be
ver}- careful in judging a vapor-density determination.
Several \-apor-density determinations must alwa}'s be
carried out at different temperatures, except in simple
cases as with organic substances, where a single
determination of the density suffices to establish
the molecular weight. Only when these different
determinations give a constant value, are we justified
in drawing a conclusion in reference to the composi-
tion of the molecule corresponding to it. It can also
occur, especially with inorganic substances, that in
addition to the one kind of molecule, a second kind
may exist at much higher or lower temperature. The
THE RESULTS 57
latter are to be regarded as decomposition or conden-
sation products of the first. Examples are iodine and
arsenious acid.
In a number of cases, as acetic acid, nitrogen diox-
ide, sulphur, it is possible to prove the presence of
only one kind of molecules, — the smaller, — by means
of the vapor-density method, because the more com-
plex molecules begin to decompose already at the
boiling-point, and dissociation values are obtained just
above this temperature. The method of vapor-density
determination does not suffice in this case to ascertain
the molecular weight of the more complex molecules.'
Other methods must be utilized here to furnish
unquestionable proof of their existence. This has,
indeed, been accomplished for the substances named
above, and many others, by the aid of the freezing-
point and boiling-point methods. These methods
have shown that there are molecules of acetic'' acid
having the composition (CH COOH)^, of nitrogen
dioxide^ having the composition N,0 , and of sul-
phurt Sg.
The osmotic methods just named are, in turn, often
■not able to demonstrate the existence of smaller mole-
cules, as with iodine, sulphur, and arsenic trioxide.
These methods establish in these cases only the
molecular weights corresponding to the formulas
I^, S3, and As O,.
' H. Biltz: Ztschr. phj's. Chem., 3. 228 (1889).
2 E. Beckmann : Ibid., 2, 729 (1888).
" W. Ramsay : /bid., 3. 66 ( 1889) ; E. Beckmann : /bid., 5. 80
{1890).
■• J. Hertz : Ibid., 6, 358 ( 1890) ; H. Biltz : /bid., 19, 425 (1896).
58 MOLECULAR WEIGHTS
The neglect of this consideration easily leads to
error, as is shown by the assumption of the existence
of the molecules S^, which prevailed for many years.
The question has not yet been solved whether double
molecules always exist in many important cases, such
as the chlorides of iron and aluminum, together with
the simple molecules FeCl and AlCl . Their exist-
. . . 3 3 _
ence is, however, indicated by the higher vapor-
densities found at lower temperatures. This question
has not yet been answered by other methods in a
manner which is free from objection. The more
recent experiments of Werner are not adapted to this
purpose, since the boiling-point method was used.
3. Difference between the Results of the Dumas
and the Gas-displacement Method. — As far as the
determination of the molecular weight of an un-
dissociated substance is concerned, the method
of Dumas and the gas-displacement method give
results of equal value, so that when very accurate
measurements are not required the gas-displacement
method of V. Meyer is to be preferred, since it is
the more convenient. It is different for dissociating
substances. Here the two methods give different
values ; those found by the method of Dumas being
uniformly higher than by the method of V. Meyer.
The reason for this lies in the fact that in the gas-
displacement method the foreign gas mixed with the
vapor dilutes it, producing thereby a corresponding
increase in the dissociation. The determinations of
the vapor-density of sulphur,' carried out by the two
■ H. Biltz : Ztschr. phys. Chem., z, 920 (1888).
Dumas Method.
Method.
7.04
5.4 mean
4-73
3-6 "
THE RESULTS 59
methods at the same temperature, show this difference
very clearly.
Gas-displacement
Temperature. "' " ' __ . .
518°
606°
The results' for aluminum chloride obtained by
Nilson and Pettersson confirm the foregoing.
The dissociating influence of a foreign gas mixed
with the vapor of the substance, manifests itself in
still another way. A more or less intimate mixture
of the vaporized substance with the foreign gas takes
place in the V. Meyer method, according to the
amount of substance which is to be converted into
vapor. A more intimate mixture is obtained when
the amount of substance used is small, than when a
larger quantity is employed.
Consequently, in the former case the dissociation
proceeds further than in the latter, and a smaller
value for the vapor-density is found. The fluctuations
caused thereby in the density values of dissociating
substances are, in general, not great, as e. g. is shown
by the experiments of Nilson and Pettersson^ with
aluminum chloride. They found for aluminum
chloride, at the boiling-point of sulphur :
Gram substance 0.1102 0.0963 0.0859
Density 7.79 7.5 7.4
This dependence of the vapor-density upon the
amount of substance employed, is very unustially
' L. F. Nilson and O. Pettersson: Ztschr. phj-s. Chem.^ 4, 206,
224 (1889).
''■ L. F. Nilson and O. Pettersson : Ibid., 4, 214 (1889).
6o MOLECULAR WEIGHTS
great for sulphur' within its stages of dissociation ^
since the breaking down of the molecule Sg into mole-
cules of S,, produces a marked change in the density.
Gram substance 0.1067 0.0888 0.0675 0.0555 0.0450
Density 7.1 6.4 5.7 4.9 4.5
The form' of the vaporizing vessel in the gas-
displacement method, has also an influence in the
investigation of dissociating substances. The wider
the vessel the better the mixing of the vaporized
substance with the gas contained in it ; the narrower
the vessel, the less perfect the mixing. As a matter
of fact, methylene bromide at 100°, and sulphur at
518°, behave similarly in this re.spect.
All these obser\ations show that the Dumas method
is better adapted to the investigation of dissociation
phenomena than the gas-displacement method. The
disturbing factors above mentioned disappear and
much simpler relations obtain. But the experimental
difficulties presented by the Dumas method above
700°, are so great that the gas-displacement method
must be resorted to. This- latter method also gives
uniform values at these high temperatures, and still
better at the very highest temperatures employed,
because the movement of the molecules, as such, is so
rapid at these high temperatures that an intimate
mixings of the gases is, in every case, quickly brought
' H. Biltz: Ztschr. phys. Chem., 2, 926, 944 (1888); Ber. d.
chem. Ges., 21, 2013 (1888).
" H. Biltz: Ber. d. chem. Ges., 21, 2772 (1888).
■' Consequently the dissociation will always increase, for an
equal rise in temperature, more rapidly at higher temperatures than
at lower. A dissociation curve must therefore fall more rapidly at
very high than at moderate temperatxires, as is shown by the disso-
ciation curve of arsenious acid (Ztschr. phys.Chem.,ig, 422 (1896)).
THE RESULTS 6 1
about. Values are indeed found, which differ from
those which would be obtained by the Dumas method,
but these remain constant in repeated experiments, so
that the dissociation can be followed step by step by
the gas-displacement method.
OSMOTIC METHODS
There is the tendency on the part of a dissolved
substance to distribute itself uniformly throughout the
entire volume of the solution, just as a gas tends to
fill uniformly the space placed at its disposal. The
osmotic experiments of Graham' and others, in which
a layer of the pure solvent was placed over the con-
centrated solution, have shown this; the dissolved
molecules migrating from the solution into the pure
solvent, and the reverse, the molecules of the pure
solvent wandering into the solution. The final condi-
tion which is reached, however, only after a long
time, is one in which a sufficient number of molecules
have wandered from the solution into the solvent to
make the concentration in both equal. The measure
of this tendency of the dissolved molecules to fill the
space uniformly is the osmotic pressure.''
Osmotic pressure has been measured directly with
suitable devices. These measurements have shown
that, apart from temperature and concentration,
osmotic pressure is dependent only upon the number
of dissolved molecules, but not upon their size.
Therefore, equimolecular solutions, /. e., solutions
■ Th. Graham: Ann. Chem. und Pharm., 77, 56, 129 (1851);
80, 197(1851); 121,1(1862).
2 J. H. van't HofF: Ztschr. phys. Chem., i, 481 (1887).
OSMOTIC METHODS 63
which contain an equal number of molecules of any
substance in equal volumes, have the same osmotic
pressure at the same temperature.
Equimolecular solutions are defined differently, as
Raoult and others have done, in investigations in
which measurements are to be made. Equimolecular
solutions are those which contain an equal number of
molecules in an equal mass of the solvent. By using
this definition the calculation of the results of experi-
ment is considerably simplified, so that at present it is
almost exclusively used. Abegg' has tried to furnish
a rational basis for it.
A naethod for determining molecular weights is based
upon this. Two solutions of different substances in
the same solvent are brought to the same osmotic
pressure.^ It follows from what has been said, that
in the two solutions an equal number of molecules of
the two substances are present in the same amount of
the solvents. If we designate the molecular weights
by m, and m^, and the number of grams of the sub-
stance dissolved in loo grams of the solvent by
r^ and r^ :
m, r,
m, ~ r/
If now the molecular weight of one of the dissolved
substances, m , is known, the unknown molecular
■ R. Abegg: Ztschr. phys. Chem., 15, 248 (1894).
2 Compare the work of H. de Vries : Ztschr. phys. Chem., /.,
415, 430 (1888); and of K. Schreher : Mitteilungen aus dem
naturwissenschaftl. Verein f. Neupommern und Riigen, 26, 161
(1895)-
64 MOLECUIvAR WEIGHTS
weight of the other is calculated from the equation :
ni,
m, ^ — -
But since it is difficult to carry out a direct meas-
urement of the osmotic pressure, an indirect method is
employed. Instead of ascertaining the pressure which
a dissolved substance exerts in its effort to fill the
larger volume occupied by the solvent, the work
(osmotic work) is determined in a solution of definite
concentration, which is necessary to separate the
solvent and the dissolved substance. Nemst' has
shown that there are several possible ways of doing
this, and how these may be used as methods for
measuring osmotic pressure.
Only three of these find practical application in the
laboratory as methods for determining molecular
weights: (i) The freezing-point method; (2) the
boiling-point method; and (3) the method of Nernst,
based upon the principle of lowering of solubility.
The first is based upon the fact that when a solution
freezes only the solid solvent separates, while the
liquid solution becomes more concentrated. But
since a part of the solvent is thus removed from the
solution and the dissolved molecules are confined to a
smaller volume, the osmotic pressure of the dissolved
substance must be overcome by external work. More
heat must therefore be removed from a solution before
it freezes, than from the pure solvent. Inasmuch as
the latent heat of fusion remains nearly constant, the
■ W. Nernst: Theoretische Chemie, p. 121 (1893).
OSMOTIC METHODS 65
larger removal of heat is expressed in a depression of
the freezing-point.
A separation of a part of the solvent from the solu-
tion also takes place when a solution is boiled, and
upon this the second method rests. A special expen-
diture of work is necessary also here, to confine the
dissolved substance to a smaller quantity of the
solvent. More heat must be added than is necessary
to boil the pure solvent, and this larger addition of
heat is expressed in a rise of the boiling-point, since
the heat of vaporization is only slightly changed.
The third method attempts to remove the solvent
from the solution in a manner different from those
already described, by adding another solvent which
dissolves the primary solvent to a certain extent, but
does not dissolve the substance in solution in the
primary solvent. A part of the solvent is removed
from the primary solution by means of this second
solvent, and the more of it the smaller the osmotic
pressure of the dissolved substance in the primary
solvent.
The real theoretical foundation of these methods,
which could be only indicated here, is discussed more
fully in the text-books of physical chemistry.^ In the
following presentation of the several methods, each is
built up for itself on an experimental foundation, and
is empirically developed.
' W. Ostwald: Lehrb. d. allg. Chemie( Leipzig, 1891). W. Ost-
wald: Grundriss d. allg. Chemie (Leipzig, 1889). W. Nernst :
Theoretische Chemie vom Standpunkte der Avogadroschen Kegel
und der Thermodynamik (Stuttgart, 1893).
66
MOLECUI.AR WEIGHTS
^i
Beckmann's Differential Thermometer
Since we are not dealing with absolute measure-
ments of temperature in determining molecular
weights by the boiling-point and freezing-
n point methods, but only determined how much
higher a solution boils than the pure solvent
or how much lower it freezes, a differential
thermometer with an arbitrary scale is em-
ployed for this purpose. The numbers on
the scale do not indicate the real tempera-
ture, but the difference between the two
positions of the mercury column, read on the
scale, corresponds to the difference in tem-
peratures in degrees Celsius.
Thermometers adapted to this purpose
have been constructed by Beckmann. ' They
are furnished in complete form by F. O. R.
Gotze, in Leipsic. There are two forms upon
the market : those having a larger mercury
bulb, about 5 cm. long and 0.9 cm. in diam-
eter, and those having a smaller mercury
bulb, about 2.3 cm. long and i.i cm. in
diameter. The length of a degree is, in the
first case, about 4.5 cm., in the latter about
3.5 cm. The scale includes from 5 to 6
Each degree is divided into hun-
Fig. 10.
Reservoir of QegTeeS.
the Beck- °
mann differ- drcdths, and each hundredth is sufficiently
ential ther- ' •'
NaTurT^size l^^gc that the thousaudths can be estimated
accurately by means of a lens. Care must be
taken in reading, that the eye, the mercury meniscus,
'E. Beckmann : Ztschr. phys. Chem., 2, 643 (i
OSMOTIC METHOD 67
and the line to be read, are all on the same plane,
that parallax may be avoided.
Thermometers with smaller bulbs are generally
employed at present, because they can be used for
investigations with both the freezing-point and boiling-
point methods, while thermometers with long bulbs
can be used only up to 80°. However, when it is
desired to procure a thermometer, attention should be
paid to what is stated later (note page 69).
A small reservoir is joined to the capillary above, as
shown in Fig. 10, in order that the same thermometer
can be used at different temperatures. If observation^
are to be made at a lower temperature, in the neigh-
borhood of 0°, the bulb of the thermometer must
contain much mercury, and only a small residue is
left in the reservoir. But if the same thermometer is
to be used at about 100°, a considerable quantity of
mercury must be transferred from the bulb of the
thermometer to the reservoir. In determining
molecular weights by the boiling-point method, in
which a rise in boiling-point is to be observed, the
adjustment must be so made that the top of the
mercury column comes to rest on the lower part of
the scale, when the thermometer is immersed in the
vapor of the pure solvent; while in the freezing-
point method, where a depression of the freezing-
point is to be observed, the mercury should come to
rest near the upper end of the scale, wbett' the ther-
mometer is immersed in the freezing solvent. It is a
matter of indifference, as alrea-Toluidine must be carefully dehydrated. Compare M. Ste-
phani : Disst., Ziirich (1896), p. 25.
FREEZING-POINT METHOD 109
cedure is adopted with formic acid, if a sufScient quan-
tity is available.
When water is to be used, ordinary distilled water
suffices. It is generally necessary to make it freeze
by inoculation.
It is necessary to vigorously stir naphthalene^ phenol^
■ azobenzene^ and stearic acid, near the point of solidifi-
cation, and to wait until the mercury has reached the
highest point, which usually requires considerable
time. To obtain a sufficient undercooling the liquid
is stirred very slowly, until it is about o.i° below its
freezing-point, and then stirred vigorously. It is im-
portant that the entire mass of the liquid should be
agitated.
Stearic ««'rf recommended by Eyckmann,' proved to
be useful in some experiments in which the Beck-
mann apparatus was employed. When it is used, the
temperature of the cooling-bath must be kept six or
seven degrees below the melting-point of the substance
used, which must be previously ascertained, and a
greater undercooling of, indeed, 0.5" to 0.6° must be
effected. The adjustment of the thermometer for
stearic acid requires some attention.
Nitrobenzene is not so well adapted to more ex-
act determinations, because constant values for the ad-
justment cannot be easily obtained with it.
Azobenzene behaves like naphthalene. It presents
this advantage, that it has a smaller tendency to sub-
lime. On the other hand, the determination of a
' J. F. Eyckmann : Ztschr. phys. Chem., 4, 500 (1889).
no MOLECULAR WEIGH! S
constant freezing-point is more difficnlt. It is also
necessary at times to prevent too strong undercooling
by inoculation.
Naphthalene and phenol easily sublime into the
upper part of the freezing-vessel, and can be returned
to the lower portion only, in part, by melting. In the
later experiments of a longer series, a small quantity
(o.i to 0.3 gram) is to be subtracted from the amount
of the solvent to be employed in the calculation, as a
correction. It is especially necessary with naphtha-
lene to have the same undercooling in ever)- determi-
nation.
As regards the amount of tinder coolings it should
be greater for solvents with a large heat of fusion,
(about o.3°-o.5°), since otherwise so little ice would
separate, that when mixed with the remaining mass
of the solvent, it would not suffice to bring this up to
the true freezing-temperature. It is especially desir-
able to have considerable undercooling (about 0.5°)
when formic acid, acetic acid, and water' are used.
Solvents which have a \'er}' small heat of fusion, as
nitrobenzene and phosphorus, show freezing-points
which sometimes var}- some hundredths of a degree.
This is due to the fact that their crystals effect onl)- small
changes in temperature, when, on mixing with the
solution, they increase in size or melt. But since the
molecular depression of these substances (especially
phosphorus) is ver^- considerable, the results can be
used for a molecular weight determination.
' M. Wildermann recommencls an undercooling of at least
0.6° to 0.7° with water. Ztschr. phys. Chem., 15, 359 (1894).
FREEZING-POINT METHOD III
Acetic acid^'^ which has been. strongly recommended
by V. Meyer and Auwers, is admirably adapted for
laboratory practice ; first, because it can be worked
with conveniently, and second, as will be shown later,
considerable irregularities are scarcely ever found in
the results. Further, benzene is well adapted to this
purpose, and can be worked with more conveniently
than acetic acid, and although it sometimes gives irreg-
ular results, nevertheless it is very useful in determin-
ing molecular values when the explanations to be given
later (chapter containing results) are taken into
account. It is all the more useful, since the large
value of the constant diminishes the effect on the
result of small errors in the measurement of tempera-
ture. Naphthalene^ which in other respects is as good
for this purpose as benzene, at its melting-point, 80°,
is an excellent solvent for many substances which are
only slightly soluble in bezene at 5°, Finally phenol
is to be mentioned. This, like acetic acid, gives
results which are simpler in their relations.
Solvents Which Cannot Be Used in Certain
Cases. — Solvents which are isomorphous with the
substance to be dissolved in them, or which are closely
related to it chemically, cannot be used for molectilar
weight determinations. These solvents do not sepa-
rate as pure solids, but there separates a mixture of
the solid solvent and the dissolved substance, which
' K. Auwers : Ber. d. chem. Ges., 21, 707 ( 1888). K. Auwers
and V. Meyer : Ibid., 21, 1068 (1888). E. Beckmann : Ztschr. phys.
Chem., 2, 742 (1888).
112 MOLECULAR WEIGHTS
is to be regarded as a solid solution.' In these cases,
a smaller quantity of the dissolved substance remains
in the solution than was added to the solvent. The
depressions of the freezing-point found, are, therefore,
too small, and the molecular weights calculated are
too large.
This irregularity is shown by : Solutions in benzene^
of thiophene, pyrrol, pyrroline, pyridine, pyrroleine,
piperidine, quinoline, tetrahydroquinoline.
Solutions in naphthalene^ of indol, indene, quinolene,
isoquinolene, tetrahydroquinoline, /3-naphthol, pyrrol,
pyrrolene.
Solutions in phenanthrene, of carbazol, anthracene,
acridine, tetrahydrocarbazol, diphenylene oxide, naph-
thoquinolene.
Solutions in diphenyl^ of dipyridil, tetrahydrodi-
phenyl.
Finally, solution in benzoic acid of salicylic acid,
a-carbopyrrolic acid, in succinic acid anhydride^ of ma-
leic acid anhydride, and in acetophenone^ of acetylpyr-
rol, acetothienone.
This irregularity is not found for substances with
open chains; e. g., butyric acid in crotonic acid, oleic
acid in stearic acid, give normal values.
The presence of side chains either in the solvent or
in the dissolved substance, tends to give normal val-
ues. Pyrrol and thiophene dissolved in p-xylene, and,
further, methyl pyrrol dissolved in benzene, give nor-
mal depressions.
' J. H. van't Hoff : Ztschr. phys. Chem., 5, 322, 334 (1890).
FREEZING-POINT METHOD II 3
It was possible in some of these cases, to prove di-
rectly that some of the dissolved substance had sepa-
rated on freezing. The solid which had separated was
isolated and analyzed, the amount of the dissolved
substance present in the mother-liquor included in the
crystals, being determined by a peculiar device," and
left out of account.
Iodine dissolved in benzene showed the same pecul-
iarity as the above-mentioned ring compounds. Its
behavior has been shown very clearly, through an in-
vestigation by Beckmann' and Stock, by studying it,
on the one hand, in other solvents, which allowed no
iodine to crystallize out with them, and on the other,
by determining the amount of iodine in the solid ben-
zene which separated out.
Antimony^ dissolved in tin, behaves just as irregu-
larly.
Increase in Accuracy in Investigating Very-
Dilute Solutions. — In studying scientifically the law
which lies at the foundation of the freezing-point
method, pains has been taken to refine the method,
and thus to increase, as far as possible, the accuracy of
the results. Since the laws of osmotic pressure
appear clearly, only in very dilute solutions, this in-
vestigation must extend to such solutions, and to the
very small depressions of the freezing-point given by
' A. V. Bijlert : Ztschr. phys. Chem., 8, 343 (1891). Compare
also E. Beckmann: Ibid., 27, 609 (1897).
