REESE LIBRARY
OK THE
UNIVERSITY OF CALIFORNIA.
Deceived , igo .
Accession No . 830 .(> .L Class No .
HARPER'S SCIENTIFIC MEMOIRS
EDITED BY
J. S. AMES, PH.D.
PROFESSOR OF PHYSICS IS JOHNS HOPKINS UNIVERSITY
IV.
I
THE MODERN THEORY OF SOLUTION
THE MODERN
THEORY OF SOLUTION
MEMOIRS BY PFEFFER, VAN'T HOFF
ARRHENIUS, AND RAOULT
TRANSLATED AND EDITED
BY HARRY C. JONES, PH.D.
ASSOCIATE IS PHYSICAL CHEMISTRY IN JOHNS HOPKINS UN1VEUSIT*
NEW YORK AND LONDON
HARPER & BROTHERS PUBLISHERS
1899
HARPER'S SCIENTIFIC MEMOIRS.
EDITED BY
J. S. AMES, PH.D.,
rilOFKSSOK OF P11YSIOS IN JOHNS J1OPKINB UNIVKK61TY.
READY:
THE FREE EXPANSION OF GASES. Memoirs
by G;iy-Lussac, Joule, and Joule ;uul Thomson.
Editor, Prof. J. S. AMISS, Ph.D., Johns Hopkins
University. 75 cents.
PRISMATIC AND DIFFRACTION SPECTRA.
Memoirs by Joseph von Fraunhofer. Editor, Prof.
J. S. A MICS, Ph.D., Johns Hopkins University.
00 cents.
RONTGKN RAYS. Memoirs by Rontgen, Stokes,
and J. J. Thomson. Editor, Prof. GKOKGK F.
B A UK KB, University of Pennsylvania.
THE MODERN THEORY OF SOLUTION. Me-
moirs by Pfeffer, Van'r. Hoff, Arrhenins, and Raonlt.
Editor, Dr. II. C. JONKS, Jolins Hopkins University.
IN PREPARATION:
THE LAWS OF GASES. Memoirs by Boyle and
Ainnga t. Editor, Prof. C A uuBAitrs, BrownUniversity.
THE SECOND LAW OF THERMODYNAMICS.
Memoirs by Carnot, Clausing, and Thomson. Editor,
Prof. W. F. MAGIK, Princeton University.
THE PROPERTIES OF IONS. Memoirs by
Kohlransch and Hittorf. Editor, Dr. II. M. GOOD-
WIN, Massachusetts Institute of Technology.
THE FARADAY AND ZEEMAN EFFECT. Me-
moirs by Faradav, Kerr, and Zeeman. Editor, Dr.
E. P. LKWIS, University of California.
WAVE-THEORY OF LIGHT. Memoirs by Younjr
and Fresnel. Editor, Prof. HENRY CIIF.W, North-
western University.
NEWTON'S LAW OF GRAVITATION. Editor,
Prof. A. S. MAOKKNZIK, Bryn Mawr College.
NEW YORK AND LONDON:
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Copy right, 1899, by HAUTEI: & BUOTIIKKB.
All rights reserved.
PREFACE
IT is well known that great progress has been made in phys-
ical chemistry daring the last ten or fifteen years. Indeed,
this has been of such a character that what is now studied
and taught under the head of physical chemistry differs fun-
damentally from what was included under that subject a few
decades ago.
The papers in this volume have been selected and arranged
with the idea of showing how the two leading generalizations,
which underlie these recent developments, have been reached.
Previous to 1885, physical chemistry dealt chiefly with the
physical properties of chemical substances, and the relations
between properties and composition on the one hand, and prop-
ertiejs and constitution on the other. How would the differ-
ence in composition of an oxygen atom, or a CH 2 group, affect
the physical properties, or what would be the effect of an oxygen
atom united to hydrogen with respect to an oxygen atom united
to carbon, were questions which investigators were endeavoring
to answer.
The first important advance was made possible by the work
of the botanist Pfeffer. He undertook to investigate the os-
motic pressure which solutions of substances exert against the
pure solvent. His work, which was published in an extensive
monograph, Osmotische Untersuchungen, was carried out pure-
ly from a physiological-botanical stand-point, and Pfeffer did
not indicate its bearing upon any physical - chemical prob-
lem. Enough of his work is given to show the method which
he used and the apparatus which he employed. He worked
with solutions of several substances in water, but from our
point of view it is important to note that he worked with dif-
ferent dilutions of the same substance in the same solvent, and
83061
PREFACE
also determined the temperature coefficient of osmotic press-
ure. Just enough of his results are given to bring out these
two important points.
The paper of Van't Hoff, given in full in this volume, was
published in the first volume of the ZeitscJirift fur Physika-
UscJie Chemie in 1887. In this, the relation between dilute
solutions and gases was pointed out for the first time. The
law 'of Boyle for gas-pressure was found to be applicable to the
osmotic pressures of solutions of different concentrations.
That osmotic pressure is proportional to concentration was
found to be true from the results of Pfeffer's investigations.
This was the first important generalization showing the rela-
tion between gases and dilute solutions.
Van't Hoff showed,. further, from Pfeffer's results, as well as
theoretically, that the law of Gay-Lussac for the temperature
coefficient of gas - pressure, applies to the temperature coef-
ficient of osmotic pressure, which was the second important
step. Then Van't Hoif took another and even more important
step, showing that the osmotic pressure of a dilute solution is
exactly equal to the gas-pressure of a gas at the same temper-
ature, containing the same number of molecules in a given
space as there are molecules of dissolved substance. Thus,
two grams of hydrogen (H^ = 2) will exert a gas-pressure in a
space of a litre which is exactly equal to the osmotic pressure
which three hundred and forty - two grams of cane - sugar
(C 12 H 22 U = 342) will exert in a litre of aqueous solution.