= E. Beckmanri and A. Stock: Ibid., 17,107(1895).
'' C. T. Heycock and E. H. Neville : Chem. News, 59, 157
(1889).
114 MOI.ECULAR WEIGHTS
them. These experiments have partly accomplished
their purpose. Numerous sources of error have been
discovered, but others are not yet sufficiently under-
stood to enable one to make a proper correction for
them.
Much larger volumes of liquid (about i liter') are
used for exact measurements. The surface is then
small in proportion to the mass, and variations in the
external temperature have a smaller influence. The
pure solvent is poured at first into the apparatus, —
water alone having been used up to the present, — and
the freezing-point of the water ascertained. A definite
\-olume of the solvent is then removed by means of a
pipette, and an equal volume of a standardized solu-
tion of the substance to be investigated, added. A
solution of known concentration is thus conveniently
prepared in the apparatus.
A plate, with openings cut opposite one another,
serves as a stirrer. It is placed horizontal, and moved
up and down by means' of a rod. A vigorous move-
ment of the liquid particles is effected b}- a special
arrangement^ of the sections. Hitherto stirrers of
porcelain, silver, and brass have been used. The use
of a platinum stirrer appears desirable also in this case,
and all the more so, since working with a platinum
stirrer is not so expensive as we generally think, since
the larger platinum wor^s — e. g.^ Heraeus in Hanau
' H. C. Jones: Ztschr. phys. Chem., ii, in, 529; 12, 623
(1893); P. B. Lewis : Ibid., 15, 367 (1894).
^H. C. Jones: Ibid., 11, 533 (1893); P. B.Lewis: Ibid.,
15, 368(1894).
FREEZING-POINT METHOD 115
— are generally ready to take back platinum appara-
tus furnished for scientific investigations, after the in-
vestigation is finished. It is therefore necessary to
pay only for making the apparatus.
The velocity of the stirrer has a marked influence,
according to the experiments of Nernst and Abegg,'
since heat is continually being produced in the liquid by
stirring, and this raises the real freezing-point. Con-
sequently, they employed a device for driving the
stirrer, whose speed can be accurately regulated. The
effect of the stirrer is ol less significance in ordinary
molecular weight determinations, in which the liquid
has relatively a larger surface.
Thermometers'" have been occasionally employed
whose scale was graduated to thousandths of a degree,
and which, accordingly, had a range of from only }4°
to i". Also, thermometers graduated to hundredths,
have been read with a microscope^ with ocular microm-
eter, which made it possible to estimate the ten-
thousandths of a degree. Readings of equal accuracy
■were possible by these two devices, provided the
^aduation on the thermometer divided into hun-
dredths, is made fine enough. It is, however, a ques-
tion whether the use of a thermometer graduated to
thousandths is not to be abandoned, because the bulb
required is too large. The possibility of heating a
mass of about 300 grams of mercury, with sufficient
' W. Nernst and R. Abegg : Ztschr. phys. Chem., 15, 687
1(1894); R. Abegg: /bid., 20, 212 (1896).
' H. C. Jones: /bid., 11, no (1893); P. B. Lewis: /bid.,
15,366(1894).
^ E. H. Loomis: Wied. Ann., N. F., 51, 506 (1894).
Il6 MOLECULAR WEIGHTS
uniformity with the arrangement used, appears to be
doubtful. At all events, the sources of error inherent
in the method of work, are, up to the present, of more
consequence than the errors due to the inexact read-
ing of the temperature.
The influence of the cooling-vessel, whose tempera-
ture must be kept very constant, is of the very great-
est significance. Nernst and Abegg' surrounded the
freezing-vessel on all sides, also above, with a freezing-
mixture which was contained in a vessel protected
from the temperature of the room by a thick layer of
felt. The temperature of the room should be as near
as possible to the freezing-temperature. A correctidn
for the effect of the temperature of the freezing-bath,
and for the action of the stirrer, obtained from obser-
vations, was first applied by Nernst,'' through a method
of calculation which still needs some modification.
This method was discussed by Wildermann,^ who
endeavored to so arrange the conditions of his exper-
iments, that corrections could be done away with.
Raoult" sought to solve the problem in a simple man-
ner, which was the more desirable, since the values of
Nernst's correction cannot be determined with any
great degree of certainty. His method is, moreover,
\'er)- closely related to the procedure of Wildermann
above referred to.
' W. Nernst anrl R. Abegg : Ztschr. phys. Chem., 15, 685
(1894) ; R. Abegg: Ibid., 20, 211 (1896).
MV. Nemst and R. Abegg: Ibid., 15, 682 (1894).
^ M. Wildermann : Ibid., 19, 63 (1896).
^ F. M. Raoult : Ibid., 20, 601 (1896).
CRITICAL EXAMINATION OF THE RESULTS
Smaller Anomalies Inherent in the Method. — If a
series of molecular weight determinations is carried
out, with increasing concentration of the same sub-
stance in the same solvent, it would be expected that
all of the determinations would give the same value.
But such is not the case. The results do not vary
irregularly about a mean value, but show a quite
regular decrease or increase. The smallest values are
generally found at the greatest dilution. The molec-
ular weight found, increases with increasing concen-
tration. . This particular kind of increase is shown
by the following values for the molecular weight
of naphthalene (m = 128) in benzene, published by
Beckmann.'
Concentration.
Molecular weig^ht.
Concentration.
Molecular weight.
I.I
, 120
10.6
126
2.6
122
12.7
127
4,0
123
^■3
128
51
123
16.6
130
6.6
124
20.5
132
8.1 125
The deviations from the calculated value, 128,
shown by the individual determinations, are not great,
but their regularity indicates that these are not due
to experimental error, but that a cause inherent in
the nature of the experiment, lies at the base of this
phenomenon.
A decrease in the molecular weight with rise in tern^
piS:^¥e-is seldom found. Chloral (CC1CH0 = 147.5)
' E. Beckmann : Ztschr. phys. Chem., x, 734 (1898).
ii8
MOI.ECULAR WEIGHTS
in glacial acetic acid, is an example, according to the
experiments of Beckmann.'
Concentration.
Molecular weight.
0.76
179
2.8
172
5-4
J 66
I0.4
164
14.6
162
Sometimes the values for the molecular weight de-
crease, at first, with increasing concentration, reach a
minimum, and then begin to increase, as is shown by
the example given on page 93 of acetic ether in ben-
zene.
The results obtained are very clearly shown in a
curve,° in which the depressions are plotted as abscis-
sae, and the molecular weights as ordinates.
^
-^-~
■q>^,
/iO
""
■"
1
"
A
J
•
H
r c
■ ■
'' 8'
Freezing-point lowering.
Fig. 19.
Naphthalene in solution in glacial acetic acid.
These curves can be used to derive the molecular
weight at infinite dilution, by graphic extrapolation
Beckmann^ found the following values for phenetol
(CgHjOC^H^ ==; 122) in glacial acetic acid.
■ E. Beckmann : Ztschr. phys. Chem., 2, 724 (1888).
' E. Beckmann : Ibid., 2, 719 (1888).
" E. Beckmann : Ibid., 2, 732 (1888).
EXAMINATION OF THE RESULTS
119
Lowering 0.324° 1.602° 2.522° 4.162° 5.252°
Molecular weight 125 136 143 159 171
If the curve is drawn with these values, it will be
found to be almost a straight line. The value which
would be found for the molecular weight at infinite
dilution, can be determined by prolonging the curve
to the left, until it intersects the perpendicular drawn
through the zero point. The distance cut off on this
perpendicular by the curve, corresponds to the molec-
ular weight at infinite dilution. Our example gives
the value required, 122.
Other examples are found in the works of Beck-
S/60
iJ'iO
no
*
^
-^"
Q/v,„(
0' r x" 3" 1
Freezing-point lowering-.
J'
Fig. 20.
Phenetol in solution in glacial acetic acid.
mann. The reason for this procedure lies in the fact
that the laws of osmotic pressure, and the methods for
determining molecular weights based upon them, hold
most rigidly in very dilute solutions. The true value
of the molecular weight would, therefore, be expected
at infinite dilution, which cannot be tested experimen-
tally with the thermometer.
I20
MOI^ECULAR WEIGHTS
This method of graphically extrapolating the value
for the molecular weight, is to be recommended, when
the curve is not a straight line nearly parallel to the
abscissae, but when it is a straight line deviating
widely from this direction, or is bent. In every case,
several observations must be made in very dilute
solutions (depression 0.05'^ to 0.25°), because many
curves are strongly bent in this part of their course,
especially those of the acids and oximes, (Figs. 22 and
MOio
U
taoio
>
p
y
y
/
/
•■>
^
/
/
/'
/
/
, ,
^
U)
*t
Hundredths grams-molecule to loo grams of solvent
Fig. 21.
(i) ^-oxybenzaldehyde. (2) ;>-Cresol in solution in naphthalene.
(Drawn by the method of Auwers.)
23) and the neglect of this portion of the curve would
lead, on extrapolation, to erroneous results.
Auwers' undertook a recalculation of the numerical
values, in order that the results obtained with differ-
ent substances in the same solvent, could be so brought
' K. Auwers: Ztschr. phys. Chem. 21, 339 (1896).
ELECTROLYTIC DISSOCIATION 121
together in a table of curves, that the different curves
would be directly comparable. The concentrations,
multiplied by loo and divided by the molecular weight
(hundredths gram-molecular weight substance to loo
grams solvent), were taken as abscissae, and the per-
centage deviations of the molecular weight found,
from the theoretical, as ordinates. The results ob-
tained f or ^-oxybenzaldehyde and ^-cresol, are drawn
in the above table of curves, according to the method
of Auwers. Many curves thus drawn, are contained in
the tables in the work of Auwers already mentioned.
In these, any regularities which exist, can be easily
recognized, but they suffer from the unavoidable defect,
that the initial portions of the different curves lie very
close to one another, so that it is not very easy to keep
them apart. But as is shown in the above mentioned
publication, a larger number of curves can be drawn
with the same coordinates, without becoming con-
fused, if the drawing is neatly done.
ELECTROLYTIC DISSOCIATION
The investigation of aqueous solutions of salts, leads
to very irregular results, especially those of the strong
inorganic acids and bases, and further, solutions of
strong acids and bases themselves. Sodium chloride, ■
for example, in dilute solution, gives a depression
almost double that which would be expected from the
formula, whereas, the molecular weight calculated
from this, would be only a little more than half the
theoretical. Some salts, such as barium chloride,
magnesium chloride, potassium sulphate, show still
greater deviation.
122 MOI.ECULAR WEIGHTS
This phenomenon has been explained by Arrhenius'
with the aid of the following assumption. The sub-
stances which show this irregularity, on dissolving,
dissociate into part molecules, the so-called ions : e. g.^
Sodium chloride, NaCl, into Na + CI,
Potassium sulphate, K^SO, into K + K+ SO,, or
into K + KSO,.
The ions are to be distinguished from the free atoms,
in that they are charged with large quantities of
electricity. The number of dissolved molecules con-
tained in the solution, is largely increased by this dis-
sociation, since the ions act as molecules. In the case
of sodium chloride it was almost doubled, consequently
the mean molecular weight is almost half that which
would be expected from the formula NaCl ; NaCl =
58. 5, mean molecular weight of the ions := 2 9. 2.
The dissociation is greatest in very dilute solutions ;
the greater the concentration of a solution, the smaller
the fraction of dissociated molecules. The amount of
the dissociation depends, further, upon the chemical
properties of the substance. The weak acids and weak
bases are im4 the least dissociated, their salts are more
strongly dissociated, while the strong acids and bases
and their salts are the most strongly dissociated.
Weak acids and weak bases give, therefore, nearly
normal values for the molecular weights ; examples
are, lactic acid, formic acid, butyric acid, ethylamine.
The, halogen compounds of bivalent mercury, as well
' Svante Arrhenius : Ztschr. phys. Chem., i, 631 (1887).
ELECTROLYTIC DISSOCIATION 123
as the cyanide, are but little dissociated. The cor-
responding cadmium salts are somewhat more disso-
ciated, and the corresponding zinc salts still more.
Formic acid,' like water, is a strong dissociating
agent, though it is not as strong as water. Methyl
alcohol ^ dissociates less strongly than formic acid.
The amount of dissociation can be ascertained from
a determination of the molecular weight by the freez-
ing-point method, in a manner similar to that employed
in ascertaining dissociation from the determination of
vapor-density. lyCt M represent the molecular weight
calculated from the formula, M' the molecular weight
found (smaller than M), n the number of ions into
which a molecule dissociates, and 7 the degree of dis-
sociation ; i. e.^ the fraction of the molecules originally
present in the undecomposed condition, which is broken
down into ions, then we have :
M — M'
' (n— i)M'
All solutions which conduct the electric current
contain such dissociated molecules. Indeed, it is the
ions which make conductivity possible ; the larger the
number of ions the greater the conductivity of the
solution. Upon this fact is based a second method
for determining the amount of dissociation, which
gives the same values as the cryoscopic method, for
molecules which break down into only two ions.
'H. Zanninowicli-Tessarin : Ztschr. phys. Chem., 19, 251
(1896).
* G. Carrara : Ibid., 21, 680 (1896).
124 MOLECULAR WEIGHTS
Since the experimental errors of this electrical method
are smaller, it gives more accurate results. The results
of the two methods are different for substances which
break down into more than two ions.
Since, then, only conductors of the current break
down into ions, this kind of dissociation has been
termed " Electrolytic dissociation.'" It must, however,
be clearly borne in mind, that this condition of dis-
sociation is not brought about by the passage of the
current through the liquid, but is completely inde-
pendent of it, existing in the liquid through which no
current is passing. The capability of a liquid to con-
duct the current, is but an expression of the fact that
it contains free ions.
Another kind of splitting-up which certain sub-
stances undergo in solution, is to be distinguished from
electrolytic dissociation, although it is very similar to
the latter in its effect upon the molecular weight found.
It is the breaking down which certain chemical com-
pounds undergo, when formed of two substances loosely
held together. Quinhydrone decomposes in solution
into quinone and hydroquinone, losing its intense
color. Belonging to this same class are the com-
pounds of the hydrocarbons with picric acid.^ Chloral
hydrates belongs also in this class, since in solution in
acetic acid, it gives considerably smaller values than
would correspond to the formula CCl .CH(OH^, evi-
' Fitzgerald proposed the name ionization : Ztschr. phys.
Chem.. 7, 400 (1891).
= R. Anschiitz : Ann. d. Chem., 253, 343 (1889) ; E. Patemo and
R. Nasini : Ber. d. chem. Ges., 22, R. 644 (1889).
' E. Beckmann : Ztschr. phys. Chem., i, 724 (18
ELECTROLYTIC DISSOCIATION 125
dently because it is partially broken up into chloral
and water. This decomposition is not shown in
aqueous solution, since the dissociation is driven
back by the large quantity of one of the possible
products of dissociation. The same phenomenon
is exhibited by chloral alcoholate,' which decomposes
into its components in benzene, and .still more in acetic
acid and water. Finally, attention should be called
to salts containing water of crystallization, which lose
their water of crystallization in aqueous solution. In
none of these cases does electrolytic dis.sociation take
place.
A substance like ammonium chloride can decom-
pose by dissociation, in two ways. In the gaseous con-
dition it is split up into ammonia and hydrochloric
acid :
NH,C1 = NH3-|-HC1.
In aqueous solution, on the other hand, the compo-
nents are the ammonium and the chlorine ions :
NH,Cl = NH,-fCl.
The determination of the molecular weight gives
half the true value, in both cases, but as the equations
just given show, this is explained differently in the
two cases..
More Complex Molecules. — While the electrolytic
dissociation in aqueous solutions, can lead to smaller
molecular weights than would be expected from the
formula of the substance, the reverse can take place in
some other solvents ; i. e., a condensation of several
' E. Beckniann : Ztschr. phys. Chem., 2, 724 (if
126
MOLECULAR WEIGHTS
simple molecules to form, a more com.plex ?nolecule.
The determination of. the molecular weight in this
case, gives values which are too large. The term
"association " has recently been proposed for this kind
of condensation. This phenomenon depends upon.the
nature of the solvent, the nature of the dissolved sub-
stance, and the concentration.
The following solvents favor the formation of more
complex molecules :
ASSOCIATING SOLVENTS.
Anethol,
Azobenzene,
Benzene,
Bromoform ,
Dimethylaniline ,
Diphenyl,
Diphenylmethane ,
Methyl oxalate,
Naphthalene,
Nitrobenzene,
Phenanthrene,
/■-Propylanisol,
/Ji-Toluidine.
On the other hand, we find the simple molecules in
the following solvents :
NON-ASSOCIATING SOLVENTS
Acetoxime,
Formic acid,
Aniline,
/-Brompheuol,
Cetyl alcohol,
Chloral alcoliolate.
Acetic acid,
/-Cresol,
Phenol,
Phenylpropionic acid,
Stearine,
Stearic acid,
Thymol,
Urethane,
Urethylane.
Acetophenone has a weaker action than these, while
the strongest of the above are formic and nitric acids.
The hydrocarbons are, then, most favorable to the
formation of complex molecules, and solvents contain-
ing hydroxyl to simple molecules.
ELECTROLYTIC DISSOCIATION 127
If it is a question of establishing the simplest
molecular weight, which is of the most interest to the
chemist, a solvent with dissociating power is chosen
for this purpose from the second table. But this pre-
caution is necessary onl)- when the substance whose
molecular weight is to be determined, tends to form
complex molecules.
Experience has shown that only those substances
which contain kydroxyl-, and such, substances which,
through desmotropism, can easily pass over into
hydroxyl compounds, form double molecules and still
larger molecular aggregations. Very typical of this
is the tendency of the organic acids to form double
molecules, a tendency which had already been earlier
obser\-ed in vapor-density determinations. The ten-
dency towards the formation of molecular aggre-
gates was first shown for the remaining classes of
substances containing hydroxyl (oximes, alcohols,
pijenols, acid amines, etc.), through crjoscopic obser-
vations. These substances form, therefore, in addition
to the ordinary simj^le moleculesj which in general
were to be observed in the gaseous state, one or more
kinds of more complex molecules, which have been
formed through a more or less stable union of simple
molecules. This phenomenon is of great significance
for our knowledge of the nature of the liquid state of
aggregation, or still more, for our knowledge of the
condition of dissolved substances.
Finally, the formation of complex molecules is
largely dependent upon the concentration. In very
dilute solutions, the cryoscopic determinations of the
128
MOLECULAR WEIGHTS
molecular weights of the classes of substances indi-
cated in the solvents contained in Table I, either give
values which correspond to the simple molecule, or
which are only a little higher. In the latter case, the
simple molecular weight is always obtained by extra-
polating the curve. A greater or less number of
simpler molecules unite to form double molecules, and
still higher molecular aggregates, in somewhat more
concentrated solutions. Higher values are accord-
ingly found for the molecular weights, which increase
with increase in the concentration.
The acids and oximes form double molecules in
concentrated solutions, as already observed. As far
■3. go
I'fO
JO^H
■0^^-
3^
(3)
"^
'/
'^v-H.A
% AOO
^ fCO
no
7° r .?" v° 5°
■ Freeziug-poiut lowering:.
Fig. 22.
(i) Benzoic acid in .solution in benzene ; (2) In naphthalene ;
(3) In azobenzene.
as investigations have been carried up to the present,
there is no reason to think that they form still more
complex molecules. Therefore, their dissociation
ELECTROLYTIC DISSOCIATION
129
curves represent a simple dissociation of double
molecules into single molecules, similar to the curves
which represent the dissociation of vaporized sub-
stances, as determined by vapor-density methods.
The remaining substances containing hydroxyl,
differ from the acids and oximes in that, as far as is
known up to the present, they form larger molecular
complexes. Their curve is, therefore, not parallel to
the axis of the abscissae at any point, but there is an
J«'0
s
/60
^^
{C,H,,
vo;^
/
(
/iO
A^?
NO
/
" J
» s
' ■>
J
Freezing-point lowering.
Pig. 23-
Acetophenoneoxime in solution in benzene.!
indication that such would be the case at greater con-
centration. Let a curve of ethyl alcohol,'' and that of
/-oxybenzaldehyde be chosen as examples.
' From E. Beckmann's determination : Ztschr. phys. Chem.,
2,717(1888).
^ It has not been shown in the investigation of ethyl alcohol in
solution in benzene, whether a mixture of alcohol and benzene may
not perhaps have separated, which would explain the higher
molecular values found.
I30
MOLECULAR WEIGHTS
3iO
Jif(0
JJiO
■^:loo
V./60
no
no
to
(QJiQ)^
jQHj^Oj,
(Q
^tuOL
(C.JjM
i^ii
(yjiiOji
(S\tij.Q).
0° r 2° 3' y
Freezing-point lowering.
Fig. 24.
Ethyl alcohol in solution in beijzene.l
An exception is furnished among the alcohols in
the derivatives of vinyl alcohol," CH^=CHOH, in
which the carbon atom, in combination with the
hydroxyl group, is united by double union with a
neighboring carbon atom. All substances which we
at present regard as being built up according to this
■ E. Beckmann : Ztschr. phys. Chem., 2, 728 (1888).
= K. Auwers : /did., 15, 40, 41 ( 1894).
ELECTROLYTIC DISSOCIATION
131
/- A' 3
Freezingr-point lowering.
Fig. 25.