From this, the law of Avogadro for gases applies at once to
dilute solutions, and we can then say that solutions having
the same osmotic pressure, at the same temperature, contain
the same number of ultimate parts in unit space.
Thus, the three fundamental laws of gas-pressure apply to
the osmotic pressure of dilute solutions, and we are therefore
justified in attempting to apply other laws of gases to dilute
solutions. We have said dilute solutions, and have thus in-
dicated that the gas laws would not apply to concentrated so-
lutions. This is true, and in this, again, solutions are analo-
gous to gases, since the ordinary gas laws do not apply to very
concentrated gases i.e., gases near the point of liquefaction.
But if the laws of gas-pressure apply to the osmotic pressure
of dilute solutions, then we would naturally ask if any excep-
tions to the laws of gas-pressure find their counterpart in the
PREFACE
osmotic pressure of solutions. We 'know that certain vapors,
as that of ammonium chloride, exert a greater pressure than
they would be expected to do from Avogadro's law. These
vapors, then, are exceptions to the gas laws.
We find their strict analogues in the osmotic pressures of
certain solutions. The laws of gas-pressure apply to the os-
motic pressures of dilute solutions of substances of the class
of cane-sugar i. e., those substances whose solutions do not
conduct the electric current. As quickly as we turn to solu-
tions of the strong acids and bases, and salts, we find that all
of them, when dissolved in water, exert an osmotic pressure
against the water which is greater than would be calculated
from the concentration. Just as the vapor-pressure of ammo-
nium chloride is abnormally large, so the osmotic pressure of
solutions of substances such as those named above is abnor-
mally large. The gas laws not only apply to the osmotic press-
ure of solutions, but just as there are exceptions to these
laws in gas-pressure, so, also, there are exceptions in osmotic
pressure.
What is the explanation of these apparent anomalies ? This
phenomenon was, for a long time, unexplained for gases. It
was pointed out that here were exceptions to the law of Avoga-
dro, and this law could, therefore, not be generally applicable.
But the anomalies were finally accounted for with gases by
showing that vapors like those of ammonium chloride disso-
ciated or broke down into constituent parts, the amount of the
dissociation depending in part upon the temperature. That
the vapor of ammonium chloride is partly broken down into
ammonia and hydrochloric acid was shown, in a perfectly sat-
isfactory manner, by the work of Pebal and others.
But of what aid was this explanation for anomalous gas-
pressure, in ascertaining the cause of the abnormal osmotic
pressure of dilute solutions of acids, bases, and salts ? It was
simple enough to conceive of a molecule of ammonium chloride
being broken down by heat as follows :
especially after it had been proven experimentally that the
vapor of ammonium chloride contains both free ammonia and
free hydrochloric acid ; and this increase in the number of
parts present would explain the abnormally large gas-pressure,
and still allow the law of Avogadro to be generally applicable.
vii
PREFACE
But could we conceive of any analogous explanation for the
abnormal osmotic pressures ? How could water break down
stable compounds, such as the strong acids and bases ? Ar-
rhenius explained these abnormal osmotic pressures in a paper
published also in the first volume of the Zeitschrift fur Pliysi-
kalische Chemie, and which is also given in full in this volume.
According to him,, those substances which give abnormally
large osmotic pressures are broken down in solution, not into
molecules as ammonium chloride is broken down into molecules
by heat, but into ions, which are atoms, or groups of atoms,
charged with electricity. It is very important in this connec-
tion to distinguish between atoms and ions. A compound like
potassium chloride is, according to Arrhenius, broken down, or,
as he would say, dissociated into potassium ions and chlorine
ions, which exist in the presence of water. If a potassium ion
had properties at all similar to a potassium molecule the sug-
gestion of Arrhenius would be absurd, since it is well known
how vigorously ordinary potassium acts upon water, while
potassium chloride dissolves in water without any such action.
The fundamental distinction between molecules and ions is
that the latter are charged either positively or negatively, and
by virtue of their charge do not have properties similar to those
of the molecules.
This assumption, that the molecules of those substances
which give abnormally large osmotic pressures are broken
down in solution into a larger number of parts, if true, shows
that the law of Boyle holds for the osmotic pressure of all
dilute solutions i. e., the osmotic pressure is proportional to
the number of parts present. In the case of those substances
whose solutions do not conduct the current non-electrolytes
the molecules exist in solution as such, and each exerts its own
definite osmotic pressure. But in solutions of those substances
which conduct the current, at least some of the molecules are
broken down into ions, the number depending upon the dilu-
tion, and each ion exerts just the same osmotic pressure as a
molecule. Since a molecule cannot break down into less than
two ions, those substances whose solutions are even partly dis-
sociated into ions must exert greater osmotic pressure than
those whose solutions are completely undissociated.
The suggestion that solutions of electrolytes contain ions
which conduct the current is not new with Arrhenius.
,
PREFACE
Grotthuss attempted to explain how the current is able to pass
through a solution of an electrolyte, and Clausius assumed
the presence of free ions in electrolytic solutions. The chem-
ist Williamson, as the result of his now classic synthesis of
ether, also concluded that molecules of substances are broken
down in solution. But the application of electrolytic dissocia-
tion, as it is called, to explain the abnormally large osmotic
pressures of electrolytes, we owe to Arrhenius. And what is
even more important, he did not simply assume that solutions
of electrolytes are partly broken down or dissociated into ions,
but showed how the amount of such dissociation could be
measured quantitatively.
It was found that those substances which give abnormally
large osmotic pressures, give abnormally great depressions of
the freezing-point of the solvent, and, further, solutions of
such substances conduct the current. Arrhenius showed that
if the assumption of electrolytic dissociation to account for
abnormally large osmotic pressures was true, then it must
also account for the abnormally large depressions of the freez-
ing-point. The amount of dissociation of a given solution, cal-
culated from its osmotic pressure, should then agree with the
dissociation calculated from the lowering of the freezing-point.
But since direct measurements of osmotic pressure will be seen
from Pfeffer's work to be difficult, this comparison could not
be made directly.
But if Arrhenius's theory of electrolytic dissociation is true,
then it must account for the property of solutions to conduct
the current; and since conductivity is due only to ions, the
amount of conductivity could be used to measure the amount
of dissociation. Arrhenius did not compare the dissociation
as calculated from the freezing-point lowerings, directly with
that calculated from conductivity, but compared the values of
it certain coefficient, i, obtained by the two methods for a large
number of substances, and found a striking agreement through-
out. This agreement, then, made it probable that the theory
of electrolytic dissociation corresponds to a great truth in nat-
ure, and that the analogy between solutions and gases is even
more deeply seated than was at first supposed.
It is impossible to show here the wide-reaching significance
of this analogy, and of the theory of electrolytic dissociation.
This would require a fairly comprehensive survey of the field of
ix
PREFACE
physical chemistry. Suffice it to say here that all of the more
important advances in physical chemistry during the last ten
or twelve years have centred around these two generalizations,
which may be termed the corner - stones of modern physical
chemistry.
It has already been stated that those substances which give
abnormally large osmotic pressures, give abnormally great de-
pressions of the freezing-point of the solvent. This brings us
to the work of Raoult on the freezing-point depression, and
lowering of vapor-tension, of solvents by substances dissolved
in them. Three of the more important papers of Raoult along
these lines are given in this volume.
Raoult showed that the depression of the freezing-point of a
solvent, or of its vapor-tension, depends upon the relation be-
tween the number of molecules of solvent and of dissolved sub-
stance. He showed from this how it was possible to determine
the unknown molecular weights of substances, by determining
how much a given weight of the substance would lower the
freezing-point, or lower the vapor-tension, of a given weight of
a solvent in which it was dissolved. These methods, the theo-
retical development of which we owe to Raoult, have been
greatly improved by others from an experimental stand-point,
and have been very widely applied, especially to the determina-
tion of the molecular weights of substances. It should be es-
pecially mentioned that the method of measuring the depres-
sion of the vapor-tension has been almost entirely supplanted
by the method of determining the temperature at which solvent
and solution boil. From the rise in the boiling-point of the
solvent produced by the dissolved substance we can calculate
the molecular weight of the latter. This improvement on the
Raoult method of measuring the depression in vapor- tension
we owe to Beckmann.
The freezing-point method especially has now been improved
until it can be also used as a fairly accurate measure of elec-
trolytic dissociation. And it can be stated that electrolytic
dissociation, measured by the freezing-point method, agrees
within the limits of experimental error, with that measured by
the conductivity method.
The following papers will show, then, how the analogy be-
tween dilute solutions and gases was first recognized and point-
ed out, and how the theory of electrolytic dissociation arose to
PREFACE
account for the abnormal results obtained with electrolytes
abnormally large osmotic pressures, depressions of freezing-
point, and depressions of vapor-tension.
Since the theory was proposed it has been tested both theo-
retically and experimentally from many sides; with the result
that, when all of the evidence available is taken into account,
the theory of electrolytic dissociation seems to be as well es-
tablished as many of our so-called laws of nature.
HARRY C. JONES.
Johns Hopkins University.
GENERAL CONTENTS
PAGH
Preface v
Osmotic Investigations. [Selected Sections.] By W. Pfeffer 3
Biography of Pfeffer 10
The Role of Osmotic Pressure in the Analogy between Solutions and
Gases. By J. H. Van't Hoff 13
Biography of Van't Hoff 42
On the Dissociation of Substances Dissolved in Water. By S.
Arrhenius 47
Biography of Arrhenius 66
The General Law of the Freezing of Solvents. By F. M. Raoult 71
On the Vapor-Pressure of Ethereal Solutions. By F. M. Raoult 95
The General Law of the Vapor-Pressure of Solvents. By F. M. Raoult. 125
Biography of Raoult 128
Bibliography 129
Index.. <&.^.. ... 133
OSMOTIC INVESTIGATIONS
BY
DR. W. PFEFFER
Pj-ofessor of Botany in the University of Leipsic
SELECTED SECTIONS
CONTENTS
PAGK
Preparation of the Cells 3
Measurement of the Pressure 7
Experimental Results 9
OSMOTIC INVESTIGATIONS*
BY
DR. W. PFEFFER
SELECTED SECTIONS
A. APPARATUS AND METHOD
1. PREPARATION OF THE CELLS
CERTAIN precipitates can be obtained as membranes if they
are formed at the plane of contact of two solutions, or of a so-
lution and a solid. Traube, as is known, was the first to pre-
pare such membranes, and he, at the same time, worked out
the conditions under which they can be formed, conditions
which later will be briefly explained. The author of this im-
portant discovery tested membranes obtained from different
substances as to their permeability to dissolved bodies ; and
it was shown that substances in general pass less easily through
such membranes than through those formerly employed in dios-
motic investigations. Indeed, many substances which easily
diosmose through the latter were incapable of passing through
definite precipitated membranes.
Traube carried out diosmotic investigations, for the most
part, with membranes which closed one end of a glass tube, into
which the substance whose diosmotic properties were to be
tested was introduced. Such an apparatus is, in most cases,
easily prepared ; a small quantity of one of the solutions neces-
sary to produce a precipitate being introduced into the glass
* Selected paragraphs from Pfeffer's Osmotische Untwsuchungen. Leipsic,
1877.