^-oxybenzaldehyde in solution in naphthalene. 1
formula, give the same values for the molecular weight
at different concentrations. Examples are : Triphenyl-
vinyl alcohol, CH3COH OHCCH,
II II
CH CH
\ /
CO
diacetyl acetone, dibenzoyl acetone, formyl camphor
with the group, \ H
-" C=C
I OH
CO
hrlpl
'K. Auwers: Ztschr.lphys. Chem., 18, 606 (1895).
132
MOLECULAR WEIGHTS
r 4° j°
Freezing-point lowering.
Fig. 26.
Formanilid in solution in benzene. 1
It is interesting to note that the thioalcohols^ and
thiophenols also behave normally.
The acid amides are to be added to the substances
which contain hydroxyl.3 This indicates that, in
these cases, a rearrangement has taken place through
the migration of the hydrogen ion, which led to
the formation of a hydroxyl group; e. g., diphen-
'E. Beckmann : Ztschr. phys. Chem., 12, 711 (1893).
^ K. Auwers: Ibid., 12, 693; 711 (1^893).
'' K. Auwers : Ibid., 15, 45, 50 (1894) ; A. Lachmann : Ibid.,
22, 170 (1897).
ELECTROLYTIC DISSOCIATION 1 33
oxyacetamide, (CgHjO)^CH.CO.NH^, passes over into
(C,Hp)CH.C.NH.
OH
This phenomenon has been investigated most ad-
vantageously with the acid derivatives of the organic
hases, especially with the formic acid derivatives, of
which a large number has been studied by Auwers,'
e. g., formanilid, C^H NH.COH, behaves as if it were
CeH.N : CH
OH
To these are to be added some of the amides of car-
bonic acid, such "as ordinary urethane,
/NH,
C0<
\0C,H.
which acts like a substance,
C:^.OH
V0C,H,
The fact that acid derivatives of the secondary bases
behave normally,'' indicates that the cause of the
anomaly is a rearrangement, with the formation of a
hydroxyl group; e. g.,
CsH^.N.CeH.
CO
H
formyldiphenylamine and
CeH^.N.CH
CO
H
formylmethylaniline.
' K. Auwers : Ztschr. phys. Chem., 15, 49 (1894).
=■ K. Auwers : /bid., 15. 44 ; 45 (1894).
134 MOLECULAR WEIGHTS
These substances contain in combination with the
nitrogen, no available hydrogen which can take part in
the formation of a hydroxyl group. That it is not the
imide group which favors the molecular condensation,
is shown by the fact that pure imide substances, which
cannot pass over into hydroxyl compounds by the
migration of a hydrogen atom, behave normally ; e. g.^
monomethylaniline, monoethylaniline,' acridine,^ ska-
tol.=
Finally, the nitroso compounds of the tertiary
aromatic bases,^ show inclination to form molecular
complexes, although, according to our present view,
they do not contain a hydroxyl group. It should,
however, be observed, that the constitution of this re-
markable class of substances is not completely cleared
up.
On the other hand, nitric acid" dissolved in nitro-
benzene gives normal values, nothwithstanding that it
contains a hydrox)'l group.
The class of the phenols has been studied with un-
usual thoroughness and with success, in the beautiful
work of Auwers^ and his pupils, using naphthalene as
a solvent. It has been shown that the capability of
the phenols to form complex molecules, depends essen-
tially upon the substituents already present in the
molecule, these either favoring or hindering conden-
sation, depending upon their position and their chem-
" H. Hof : Dissertation, Erlangen 1895, p. 26.
2 K. Auwers : Ztschr. phys. Chem., 12, 712, 713 (1893).
' K. Auwers: Ibid., 12, 715 (1893).
" H. Hof : Dissertation, Erlangen 1895, p. 11.
' K. Auwers ; Zeit. phys. Chem., 18, 595 (1895) ; 21, 337 (1896).
ELECTROLYTIC DISSOCIATION
135
J 60
3J0
J.SID
I MO
/60
/S.0
/
(para
/
(CyH,Ojj
/
/
^meto.
/
y
/^
/^
y
ortho
'
(^,
HA)
r
J° • ol° J"
Freezing-point lowering.
Fig. 27.
The three oxybenzaldehydes in solution in naphthalene.!
ical composition. Ordinary phenol is to be classed
with the alcohols, as also the parasubstituted phenols.
The m eta-derivatives show a somewhat lighter ten-
dency in this direction. It has completely disappeared
in the ortho-derivatives. These behave like substances
which do not contain hydroxyl, and give constant
values with increasing concentration.
In addition to the position, the composition of the
substituents is to be taken into account. The alde-
hyde group, — COH in the para position to the
hydroxyl group, is most favorable to the formation of
complex molecules. Next comes the carboxethyl
K. Auwers : Ztschr. phys. Chem., 18, 605, 606 (1895).
136
MOLECULAR WEIGHTS
group, — COOR, then the cyanogen group, — CN, and
then the nitro group, NO^. Then follow the halogen
atoms in the order, I, Br, CI, and the least active of
all are the alkyl groups. On the contrary, values are
obtained which deviate but slightly from the calcu-
lated molecular weight, if one of these groups is in the
J()Or
/" =2° J" ^^
Freezing-point lowering:.
Fig 28.
(I) ;S-Oxybenzaldehyde, and (2) >-cresol in solution in naphthalene. 1
ortho position to the hydroxyl group. This deviation
is least with the aldehydes and nitro compounds.
Larger deviations appear, corresponding to the order
of succession, on introducing the remaining substitu-
ents. In conformity with the rule that the para-
■ K. Auwers : Ztschr. phys. Chem., 18, 599, 6o5 (1895).
ELECTROLYTIC DISSOCIATION
137
phenols tend to form double molecules, and the ortho-
phenols single phenols, it can be said that the aldehyde
and nitro groups tend to give normal results. The
fairly normal curve of /-cresol, and the rapidly
/" r 3"
Freezing-point lowering.
Fig. 29.
o-^-dinitrophenol in solution in naphthalene. i
ascending curve of jzJ-oxybenzaldehyde, may be taken
as examples.
If there are several substituents present in the
phenol, the one in the ortho position to the hydroxyl
r -2
Freezing-point lowering.
Fig. 30.
/-oxy-OT-methylbenzaldehyde in solution in naphthalene. 2
has the strongest action. Its effect can be overcome only
when it itself is. a weakly acting substituent (alkyl),
and a strongly acting substituent stands in the para
position. The curve of -cresol.
H \ /
O
K.AuwersandK.Orton ; Ztschr. phy s. Chem . , 21,355 {1896).
ELECTROLYTIC DISSOCIATION
139
It is a general rule, that in those classes of substances
which give abnormal molecular weights, the devia-
tions are greatest in the lowest members of the series,
and least in the highest members. Auwers' found
this rule for alcohols, Hof'' for anilides. This same
relation was shown in the abnormal vapor-densities, as
already observed.
To recapitulate briefly, it was found that the con-
centration curves for acids and oximes, which were
/"
o2
7'
T
J" i" J" 6
Freezing-point lowering.
Fig. 31.
(i) Benzoic acid ; (2) phenol ; (3) ethyl alcohol in solution
in glacial acetic acid 3
investigated in solvents of the first table, were bent,
their concave side being turned towards the abscissae.
For all other substances it is represented by a straight
line, which, as a rule, is only a little inclined. But,
on the other hand, for substances containing hydroxyl
it rises more or less rapidly, depending on the concen-*
tration, and only in a few cases, behaves normally.
■ K. Auwers : Ztschr. phys. Chem., 12, 705 (1893).
= H. Hof ; Dissertation, Erlangen 1895, p. 19.
= E. Beckmann: Ztschr. phys. Chem., 2, 732 (1888).
w
140
MOLECULAR WEIGHTS
The simple molecular weight for every one of these
'■'■ abnormal substances " can be derived from a series
of molecular weight determinations plotted in a curve.
But the interpretation of one singular molecular weight
determination is often difficult, and at times impossible.
Curves which are always normal, and therefore
almost horizontal, are found in solvents of the second
table. Benzophenone and benzoic acid anhydride, in
J60
/'■ r J" V 6°
Freezing-point lowering.
Fig"- ."2-
(i) Benzoic acid anhydride; (2) benzophenone, in solution in
glacial acetic acid.l
solution in glacial acetic acid, are exceptions. Their
curves rise rapidly, according to the investigation of
Beckmann,' and look like a curve of an alcohol in
benzene. Dicyandiethyl, C^H^^N^, in benzene, behaves
in the same way. No explanation, whatever, of these
remarkable exceptions, has thus far been furnished.
' E. Beckmann : Ztschr. phys. Chetn., 2, 722 ; 732 (i
bETERMINATION OF MOLECULAR WEIGHTS BY
THE BOILING-POINT METHOD
Three fundamental statements can be made at first
in considering the boiling-point method :
(i) A solution boils higher than the solvent. '
(2) The .rise in boiling-point is .proportional to the
concentration.
(3) Equimolecular solutions in the'same solvent,
show the same rise in boiling-point.
The generalizations which have led to the boiling-
point method, have not been found directly in this
form, but were derived, at first, rather from observations
on the vapor-pressure of solutions and solvents, by
Wiillner, Ostwald, and Raoult. But diminution in
vapor-pressure and rise in boiling-point are propor-
tional, within limits which are not too wide. This
historical development can thus be explained : There
are disturbing complications involved in the determi-
nation of the boiling-points of a solution, which, only
very recently, have been overcome, while there are no
difficulties in the method involved for determining va-
por-pressure. The thermometer must dip into the solu-
tion to determine its boiling-point. But overheating,
warmer and colder currents, small changes in the
amount of heat supplied, produce considerable varia-
tions in the position of the thermometer, which can
amount to more than a degree.
It was Beckmann,' who overcame these difficulties,
' E. Beckmann : Ztschr. phys. Chem., 4, 539 ('
142 MOLECULAR WEIGHTS
after Raoult, some years before, had carried out ex-
periments along this line, which, at first, were only
partially successful. Beckmann accomplished his aim
through two new improvements. First, he fused a
platinum rod into the bottom of the boiling-vessel,
which prevents bumping, and second, he partly filled
the boiling-vessel with some coarsely granular material,
which prevents overheating. These two devices work
so well that it was no longer difficult to keep the
boiling-point of a solution constant for several hours,
to within a few thousandths of a degree. The best
guarantee that Beckmann has completely accomplished
his aim, and that an overheating of the boiling liquid
is entirely avoided by his method, is that a pure sub-
stance shows the same boiling-point, whether the ther-
mometer is heated by the vapor of the boiling liquid,
or -^vhether it dips into the liquid itself, provided the
Beckmann apparatus is used.
The ^'■Molecular rise in boiling-point^'' or ^^Boiling-
point constant^'' K', is used as the value for compari-
son in calculating molecular weights. K' is the
number of degrees, which the boiling-point of loo
grams of the solvent is raised by a gram-molecular
weight of the substance dissolved in it. An equation
for the determination of the molecular rise in boiling-
point, is derived from the above fundamental propo-
sitions, ex^tly as in the freezing-point method.
An experiment has shown that the boiling-point of
V grams of solvent, is raised E degrees by dissolving
S' grams of the substance in it. By dissolving one
gram of the substance, the rise — would be obtained
BOILING-POINT METHOD
143
(fundamental proposition 2). If one gram of the sol-
vent had been employed, the rise would have been
EL'
— - ; and if 100 grams of the solvent had been em-
EL'
ployed, - — — . Finally, if a gram-molecular weight
of the substance had been dissolved, the rise would
ET 'M
have been — . From the third fundamental prop-
100 S ^ ^
osition this expression, for one and the same solvent
in which any substance is dissolved is :
^^,^EL'M
IOCS''
If the molecular weight of the dissolved substance
is known, the constant K' is found from a determina-
tion of the rise in boiling-point which the substance
produces.
Example : 0.5475 gram benzil, (C^ H^^O^ = 2io) in
38.09 grams of benzene, gave a rise in boiling-point of
0.174°.
^,^ 0.174 X 38.09 X 210 ^
100 X 0.5475
The mean of a large number of experiments is
26.1. Furthermore, the boiling-point constant K''
■ The constant K' can, further, be approximately derived from
the law of Trouton. K' = 0.00096 TM ; T is the absolute boiling
temperature, and M the molecular weight of the solvent. E. Beck-
mann, G. Fuchs, and V. Gernhardt : Ztschr. phys. Chem., 18, 473
(1895). In the same place a method is described for deriving the
heat of vaporization, from a determination of the boiling-point of a
solvent under different pressures. The boiling-point constant is
then calculated from this.
144 MOLECUI^AR WEIGHTS
can be derived in the same manner as the freeziiK
point constant K. Let T^ be the absolute tempera-
ture, W, the latent heat of vaporization, then :
,„ 0.0198 T;'
^ - w. ■
On the contrary, if the heat of vaporization of a
substance is not known, this is derived from the
determination of the rise in boiling-point which! is
produced, by dissolving in it another substance of
known molecular weight. K' is at first derived from
this observation, and finally, W^ found by introduci^
this into the last formula. This method has been
used by Beckmann and Fuchs^ for determining the
heat of vaporization of a large number of substances.
If the boiling-point constant of a solvent is known,
it can be used for determining the unknown molecular
weights of other substances which are soluble in this
solvent. The molecular weight is obtained from the
equation :
^^ 100 S'K'
This method for determining molecular weights was
discovered and developed by Raoult.^ It has been
used by Walker, Lob, Tammann, Will, and Bredig, in
a modified form adapted to the chemical laboratory.
Raoult, already in 1878, had demonstrated the possi-
bility of obtaining the same" results through boiling-
■ Sv. Arrhenius : Ztschr. ph5-s. Chem,, 4, 550 (18S9).
'■^ E. Beckmann and G.Fuchs: /did., 18, 473 (1895).
^ F. M. Raoult: Compt. rend., 87, 167 (1878) ; 103, 1125 (1886);
104, 976, 1430 (1887),; 105, 857 (1887) ; 107,442(1888).; Ann. Chim.
Phys. [6], 15, 375 (i888) ; Ztschr. phys. Chem., 2, 353 (1888).
BOILING-POINT METHOD 145
t-'^itit determinations, as through observations of the
vapor-pressure, but regarded the latter method as
preferable even up to 1889. In the same year, Wiley
employed the boiling-point method for determining
the molecular weights of some salts ; but Beckmann'
was the first to develop it into a really practicable
method. He submitted the apparatus constructed by
himself, to the German Society of Scientists, on Sep-
tember 21, 1889, and shortly afterwards published a
description of it. At the same time, Arrhenius^ fur-
nished the theoretical basis for the method. An improved
form of apparatus was described by Beckmann' in 1891.
We owe the principle of both the freezing-point
and boiling-point methods to the physicist, Raoult, the
practical development to the chemist, Beckmann.
The Simple Boiling-point Apparatus of Beckmann. ■*
— The boiling liquid is contained in a test-tube {a),
' E. Beckmann :Ztschr. phys.Chem., 3,603(1889); 4,532 (1889).
2 Sv. Arrhenius : /did., 4,550 (1889).
^ E. Beckmann : Ibid., 8, 223 (1891).
■* The description of the first Beckmann boiling apparatus, with-
out vapor-jacket, which is adapted only for low-boiling solvents,
is given in Ztschr. phys. Chem., 4, 539 (18S9). An account of ex-
periments performed with it is given by E. Beckmann in Ztschr.
phys. Chem., 6, 437 (1890). This apparatus has been recently im-
proved and also adapted to high-boiling solvents ; E. Beckmann :
Ztschr. phys. Chem., 21, 245 (1896). The apparatus described in
the text, with vapor-jacket, was described by E. Beckmann in
1891 in Ztschr. phys. Chem., 8, 223 (1891). Some modifications,
together with a criticism of changes proposed in other places, in
Ztschr. phys. Chem., 15, 656 (1894). For carrying out boiHng-
point experiments under changing pressure, the apparatus of E.
Beckmann and G. Fuchs has been somewhat modified. Ztschr.
phys. Chem., 18, 492 (1895) : E. Beckmann: Ztschr. phys. Chem.,
18, 661 (1894).
146 MOI,E.CUlvAR WEIGHTS
the " boiling-vessel") provided with a side tube. It
has the same form, and also nearly the same dimen-
sions as the freezing-vessel in the freezing-point appa-
ratus. A thick platinum rod about ]/.,. cm. long, is
fused into the bottom of the boiling-vessel with the aid
of fusion glass, to prevent the boiling liquid from
bumping. The rod projects externally only a little
beyond the surface of the glass, and is notched along
that portion which projects into the vessel. The
formation of bubbles takes place easily on the sharp
edges, because small bubbles of vapor, which really
produce the boiling, adhere to these. Moreover, heat
is conducted from the outside into the interior of the
liquid, through the platinum rod, which can be re-
placed also by a rod of red fusion glass. This boiling
device can be dispensed with without any serious dis-
advantage.' A Beckmann thermometer is placed in
position, by means of a cork, which had been extracted
with ether before using, so that the mercury bulb
stands about 3 }^ to 4 1^ cm. from the bottom of the
boiling cylinder. A light glass condenser with a
straight condenser tube, is fitted to the side tube with
a cork which has also been cleansed with ether. The
boiling-vessel fits loosely into the hollow of the glass
boiling-jacket {b\ so that it scarcely protrudes below^
The inner space of the boiling-jacket, closed on all
sides, is connected above (left in the figure) with a
small condenser which is bent upward. The effect of
the temperature of the air is excluded by introducing
' E. Beckmann : Ztschr. phys. Chem., 15, 65i (1894).
Fig. 33-
Beckmann boiling-point apparatus. One-6fth natural size.
148
MOLECULAR WEIGHTS
into the outer vessel the same solvent as in the inner.
This device is of great advantage for experiments
with high-boiling solvents, boiling from 100° to 200°.
Both systems were placed on a heating-box, made
with strong asbestos board held together with wire
clamps and" water-glass. Its arrangement is shown in
Figs. 33 and 34. The bottom rests on an iron sup-
port (Fig. 33, d\ together with the side walls 5 cm.
s
i/
Fig. 34.
Diagonal section through the heating-box.
One-third natural size.
in height, a mica window' having been inserted into
one of these. It has an opening in the center 8 cm.
in diameter, which is covered with a piece of brass
gauze (Fig. 34, a). On the shelf on which the brass
gauze rests, is placed a ring of asbestos board, bent
upward, as shown in the figure (Fig. 34, b), protruding
' The object of the mica window is to allow the flames to be
observed, and is strongly to be recommended when the circular
burner, to be described later, is used. When a Bunseu burner is
used, the flame can be observed just as well from below, and a box
without a mica window is preferable, since it is more durable.
BOILING-POINT METHOD
149
over the gauze, and having a hole in the center about
6 cm. in diameter. The boiling-jacket with boiling-
vessel is placed upon this. Two concentric rings of
asbestos board, 3 and 5 cm. in diameter (Fig. 34, c),
and 3 cm. in height, and fastened below, are placed
near the center of the gauze. They are united at the
level of the gauze, by a ring of asbestos (d) with a hole
cut in the center. The brass gauze is cut out in the
middle, leaving an opening of the diameter of the
inner ring. This opening is just beneath the bottom
of the boiling-vessel. The 'rings prevent the direct
action of the surrounding flames on the boiling-vessel
itself. Finally, two asbestos chimneys ((f) are placed
in two corners of the cover of the heating-box.
These serve to carry off the gaseous products of com-
bustion. Two Bunsen burners, or gas burners of a
form to be described later, are placed below the heat-
ing box, so that their flames strike the gauze at places
removed as far as possible from the chimney.
Carrying Out a Simple Molecular Weight Determi-
nation with the Simple Boiling-point Apparatus of
Beckmann. — It is recommended in learning the
method to carry out a molecular determination with
benzene as a solvent, and a high-boiling, solid hydro-
carbon, perhaps phenanthrene, as the substance to be
investigated.
The thermometer is at first so adjusted that the
top of the mercury column comes to rest between the
divisions o and i (say about half way between them),
when the bulb of the thermometer is placed in the
vapor of some benzene, boiling in a wide test-tube.
I50 MOIvECULAR WEIGHTS
Sometimes the bulb of the thermometer available, is
just far enough from the lower end of the scale, that
when the thermometer is properly introduced into the
apparatus, this portion of the scale is covered by the
cork. In this case the thermometer is, of course, so
adjusted, that the top of the column comes to rest just
above the cork, when the benzene boils. The ther-
mometer with short bulb, is best adapted to boiling-
point measurements. The older freezing-point ther-
mometers, with long bulb (4.5 to 5 cm.), can also be
used when necessary. They can, however, be used
only with solvents which do not boil above 100°.
Sixteen to seventeen grams of pure, dry, benzene,
are weighed oil accurately to centigrams in the boil-
ing vessel,' then the thermometer with cork put in
place, and the position of the thermometer so regu-
lated that its lower end is about 4 cm. from the bot-
tom, and dips well into the benzene. Then some
heavy glass beads of about 3 mm. diameter, or garnets
of from 2 to 3 mm. diameter, are introduced through
ths side tube, until the vessel is filled with them up to
the bottom of the thermometer. The thermometer
itself must not touch them, since if it did, an exact
determination of the zero point would be difficult.