3
MEMOIRS ON
tube, which is then dipped into the other solution. With cor-
rect procedure, the precipitate is formed as a membrane clos-
ing the tube, at the surface where the solutions of the two
"membrane-formers" come in contact.
Traube worked in every case with cells protruding free into
the liquid. These are, on the one hand, not very resistant ;
and, further, they continually increase in size as long as an
osmotic current of water flowing in produces a pressure in
the interior which tends to distend the membrane. By this
means a new membrane particle is inserted as soon as the two
membrane - formers meet in the enlarged interstices an in-
crease in surface by intussusception which these membranes
very beautifully demonstrate. But even if it were possible to
overcome these and other difficulties when the problem is to
study diosmotic exchange, yet it is impossible, in freely sus-
pended cells, to measure the pressure brought about by osmotic
action. To render this possible the membranes must be placed
against a support, which can offer resistance to ordinary press-
ure, but which is relatively easily permeable to water and salts.
The plant cells furnish us with the model desired for imitation.
In these the plasma membrane, which, in its diosmotic prop-
erties, is similar to the artificially precipitated membranes, is
pressed against the cell wall.
In my first experiments, freely suspended membranes were
allowed to increase by osmotic pressure until they finally rested
on a support which closed one end of a glass tube. If, finally,
with some trouble, this was accomplished, other difficulties ap-
peared, in reference to measurement of pressure, which induced
me to adop,t another course. The precipitated membrane, even
under slight pressure, would be squeezed through the pores even
of the thickest linen and silken textures i. e., the continually
growing membrane appeared on the other side of the texture,
in different places, in the form of small sacs, which further in-
creased in size and finally burst.
Attempts to use thicker material as supports, such as parch-
ment paper or porcelain cells, did not yield favorable results,
for reasons which I shall leave undiscussed here.
I obtained the first favorable result by proceeding as follows :
I took [unglazed] porcelain cells, such as are used for electric
batteries, and, after suitably closing them, I first injected them
carefully with water, and then placed them in a solution of cop-
4
THE MODERN THEORY OF SOLUTION
per sulphate, while, either immediately or after a short time, I
introduced into the interior a solution of potassium ferrocya-
nide. The two membrane-formers now penetrate diosmotically
the porcelain wall separating them, and form, where they meet,
a precipitated membrane of copper ferrocyanide. This ap-
pears, by virtue of its reddish-brown color, as a very fine line in
the white porcelain which remains colorless at all other places,
since the membrane, once formed, prevents the substances
which formed it from passing through.
These membranes, deposited
in the interior of porcelain walls,
I have used, moreover, almost ex-
clusively for preliminary experi-
ments, the investigation proper
being carried out with mem-
branes which were deposited on
the inner surface of porcelain
cells. All the experiments to be
described are carried out with
the latter kind of membranes, if
not especially stated to be other-
wise. To prepare these, the por-
celain cells were completely in-
jected with, e.g., a solution of
copper sulphate, then quickly
rinsed out with water, and a solu-
tion of potassium ferrocyanide
afterwards added. More minute
details as to the preparation of
the apparatus will be given later,
after this general account.
In Fig. 1, the apparatus ready
for use, with the manometer (m)
for measuring the pressure, is
shown, at approximately one-half
the natural size. The porcelain
cell (z) and the glass pieces v and
/, inserted in position, are shown
in median longitudinal section. a |
The porcelain cells which I -used
were, on an average, approximate-
5
MEMOIRS ON
ly 46 millimetres high, were about 16 millimetres' internal diam-
eter, and the walls were from li to 2 millimetres thick. The
narrow glass tube v, called the connecting-piece, was fastened
into the porcelain cell with fused sealing-wax, and the closing
piece t was set into the other end of this tube in the same
manner. The shape and purpose of this are shown in the
figure. The glass ring r was necessary only in experiments at
higher temperature, in which the sealing-wax softened. The
ring was then filled with pitch, which also held together firmly
the pieces inserted into one another.
[Two pages omitted.]
All porcelain cells were treated first with dilute potassium
hydroxide, then with dilute hydrochloric acid (about 3 per
cent.), and, after being well washed, were again completely
dried, before they were closed as already described. Substances
which are soluble in these reagents, such as oxides and iron,
which under certain conditions can do harm, would thus be re-
moved.
After the apparatus was closed, the precipitated membrane
was formed, either in the wall or upon the surface, according
to the principle already indicated. In order that this should
be done successfully, a number of precautionary measures are
necessary, and these will now be discussed. Since I experi-
mented chiefly with membranes of copper ferrocyanide, which
were deposited upon the inner surface of porcelain cells, I will
fix attention especially upon this case.
The porcelain cells were first completely injected with water
under the air-pump, and then placed, for at least some hours, in
a solution containing 3 per cent, of copper sulphate, and the
interior was also filled with this solution. The interior only
of the porcelain cell was then once rinsed out quickly w r ith
Avater, well dried as quickly as possible, by introducing strips
of filter paper, and after the outside had dried off somewhat
it was allowed to stand some time in the air until it just felt
moist. Then a 3-per-cent. solution of potassium ferrocyanide
was poured into the cell, and this immediately reintroduced
into the solution of copper sulphate.
After the cell had stood for from twenty-four to forty-
eight hours undisturbed, it was completely filled with the solu-
tion of potassium ferrocyanide, and closed as shown in Fig. 1.
A certain excess of pressure of the contents of the cell now
6
THE MODERN THEORY OF SOLUTION
gradnally manifested itself, since the solution of potassium
ferrocyanide had a greater osmotic pressure than the solu-
tion of copper sulphate. After another twenty-four to forty-
eight hours the apparatus was again opened, and generally a
solution introduced which contained 3 per cent, of potassium
ferrocyanide and 1^ per cent, of potassium nitrate (by weight),
and which showed an excess of osmotic pressure of somewhat
more than three atmospheres. If the cell should, moreover, he
used for experiments in which a higher pressure was produced,
it was also tested at a higher pressure by using a solution
richer in potassium nitrate. In these test experiments, of
course, any home-made manometers can be used.
[Eleven pages omitted.]
4. MEASUREMENT OF THE PRESSURE
The osmotic pressures were measured chiefly with air-
manometers, open manometers being applicable only where
smaller pressures were involved. The form of my air-manom-
eter is shown in Fig. 1, in approximately half its natural size.
The longer closed limb is connected with the shorter open
limb by means of the glass cock already mentioned. An en-
largement is blown upon the shorter limb for the reception
of mercury. There is a millimetre scale upon both limbs,
starting from the same zero point. The scale upon the closed
arm is 200 millimetres in length. This arm was selected of
small diameter (in the three manometers which I employed
it was between 1.166 and 1.198 millimetres), so that the os-
motic pressure can be established more quickly, and without
any considerable amount of water entering the apparatus.
The diameter of the arm, bent twice at right angles, was
larger throughout, and was from 7.5 to 8 millimetres in the
enlarged space.
[One page omitted]
In use, the space in the open arm of the manometer which
was not filled with mercury, was filled with the liquid whose
osmotic action was to be tested. The cell was then also
filled with this, after the manometer was attached, as shown
in Fig. 1, and then the final closing made without leaving
any air in the apparatus, in the manner already given, with
the aid of a glass tube drawn out to a capillary. After the
capillary point is melted off, it is recommended to produce
7
MEMOIRS ON
some pressure in the cell, by pushing the glass tube farther
in, in order to lessen the time required to reach the final
pressure, and at the same time to diminish the amount of
water which enters the apparatus. The apparatus can be
opened again without any difficulty, after the experiment is
over, by blowing open the capillary point in the flame. If
the form of the glass tube t allows the rubber corks to ex-
pand somewhat at their inner ends, they acquire thus a con-
siderable support. Yet, for higher pressures, they were always
secured by tying them
down with metal wire
(copper or silver wire),
as champagne bottles
are closed. I have been
able to close the appa-
ratus easily, so that it
would withstand, per-
fectly, a pressure of sev-
en atmospheres.
The closed cell, as
seen in Fig. 2, is fast-
ened to a glass rod pass-
ing through a cork, and
was introduced into a
bath in such a manner
that the manometer, as
well, was entirely im-
mersed in the liquid.
The temperature was
measured by two accu-
rate thermometers. By
covering that portion of
the bath not closed with
corks with a brass plate,
evaporation of the liq-
uid was diminished when
the bath was filled with
a dilute solution of a
membrane-former. The apparatus is represented in the figure
at approximately one-fourth its natural size. The baths held
from 2 to 2J litres of liquid.
8
THE MODERN THEORY OF SOLUTION
It is best to place the baths in dishes filled with sand,
in order that the manometers may be easily adjusted with
accuracy to a vertical position. If the entire apparatus is
covered with a bell-jar, and kept in a room of uniform tem-
perature, it is not difficult to keep the thermometers con-
stant for several hours to within less than T V. This constancy
of temperature is of significance, because the final condition
of equilibrium between the osmotic inflow and filtration un-
der pressure is established very slowly, especially at low tem-
peratures, and therefore, before the experiment is completed,
we are compelled to assure ourselves that the mercury stands
at the same height in the manometer for several hours.
In determining osmotic pressures at higher temperatures,
the entire vessel was placed in a heating apparatus which
was filled with sand and covered with a bell-jar, and whose
temperature was accurately regulated. Care must be taken,
in passing from lower to higher temperatures, that the junc-
tions of the apparatus are not injured by the increased press-
ure which is caused by the expansion of liquid and air.
Small osmotic pressures were, indeed, measured with an
open manometer, whose longer arm was made of a narrow
tube of approximately 0.3 millimetre diameter, in order that
the condition of equilibrium might be quickly reached. The
form and method of using this manometer requires no special
explanation. It should be observed, in passing, that the error
of measurement is, in any case, less than 3 millimetres.
[Thirteen sections omitted.]
17. EXPERIMENTAL RESULTS
NO. VII.
Pressures for Cane- Sugar of Different Concentration.
CONCENTRATION IN PER
CENT. BY WEIGHT. PRESSURE.
1 535 mm.
2 1016 "
2.74 1518 "
4 2082 "
3075 "
1 535 "
Surface of membrane, 17.1 square centimetres.
9
THE MODERN THEORY OF SOLUTION
TABLE 12*
EXPERIMENTS WITH A ONE -PER -CENT. SOLUTION OF CANE-
SUGAR
[Change in Osmotic Pressure ivith Change in Temperature.]
TEMPERATURE. PRESSURE.
J14.2C 51.0 cm.
a (32.0C 54.4 "
6.8 50.5 cm.
13.7 C 52.5 "
22.0 C 54.8 "
15.5 C 52.0 cm.
36.0 C.. . 56.7 "
WILHELM FRIEDRICH PHILIPP PFEFFER was born March 9th,
1845, at Grebenstein, Cassel. He received the Degree of Doc-
tor of Philosophy at Gottingen in 1865, was appointed Privat-
docent in Marburg in 1871, and in 1873 was elected to a sub-
ordinate professorship in Bonn. He became professor in Basel
in 1877, and was called to Tubingen in 1878. He is at present
Professor of Botany in the University of Leipsic. Some of his
more important papers, in addition to his investigations of os-
motic pressure, are : Physiological Investigations, Leipsic, 1873 ;
Action of the Spectrum Colors on the Decomposition of Carbon
Dioxide in Plants; Studies on Symmetry and the Specific
Causes of Growth; Plant Physiology, Vol. I., 1881 ; Construc-
tion of a Number of Pieces of Apparatus for Investigating the
Growth of Plants. His measurements of osmotic pressure are,
with perhaps one slight exception, the only direct measure-
ments which have been made up to the present.