The benzene is thus made to rise over the bulb of the
thermometer. The properly selected beads or garnets
are cleansed, by warming with concentrated hydro-
' The boiling-vessel must be thoroughly cleansed, otherwise
the liquid condensing in the upper part flows down with difficulty,
thereby producing an increase in the concentration of the boiling
solution. This fault is remedied, by cleaning the vessel with warm
concentrated sulphuric acid and potassium chromate.
BOILING-POINT METHOD
151
chloric acid, washing with water and alcohol, and
then drying. Platinum is especially well adapted
for use, and has been recommended by Orndorff and
Cameron,' and also recently by Beckmann.^ The
good conductivity of the metal facilitates the equaliza-
tion of temperature, and makes possible a better adjust-
ment of the thermometer, than glass beads or garnets.
Platinum foil is bent for this purpose into balls or
tetrahedra, cleansed, and heated to redness before
using.
The introduction of a solid filling-material into the
boiling-vessel is of the greatest significance, because it
prevents a superheating of the boiling liquid. The
bubbles of vapor, rising from the bottom, have their
movements frequently checked by striking against the
glass beads which block up their paths. The bubbles
must then pass around these, and in doing so they
give up their excess of heat to the liquid, so that when
they emerge from the filling-material, they have exactly
the temperature of the boiling-point. This exception-
ally important means of preventing superheating,
without which it would be almost impossible to deter-
mine the boiling-point of a solution, has been intro-
duced into practical work by Beckmann.
When the condenser is attached, the boiling-vessel
is ready for the experiment. Ordinary benzene is
poured into the boiling-jacket, until it is filled half-way
up the filling-material in the boiling-vessel, and some
' W. R. Orndorff and F. K. Cameron : Ztschr. phys. Chem.,
17,638(1895).
" E. Beckmann : /did., 21, 248 (1896).
152 MOLECULAR WEIGHTS
pumice-stone or some pieces of porous porcelain thrown
in. The proper condenser is attached, and now the
whole apparatus is set up as shown in Fig. 33, the
boiling-vessel being clamped at the upper end in a
retort holder.
If the apparatus thus described, is used at once for
experiment, a considerable fault would be met with.
Some of the hot gases from the flame would ascend
through the brass gauze of the heating box, and rise
well up between the boiling-vessel and boiling-jacket.
Since this would not take place uniformly, the boiling
apparatus would be supplied, now with more, now with
less heat, so that an accurate adjustment of the mer-
cury meniscus would not be possible. This current of
air is prevented by two devices. First, a tube made
by rolling up asbestos paper into several layers, is
placed in the inner asbestos ring of the heating box,
as shown in Fig. 34, so that it reaches up into the
boiling-jacket. The boiling-vessel is now introduced
into the jacket, while the asbestos tube is held in
position below by the finger, that it will not be pushed
down. The boiling vessel then slips right down into
the asbestos tube. Second, some loose asbestos is
packed in above, between the boiling-vessel and the
boiling-jacket, so that here, again, is another obstruc-
tion which prevents the gases from rising. Instead of
using loose asbestos, the boiling-vessel, before it is in-
serted into the jacket, can be wound around with
several layers of strips of asbestos paper, even up to
the side tube. This, then, accomplishes the same pur-
pose as the loose asbestos. Neither of these asbestos
BOILING-POINT METHOD 1 53
packings is shown in the drawing of the apparatus as
a whole, that the figure should not thereby be rendered
indistinct.
If the whole apparatus is set up on a wooden table,
it is necessary to place a slab of slate beneath it,
because the wood would be heated too strongly by
the heat radiated down upon it from the heating box.
The apparatus is heated by two Bunsen burners, in
the manner already described. Two sheets of metal,
bent in the form of semicircles, and which together
form a ring about 20 cm. high, are placed around the
apparatus to prevent any possible air-currents from
affecting the apparatus. If a boiling apparatus with
high heating box is used, the burners are placed on
small blocks of wood, or the Beckmann adjustable
burner, to be described later, is used.
After the apparatus has been set up and filled, which
requires from ten to fifteen minutes if everything is
at hand and no cleansing is needed, the water is
turned into the condenser and the gas lighted. A
small flame is used at first. The height of the flame
can be somewhat increased after five minutes, so that
it reaches the gauze. A cracking of the glass is not
to be feared, even if less care is taken. The benzene
in the jacket quickly begins to boil. The first bub-
bles of vapor emerge somewhat later from the filling-
material in the boiling-vessel. The rate of boiling is
now so regulated, by adjusting the height of the flame,
that a drop falls from the condenser of the boiling-
vessel every five to ten seconds. It is self-evident that
a "luch more vigorous boiling goes on in the jacket.
154 MOI.ECULAR WEIGHTS
It is important to maintain this rate of dropping,
because the thermometer will then quickly reach the
true boiling-point, and show only small fluctuations of
a few thousandths of a degree. It is well, after the
proper rate of dropping has been established, to read
the thermometer from time to time, say every five
minutes, and to note the readings together with the
time. An estimate of the rate of movement of the
mercury can best be obtained in this way. The fol-
lowing fact is to be taken into account in making the
readings: The movement of the mercury in the
capillary is hindered, because of the small diameter
of the capillary, and therefore the mercury does not
accurately respond to small changes in temperature.
The error thus introduced, and to which attention has
been called in discussing the freezing-point method, is
avoided, if just before and during the reading the
upper end of the thermometer is gently tapped with
an empty thermometer case, held in the right hand,
the lens being held in the left. The capillary is thus
thrown into gentle vibrations. The tapping is con-
tinued from one-half to one minute, and then the read-
ing is made. A mechanical tapping-device can be
used instead of the hand. Loom is' recommends a
device like the hammer of an electric clock, which
strikes on the top of the thermometer. The large
"E. H. Loomis: Wied. Ann., N. P., 51,506(1894); W. R.
Omdorff and F. K. Cameron : Ztschr. phys. Chem., 17, 640
(1895); M. Kaehler and Martini: W. Berlin, Nachtragscatalog,
1897 ; electro- and physicochemical apparatus, p. 37, Nr. 6305 ;
The mechanic, H. Wittig, in Greifswald, furnishes suitable electri-
cal clock-works for about 7 marks each.
BOILING-POINT METHOD 155
number of slight taps jar the thermometer uniformly
throughout, but each blow only so slightly that no
oscillation of the capillary- can be observed. Conse-
quently, the reading can be made very accurately.
The use of this device is, strongly to be recommended.
Blows on the side, can be given by a cork rotating on
an axis. One side of the cork must be partly cut ofF,
and the remainder allowed to strike the thermometer
once in every turn. The cork is driven by a cord
attached to a small water turbine. Turbine and cork
are fastened to a wooden lath about 40 cm. long, sup-
ported on a stand.
The electrical clock-work already mentioned, is
preferable. But it is sufficient in an ordinary molec-
ular weight determination, to tap with the hand in the
manner described.
It usually requires one hour, but often two, and
sometimes, indeed, several hours, to obtain a constant
temperature in the boiling-vessel. If one is already
familiar with the method, it is sufficient to observe the
position of the mercury thread every quarter of an
hour, and to begin the readings proper, only when the
mercury has about come to rest.
The tablets, molded in exactly the same manner
as described in the chapter on the freezing-point
method, are meanwhile gotten ready and weighed.
When the thermometer ceases to rise, and oscillates
only slightly about a fixed point on the scale, which
is explained by irregularities in boiling, the point is
determined accurately by taking the mean of several
readings. It should not oscillate more than two- or
156 MOLECULAR WEIGHTS
three-thousandths of a degree, in ten to fifteen minutes,
otherwise the experiment cannot be begun. Since the
constants of the solvents are, indeed, considerably
smaller in the boiling-point method than in the freez-
ing-point, the rise as read on the thermometer in the
former case, is less than the fall in the latter. Con-
sequently, the elevations of the boiling-point must be
determined with the greatest care, in order to make
accurate molecular weight determinations. This is
to be taken into account, especially for substances with
high molectilar weights, and in dilute solutions where
a rise of a few hundredths of a degree must be read.
After uniform boiling has been secured in the appa-
ratus, and the boiling-point established, the determina-
tions proper present no further difficulties. The first
tablet is slipped into the boiling-vessel, through the
tube of the condenser. The temperature falls at first,
because the cold tablet, and further the process of
passing into solution, absorb heat. But it soon begins
to rise above the original position as the substance
dissolves, and within five minutes registers the boil-
ing-point of the solution. One should wait a few
minutes to determine whether the temperature re-
mains constant, and then make the final reading. A
determination usually requires from ten to fifteen
minutes, from the time the substance is introduced
until the final reading is made. A second tablet is
then introduced, and the boiling-point of the new solu-
tion determined, the total amount of substance con-
tained in the solution, and the total rise in tempera-
ture being taken into account. Four or more deter-
BOILING-POINT METHOD
157
minations can be conveniently carried out in this
manner, according to the purpose of the investigation,
and the solubility of the substance to be investigated.
The boiling of the solvent must not be discontinued
during the introduction of the tablet. Every liquid
which is kept exposed to the air, contains some air in
solution, and the formation of the first vapor-bubbles
during the warming of the liquid, is due to this small
quantity of dissolved air. The air-bubbles adhere to
the walls and to the bottom, but they soon pass over
into bubbles, the air being gradually driven out by the
particles of vapor formed, and replaced by vapor.
Uniform boiling depends upon the presence of such
bubbles.
When the liquid ceases to boil, the small bubbles of
vapor disappear, and if the temperature again rises,
there are no places present from which boiling can
begin. Overheating is the result, and consequent
bumping, which interferes with the experiment.
It is very convenient in introducing the round
tablets, to allow them to roll down through the con-
denser into the apparatus. In this way, we can be
certain that the tablet enters the boiling-vessel as it is
weighed, without any loss. This is accomplished by
means of the tablet thrower, shown in
Pig- 35) which is made by bending a
piece of sheet-zinc, or brass, into the proper
form. The tablet is placed in the box- '''s- 35-
shaped groove open in front, the thrower one-haifnat^rli
seized by the bent portion, lifted up to the
edge of the condenser, and the tablet started rolling, by
158 MOLECULAR WEIGHTS
tilting downward the front, open end of the groove, the
walls of the groove giving it an upright position. If
the tablets are more than 4 mm. thick, they can no longer
be rolled through the condenser. They are then allowed
to slide down, the axis of the cylindrical tablet in the
axis of the condenser; this being assisted by a long
glass rod. It is desirable that the tablet should be
introduced without allowing the glass rod to come in
contact with the liquid condensed in the lower end of
the condenser. If this should occur, the rod is slowly
drawn backward, and repeatedly touched against the
walls of the condenser, so that the particles of solvent
clinging to it, are wiped off. as much as possible, and
thus only a small loss of solvent results. It is simplest,
however, to prepare the tablets of such size that they
can be rolled into the apparatus. When larger
amounts of substance are to be introduced, instead of
one tablet, several are to be thrown in at once. This
has the further advantage that the tablets glide past the
thermometer into the boiling solvent, while larger
tablets remain suspended at the junction of the side
tube, between the thermometer and the wall of the
vessel, and are here gradually dissolved by the con-
densed liquid as it runs down, and by the rising
vapors, until it can slip down through the intervening
space. It is convenient in the boiling-point method,
that any small particles of the substance which remain
suspended, are washed down by the recondensed sol-
vent. Further, a rapid and uniform mixing of the
solution is effected with certainty by the boiling pro-
cess, through the movement produced by the bubbles
of vapor as they ascend in the boiling-vessel.
BOILING-POINT METHOD 159
The solution constantly undergoes small changes
in concentration, through the drops which fall from
the condenser, every such drop increasing in dilution,
while the concentration is again increased in the fol-
lowing moment, by the distillation of the solvent high
up into the apparatus, until a new drop dilutes it
again. These changes in concentration are very per-
ceptible in stronger solutions, and prevent the mer-
cury column from adjusting itself as sharply with
more dilute solutions, or with the pure solvent. But
since the total elevations observed in these cases are
large, an error of reading which does not amount to
more than o.oi°, is not of much consequence.
The calculation is made with ttje aid of the formula
already developed, taking into accounf'.the following*-
correction. A part of the soiw^t is alwS^sjjresent in
the form of vapor, in the upper paTt,«vof me '%oilmg-
vessel, due to the boiling "jprocess. ArfdtJ]^r portioit
adheres to the walls in small drops', «!\ih,ile stiU another
portion is absorbed by the cofks with which the
vapors come in contact. Consequently, tfi&i««^s
always somewhat less solvent below in the boiling-
vessel, than had been weighed in it, and the solution
is somewhat more concentrated. The error thus pro-
duced, is corrected by subtracting a small amount,
about 0.15 to 0.2 gram, from the weighed mass of the
solvent. Only when water is used should about 0.35
gi-am be subtracted.
Furthermore, a correction for the value of the degree
on the thermometer, as was stated in the description
of the thermometer, should be introduced into the calcu-
l60 MOI.ECUI.AR WEIGHTS
lation of molecular weight determinations by the boil-
ing-point method, when solvents are used which boil
above ioo°.
Example. — Phenanthrene in solution in benzene.'
C H == 178. In 22.95 grams benzene (22.75 used
in the calculation) gave :
Grams
Rise in
Molecular
substance.
boiling-point.
weight.
0.1983
0.125°-
182
0.6187
0.389°
182
I.0177
0.639°
183
1. 6481
1.023°
185
2.2634
1.391°
187
3-0476
-833°
191
3-9025
2-393''
187
4.6718
2.772°
194
The value 26.1, contained in the table to be given
later, is used in the calculation, as the boiling-point
constant.
The flames are extinguished after the molecular
weight determination is completed, and the apparatus
immediately taken apart. Special attention is to be
paid, in cleaning the apparatus, to the removal of
every trace of substance and solvent from the filling
material. This is collected in a funnel with narrow
neck, and washed at once with a little of the solvent.
The substance used in the investigation, can generally
be removed by evaporating the filtrate, or volatilizing
it with water vapor. The filling material is boiled
repeatedly with alcohol, or some other solvent for the
substance, and well dried before a new determination,
' From experiments by William Biltz. Next to the last experi-
ment probably contains an experimental error.
BOILING-POINT APPARATUS OF JONES l6l
in order that no liquid should remain unobserved in
the small crevices and depressions. The cleansed and
dried filling material is, after a number of determina-
tions, warmed with concentrated sulphuric acid, then
boiled repeatedly with distilled water, finally with
alcohol, and then dried again.
THE BOILING-POINT APPARATUS OF JONES
A modification of the boiling-point apparatus of
Beckmann has been proposed by H. C. Jones.' Of all
the forms of boiling-point apparatus described, onh-
those of Hite,^ Sakurai,^ and Landsbergert prevent the
cold sohent from the condenser, from coming in
contact with the bulb of the thermometer, before the
liquid has been reheated to the boiling-point. But in
no form thus far. devised, has the effect of radiation
outward from the hot bulb of the thermometer been
properly prevented. This is accomplished by the
apparatus described b>- Jones, which also prevents the
cold, recondensed, solvent from coming in contact with
the thennometer, before it is heated again to the
boiling-point.
The apparatus is sketched in Fig. 351?. It is drawn
approximate]}' to scale. A is a glass tube 18 cm.
high and 4 cm. wide. At the top it is drawn out to a
diameter of about 234 cm., and ground to receive a
ground-glass stopper. This tube is filled to a depth
of from 3 to 4 cm. with glass beads. P is a cylinder
' Am. Chem. J., 19, 581.
^ Ibid. 17, 507.
■' J. Chem. Soc. (London ), 61, 989.
■* Ber. d. chem. Ges., 31, 458.
Fig. 35a-
BOILING-POINT APPARATUS OF JONES 1 63
of platinum 8 cm. high and 2 >^ cm. wide, made by
rolling a piece of platinum foil, and fastening it in
position by wrapping it near the top and bottom with
platinum wire. It would be better if the edges of the
cylinder were closed by welding, so that none of the
liquid could pass through from one side to the other.
A cylinder of some other metal, such as copper, zinc,
or silver, could be employed in many cases where they
would not be acted upon by the solvent or the solu-
tion, but platinum is to be preferred, because of its
greater resisting power to the action of such agents.
Into the cylinder P, some pieces of platinum foil are
thrown. These are made by cutting foil into pieces
about ^ cm. square, bending the corners alternately
up and down, to prevent them from lying too closely
upon one another, and serrating the edges with
scissors, to give a greater number of points from which
the boiling can take place. The bulb of the ther-
mometer is thus entirely surrounded by metal at vefy
nearly its own temperature, except directly above.
The thermometer could be forced through a hole in a
sheet of platinum, which would remain suspended just
over the cylinder, but in consideration of the small
angle through which radiation can take place in an
upward direction, this seems to be a superfluous refine-
ment. A condenser (C), about 40 cm. long, is attached
to the tube (A) which is 2 to 2^ cm. in diameter, by
means of a cork. When it is desired to protect the
solvent from the moisture in the air, the top of the
condenser tube should be provided with a tube con-
taining calcium chloride, or phosphorus pentoxide.
164 MOLECULAR WEIGHTS
During an experiment the vessel (A), is closed by a cork,
through which the Beckmann thermometer (T), passes.
M is a jacket of asbestos, 12 cm. high and lyi cm.
thick, over the top of which the rate of boiling can
be observed very satisfactorily. It is constructed by
bending a thin board of asbestos tightly around the
tube (A), and fixing it in place by means of copper
wire. Thick asbestos paper is then wound around
this, until the desired thickness is reached. The
apparatus is supported on a small iron tripod (S), 8 cm.
in diameter, on which rests an asbestos ring (R), about
9 cm. in external diameter. A circular hole is cut in
the center of this ring, about 3 % cm. in diameter, and
over this is placed a piece of fine copper gauze. The
source of heat is a Bunsen burner (B), surrounded by
an ordinary metallic cone (I), to protect the small flame
from the effect of air currents. The glass vessel (A) is
shoved down until it comes in contact with the wire
gauze. Under these conditions, a very small flame
suffices when low-boiling solvents are employed, and
not a large flame is required when a solvent like
aniline is used.
CARRYING OUT A DETERMINATION WITH THE JONES
APPARATUS.
The glass beads are poured into the glass cylinder,
the platinum cylinder inserted, and pressed down into
the beads to a distance of from ^ to i cm. The
platinum plates are then introduced into the platinum
cylinder, the end of the tube (A) closed with a cork,
and the ground-glass stopper inserted in A. The
apparatus is then set in a small beaker glass and
DETERMINATION WITH THE JONES APPARATUS 1 65
weighed. The solvent is then introduced, and the
whole reweighed. Great care must be taken that not
enough solvent is employed to boil over from one side
of the platinum cylinder to the other. In case a
laboratory is not provided with a balance capable of
weighing accurately 200 or 300 grams, the solvent
must be weighed directly, and then poured into the
apparatus. This, for low-boiling solvents, is neces-
sarily less accurate than the above-described method
of procedure. After the solvent is weighed the glass
stopper is removed, and the thermometer, fitted tightly
into a cork, is placed in position, as shown in the
drawing. The apparatus is then placed upon the
stand in the mantle of asbestos, the cork removed
from A, and the condenser attached. Heat is then
applied and the solvent boiled. The size of the flame
must be so regulated by means of a screw pinch-cock,
that the boiling is quite vigorous, but not so violent
as to be of an irregular or explosive character. A
quiet but very active boiling is absolutely essential to
the success of the experiment. The time required to
establish the true temperature of equilibrium between
the pure liquid solvent and its vapor, is very much
greater than in the case of a solution. This is strictly
analogous to what is observed with the freezing-point
method. Before taking a reading on the Beckmann
thermometer, it is always necessary to give it a few
sharp taps with a lead pencil, and, indeed, this should
be done occasionally while the mercury is rising, and
especially when it is near the point of equilibrium.
The use of an electric hammer to accomplish this
1 66 MOLECULAR WEIGHTS
object, is an unnecessary complication. A small hand
lens, magnifying a half-dozen times, is quite sufficitot
to use in making the readings. It is always best to
redetermine the boiling-point of the solvent. After
the boiling-point of the solvent has been determined,
a tube containing the substance pressed into pellets, is
weighed, and a convenient number of these poured
into the solvent, either through the condenser, or
directly through the tube A, when the solvent is not
too volatile, and has ceased to boil. The tube is then
reweighed, the amount of substance introduced being
thus ascertained. The boiling-point of the solution is
then determined. The carrying out of a determina-
tion with a low-boiling solvent, is a much easier pro-
cess than with one boiling at a considerably higher
temperature.
Thus, when anisol or aniline is employed, much
care and some experience are necessary to determine
the rate of boiling which must be adopted. If the
boiling is too slow, the thermometer will never reach
the temperature of equilibrium. If so rapid that it is
irregular and explosive, the thermometer may rise
above the true boiling-point, and then suddenly drop
below it, at the moment when a large amount of
vapor is formed. In a word, for high-boiling solvents
the rate of boiling must be as vigorous as possible, in
order to proceed with perfect regularity.
All the forms of apparatus thus far described, are
somewhat dependent upon the size of flame used.
This is probably due, in part, to the corresponding
change in rate at which the condensed solvent is
returned to the boiling liquid. If this be true, then
DETERMINATION WITH THE JONES APPARATUS 1 67
that form of apparatus which prevents the condensed
solvent from coming in contact with the thermometer
until it has been reheated, should be least affected by
the size of flame used, and such is the fact.
The barometer must be very carefully noted before
and after each boiling-point determination, and a
correction introduced for any change in the baro-
metric height.
This boiling-point method has been applied to the
determination of molecular weights,' and has been
found capable of yielding excellent results, with both
low- and high- boiling solvents. It has also been ap-
plied by Jones and King," and subsequently, far more
extensively by Jones,^ to the measurement of electro-
lytic dissociation in methyl and ethyl alcohols. This
apparatus is simpler than the best forms devised by
Beckmann, and eliminates experimental errors which
are present in all of the modifications thus far proposed.
Modifications of the Boiling- vessel/ — The boiling-
' Am. Chem. J., ig, 590.
^ Ibid., 19, 753.
^ Results will soon be published in the American Chemical
Journal.
' Different modifications of the Beckmann apparatus have been
described. These appear to differ in their general applicability,
and some of them must be regarded as complications. Compare
B. H. Hite: Am. Chem. J., 17, 507 (1895); W. R. Orndorff and
F. K. Cameron : Ztschr. phys. Chem., 17, 637 (1895) ; P. Fuchs :
Ztschr. phys. Chem., 22, 72 (1897). Other modifications have been
proposed by Beckmann : Ztschr. phys. Chem., 15, 656 (1894).
Another form of boiling-point apparatus, based upon the principle
of the Sakurai apparatus, has recently been described by Lands-
berger : Ber. d. chem. Ges., 31, 458, and very recently simplified
by Walker and Ivumsden, J. Chem. Soc, 502 {1898).
1 68 MOLECULAR WEIGHTS
vessel described, nearly always suffices for the purpose
of a chemical laboratory, and is to be very highly
recommended on account of its convenient manipula-
tion. Some changes made for definite purposes, have
been described recently by Beckmann.'
In case the vapor of the solvent attacks cork, the
apparatus should be closed with asbestos packing,
instead of with cork. But since this easily absorbs a
large quantity of liquid, it is better to fuse the con-
denser tube direct!}- on to the boiling-vessel, thus en-
tirely avoiding the use of the side tube. In conse-
quence of this arrangement, no drops fall, from time to
time, from the condenser, which, as alread}' observed,
produce small changes in the concentration. The
condensed liquid thus flows down the walls at a uni-
form rate, preventing the changes in concentration
and in temperature, which are produced by the intro-
duction of a cooler drop into the boiling liquid. On
the other hand, the con\-enient means of determining
the amount of boi-ling from the rate of dropping, is no
longer available. Since the error due to the cause
first mentioned, is only slight, the tube of the conden-
ser should be so fused into the side tube of the boiling-
vessel, that it projects somewhat into it. The drops
then fall from the protruding end, just as when the ap-
paratus is set up simpl}- with a cork.
It is difficult to avoid the use of a cork to close the
second opening in the boiling-vessel, where the ther-
mometer enters. To reduce to a minimum the amount
of solvent which distils against the cork, the boiline-
' E. Beckmann : Ztschr. pliys. Chem., 15, 666 (1894).
MODIFICATIONS OF BOILING VESSEL 1 69
\essel is lengthened above the side tube, until the cork
stands at about the middle of the condenser along by
its side, I. e., somewhat higher than is shown in draw-
ing ( Fig. 2,2,)- This lengthening is all the more possible,
now, since boiling-point thermometers are recently
obtainable with a very long stem between bulb and
scale. The vapors in this arrangement scarcely rise
up to the cork, in which the thermometer is inserted.
Tliere is another expedient which can be resorted to
witli substances of great activity, such as bromine.
The boiling-vessel is narrowed somewhat above the
attachment of the side tube, and made long enough
to receive the thermometer even up to the mercury
reservoir. The position of the mercury is then read
tlirongh this lengthened portion of the apparatus.
Tlie apparatus is closed with a piece of rubber tubing,
or w itli a cork in case a somewhat wider portion is
attached to the narrower portion. The boiling-vessel
must not be made so narrow that liquid will be drawn,
b\- capillary attraction, well up into the space between
tlie thermometer and the surrounding glass wall.
To prevent the boiling-vessel from cracking below,
wliere the platinum rod is fused in, a small piece of
mica or asbestos paper, with a hole cut in the center
for the platinum rod, is glued around the projecting
end (^f the rod, with a drop of water glass. The plati-
num rod, in this case, must protrude about o.t, mm.
from the glass. The boiling-vessel, according to my
experience, does not crack at this place during use, so
that any special protection appears to me to be super-
fluous. The vessel is much more liable to crack if.
170 MOLECULAR WEIGHTS
when filled with any solvent for cleansing, it is ex-
posed to great differences in temperature. It is best
to entirely avoid heating it with a free flame, and in
cleansing it to warm it in a water-bath.
Some glass wool is placed on the bottom of the
boiling-vessel, as a further protection, to prevent the
garnets or glass beads from striking against the bot-
tom and scratching it. This precautionary measure
is not necessary when platinum is used as the filling
material.
Modifications of the Boiling-jacket. — The glass
boiling-jacket' described, can be employed under all
conditions, at high temperatures as well as at low, and
on account of its transparency, is to be strongly recom-
mended for every one who wishes only to learn the
method. Boiling-jackets made of porcelain are more
durable. These have, in general, the form of the
glass apparatus, without the bulge above and below,
so that their form is exactly cylindrical, as shown in
section in Fig. 36. They have a tube («), into which
the condenser is inserted, like the glass apparatus,
and generally a tube is, also, placed upright above
this one in the upper wall, into which a thermometer
can be introduced to determine the temperature in the
vapor-jacket. Two windows, through which the boil-
ing-vessel can be observed, are cut opposite one
another. (These windows are shown in the figure.)
' The glass boiling-jackets fviniished by F. O. R. Gotze are
especially well constructed. I have had some in use for years, and
have subjected them to a very wide range of temperature without
injuring them.
MODIFICATIONS OF BOILING JACKET 171
Eacli of these windows is closed inside and outside, in
the planes of the inner and outer walls, with a piece
of mica, which is cemented on with a paste of water-
glass and chalk. This can be easily accomplished,
since, in the newer pieces of apparatus, a ridge projects
for this purpose from the inner side, and a correspond-
Fig. 36.
Porcelain boiling-jacket. One-third natural size.
ing groove is made in the outer side, as can be recog-
nized on the left side of the figure. The object in
closing the apparatus in this way, is to keep away cur-
rents of air which would cool the boiling-vessel. The
jacket with the central opening from top to bottom, is
also provided below with a narrow ledge, which can
likewise be recognized in the cross section. A ring
cut out of soft asbestos board, is placed upon this, and
the boiling-vessel fits into the opening. The space
between the boiling-vessel and boiling-jacket is thus
closed below. Some fibrous asbestos, or several layers
172 MOLECULAR WEIGHTS
of strips of asbestos paper, are used above in the same
manner, and for the same purpose. The tube of asbes-
tos paper, which reaches from the boiling-vessel down
into the ring of the heating-box, is thus dispensed
with.
These porcelain boiling-jackets, like those of glass,
are filled with the solvent until the level of the liquid
is about half-way up the filling material in the boiling-
vessel. If an upright tube is attached above to the
jacket, the height of the liquid column can be easily
ascertained by introducing a glass rod into it.
If the solvent attacks the cork vigorously, the con-
denser is attached to the boiling-jacket with some
asbestos cord. When expensive solvents are employed,
■ some other substance, having nearly the same boiling-
point, is introduced into the boiling-jacket. The
boiling-point of the latter can then be changed by add-
ing another volatile substance. This is added through
the condenser, until the thermometer, immersed in the
vapor, registers the boiling-point desired. The boiling-
points of the two substances in the vapor-jacket, should
not differ more than 50°. Beckmann' has described
other forms of boiling-jackets.
The Heating. — The heating-box is warmed by two
burners placed beneath it. As already observed, these
are so arranged that their flames do not directly enter,
the chimneys. In the case of high-boiling liquids,
which require the burners to be turned on full, care
must be taken that the flames do not strike under the
asbestos rings of the heating-box, and fall directly
' E. Beckmann : Ztschr. phys. Chem., 15, 666 (1894).
THE HEATING
173
upon the boiling-vesse], because an irregular supply of
heat would thus result, and there would be danger of
overheating. The boiling-vessel is warmed only in-
directly and, indeed, chiefly through the boiling-
jacket. The small additional amount of heat neces-
sary to mountain the boiling, is obtained through the
tube of asbestos paper, from the closed air-chamber,
which is terminated below by the gauze of the heating-
box, and above by the boiling-jacket. Solvents hav-
ing greater heat of vaporization, require more heat to
boil them. The tube of asbestos paper is then aban-
doned, so that the boiling- vessel projects directly into
the air-space already mentioned.
A direct heating with a flame is necessary, only
when water is used, which is distinguished by a very
high heat of vaporization, and with some very high-
boiling solvents, as nitrobenzene. A small, luminous
flame, about ^ to ^ cm. high, is suitable for this
purpose. It is placed far enough below the boiling-
vessel to prevent the deposit of soot upon the vessel.
A lead tube, bent in the form of an ty^ , with one end
narrowed to a small opening from which the flame es-
capes, serves as the burner. The lead tube is supported
on a laboratory stand, placed near the boiling apparatus.
The Beckmann burner (Fig. 37) can be used instead
of this primitive device, which is, however, quite suf-
ficient. If the burner tube is screwed off, a burner is
obtained whose use is apparent from what has been
said. The burner already set up, is used conveniently
instead of the Bunsen burner, for heating the appara-
tus. It is especially convenient with very high-
174
MOLECULAR WEIGHTS
boiling solvents, since three or four such burners can be
placed under the heating-box, while the large bases of
Bunsen burners are in the way. A circular burner,
which gives about 35 small flames, can be attached to
these burners furnished by the mechanic, J. G. Bohner
of the Physical Institute in Erlangen, by means of a
small porcelain tube and asbestos packing. When the
Fig- 37-
Adjustable burner. One-sixth natural size.
burner is used, the circle of burners is placed some-
what below the outer asbestos ring of the heating-box.
Higher iron stands are necessary for the heating-boxes,
that these burners may be used conveniently. They
can be obtained 25 cm. high.
Marked changes in the gas-pressure in the city
mains, which usually take place toward evening, can
sometimes do harm. The introduction of a gas-regu-
lator makes us independent of the pressure of the gas
in the conduit tube. Beckmann recommends the use
of the one attached to the Gulcher thermopile made by
the firm of Julius Pintsch in Berlin. Smaller variations,
INTRODUCTION OF THE SUBSTANCE 1 75
whicti sometime occur during the day, have no appre-
ciable effect.
The Introduction of the Substance. — Solid sub-
stances are compressed into tablets, exactly as de-
scribed under the freezing-point method. Generally,
the tablets can be fairl}' tightly compressed, since they
are usually dissolved easily and quickly in the boiling
solvent.- When the substances are more difficultly
soluble, the tablets are, of course, not compressed so
tightly, so that they break up in dissolving ; or small
vessels of fine platinum gauze are prepared, filled with
the substance in the form of powder, and closed above
by bending the walls together. Glass, or metallic ves-
sels cannot be used, because the substance is dissolved
out of them only very slowly. A layer of concen-
trated solution forms over the substance lying on the
bottom of the vessel, which prevents or delays further
solution. Small flat boxes, or boats of thin platinum
foil, have occasionally proved to be satisfactory. Small
conical glass tubes, open below, can also be employed.
These remain suspended between the thermometer and
the wall of the boiling-vessel, their contents being
washed out by the condensed liquid as it flows down.'
But tablets are to be used whenever it is possible, that
the height of the column of liquid should not be un-
necessarily, increased through the introduction of for-
eign substances. A rise in boiling-point accompanies
a rise in the liquid column, which, although it is not
great, yet, whenever possible, should be avoided.
■ C. Schall : Ztschr. phys. Chem., 12, 147 (1893).
176 MOtECULAK WEIGHTS
According to the statements of Beckmann^ the rise in
the boiling-point of ether, under 760 mm. pressure, is
0.002'' for each millimeter increase in the heiglit <>f
the layer of ether.
Liquids are introduced with a weighing pipette,
which is quite similar to that used in cryoscopic de-
terminations, but is to be distinguished from it in that
the capillary is much longer, indeed, somewhat lonuer
than the condenser. In introducing the liquid, the pipette
is shoved into the condenser until the end of the exit
tube is exactly at the place where the vapor of the sol-
vent condenses. Only such a small trace of tlie sol-
vent condenses, then, on the point of the pipette, that
it can be neglected. But it is always desirable not to
allow the liquid contained in the capillary of the yjipette
to flow back, until the pipette has been raised into the
upper portion of the condenser, so that none of the sol-
vent will be drawn into the pipette. The following pro-
cedure can also be adopted. The desired amount of
liquid can be dropped into the condenser, just aljoxe
the point of condensation of the vapors, when no trace
of the solvent can condense upon the pipette, and then
about i'2 cc. of the solvent can be dropped in from a
second pipette, to rinse down the substance. The
amount of solvent introduced, can be determined 1)\
weighing the second pipette, and this is added to tlie
amount already in the apparatus.
The boiling-point method is, in general, rareh- em-
ployed for liquids, since the freezing-point method is
better adapted to them, and, indeed, a suitable solvent
' E. Beckmann ; Ztschr. phys. Cheni., 4, 549 ( j8Sg ,
USE OF THE DIFFERENT SOLVENTS 1 77
can always be found when it is to be used. Very vis-
cous liquids are most simply introduced into the boil-
ing apparatus by means of a small box made of plati-
num foil.
The Use of the Different Solvents. — The boiling-
point method has the advantage over the freezing-point,
that the different solvents can be employed with it
without any essential change in the manner of using
the apparatus ; while with the freezing-point method,
different devices are necessary for keeping the tempera-
ture of the thermostat constant. In addition to the
high-boiling solvents, water, as already observed, is
the only exception. It requires a direct heating of
the boiling-vessel with a flame, since its heat of vapor-
ization is enormously high.
A thick layer of fine-grained filling material, say gar-
nets, is introduced into the boiling-vessel, when
solvents are used with large heats of vaporizations, in
order that the superheated bubbles of vapor, rising
from below, should be very often checked in their
path, slowly turned aside, and given time and abun-
dant opportunity to part with the excess of heat. They
would then not reach the layer of liquid surrounding
the thermometer, until all superheating had been done
away with. A layer of garnets from 4 to 5 cm. in
thickness, should be employed with water as a solvent.
On the other hand, a layer of glass beads, from 3 to
3 ^ cm. in thickness, suffices for solvents whose heat of
vaporization is small.
Hygroscopic solvents, e. g., ethyl acetate and acetic
acid, are protected from the outer air by a small tube
178 MOLECULAR WEIGHTS
about 5 cm. long, filled with calcium chloride. This
is attached to the condenser, with a cork, and is re-
moved for a moment while the substance is being in-
troduced.
Ethyl ether is an especially convenient solvent. It
can be easily obtained of sufficient purity, readily dis-
solves many substances, boils at a convenient tem-
perature, so that generally a constant temperature is
quickly reached, gives results which are simple to in-
terpret, and permits the substance used to be easily
recovered.
It is more difficult to carry out molecular weight
determinations correctly with water, since the eleva-
tions obtained with dilute solution are very small, be-
cause of the small value of its boiling-point constant.
Satisfactory values can, however, be obtained with it,
especially at medium concentrations, by working
carefully and slowly.
A careful purification of the solvent to be used, is of
the greatest importance for the boiling-point method.
Special directions for the purification of the several
solvents have been given by Beckmann, Fuchs, and
Gerhard t.' It generally suffices to purify the liquids
by the usual chemical methods, to carefully dry them,
and to distil them, using a fractionating apparatus.
The substance to be employed, must pass over within
a few tenths of a degree. The pure preparation
should be kept in glass flasks with tightly fitting glass
stoppers, or still better, in small pipettes whose ends
' E. Beckmann, G. Fuchs, V.Gerhardt : Ztschr. phys. Chem., 18,
496 and following (1895).
USE OF THE DIFFERENT SOLVENTS 1 79
are fused together, of the form of theOstwald pycnom-
eter.' Many solvents, such as aniline, ethylene
bromide, the ethyl compounds of the halogens, chloro-
form, some ethereal salts, decompose easily in the
light, and are therefore kept in the dark.
Boiling- Molecular heat Boiling-point
point. of vaporization. 2 constant.
Acetone 56° 125 17. i
Acetonitrile' 81° 139 170
Ethyl acetate* 77° 90 26.8
Ethyl ether* 35° 87 21.6
Ethyl alcohol 78° 208 11.7
Ethyl bromide . . 38° 69 27.9
Ethylene bromide 130° 50 64.5
Ethylene chloride 83° 81 30.9
Ethyl formate 54° 100 21 .2
Ethylidene chloride 57° 69 31.3
Ethyl iodide 72° 46 51.6
Ethyl mercaptan 37° 100 19.0
Ethyl sulphide" 90° 80 32 .6
Amyl alcohol (Iso) 131° 125 25.8
' E. Beckmann : Ibid., 21, 251 (1896).
^ The heats of vaporization have been calculated by means of
the formula already given, from the boiling-point constant and the
absolute boiling temperature.
^ Acetonitrile undergoes slow change when boiled, and there-
fore does not give a sharp boiling-point.
' It is best to purify ethyl acetate just before the experiment,
by shaking it repeatedly with water, carefully drying it, and then
distilling it, since older preparations usually contain some alcohol
and acetic acid. The same holds for methyl acetate. Since these
ethereal salts are very hygroscopic, the condenser must be closed
with a calcium chloride tube.
* Ethyl ether is to be shaken with mercury, after it is cleaned
and dried, thus removing a product which raises the boiling-point.
W. Ramsay and J. Shields : Ztschr. phys Chem., 12, 448 (^1893).
* Ethyl sulphide is adapted as a solvent for many inorganic
salts. Compare M. Stephani : Dissociation Ziirich., p. 29 (1896).
l80 MOLECULAR WEIGHTS
Boiling- Molecular heat Boiling-point
point. of vaporization. constant.
Amylene hydrate (tertiary
amyl alcohol ) 102° 113 24.6
Aniline 184° 129 S^-O
Anisol 155° 92 44-3
Benzene 79° 94 26. 1
Benzonitrile 191° "7 S^-S
Bromine ■ 58° 46 47
Chloroform 61° 61 35-9
Cymol 173° 71 55-2
Diethyl sulphide 92° 66 4°
Dipropylamine 106° 62 46.0
Acetic acid' 118° 120 25.3
Isoamyl acetate 142" 7' 48-3
Isobutyl alcohol 108° 143 20. i
Isopropyl alcohol 83° 194 12-9
Camphor 204° 77 58-5
Menthol 212° 71 65.2
Menthone 206° 73 62,5
Methyl acetate 56" 104 20.6
Methylal 42° 93 21. i
Methyl alcohol 66° 259 8.8
Methyl formate 32° 116 158
Methyl iodide ■...- 42° 46 42-3
Methyl-propyl ketone .. • 102° 92 30.3
Nitroethane 114° "6 25.5
Nitrobenzene^ 209° 92 50.0
Paraldehyde^ 123° 74 41-8
Phenol 183" 13s '30.4
Propionitrile" 97° 120 22.6
' Acetic acid, when boiled for a long time, strongly attacks
the corks.
= The constant for nitrobenzene is calculated from the best
determinations available. Ztschr. phys. Chem., 19, 424 (1895).
' Paraldehj^de, on boiling, partly passes over into acetaldehyde,
so that the boiling-point is difficult to determine : Ztschr. phys.
Chem., 18, 507 (1895J.
■" Nitriles of the fatty series undergo change on boiling, and
therefore do not give a boiling-point which remains constant for
any length of time. Compare Werner : Ztschr. anorg. Chem., 15,
33 (1897)-
SOLVENTS WHICH CANNOT ALWAYS BE USED l8l
Boiling- Molecular heat Boiling-point
point. of vaporization. constant.
Propyl alcohol ( normal ) . 97° 170 ic g
Mercury 357O 60 130.0
Carbon bisulphide 46° 85 23.5
Carbon tetrachloride- .... 76° 50 48.0
Water loo"^ 540 5. i
Some Solvents Which Cannot be Used in Certain
Cases. — All solvents cannot be indiscriminately used
with the boiling-point method, just as with the freez-
ing-point method, and indeed for a very similar rea-
son. As in the latter case, a mixture of solvent and
the dissolved substance sometimes separates on solidi-
fication, so it can happen here, that the dissolved sub-
stance also volatilizes with the vapor of the solvent.
The concentration of the solution remaining behind, is
therefore smaller, and the molecular weights found are
too large.
A correction can be made, as Beckmann and Stock'
have shown, on the assumption that the dissolved sub-
stance has the same molecular weight in the gaseous
and liquid states of aggregation, by multiplying the re-
sult found for the molecular weight M', leaving out a
correction, with the expression ( i — a), a is the rela-
tion of the concentration (£ e., the number of grams
of dissolved substance to 100 grams solvent) in the
space occupied by the vapor, to the concentration in
the liquid solution. This relation, from Henry's law,
is constant for solutions of any concentration of the
same substance in the same solvent. It is ascertained
as follows : A solution of known concentration of the
' E. Beckmann and A. Stock: Ztschr. phys. Chem., 17, no
(1895).