* Osmotische Untersuchungen, p. 85.
10
THE ROLE OF OSMOTIC PRESSURE IN
THE ANALOGY BETWEEN SOLUTIONS
AND GASES
BY
J. H. VANT HOFF
Professor of Physical Chemistry in the University of Berlin
(Zeitschrift fur Physikalische Chemie, I., 481, 1887)
CONTENTS
PACK
Introduction 13
Osmotic Pressure 13
ttoyle's Laic for Dilute Solutions 15
Gay-Lussac's Law for Dilute Solutions 17
Avogadro's Laic for Dilute Solutions 21
General Expression of Above Laws for Solutions and Gases 24
Confirmation of Avogadro's Law as applied to Solutions:
1. Osmotic Pressure 25
2. Loitering of Vapor- Pressure 26
3. Lowering of Freezing -Point 29
Application of Avogadro's Law to Solutions 31
Guldberg and Waage's Law 31
Deviations from Avogadro's Law in Solutions 34
Variations from Guldberg and Waage's Law 34
Determinations of "i " for Aqueous Solutions ; 36
Proof of the Modified Guldberg and Waage Law 37
THE ROLE OF OSMOTIC PRESSURE IN
THE ANALOGY BETWEEN SOLUTIONS
AND GASES*
BY
J. H. VAXT HOFF
Ix an investigation, whose essential aim was a knowledge
of the laws of chemical equilibrium in solutions,! it gradually
became apparent that there is a deep-seated analogy indeed,
almost an identity between solutions and gases, so far as their
physical relations are concerned ; provided that with solutions
we deal with the so-called osmotic pressure, where with gases we
are concerned with the ordinary elastic pressure. This anal-
ogy will be made as clear as possible in the following paper, the
physical properties being considered first :
1. OSMOTIC PRESSURE. KIND OF ANALOGY WHICH ARISES
THROUGH THIS CONCEPTION.
In considering the quantity, with which we shall chiefly have
to deal in what follows, at first from the theoretical point of
view, let us think of a vessel, A, completely
filled, for example, with an aqueous solution
of sugar, the vessel being placed in water, B.
If, now, the perfectly solid wall of the vessel
is permeable to wa'ter, but impermeable to the
dissolved sugar, the attraction of the water by
the solution will, as is well known, cause the
water to enter A, but this action will soon
reach its limit due to the pressure produced by the water which
enters (in minimal quantity). Equilibrium exists under these
*Ztschr. Phys. Cliem.. 1., 481, 1887.
\Etudes de Dynamique Chimie, 179; Archives Neerlandaisex, 2O ;
k. Scenska Akademiens Handl., 21.
13 XS^SE US*:
MEMOIRS ON
conditions, and the pressure exerted on the wall of the vessel
we will designate in the following pages as osmotic pressure.
It is evident that this condition of equilibrium can be estab-
lished in A also at the outset, that is, without previous entrance
of water, by providing the vessel B with a piston which exerts
a pressure equal to the osmotic pressure. We can then see that
by increasing or diminishing the pressure on
the piston it is possible to produce arbitrary
changes in the concentration of the solution,
through movement of water in the one or
the other direction through the walls of the
vessel.
m t'' ket ^ s osm tf c pressure be described from
an experimental stand-point by one of Pfef-
fer's* experiments. An unglazed porcelain cell was used, which
was provided with a membrane permeable to water, but not to
sugar. This was obtained as follows : The cell, thoroughly
moistened, so as to drive out the air, and filled with a solution
of potassium ferrocyanicle, was placed in a solution of copper
sulphate. The potassium and copper salts came in contact,
after a time, by diifusion, in the interior of the porous wall,
and formed there a membrane having the desired property. Such
a vessel was then filled with a one-per-cent. solution of sugar,
and, after being closed by a cork with manometer attached, was
immersed in water. The osmotic pressure gradually makes its
appearance through the entrance of some water, and after equi-
librium is established it is read on the manometer. Thus, the
one-per-cent. solution of sugar in question, which was diluted
only an insignificant amount by the water which entered,
showed, at 6.8, a pressure of 50.5 millimetres of mercury,
therefore about T ^ of an atmosphere.
The porous membranes here described will, under the name
" semipermeable membranes," find extensive application in
what follows, even though in some cases the practical applica-
tion is, perhaps, still unrealized. They furnish a means of
dealing with solutions, which bears the closest resemblance to
that used with gases. This evidently arises from the fact that
the elastic pressure, characteristic of the latter condition, is
now introduced also for solutions as osmotic pressure. At the
* Osmotische Untersuchungen, Leipsic, 1877.
14
THE MODERN THEORY OF SOLUTION
same time let stress be laid upon the fact that we are not deal-
ing here with an artificially forced analogy, but with one which
is deeply seated in the nature of the case. The mechanism
by which, according to our present conceptions, the elastic
pressure of gases is produced is essentially the same as that
which gives rise to osmotic pressure in solutions. It depends,
in the first case, upon the impact of the gas molecules against
the wall of the vessel ; in the latter, upon the impact of tke.
molecules of the dissolved substance against the semipermeaDre
membrane, since the molecules of the solvent, being present
upon both sides of the membrane through which they pass, do
not enter into consideration.
The great practical advantage for the study of solutions,
which follows from the analogy upon which stress has been
laid, and which leads at once to quantitative results, is that
the application of the second law of thermodynamics to solu-
tions has now become extremely easy, since reversible processes,
to which, as is well known, this law applies, can now be per-
formed with the greatest simplicity. It has been already men-
tioned above that a cylinder, provided with semipermeable
walls and piston, when immersed in the solvent, allow any
desired change in concentration to be produced in the solution
beneath the piston by exerting a proper pressure upon the
piston, just as a gas is compressed and can then expand ; only
that in.^he first case the solvent, in these changes in volume,
moves through the wall of the cylinder. Such processes can,
in both cases, preserve the condition of reversibility with the
same degree of ease, provided that the pressure of the piston
is equal to the counter-pressure, i.e., with solutions, to the
osmotic pressure.
We will now make use of this practical advantage, especially
for the investigation of the laws which hold for "ideal solu-
tions," that is^ for solutions which are diluted to such an ex-
tent that they are comparable with " ideal gases/' and in which,
therefore, the reciprocal action of the dissolved molecules can
be neglected, as also the space occupied by these molecules, in
comparison with the volume of the solution itself.
2. BOYLE'S LAW FOR DILUTE SOLUTIONS.
The analogy between dilute solutions and gases acquires at
once a more quantitative form, if we consider that in both
15
MEMOIRS ON
cases the change in concentration exerts a similar influence on
the pressure ; and, indeed, the values in question are, in botli
cases, proportional to one another.
This proportionality, which for gases is designated as Boyle's
law, can be shown for osmotic pressure, experimentally from
data already at hand, and also theoretically.
Experimental Proof. Determination of the Osmotic Pressure
Different Concentrations. Let us first give the results of
offer's determinations* of osmotic pressure (P) in solutions
of sugar, at the same temperature (13.2-16.1) and different
concentrations (C) :
\<f c .......... 535 mm .......... 535
2f c .......... 1016 " ...... ....508
2.74$ .......... 1518 " .......... 554
4$ .......... 2082 " .......... 521
Qf c .......... 3075 " .......... 513
p
The nearly constant value of indicates that, in fact, a pro-
\j
portionality between pressure and concentration exists.
Experimental Proof. Comparison of Osmotic Pressure "by
Physiological Methods. The observations of De Vriesf can be
placed with the above as a second line of evidence. From
these it follows that equal changes in concentration of solu-
tions of sugar, potassium nitrate, and potassium sulphate, ex-
ert the same influence on the osmotic pressure. The above-
named investigator compared, by physiological methods, the
osmotic pressure of these with that of the contents of a plant
cell whose protoplasmic sac contracts when the cell is in-
troduced into a solution which has stronger attraction for
water. By a systematic comparison of different solutions of
the three substances named, with the same cells, three so-
called isotonic liquids were obtained, i. e., solutions of equal
osmotic pressure. Then cells of another plant were used,
and thus four such isotonic series were prepared, whereby a
similar relation appeared in the respective concentrations, as
* Otmotisdie UntersucJiungen, p. 71. [This volume, p. 10.]
\ Eine Methode zur Analyse der Turrjorkraft, Pringslieim's Jahrb., 14.
10
THE MODERN THEORY OF SOLUTION
is shown in the following table, in which the concentration
is expressed in gram-molecules* per litre :
Series KNO 3 C ia H 22 O n K 2 SO 4 KNO 3 =1 C 12 H 22 O n R.,SO 4
I. 0.12 0.09 1 0.75
II. 0.13 0.2 0.1 1 1.54 0.77
III. 0.195 0.3 0.15 1 1.54 0.77
IV. 0.26 0.4 1 1.54
Theoretical Demonstration. Although the observations men-
tioned make it very probable that there is a proportionality
between osmotic pressure and concentration, yet the theoret-
ical demonstration is a welcome supplement, especially since
it is almost self-evident. If we regard osmotic pressure as of
kinetic origin, therefore as being produced by the impacts of
the molecules of the dissolved substance, the demonstration
depends upon the proportionality between the number of im-
pacts in unit time and the number of molecules in unit space.
The demonstration is, then, exactly the same as that for Boyle's
law with ideal gases. If, on the other hand, we regard osmotic
pressure as the expression of an attraction for water, the value
of this is evidently proportional to the number of attracting
molecules in uui-t volume, provided the dissolved molecules
have no action upon one another, and each exerts, therefore,
its own special attraction, as can be assumed with sufficiently
dilute solutions.
~Hh
' ^_
3, GAY-LUSSAC'S LAW FOR DILUTE SOLUTIONS.
While the proportionality between concentration and osmot-
ic pressure at constant temperature is self-evident, it is dif-
ferent with the proportionality between osmotic pressure and
absolute temperature at constant concentration. Neverthe-
less, this proposition can be demonstrated on thermodynamic
grounds, and experimental data can also be cited which are
very favorable to the results obtained thermodynamically.
Theoretical Demonstration. It has already been mentioned
that reversible transformations can be carried out by means of
* [A gram-molecule of a substance is the molecular weight of the substance
in grams, e.g. 58.5 grams of sodium chloride.}
B 17
MEMOIRS ON
a piston and cylinder with semipermeable walls, which we will
now use to complete a cycle. If we express this in the way
which is well known for gases, volume and pressure are rep-
resented on the axes 0V and OP, only that we must again
deal here with the osmotic pressure. Let
the originaLxohime ( FJf/- 8 )* be repre-
sented by OAj the original pressure on
the piston (PK), which is 1 Mr' ', by Aq,
the absolute temperature by T; now let
the solution undergo a minimum increase
in volume of dVMr 3 ( = AB) by moving
A DEC v the piston a distance d VMr, while the
Fig. 3. temperature of the solution is main-
tained constant by adding the requisite
amount of heat. But this amount of heat can be determined
at once, since it just serves to perform the known external
work PdV, by moving the piston. No internal work is done,
since we are dealing with a dilution which is so great that the
dissolved molecules have no action upon one another. This
isothermal change ab is followed by the so-called isen tropic
change be, during which heat is neither given out nor absorbed.