1 82 MOIvECUI^AR WEIGHTS
substance to be investigated, in the solvent chosen, is
distilled, taking the precaution that the vapors are
condensed only in the condenser. The distillation is
interrupted after a time, and the amount of the distil-
late and of the dissolved substance contained in it, are
determined analytically. The concentration of the
distillate, which is equal to that in the space occupied
by the vapoi g^, is calculated from this. The original
concentration of the boiling solution is known. The
final concentration, which obtains after the first portion
is distilled off, can be calculated from the amounts of
solvent and dissolved substance which have passed
over. Let g^ be the mean of the concentrations at the
beginning and end ; i. e., the mean concentration of
the boiling solution. The relation between the con-
centration of the portion which has distilled over, and
that of the distilling solution, is then : _°1 = a. Sev-
eral values for a, the mean of which can be used for
correcting the molecular weight, can be obtained, by
distilling over after the first portion, a second portion,
etc., and investigating it.
This method of introducing correction is simple,
only when the fractions can be easily analyzed, as by
titration ; or in case only one of the two substances
to be taken into account contains nitrogen or a halo-
gen, by an analytical determination of these elements.
It is not practicable when analytical determinations
present difficulties, e. g., when both substances are
hydrocarbons.
The investigation of the molecular weight of iodine,
SOLVENTS 183
by Beckmann and Stock, serves as an example. Iodine
sublimes at no'' to 120°; carbon tetrachloride boils
at 76.5°.
Determination of a for Iodine in Carbon Tetrachloride.
Number of the fraction i 2 3
Concentration of the distillate = ^1 0.579 0-732 0.899
Mean concentrations of the boiling solu-
tions =^2 1.656 1.947 2.348
" 0.35 0.38 0.38
Mean value of a from all the experiments is 0.37.
The corrected molecular weight M, is obtained from
the uncorrected molecular weight M^, by introducing
this value into the above formula.
Uncorrected and Corrected Molecular Weights of Iodine
IN Carbon Tetrachloride.
Ml 370 365 374 382
M 233 230 236 241
Calculated 1^ = 254.
The value of a is smaller the greater the difference
between the boiling-points of solvent and of dissolved
substance. Beckmann and Stock found the value of
a to be 0.1, when methylal, whose boiling-point is
about 42°, was used as solvent for iodine. The intro-
duction of this value diminished only slightly the
value of M . If the dissolved substance boils more
I
than 130° higher than the solvent, the effect of the
part carried along with the vapor, is so small, that it no
longer needs to be taken into account. Only in this
case can the molecular weight be derived from the re-
sults of experiment, without further correction. To
avoid the troublesome correction^ always choose a
1 84 MOLECULAR WEIGHTS
solvent whose boiling-point lies at least ijo° below
that of the dissolved substance.
A corresponding correction can be introduced, also,
for substances which have a different molecular weight
in the gaseous form than when dissolved in a liquid.
The theoretical foundations fot this have been fur-
nished by Nernst.' That the molecular weight of a
substance in the form of gas is the same as in solution
in a liquid, can be shown, on the one hand, by the
fact that the uncorrected molecular weights obtained
by the boiling-point method, are found to be constant
within certain narrow limits, independent of the con-
centration, which would not be the case if the molec-
ular weights were different in the two states of aggre-
gation. It is further shown, in that the value of a, de-
termined experimentally, is always found to be the
same, independent of the concentration of the solu-
tion.
Effect of Atmospheric Pressure. — The boiling-
point of a liquid is dependent upon the pressure of
the atmosphere resting upon it. Annoying disturb-
ances can be produced in the exact determinations of
the boiling-point, b)- the Beckmann method, by changes
in the height of the barometer. An idea of the mag-
nitude of these can be obtained, by noting that a
change in pressure of i mm. corresponds to a change
in the boiling-point of 0.03° to 0.04".= A change in
pressure of several millimeters can occur within a few
hours, on storm >' days.
' W. Nernst : Ztschr. phys. Chem., 8, 128 (1891).
^ H. Landolt and R. Bornstein : Physikalisch-chemische Tabel-
len, 2nd Edition, Tables 25 to 37.
EFFECT OF ATMOSPHERIC PRESSURE 1 85
It is difficult to remedy this. One way out of the
difficulty is to measure the pressure on an exact
barometer from time to time, ""during the molecular
weight determination, and to take the corresponding
changes in boiling-point from the tables at hand.' The
boiling-points, read on the thermometer, are then cor-
rected by these amounts. This correction can be ap-
plied only with the more common solvents, for which
the corresponding tables are available.
The exact reading of the barometer, which gener-
ally is not practicable in the chemical laboratory, can
be avoided by observing the changes in the boiling-
point of water with an accurate thermometer, and
taking from a table the changes in pressure corre-
sponding to these.
An attempt has also been made to introduce a cor-
rection by allowing the pure solvent to boil in a sec-
ond apparatus, and to use the changes in the boiling-
point as correction values. But this method does not
appear to be very reliable.
Although the effect of changes in the barometer can
be so considerable, yet no serious disturbances are thus
produced in simple molecular weight determinations,
as carried out in the laboratory. Since, in the short
time required to make some molecular weight deter-
minations, after the boiling is constant (I allowed ten
minutes for each experiment, Beckmann a still shorter
time^), the pressure changes so little that such changes
■ H. Landolt and R. Bornstein : Physikalisch-chemische Tabel-
len, 2nd Edition, Tables 25 to 37.
= E. Beckmann : Ztschr. phys. Chem., 15, 676 (1894).
1 86 MOI.ECUITASS1UM
Nitrate in Water.
Boiling-point Method
Grams
Molecular
substance.
Rise.
weight.
0.2062
0.085°
48.4
0.4910
0.183°
53-6
0.9175
0-334°
54-6
1-7774
0.615°
57-7
2.2430
0.755°
58.0
3.2870
1-055°
62.2
4-3091
1-365°
63.0
I go MOLECULAR WEIGHTS
Normal molecular weights are obtained with electro-
lytes in other solvents, e. g., ethyl alcohol, as the
investigations of Raoult' have shown for a nnmber
of salts, such as potassium acetate, lithium chloride,
calcium chloride, calcium nitrate. Normal values for
the molecular weight also of zinc chloride,^ are ob-
tained in solution in ethyl alcohol.
In 18.56 grams of ethyl alcohol (18.37 ^^ the calcu-
lation) gave :
Zinc Caloride in Ethyi, A^cohoi,. Bohing-point Method.
Grams
Molecular
substance.
Rise.
weight.
0.1959
0.087^
143
0.4096
0.194°
134
0.6825
0.336"
129
Other inorganic salts, the determination of whose
molecular weight in solution would be of considerable
theoretical interest, e.g.^ ferric chloride and aluminum
chloride,^ have, on the contrary, not been successfully
investigated thus far by the boiling-point method, in
organic solvents, because the}- act chemically upon the
solvent. This is shown by the quick rise in tempera-
ture, which immediately follows the introduction of
the salt into the boiling solvent. If there were no
reaction, the thermometer would have first fallen ;
therefore, this is an indication that reaction has taken
place. It is not permissible to draw a conclusion in
reference to the molecular weight in question from
-- F. M. Raoult : Compt. rend., 107, 442 { 18
* From experiments by O. Klosmann and E. Konig in Greifs-
wald.
3 P. Th. Muller: Compt. rend., 118, 644 (1894).
THE RESUI.TS
191
the values found/ which, as a matter of fact, agree
with the formula FeCK I state these details to show
how careful we must be in the critical examination of
molecular weight determinations of inorganic sub-
stances, which are investigated in organic solvents.
Recently, a comprehensive investigation has been
published by Werner=, and his co-workers, on the
molecular weight of inorganic salts in organic sol-
vents. In the majority of cases, the simple molecular
weights were found. The same was true for stannous
chloride, aluminum chloride, and ferric chloride. This
result for these three salts was, indeed, surprising,
since careful vapor-density determinations had shown
the existence of more complex molecules, and the high-
est molecular weight given by a vapor-density determin-
ation is always found in solution. Since, however, both
of the solvents used by Werner always appear to form
addition-products of the solvent, with metallic salts (and
Werner himself has furnished many instances of this),
I believe that more complicated processes take place
in the solutions, and that from his results alone, con-
clusions must not be drawn as to the size of the
molecules of the pure substance. Just as when ferric
chloride is dissolved in alcohol and acetic ether, no
reaction manifests itself by the evolution of heat, so,
according to Werner's statement, is no heat evolved
when aluminum chloride is dissolved in pyridine.
3. Complex Molecules. — The intimate relationship
From experiments by O. Klosmann and E. Konig in Greifs-
wald.
* Alf. Werner: Ztschr. anorg. Chem., 15, i (1897).
192 MOtECULAR WEIGHTS
between the freezing-point and boiling-point methods,
which has been repeatedly emphasized, holds, finally,
for those substances which tend to form complex
molecules, and for those solvents which favor such an
association. Both methods lead, in such cases, to the
same results. The difference in temperature makes a
slight difference in the results. The curve obtained
by the boiling-point method, — other conditions being
the same, — is lower than the curve obtained by the
freezing-point method, for dissociating substances, or
such which contain more complex molecules, in con-
centrated than in dilute solutions, since the dissocia-
tion has proceeded further, or the association not as
far, at the higher temperature. (Compare Fig. 42.)
These relations have, up to the present, been
worked out thoroughly only by means of the freezing-
point method. The analogous investigations for the
boiling-point method, which would undoubtedly lead
to the same results, have not yet been carried out, so
that the statements to be made here must be very
incomplete.
Of the solvents named, the following favor the
formation of complex molecules :
ASSOCIATING SOLVENTS.
Ethyl bromide,
Ethylene bromide,
Ethylene chloride,
Ethylidene chloride,
Ethyl iodide,
Benzene,
Chloroform,
Cymol,
Methyl iodide^,
Methyl-propyl ketone,
Nitroethane,
Nitrobenzene, ,
Propionitrile,
Carbon bisulphide,
Carbon tetrachloride.
THE RESULTS
193
On the contrary, simple molecules are found in the
following solvents :
NON-ASSOCIATING SOLVENTS.
Acetone,
Ethyl acetate,
Ethyl ether.
Ethyl alcohol.
Ethyl formate,
Amyl alcohol.
Acetic acid,
Isoamyl acetate,
Isoamyl alcohol,
Isobutyl alcohol,
Isopropyl alcohol.
Methyl alcohol,
Methyl acetate,
Methylal,
Methyl formate.
Phenol,
Propyl alcohol,
Water.
In general, all substances corresponding in their
constitution to the water type, and also acetone, exert
a dissociating influence.
The chemical nature of the dissolved substances,
and the concentration, so far as investigations up to
the present have shown, produce exactly the same
effect on the boiling-point curve, as on the freezing-
point. A few curves will serve to make this clear.
I AOO,
Rise in boiling-point.
Fig. 41.
Borneol in solution in benzene. ^
The boiling-point curve of benzoic acid in benzene,
is not drawn from the elevations of the boiling-point.
From experiments by William Biltz.
194
MOLECUtAR WEIGHTS
but from the concentrations, since it should be com-
pared with the freezing-point curve, which is introduced
above it in the drawing. It is seen that the dissocia-
oi^O-
iOO
s /GO
MO
...K-<^Ak
(n.
"m^
^
i'
/
Cdi J^O
UOO
/Go
/AO
/
—
yi
y
/
/
y
/
(
-fHfDIQ
Rise in boiling-poirrt.
Fig. 43-
o-Formtoluide in solution in benzene. 2
Some inorganic salts also show a tendency to form
double molecules, according to the investigations of
Werner; e. g., cuprous cyanide, and to a less degree,
cuprous bromide in solution in pyridine. Further,
silver iodide in pyridine. While values were found for
silver chloride and silver bromide, which were even
higher than would correspond to the double molecules.
' E. Beckmann : Ztschr. phys. Chem., 6, 451 (1890).
^ From experiments by G. Preuner.
196 MOLECULAR WEIGHTS
Choice of Method. — In deciding whether to use the
freezing-point, or the boiling-point method, in a given
case, the solubility of the substance to be investigated
must first of all be taken into account. If it dissolves
easily in one of the solvents used with the freezing-
point method, this method is preferable, because it
gives more accurate results than the boiling-point
method with smaller amounts of substance. Since
the freezing-point constants are larger than the boil-
ing-point constants, the difference in temperature,
determined for equal amounts of substance, is greater
when the freezing-point method is used, and errors in
the measurement of temperature have less effect.
But in very many cases the solubility of the sub-
stance to be investigated, is too small to permit the use
of the freezing-point method. The boiling-point
method can be used in such cases, and is of incalcula-
ble value.
The carrying out of a molecular weight determina-
tion by the boiling-point method is, without doubt,
more convenient than a freezing-point investigation,
in case the apparatus is ready. The apparatus, when
heated, can be left to itself, and then it is only neces-
sary to observe the temperature from time to time.
The determination proper, consists in introducing the
substance and observing the rise in temperature, and
is over in a short time. The substance dissolves
rapidly and spontaneously, while this often presents
difficulties in the freezing-point method. The danger
also of a substance crystallizing out, which sometimes
cannot be foreseen, is avoided.
LOWERING OF SOLUBILITY 1 97
The freezing-point method, as already observed, is
to be unconditionally preferred in the investigation of
liquids.
DETERMINATION OF MOLECULAR WEIGHTS FROM THE
PRINCIPLE OF LOWERING OF SOLUBILITY
It has already been mentioned in the introduction
to the chapter on osmotic methods, that a solution can
dissolve less of a second liquid than the pure solvent ;
e.g.^ an ethereal solution of anthracene dissolves less
water than pure ether. The law underlying this,
which led to a method for determining the molecular
weight of the dissolved substance, was discovered by
Nernst.' The relative lowering of the capacity to dis-
solve a second liquid, which a solvent experiences on
adding a foreign substance, is equal to the relation
between the number of molecules of the foreign sub-
stance dissolved, and the number of molecules of the
solvent.
Let L^ be the solubility of the liquid in the pure
solvent ; L the solubility in solution ; the relative
lowering of the solubility, therefore, ° . Further,
let n be the number of molecules of the substance dis-
solved, and N the number of molecules of the solvent ;
the above law can then be expressed in the following
formula :
L N-
Further, let n = — , where g represents the amount
' m
' W. Nernst : Ztschr. phys. Chem., 6, 16 (1890).
198 MOLECULAR WEIGHTS
of substance dissolved, and m its molecular weight.
By introducing this expression for n, and proper trans-
formation,' we finally obtain the equation :
g N + n-
Since n, with respect to N, is very small, it can be
neglected. It follows, then, that the right side of the
equation is a constant, when an equal quantity of the
same solvent (N therefore constant) is taken in every
experiment. If this constant is represented by C, we
have
m ^ C
g
The constant C, from this equation, can be determined
experimentally, by determining the lowering of solu-
bility L„ — L, which a constant quantity of a solvent
undergoes, with respect to a second liquid, when g
grams of a substance of known molecular weight
m, are dissolved in it. It should be observed
that the value of C, thus determined, is not a general
constant for the solvent in question, but refers to the
amount of solvent employed in the experiment, and
to the temperature which obtains.
This procedure has been worked out for the prac-
tice of the laboratory, by Tollaczko,' a pupil of Nernst.
Ether is used as the solvent, and water as the second
liquid. The method can be used for all substances
which are easily soluble in ether, but not soluble in
water. The solubility capacity of the ether is ascer-
■ St. Tollaczko : Ber. d. chem. Ges., 28, 804 (1895).
LOWERING OF SOLUBILITY igg
tained, simply by volume measurement. The follow-
ing simple apparatus is employed for this purpose. A
flask of about loo cc. capacity, is provided with a neck
about 15 cm. long, and 0.7 to 0.8 cm. wide, which is
graduated to half-millimeters. The neck can be closed
ether-tight, by means of an accurately ground-glass
stopper.
To determine C, the flask is filled up to where the
neck begins, with water saturated with ether. Then
a quantity of ether determined once for all, say a layer
of 6 cm. thick, which in turn is saturated with water,
is poured in, and finally some drops of mercury added,
so that the boundary of water and ether comes on the
lower portion of the scale. It is desirable to employ
in every case, not only the same quantity of ether, but
also the same quantity of water. After the flask has
stood for some time at a constant temperature, being
meanwhile repeatedly shaken, the mercury effecting
better mixing, the position of the bounding layer be-
tween ether and water is read exactly. A check
reading is made after a time.
A weighed amount of substance is now introduced
into the ether ; 0.05 to 0.15 gram, when the substance
has a small molecular weight, and o.i to 0.3 gram
when the molecular weight is large. The substance
is dissolved by shaking, and the new position of the
ether accurately determined by a number of readings.
The bounding layer has now risen higher into the
neck. The difference between the two readings is the
diminution in solubility, expressed in divisions of the
scale = L„ — L. C is obtained by introducing the
value into the formula.
200 MOLECtJLAR WEIGHTS
Example: 0.0655 gram benzene produce a displace-
ment of 0.45 cm. ; the molecular weight of benzene
is 78.
After the value of C has been accurately established,
by repeated experiments, it can be used for determin-
ing the molecular weight of substances whose molec-
ular weight is unknown. For the calculation, the
equation used above is solved for m :
^_ Cg
The molecular weight determination proper, is car-
ried out in exactly the same manner as the determi-
nation of C.
An example may serve to make the process clear :
Naphthalene in ether. 0.1266 gram naphthalene
depresses the solubility of water in ether about 0.55.
536 X 0.1266
m = ^^^:^ = 123.
0.55 ^
M, calculated from the formula C^^Hg, = 128.
This simple method, which can be easily carried out,
is very useful for substances which are easily soluble
in ether, but which are insoluble in water. It is to be
especially recommended for the investigation of liquids.
Its accuracy is certainly not very great, since the dis-
placement of the bounding layer between the water
and ether is only slight.
The fundamental condition for obtaining useful
values, is that the temperature must be maintained
LOWERING OF SOIvUBIWTY 20I
exactly constant in all of the readings, as well in deter-
mining the constants as in the molecular weight deter-
minations proper. The same temperature must obtain
in both cases, to a tenth of a degree. A large water-
bath, whose temperature is read with a thermometer
graduated to tenths of a degree, is employed as a ther-
mostat.
DETERMINATION OF THE MOLECULAR WEIGHT
OF HOMOGENEOUS SOLIDS OR LIQUIDS
111 the methods thus far described, the molecules
were separated for the purpose of determining molec-
ular weights, either by vaporization, or solution in a
solvent. The determination of the molecular weight
of undiluted solids or liquids, has been recently ac-
complished, a problem, whose solution a short time
ago would have appeared scarcely possible.
These methods, up to the present, have been chiefly ■
worked out with homogeneous liquids, and solids
since they are less simply dealt with, have been inves-
tigated in only a few cases. It has been shown that
the majority of organic substances, in the solid and
liquid conditions, are made up of the corresponding
simple molecules. Double, and still more complex,
molecules exist in those substances, in which, the
investigation of their solutions had pointed to a ten-
dency towards the formation of such molecular com-
plexes, as with the acids and alcohols. More complex
molecules exist, also, in some substances in the homo-
geneous solid, or liquid condition, whose presence was
not indicated from the investigation of their vapor or
solutions ; thus, solid naphthalene consists of double
molecules.
The existence of molecular complexes is shown, in-
deed, by some substances in the form of vapor ; e. g.,
by the simpler monobasic fatty acids. The same
HOMOGENEOUS SOUDS OR LIQUIDS 203
peculiarity is shown by a larger number of classes of
substances in the state of liquid solution. And the
same is shown by still other substances, also in the
homogeneous condition.
The assumption formerly made, that solid substances
consist of larger aggregations of the simplest mole-
cules, and therefore always have a much greater
molecular weight than the substance in the liquid or
gaseous condition, is thus shown not to be well
founded.
The problem of determining the molecular weight
of a homogeneous substance, is solved by different
methods. The majority of them give the " associa-
tion factor ;" i. e., the number of simple molecules
which are united to form a complex molecule. The
association factor is often a fraction; z'z>., when the
substances are in a state of dissociation of the more
complex molecules into simpler molecules, simple
molecules also being present, together with more com.
plex molecules. The association factor for acetic
acid' at 200°, is about 1.5, while at 50° it is 2. Some
of the double molecules, which are stable at 50°, are
decomposed, therefore, at the higher temperature.
More detailed information in reference to the indi-
vidual methods for determining the association factor,
can be found in the paper by Ramsay, already referred
to, and in a summary of the different methods by
Traube.'
The simplest method for determining the associa-
W. Ramsay: Ztschr. phys. Chem., 15, iii (1894).
■ J. Traube: Ber. d. chem. Ges., 30, 265 (1897).
204 MOtECULAR WEIGHTS
tion factor of homogeneous solids or liquids, has been
discovered by J. Traube, a method which shows at once
the formula of the molecule. This method differs
from those thus far described for determining molecu-
lar weights, in that an exact knowledge of the com-
position of the substance to be investigated, is neces-
sary, that it may be used. We must know the simplest
atomic composition, and also, approximately, the con-
stitution of the compound. The number of double
bonds, when they are present, must be known, and
also whether it has a ring system. Also the valence
of the nitrogen contained in it, must be known. Con-
sequently, this method can be occasionally used to de-
cide questions of constitution, in case the molecular
weight is determined by another method.
The method of Traube gives the molecular weight
of molecular complexes, for associated substances,
therefore, the molecular weight of the simplest mole-
cule, multiplied by the association factor. Conse-
quently, it is often impossible to determine, from the
result of a molecular weight determination alone,
whether the substance has really a high molecular
weight, or whether the molecular weight found is that
of a molecular complex. It is, indeed, of less inter-
est, for purely chemical investigations, to know whether
the molecules of the substance investigated, are united
homogeneoush' into more complex molecules, than to
be able to find out the size of the simplest molecules
which can exist. Whether a molecular weight found
is really the simplest, or whether it corresponds to a.
somewhat more complex molecule, is shown by solu-
METHOD OF TRAUBE
205
tion methods, at least with organic substances, from
the course of the concentration curve. The question,
as already observed, is not answered directly by the
results of experiment, when the method of Traube is
used, but through analogy, from the behavior of those
substances which are most closely related chemically
to the substance under investigation. But, since, from
some knowledge of the substance to be investigated,
it is almost always known whether more complex
molecules are to be expected, the method of Traube
can be used also to ascertain molecular weights for
chemical purposes. The simplest molecular weight
can, however, in many cases, certainly not be found,
by the method of Traube, as, for example, naphtha-
lene. Important information pertaining to the deriva-
tion of the simplest molecular weights, is contained in
the following pages.
DESCRIPTION OF THE METHOD OF TRAUBE
The method of Traube' was discovered and worked
out in the years 1895 ^^^ 1896. It is purely empir-
ical up to the present. It lacks theoretical foundation,
a deficiency which it shares, moreover, with other
important methods; £'.^., the method for determining
constitution from molecular refraction. The method
of Traube leads to the molecular formula, from certain
deviations obtained by determining, on the one hand,
the molecular volume of the substance in question.
' J. Traube : Ztschr. anorg. Chem., 8, 323, 338 (1895) ; Ber. d.
chem. Ges., 28, 410 (1895) ; Ann. Chem. (Liebig) 290, 410 (1896) ;
Ber. d. chem. Ges., 28, 2722, 2728, 2924, 3292 (1895); 29, 1023
(1896).
206 MOLECULAR WEIGHTS
directly, and on the other, by calculating it from
definite known factors.
Experimental Determination of the Molecular
Volume. — The space, measured in cubic centimeters,
which a gram-molecule of a substance occupies, when
undiluted with any foreign substance, is its molecular
volume.' This includes the space present between
the molecules of the mass. The molecular volume
Vm, is obtained by dividing the molecular weight m,
by the density d.
A'rr, — ™
\ m — -
d
In order to be able to compare different substances
in this regard, the density determinations have thus
far been carried out under comparable conditions, and,
indeed, at the boiling temperature of the substance
under investigation. Traube chose a temperature of
15", on practical grounds.
Calculation of the Molecular Volume. — Kopp had
alread)' recognized that the molecular volume is
essentially an additive property of substances. Its
value can be calculated, by adding the atomic volumes'"
of all the atoms which enter into the molecule. More
thorough investigations have subsequently shown that
the constitution, also, has an influence on the molecu-
' H. Kopp: Ann. Chem. Pharm., 96, 153, 303 (1855).
'' By atomic value is not to be understood the space occupied
by the mass of the atom (volume of the atom itself), but the space
necessary for the vibrating atom (space in which atom vibrates) .
According to Traube, the latter is about 3.5 times the former.
Ber. d. chem. Ges., 29, 2732 (1896).
METHOD OF TRAUBE 207
lar volume. The presence of double bonds, the
accumulation of halogen atoms on one carbon atom,
etc., produce deviations in the value of the molecular
volume, which cannot always be taken into account
by an extension of the formula by which the calcula-
tion is made. Also, other irregularities manifest
themselves.
-Traube understood the reason for these deviations.
He showed that the molecular volume cannot be
calculated by simply adding the atomic volumes and
some correction values, but that a numerical factor,
which is always the same, must be added. The main
point' of his work is this : An increase in volume takes
place when a molecule is formed from atoms ; this is
independent of the chemical nature of the substaitce,
and can be only slightly modified by constitution. It
amounts to 2^.^ cc. for a gram-molecule at 75° C
This space of 25.9 cc. is designated as the covolume.
The covolume represents the space which the mole-
cule requires for its oscillations.
It is, indeed, very interesting that this covolume
increases with the temperature, and, indeed, exactly
according to Gay Lussac's law for the expansion of
gases.
COV, = C0V„ ( I + at) = 24.5 ( I + at) .
Covt is the covolume at the temperature t ; CoVq is
the covolume at 0° ; a is the coefficient of expansion
of gases = 0.00367.
' J. Traube : Ann. Chem. (Liebig), 290, 89 (1896).
2o8 MOLECULAR WEIGHTS
Example :' The hydrocarbon C^ H^g has a covolume
24.4 cc. at 0° ; 33.0 cm. at 100". The coefficient of
expansion a^ is calculated from the equation 33.0 =
24.4 (i -f a^t) ; therefore a^ = 0.00353. "^^^ devia-
tion from the theoretical value is, as we see, very
small.
The temperature correction is unimportant for
the purpose of a molecular weight determination, and
can be disregarded, if the densit}' determination is car-
ried out at the mean room temperature (14°— 17°). If
greater differences in temperature occur, the correc-
tion can easily be made. The following short table
contains the covolumes at several temperatures:
Tempera- Covolumes. Tempera* Covolumes. Tempera- Covolumes.
are.
ture.
ture.
24-5
15
259
22
26.5
5
24.9
16
25-9
24
26.6
10
25.4
17
26.0
26
26.8
12
25.6
18
26.1
28
27.0
14
25.8
20
26.3
30
27.2
It is clear, from what has been said, that the molec-
ular volume can be obtained from the several atomic
volumes, taking into account the covolume, and some
correction values for any ring systems, double unions,
etc., present.
The following table^ contains the data necessary
for the calculation.
' J. Traube : Ber. d. chem. Ges., 28, 3297 (1895).
'J.Traube: Ber. d. chem. Ges., 28, 2724, 2924(1895); Ann.
Chem. (Liebig), 290, 43 (1896). In this paper the data observed
are recorded : Ber, d. chem. Ges., 29, 1024 (1896).
METHOD OF TRAUBE
209
c
9-9
CN 13.2
H
31
N'" 1.5
O'
2-3
N^ about 10.7
o"
5-5
N°8.5 to 10.7
5-5
P™ about 17.
O"
0.4
P'' about 28.5
S'
15-5
Na 3.1
S"
15-5
Ce ring' —8.1
S"
ID to 1 1.5
C,Sring — 11.4
F
5-5
N ring, small
CI
13.2
1= -1-7
Br
17.7
^ -3-4
I
21.4
In this table the symbols mean :
O'S', hydroxyl oxygen, snlphydride sulphur. (Al-
cohols, etc.)
0"S", the atom united with carbon by double union.
(Ketones, Aldehydes, etc.)
O", an oxygen atom uniting two carbon atoms.
(Ether.)
O", an oxygen atom in a carbonyl group, or which
is united to a carbon atom, which is next to a carbon
atom with a hydroxyl group attached to it. If there
are more than one hydroxyl groups close together,
one has O, oxygen atom.'' (Acids, o-dioxy benzene, etc.)
S°N°,mean the atoms connected with oxygen (sulpho-,
nitro-, etc. groups).
Cj ring, denotes every ring of six carbon atoms.
C S, denotes the thiophene ring.
' Twice this value is to be subtracted in naphthalene, and three
times the value in anthracene.
' Glycol has two oxygen atoms, one is to be introduced in the
calculation as O', the other as C ; a-oxy acids have O", O', Ob.
So also P- and other oxy-acids.
2IO MOLECULAR WEIGHTS
N ring, means a ring system containing nitrogen.
1= denotes a double union.
[= , denotes a triple union.
The values for the ring systems, and the double and
triple unions, are, as negative values, to be subtracted
from the sum of the atomic volumes.
If we designate by c the number of carbon atoms in
the molecule of a compound, by h the number of
hydrogen atoms, by O', O", C, O'', the number of dif-
ferent oxygen atoms, by r the number of Cg rings, etc.,
the molecular volume is :
Vm = 9.9c + 3.ih + 2.30' ••• — B.ir ... +25.9.
The molecular volume of a compound is calculated
with the aid of this formula, which is easily com-
pleted from the foregoing table. lyCt some examples
be given for this purpose. — gives the value found
experimentally.
Pentane, CsH,j.
C, = 49-5
H,. = 37.2
Cov. = 25.9
Benzene.
•Ce = 59-4
Ho = 18.6
Cov. = 25.9
c.
ring
3F=
= 8.1
= 5-1
1 12.6
m
^=113.7
103.9
— 13.2
13.2
90.7
^ = 88.3
DETERMINATION OF MOLECUIvAR WEIGHT
Methylal, CsHsOjV.
C, = 29.7
H, = 24.8
01 = II. o
Cov. ^ 25.9
91.4
m
d
= 88.4
lycerine
olecular
ether, C|,H
volume fc
0:
= 89.1
= 49-6
= II.
0,
Cov„.
= 5-3
= 24.5
2|= =
176.5
= — 3-4
I73-I
-^172.6
DETERMINATION OF MOLECULAR WEIGHT
The molecular weight determination proper, depends
upon this fact, that the molecular volume determined
experimentally in the manner given, agrees with that
calculated from the atomic volume, only when the
correct molecular weight is assumed for the substance.
Since, only then, does the following equation obtain :
-^- = 2 + 25.9 or _ — 2 — 25.9.
By the sign 2, is undet'stood the algebraic sum of
the atomic volumes and the correction values, with
the exception of the covolumes. If the density is
212 MOLECULAR WEIGHTS
determined at a temperature (t), which differs consider-
ably from 15°, the value introduced is 24.5 (i + at),
instead of 25.9.
If the molecular weight is estimated at one-half its
real value, the equation will appear to be divided by
two, and, accordingly, the numerical factor 12.9 appears
instead of 25.9
If a molecular weight is assumed, which is double
the real molecular weight of the substance, the
equation will appear to be multiplied by 2, and the
numerical factor upon the right will be 51.8. A few
examples will serve to make the application of the
method clear.
1. What is the molecular weight of the chloride
(CHCl^)x ivhose density is 1.6258.^
The calculation gives the following values :
tn ^
Formula assumed. d ^ Difference.
CHCl, 51.6 39.4 12.2
(CHCIJ2 103.2 78.8 24.4
(CHC1,)3 154.8 118.2 36.6
The examination of the column of differences, shows
that the substance has the formula C H CI , because
the difference corresponding to this formula, 24.4,
approaches closely to the normal covolume 25.9. The
substance is tetrachlorethane.
2. A bromide is obtained by introducing bromine
into toluene^ which^from analysis^ has the formula
C^H^Br. The density was 1.401. What is the
molecular weight?
DETERMINATION OF MOLECULAR WEIGHT 213
Formula assumed. d ^ Difference.
C;H,Br I22.I 95.5 26.6
(C,H,Br)2 244.2 191. o 53.1
(C,H,Br), 366.3 286.5 79-7
It follows from this calculation, that the simple
formula C H Br belongs to the substance ; for the
covoliime corresponding to this assumption, agrees
closely with the required value 25.9, while the other
differences are widely removed from it.
3. What is the molecular weight of naphthalene
(Cj^Hg)x, whose density is 1.1517.?
m .^
Formula assumed. d ^ Difference.
CioHg III. I 99.1 12.0
(CioHs).^. 222.2 198.2 24.0
It follows from this, that solid homogeneous naph-
thalene consists of double molecules.' On vaporization
and solution, these molecules decompose to molecules
4. Styrql^ and two isomers formed from, it^ have
the .composition (CgHg)^; the density of styrol is
o.giii-^), of the so-called distyrol, 1.016 (—3-) of the
metastyrol, 1.0^^ (-^h What are the molecular
weights of the three hydrocarbons?
' Naphthalene investigated by the freezing-point and boiling-
point methods, showed not the least inclination to form double
molecules. On the contrary, Kiister had shown, both from the law
of the division of substances between solvents, and also from the
lowering of solubility, that solid naphthalene consists of double
molecules. F. W. Kiister: Ztschr. phys. Chem., 17, 366 (1895).
214 MOtECULAR WEIGHTS
(a) Styrol.
m -y 1
Formula assumed. ~d" Difference.
CgHs 114.2 89.1 25.1
(CsHj,);, 228.4 178-2 50.2
Styrol has therefore the simple formula CgHg.
(3) Distyrol.
Formula a.'-.sumed. "d" Difference.
CgHg 102.3 89.1 13.2
(CsHs)^ 204.6 178.2 26.4
Distyrol has, therefore, the double formula, as has
also been shown by the vapor-density determination.
The high covolume suggests that when two styrol
molecules unite, the union is effected through a double
union of the side-chain in one of the molecules. The
value of S, calculated on this assumption, would be
179.9, and the difference 24.7; this cannot be decided
with certainty. As a matter of fact, distyrol takes
up only one molecule of bromine, so that the con-
jecture appears to be justified.
{c) Metastyrol.
Metastyrol cannot be vaporized without decom-
position, and is so slightly soluble in organic solvents
that its molecular weight, thus far, could not be
determined. The method of Traube, on the other
hand, led to results.
m VI
Formula assumed. d Difference.
CaHs 98.7 89.1 9.6
(C8Hg)j 197,4 178.2 19.2
(CfiHs 3 296.1 267.3 28.8
(QHg), 394.8 356.4 38.4
' In calculating the sum X. for styrol and its isomers, a
benzene ring and four double bonds are assuined to be present.
DETERMINATION OF MOLECULAR WEIGHT
215
It is not very easy to decide in this case, since the
value of the difference, which comes nearest to the
normal covolume at 13° (25.7), differs from it by 3.1.
At any rate, three styrol molecules unite to form a
metastyrol molecule ; it is probable that two double
unions in the side-chains are broken here, so that the
formula of the compound is C^ H^ , lof^, 3C5 rings.
The value of 2, calculated for this, is 270.7; the
difference thus being 25.4, while the normal covolume
at 13°, is 25.7 cc. A formula in which all the double
unions of the side-chain are broken — indeed, a formula
for which the great stability of the substance argues —
is not possible, because in it a new ring system
occurs.
H CeH,
CcH
The value 2, calculated for this, is 264.3 ; the dif-
ference would be 31.8 ; therefore, much too large.
Deviations are found in a number of cases.
Indeed, larger covolumes sometimes appear even
with the simplest possible formula, so that one could
assume a partial decomposition of the simplest mole-
cules. This anomaly, which has not yet been com-
pletely explained, is shown by substances into which
2l6 MOLECUI,AR WEIGHTS
more than one halogen atom has. been introduced,'
especially if the halogen atoms are united to one car-
bon atom; e. g., chloroform (cov. = 27.8); chloral
(cov. ^ 29.0) ; carbon tetrachloride (cov. = 31.9).
The same peculiarity exists with the highly sub-
stituted ammonias; ^. ^., with triethylamine (cov..=:
31.6) ; triisobutylamine (cov. = 37.1) ; and finally, with
the ethereal salts of nitrous acid, and also — to a less
extent — with those of nitric acid, if they contain a
higher alcohol residue ; e. g., isoamylni trite (cov. =
27.7) ; n octyl nitrite (cov. = 30.0).
This peculiarity must be taken into account in de-
termining the molecular weight of the corresponding
substances.
Example : Hexachlore thane has the density 2.01 1.
m ^
Formula assumed. ~i Differeuce.
CjClfi 117.5 99.0 18.5
(C2Cls)2 235.0 198.0 37.0
Since substances with a large number of chlorine
atoms have a high covolume, the conclusion must be
drawn that hexachlorethane consists essentially of
double molecules.
Another series of substances shows a remarkably
small covolume, from which we must conclude that
complex molecules exist. This includes substances
containing hydroxyl, with low molecular weight, and
also some other substances (as acetone) of very small
molecular weight ; e. g., water (cov. 9.6) ; formic acid
(cov. 15.5) ; acetic acid (cov. 18.7) ; valeric acid (cov.
21.7). The covolume also approaches the normal
■ J. Traube : Ber, d. chem. Ges., 29, 1027 (1896).
DETERMINATION OF MOLECULAR WEIGHT 2l'7
value with increasing molecular weight, as we see;
i. e., the association is less among the higher members
of the series, as indeed, had been earlier made probable
by vapor-density determinations. The following sub-
stances belong, also, with those of low covolumes :
Methyl alcohol (cov. 15.6) ; ethyl alcohol (cov. 17.2);
glycerine (cov. 14.9) ; acetone (cov. 19.0). The same
rule, that the association decreases with increasing
molecular weight, holds also for the alcohols ; an in-
crease in the number of hydroxyl groups in the
molecule, increases the association factor.
The slight tendency of ethyl alcohol to associate is
striking. We would conclude from the investigation
of ethyl alcohol in benzene, by the freezing-point
method (page 100), that there were molecules much
more complex than double. It was, however, pointed
out that that investigation was possibly not entirely
to be depended upon, because, when the solution solidi-
fied, a mixture of alcohol with the benzene may have
separated.
The simplest molecular weight of glycol, C^H^O ,
is found as follows, taking into account this influence
of the hydroxyl groups.
Example : Glycol has the density 1.1279 \~^ ) •
Formula assumed. "a" ^ Difference.
CjHeO 55 43 12
(QHeO.,)., no 86 24
According to this, glycol in the liquid condition
consists of double molecules. But since it contains
more than one hydroxyl group, a covolume consider-
2l8 MOLECUI,AR WEIGHTS
ably smaller than usual, is to be employed in deriving
the simplest molecular weight. Accordingly, the
simplest molecular formula of glycol is C^H^O^.
The association factor^ (x) is derived from the co-
volume (p), as follows : If c is found to be 25.9 at 15°,
X = I ; if c is found to be 12.95, x = 2. If the value
of c lies between 25.9 and 12.95, the association fac-
tor is found from the following equation :
12.95
For example :
0^=19.1, then x= 1.53.
Water has the largest association factor, 3.06 ; then
comes glycol (1.88), glycerine and nitroethane (1.82),
formic acid (1.80), acetic acid (1.56), methyl alcohol
(1.79), ethyl alcohol (1.67). Small association is
shown by benzene (1.18), and by toluene (1.08).
The Traube method of determining the molecular
weight, can be very conveniently employed in many
cases, indeed its experimental basis — a determination
of the density — is easily carried out, at least for
liquids. The density must often be ascertained by
other determinations, perhaps refractometric, and then
the molecular weight determination is limited to a
short calculation. The Traube method gives, how-
ever, useful results only when an exact knowledge of
the simplest atomic composition is obtained by analy-
sis, and when the constitution of the compound is
known exactly. It is absolutely necessary to know
' J. Traube: Ber. d. chem. Ges., 30, 273 (1897).
TRAUBE PROCEDURE FOR SOLUTIONS 219
the number and composition of the ring systems,
which can be contained in the simplest formula, fur-
ther, the valence of the nitrogen, and finally, at least
approximately, the number of double and triple unions.
The molecular weight of benzene, e. g.^ could not be
ascertained by the method of Traube, if the presence
of the ring and the three double unions were not
known. Such knowledge is not required to determine
molecular weights by the other methods. They give
the molecular weight of any substance, whatever, with-
out requiring the least knowledge as to the composi-
tion, and have, accordingly, shown themselves to be es-
pecially useful in the many cases in which the begin-
ning of a reaction is recognized most simply, and with
the greatest certainty, by a molecular weight deter-
mination, without knowing anything as to the compo-
sition of the products.
MODIFICATION OF THE TRAUBE PROCEDURE FOR
SOLUTIONS
It should be pointed out, in addition, that the Traube
method can also be employed for ascertaining the
molecular weight of dissolved substances. This is ac-
complished by deriving the molecular volume from
the density of the solution. Differences of kind, de-
pending upon the nature of the solvent, have become
apparent, only indifferent solvents free from hydroxyl,
showing no further anomalies ; so that the molecular
volume derived from the solution, just as that obtained
from the homogeneous substance, can be introduced
into the calculation. Solvents containing hydroxyl,
220 MOLECUI.AR WEIGHTS
especially water, lead, on the other hand, to entirely
different results.
A. Indifferent Solvents. The molecular volume
is derived from the density of the solution which is
not too dilute, of the substance in chloroform, carbon
bisulphide, benzene, or other indifferent solvent, in
the following simple manner. From the volume of
the solution which contains a gram-molecule of the
dissolved substance, is subtracted the volume of the
solvent contained in it. The difference is the molec-
ular volume of the dissolved substance. If a solution
of a gram-molecular weight of substance m, in i gram
of solvent, has the density d, and the pure solvent the
density S, the molecular volume of the dissolved sub-
stance Vm, is expressed thus:
m+i I
Example: A solution of naphthalene in benzene,
18.77 per cent, had a density of 0.90312 at 19.1° ; the
density of the pure benzene is 0.8804.
The amount of benzene which would dissolve a
gram-molecular weight of naphthalene (127.7 gr^™s),
giving a solution of the same concentration, is obtained
from the equation,
18.77 : 81.23 = 127.7 : 1 = 552.6
0.90312 0.8804
The molecular volume of naphthalene, calculated
by the method already given, on the basis of the
TKAUBE PROCEDURE FOR SOLUTIONS 221
simple molecule C^U^, is 125.3. On the other hand,
a considerable difference exists between the molecular
volume calculated, and that found, if the double
formula C^^H^^ is made the basis of the calculation.
Naphthalene dissolved in benzene consists, then, of
simple molecules.
The molecular weight of a dissolved substance is
also easily ascertained by the method of Traube, as is
shown by this example. This modification of the
method is of significance, especially for deriving the
simplest molecular weight of solids, since it is difficult
to determine accurately the density of solids. In-
clusions of mother-liquor, air-bubbles, etc., introduce
considerable sources of error into the direct determi-
nation of density, as is shown by the investigations of
Retgers, published in the Zeitschrift fur physikalische
Chemie. The determination of the density of solids
can also be avoided, when the substances have low
melting-points, by determining the density above the
melting-point, and including in the calculation a
corresponding covolume. To determine the association
factor of the solid, it is, of course, necessary to
determine the density of the solid.
B. Aqueous Solutions. — The method of Traube
applied to aqueous solutions, brings out very peculiar
relations, which still need to be further studied.
It has been shown' that a contraction in volume
takes place, when a gram-molecule of any substance,
whatever, is dissolved in water. The molecular
volume obtained experimentally, is about 13.5 too
'J. Traube : Ann. Chem. (Uebig), 290, 88 (1896).
MOI.ECULAR WEIGHTS
small. The equation which obtains for aqueous
solutions is, therefore,
Vni'=
_m+ I
'~d"
-S^+13.5.
It must, further, be taken into account that, strange
to say, the double and triple unions are without effect
on the molecular volume of a substance dissolved in
water. Ring systems, however, have an effect. The
sum, calculated in this way, using the atomic volumes
already given, and the necessary correction values, is
designated by S'. We have then:
Vm'=2' + 25.9
and further :
m+ I
-
d 8 "
=r + i2.4-
Example : '
I Phenol CjH„0 , 3
|=, Co ring.-
2 AUyl alcohol CjHcO. |=.
C„ =
0' =
Constants =
Caring^ -
59-4
18.6
2-3
12.4
-8.1
■ 03 = 29.7
H.= i8.6
0.= 2.3
Constants = 12.4
Vm' calc. —63.0
Found = 63.3
Vni' calc. =
Found =
84.6
84-3
It is clear that the molecular weight of substances
can be calculated also on this basis, if the density of
their aqueous solutions of definite concentration is
known. The molecular weight is to be so chosen, that
' J. Traube : Ber. d. chem. Ges., 28, 2726, (1895).
TRAUBE PROCEDURE FOR SOLUTIONS 223
the calculated value of Vm' shall agree with that
derived from the determination of the density, or that
the value of Vm', obtained from the determination, is
about 12.4 smaller than S'.
Alcohol. — A five per cent, aqueous solution of
alcohol has the density o.ggoagf— 5- j; a gram-mole-
cule of alcohol (46 grams) requires 874 grams of water
to form a five per cent, solution of alcohol. The
density of water at 15°, is 0.99916.
V.n' = i6±874 ^=54.3
0.99029 0.99916
S' is calculated as follows :
C, = i9.8
H.= i8.6
O = 2.3
2' =407.
The difference 54.3 — 40.7 = 13.6, differs only a
little from the required value. Therefore, the formula
assumed, C^H^O, is correct.
From the density of a 10 per cent, solution of alcohol,
o
d = 0.98302 i-\ \ , it follows that 1 = 41.4, and Vm' ^=
53.7; the difference is 13.0. The deviation is here
still smaller.
In consequence of the strong dissociation action of
the water, no higher molecular weights were found
for the substances containing hydroxyl, which were
investigated in aqueous solution, as indeed is shown
by ethyl alcohol. Furthermore, a large amount of
224 MOI.ECUI,AR WEIGHTS
halogen in the compound does not have any disturbing
influence, so that with aqueous solutions results are
always found which are easy to interpret.
On the other hand, electrolytic dissociation has an
influence, since it increases the number of moleculesj
therefore decreasing the mean molecular weight.
When there is complete dissociation, according to
Traube, the number 13.5 is to be subtracted from 2',
for the splitting up into two ions. Substances which
undergo electrolytic dissociation must be investigated
only in dilute solutions, since only such solutions can
be regarded as completely dissociated; in more concen-
trated solutions the dissociation is driven back.
Weak acids, which even in dilute solutions are only
partially dissociated, are investigated in the form of
their sodium salts, which are strongly dissociated in
aqueous solution.
Example :'^ An aqueous solution of sodium w«-amido-
benzoate of 3.03 per cent, has the density i.oi266( -|- ).
m= 159.11, 1== 5092.04, and Vm' = 89.1.
2' is calculated as follows :
Ce ring 8.1
Dissociation constant 13.5
He:
= 69-3
= 18.6
= 1-5
0,,:
o^
Na:
= 5-5
= 0.4
= 3-1
98.4
-21.6
2' =
= 76.8
21.6
' J. Traube : Ber. d. chem. Ges., 28, 2730 (1895).
DENSITY OF A LIQUID 225
The difference 89.1 — 76.8 = 12.3, scarcely differs
from the normal =12.4. The formula assumed,
C^HgNO^Na, is therefore correct.
DETERMINATION OF THE DENSITY OF A LIQUID
To determine the density of a liquid, a small vessel
with a narrow neck is filled up to a mark with water,
weighed, then filled with the liquid to be investigated,
and reweighed. The ' vessel is also weighed empty.
By subtracting the weight of the empty vessel from
each of the first two weights, the weights of equal
volumes of water, and substance under investigation,
are obtained.
Let m be the weight of the substance, w the weight
of the water, q the density of the water at the tempera-
ture at which the measuring vessel was filled with
it (to be taken from a table given in the appen-
dix), \ the density of the air during the weighing,
X = 0.0012 ;
then we obtain the density of the substance by means
of the following formula :
a=^(Q-x) + x.
The density, thus obtained, compares the substance
at the temperature at which it was investigated, with
water at 4° C. The weighings are reduced to vacuum
standard.
The temperature of the substance during the de-
I F. Kohlrausch : Leitfaden der praktischen Physik, Aufl. p.
61.(1896). This formula suffices for density determination whose
accuracy does not exceed one unit in the fourth decimal place.
226
MOIvECULAR WEIGHTS
termination, should then always be given with the
results of such a densit)' determination.
It is also best to state that the density has been
referred to water at 4° ; perhaps thus, B = 0.7983 ( TS" ) •
A modified formula is to be employed for density
determinations which should be accurate to the fifth
decimal place.
Pycnometers of different forms are used for weigh-
ing the liquids.
They have a capacity of from i to 10 cc. Determi-
nations which are accurate to a few units in the fifth
decimal place, can be made with the larger kinds of
these p)'cnometers. Accuracy in the third decimal
Fig. 44.
Ostwald's pycnonieter.
place is sufficient for molecular weight determina-
tions of homogeneous liquids ; somewhat greater accu-
racy is required for solutions.
Small flasks, with a neck about i mm. wide, and
marked with a line drawn around them, are much
used as pycnometers. This pycnometer is not very
convenient to fill, because small air-bubbles easily
remain in it, which, even if they are very small, can
produce considerable error.
DENSITY OF A UQUID 227
The Ostwald' form of the Sprengel pycnometer,
shown in figure 44, is very convenient to use, and is to
be recommended. The pycnometer consists of a
small pipette, whose narrow tube is twice bent. It is
provided, at A, with a mark which encircles the tube.
The other tube is capillary. The liquid to be weighed,
is drawn through the delivery-tube into the pycnom-
eter proper, until this and the tube are filled up to
the mark, by sucking on the capillary tube with an
air-pump run by a current of water, or with the mouth,
a calcium chloride tube having been placed between
the mouth and pycnometer. The pycnometer is now
completely freed from liquid particles clinging to the
outside of the capillary etc., and is brought to the
desired temperature. The liquid in the pycnometer
is then so adjusted, that the capillary is completely
filled, the other tube being filled up to the mark.
This is accomplished by the following two modes of
procedure : An excess of liquid is absorbed with a
piece of cigarette paper placed at the end of the
capillary, the liquid receding into the wider tube.
If there is too little liquid in the pycnometer, a drop
on a glass rod is brought to the end of the capillary
tube filled with liquid. This is drawn in by suitably
inclining the pycnometer, and then the final adjust-
ment is made with paper.
The pycnometer, after it is regulated, is placed
aside for some time, at a constant temperature, to see
whether any changes in the temperature of the con-
tents had taken place during the adjustment. To
• W. Ostwald : J. prakt. Cheni., (N. F.), 16, 396 (1877).
228 MOI^ECULAR WEIGHTS
avoid such, the body of the pycnometer is never
touched with the fingers, but it is always held by the
tubes. The temperature is determined with a tested
thermometer, since slight changes in temperature
greatly affect the density.
The pycnometer is suspended on the balance during
the weighing, by a small platinum hook placed above
it. The weighing of the pycnometer, with the water, is
carried out several times. The water used must be as
pure as possible, and free from air. Water free from
air is prepared by boiling it, and allowing it to cool in
a space under diminished pressure. Such a determi-
nation gives the expression — , which is independent
of the temperature. This expression is obtained with
great accuracy by taking the mean of the individual
determinations, which must differ only slightly from
one another. These, determinations are carried out as
nearly as possible at the same temperature at which
the pycnometer, filled with the substance, is later
adjusted.
If a pycnometer is thus calibrated, then a density
determination consists simply in filling the pycnom-
eter with the substance to be investigated, and
weighing it. The weight of the substance, multiplied
by the above expression, and increased by X, gives the
density.
DENSITY OF A LIQUID
229
Tension op Water-vapor.'
Temperature : t ; Tension : w.
t
w
t w
t w
t w
t W
t
w
5-5
6.7
IO-5
9-4
15-5
13- 1
20.5
17.9
255
24.2
30.5
32-4
6
7.0
II
9.8
ifa
13-5
21
18.5
26
25.0
31
33-4
"•5
7.2
"•5
10. 1
ib.5
139
21.5
19.0
2b.5
25-7
31-5
.34-3
7
7-5.
12
10.4
17
14.4
22
19.6
27
2b.5
32
.3.S.3
7-5
7-7
12.5
10.8
17-5
14.9
22.5
20.2
27.5
27-3
325
,36.3
8
8.0
13
II. I
18
15-3
23
20.9
28
28.1
33
37-4
8.5
».3
13-5
1 1 -5
18.5
i5.«
235
21-5
28.5
28.9
33-5
,38.4
9
8.5
14
II. 9
19
16.3
24
22.2
29
29.7
34
39-.')
9-5
8.8
14-5
I2.,S
19-5
ib.8
24-5
22.8
295
30. fa
34-5
40.5
10
9-1
15
12.7
20
17.4
25
23-5
30
31-5
35
41.8
Density of Air, of Water, and of Mercury.
Temperature: t ; Water of 4° as unit.
t
Air
Water
Mercury
t
Air
Water Mercury.
I
0.0012883
0.99993
13-593
16
O.OOI2213
0.99899
13-556
2
836
97
591
17
171
0.99882
554
3
790
99
588
18
129
64
551
4
743
I. 00000
586
19
088
45
549
5
698
0.99999
583
20
046
25
546
6
0.0012652
0.99997
13-581
21
0.0012005
0.99804
13-544
7
607
93
578
22
O.OOII965
0.99782
541
8
562
88
576
23
924
59
539
9
517
82
573
24
884
35
536
10
473
74
571
25
844
10
534
II
0.0012429
0.99964
13-568
26
O.OOI1804
0.99684
13-532
12
385
54
566
27
765
57
529
13
342
42
563
28
726
29
527
14
299
29
561
29
687
00
524
'5
256
14
559
30
648
0.99570
522
' The numbers in this and in the following tables, are taken
from the Physikalisch-chemischen Tabellen of Landolt and Born-
stein.
230
MOLECULAR WEIGHTS
Values for Log
Temperature: t ; = 0.00367.
t
I
t
Ino- '
t
I
'°S
i°g
log
I + at
" I +at
I +M
5.5
9.99132— 10
15-5
9-97597—10
255
9.961 15— 10
6
99054
16
97522
26
96042
6.5
16.5
97447
26.5
95969
7
98898
17
97372
27
95897
7-5
98821
17-5
97297
27-5
95824
8
98743
18
97222
28
95752
8.5
98666
18.5
97147
28.5
95680
9
98589
19
97073
29
95608
9-5
98512
19-5
96998
29-5
95536
10
98435
20
96924
30
95464
IO-5
98358
20.5
96850
30-5
95392
II
98281
21
96776
31
95320
11.5
98205
2I-5
96702
315
95249
12
98128
22
96628
32
95178
12.5
98052
22.5
96554
32.5
95106
13
97976
23
96481
33
95035
13.5
97900
23-5
96407
33-5
94964
14
97824
24
96334
34
94893
'4-5
97748
24-5
96261
34-5
94823
15
97673
25
96188
35
94752
INDEX
MCCURACY in investigating very dilute solutions, increase
in-- • 113
Acetic acid, vapor-density of, at different temperatures 50
Adjustment of the Beckniann thermometer 68
Alcohol in benzene, freezing-point lowering 130
Alcohol in glacial acetic acid, freezing-point lowering 139
Anomalies inherent in the freezing-point method 117
Anomalous results from vapor-density methods 49
Aqueous solutions, method of Traube applied to 221
Associating solvents 126, 192
Atmospheric pressure, effect of on boiling-point 184
Avogadro's hypothesis i
BECKMANN boiling-point apparatus 145
Beckmann boiling-point apparatus, determination of molecu-
lar weightswith 149
Beckmann's differential thermometer 66
Beckmann, freezing-point apparatus of 79
Beckmann freezing-point apparatus, carrying out a simple mo-
lecular determination with the 83
Benzoic acid anhydride in glacial acetic acid, freezing-point
lowering 140
Benzoic acid in benzene, according to freezing-point, and ac-
cording to boiling-point methods _ 194
Benzoic acid in benzene, freezing-point lowering 128
Benzoic acid in glacial acetic acid, freezing-point lowering 139
Benzoic acid in naphthalene, freezing-point lowering 128
Benzophenone in glacial acetic acid, freezing-point lowering.. 140
Boiling-point apparatus of Beckmann 145
Boiling-point apparatus of Jones 161
Boiling-point constant 142
Boiling-point constant, calculation of 144
Boiling jacket, modifications of the 170
Boiling-point method, determination of molecular weights by
the 141
Boiling- vessel, modifications of the 167
232 INDEX
-Boric acid in water, rise in boiling-point 188
Borneol in benzene, rise in boiling-point 193
Bott and Macnair, procedure of 46
Burner, adjustable 1 74
CHOICE of freezing-point, or boiling-point method 196
Complex molecules 125, 191
Cooling vessel, influence of temperature of 116
Coste L,a, mode of procedure 45
Cresole, para, in naphthalene, freezing-point lowering 120, 136
DATA for calculating the density, by the Dumas method 39
Density of air, water, and mercury; tables 229
Densities of gases, determination of the 43
Densities of gases, determination of, under diminished press-
ure 44
Density of a liquid, determination of 225
Determination of the boiling-point, with the Jones apparatus. . 164
Deville introduced the term ' ' dissociation " 5 r
Dinitrophenol, o- and p-, in naphthalene, freezing-point lower-
ing 137
Dissociation electrolytic 121, 189
Dissociation of vapors 49
Drops 17
Dumas and gas-displacement methods do not always give the
same results 58
Dumas bulb 37
Dumas, method of 36
Dyson, procedure of 46
EI^ECTROLYTIC dissociation 121, 189
Electrolytic dissociation, measured by the freezing-point
method 123
Ethyl benzoate in benzene, rise in boiling-point 187
F='REEZING-POINT apparatus of Beckmann 79
Freezing-point apparatus of Beckmann, carrying out a simple
molecular weight determination with the 83
Freezing-point method, anomalies inherent in 117
Freezing-point method, determination of molecular weights by
the • 73
Formanilid in benzene, freezing-point lowering 132
Formtoluide (o) in benzene, rise in boiling-point 195
INDEX
233
Furnace, Lothar Meyer's jo
GAS-BURETTE : 26
Gas-displacement method 5
Gas-displacement method, simple apparatus for the 8
Gas, filling the vaporizing vessel with an indifferent 27
Gay Lussac principle, methods based upon 34
HABERMANN 47
Heating box for boiling-point apparatus 148
Heat, source of 18
Heating the boiling-point apparatus 172
Hofmann modification of the Gay Lussac method 35
Hygroscopic solvents, procedure when they are employed 96
Hygroscopic solvents, stirrer used with 97
INDIFFERENT solvents 220
Inoculating rod 89
Iodine, vapor-density of 50
JONES, boiling-point apparatus i6r
Jones, boiling-point apparatus, carrying out a determination
with i 164
LIQUID, determination of the density of a 225
Logarithm — - — -^ values of 230
Lunge and Neuberg, the method of 45
yWALFATTi and Schoop 47
Mechanical stirring device 93
Methylbenzaldehyde, >«-, /-oxy-, freezing-point lowering 137
Methods based upon the Gay Lussac principle 34
Molecules complex i gi
Molecular depression of the freezing-point 75
Molecules more complex 125
Molecular volume, calculation of 206
Molecular volume, experimental determination of 206
Molecular weight, derivation of from vapor-density i
Molecular weights, determined by the freezing-point method- 73
Molecular weights, determined by the method of Traube 211
Molecular weights, determination of, by the boiling-point
method 141
234 INDEX
Molecular weights, determination of from the principle of low-
ering of solubility I97
Molecular weights, determination of with the Beckmann boil-
ing-point apparatus i49
Molecular weights, determination of with the Beckmann freez-
ing-point apparatus 83
Molecular weights of homogeneous solids or liquids 202
Molecular weight of solids, determination of 100
INON-ASSOCIATING solvents* • 126, 193
Naphthalene in glacial acetic acid, freezing-point lowering..- 118
OSMOTIC methods 62
Osmotic pressure 62
Oxybenzaldehydes, ortho, meta, and para, in naphthalene,
freezing-point lowering 131, 135, 136
Ostwald's pycnometer 226
PEBAL'S diffusion experiment, showing the dissociation of
the vapor of ammonium chloride 52
Perrot, gas-furnace for high temperatures 21
Phenanthrene in benzene, rise in boiling-point 188
Phenetol in glacial acetic acid, freezing-point lowering 119
Phenol in glacial acetic acid, freezing-point lowering 139
Phosphorus pentachloride, dissociation of the vapor of 52
Pipette, weighing 90
Press for preparing tablets 100
Pressure, effect of atmospheric, on the boiling-point 184
Purification of solvents • 178
Pycnometer, Ostwald 226
RAOULT developed the freezing-point method 74
Results from the boiling-point method 186
Results from the freezing-point method, critical examination of 117
Results of vapor-density methods 48
SCHALIv, procedure of 47
Solids, determination of the molecular weights of 100
Solubility, determination of molecular weights, from the prin-
ciple of lowering of 197
Solutions, increase in accuracy in investigating very dilute 1 13
Solutions, modification of the Traube method for 219
Solvents, associating -.. 126
INDEX
235
Solvents for boiling-point method i^n
Solvents, indifferent 220
Solvents used in the freezing-point method 106
Solvents, use of the different, in the boiling-point method- . . 177
Solvents which cannot be used in certain cases, with the boil-
ing-point method ' 1 8 1
Solvents which cannot be used in certain cases, with the freez-
ing-point method 1 1 1
Stirring device, mechanical ^ 93
Stirrer, effect of velocity of j 1 5
Substance, introduction of into the boiling apparatus 1 75
Substances to be used in the vapor-jacket 18
Substance used in the vapor-density determination 22
Substances which form complex molecules , 127
TABLET press 100
Tablet thrower 157
Temperature of the experiment, measuring the 32
Temperatures, the measurement of high 33
Tension of water-vapor, tables 229
Theory of a dissociating vapor 55
Thermometer, adjustment of 6S
Thermometer, Beckraan's differential 66
Thermometers, use of very large 115
Thermostat 102
Traube, description of method of 205
Traube method, as applied to aqueous solutions 221
Traube method as modified for solutions 219
Traube method, determination of molecular weight by 211
VAPOR-DENSITY, derivation of molecular weight from 1
Vapor-density determination, carrying out a simple 10
Vapor-density determination, theory of 2
Vaporizing- vessel, modifications of 14
Victor Meyer apparatus 9
Volume, calculation of the molecular 206
Volume, determination of the molecular 206
Volume of gas, determination of . ^ 24
lA/EIGHING glass 1 1
New Book on Fhvsical-Chemical Methods.
The Freezing=Point,
Boiling= Point,
and
Conductivity flethods.
BY
HARRY C. JO:^rES.
Instructor in Physical Chemistry in Johns Hopkins University.
CLOTH - $0.75.
" This book brings together in brief space the essentials of
theory and practice of these three methods, and is a val-
uable guide to students in laboratories of phys-
ical chemistry." -^fli. Lewis Hotve, in
Journal of the American Chemical
Society for April, iSgS.
Stnt post-paid on receipt of price by
The Chemical Publishing Co.,
Easton, Fenna.
Cornell University Library
QD 545.B59 1899
Practical methods for determining moiecu
3 1924 003 870 676