The temperature falls, then, dT, after which return to the orig-
inal condition follows through a second isothermal and a sec-
ond isentropic transformation, cd and da, respectively. As is
known, the se^on.d law of thermodynamics requires that a
fraction of the amount of heat PdV, imparted at the begin-
dT
ning, equal to -^PdV, is converted into work. This must,
therefore, be equivalent to the area of the quadrilateral abed ;
from which we obtain the following equation :
dT
therefore : ^~r ~ a f'
But af, in the above, is the change of the osmotic pressure at
constant volume, resulting from a change in temperature dT.
i. e., I =A dT\ from which, finally, we have :
\Cl 1 /v
* [Mr is metre. K is kilogram.]
18
THE MODERN THEORY OF SOLUTION
\dTfr
Tliis equation gives, however, on integration, keeping vol-
ume constant : p
, = constant.
That is to say, the osmotic pressure is proportional to the
absolute temperature, in case volume or concentration remains
the same, which proposition for solutions is perfectly analo-
gous to the law of Gay-Lussac for gases.
Experimental Proof. Determination of the Osmotic Pressure
at Different Temperatures. Let us next compare the theoretical
conclusion just reached with the results of Pfeffer's investiga-
tions.* This investigator found, as a matter of fact, that the
osmotic pressure, without exception, increases with rise in
temperature. We will, moreover, see that although the experi-
mental results referred to do not suffice to make the above
proposition absolutely certain, yet an excellent approximation
between observation and calculation often appears. If from
one of two experiments carried out with the same solution at
different temperatures we calculate the result of the other, on
the assumption of Gay-Lussac's law, and compare it with the
value directly obtained, we have :
1. Solution of cane-sugar.
At 32 a pressure of 544 millimetres was observed.
At 14. 15 the calculated pressure is 512 millimetres, in-
stead of 510 millimetres observed.
2. Solution of cane-sugar.
At 36 the pressure observed was 567 millimetres.
At 15. 5 the calculated pressure is 529 millimetres, instead
of 520.5 millimetres observed.
3. Solution of sodium tartrate.
At 36. 6 the pressure observed was 15G4 millimetres.
At 13. 3 the calculated pressure is 1443 millimetres, instead
of 1431.6 millimetres found.
4. Solution of sodium tartrate.
At 3 7. 3 the pressure observed was 983 millimetres.
At 13.3 the calculated pressure is 907 millimetres, instead
of 908 millimetres found.
* Osmotisclie UntersncJiurirjcn, pp. 114, 115. [77m volume, p. 10.]
19
MEMOIRS ON
Experimental Proof. Comparison of Osmotic Pressure by
Physiological Methods. Just as the law of Boyle, applied to so-
lutions, received support from the fact that isotonic solutions
of different substances preserve equality of osmotic pressure
when the respective concentrations were reduced to the same
fraction, so the law of Gay-Lussac is supported by the result
that this isotonism is likewise preserved for equal change in
temperature. This fact was also established by physiological
methods, this time by Bonders and Hamburger,* who, working
in a manner similar to that of De Vries, but now with animal
cells ( blood corpuscles ), found that solutions of potassium
nitrate, sodium chloride, and sugar, which are isotonic with the
contents of the cells in question, at 0, and, therefore, with one
another, show exactly the same relation at 34, as will be seen
from the following table :
TEMPERATURE 0. TEMPERATURE 34.
KN0 3 1.052-1.03 % 1.052-1.03 $
NaCI 0.62 -0.609$ 0.62 -0.609$
C ]2 H 22 O n 5.48 -5.38$ 5.48 -5.38$
Experimental Proof of the Laws of Boyle and Gay-Lussac
for Solutions. Experiments of Soret.\ The phenomenon ob-
served by Soret is very significant for the analogy between
gases and solutions, where we are dealing with the influ-
ence of concentration and temperature on the pressure and
on osmotic pressure respectively. It became apparent from
these experiments that, just as with a difference in tempera-
ture in gases, the warmest part is the most dilute, so, also,
with solutions the same relation obtains ; only that in the lat-
ter case the time required to establish the final condition of
equilibrium is considerably greater. The experiments were
made in vertical tubes, in such a manner that the upper por-
tion of the solution contained in them, which was perfectly
homogeneous at the beginning, was warmed at a constant tem-
perature, while the under portion was likewise cooled to a def-
inite temperature.
* Onderzoekingen gedaan in het pJiysiologisch. Labor atorium der Utreclit-
sche Hoogeschool, (3), 9, 26.
f Archives des Sciences phys. et nat., (3), 2, 48; Ann. Chim. P/<yx..
(5), 22, 293.
20
THE MODERN THEORY OF SOLUTION
If, then, the observation of Soret contains, qualitatively, a
complete confirmation of the laws developed, so, also, a wel-
come approximation to our theory is to be found in his quanti-
tative results, at least in the latest experiments. It would be
expected, as with gases, that equilibrium exists when the iso-
tonic state is reached; and where the osmotic pressure increases
proportional to the concentration and to the absolute tempera-
ture, this isotonic state of the parts of the solution will occur
when the products of the two values are equal.
If, on this basis, we calculate the concentration of the
warmer part of the solution from that which was found in the
colder part, and compare with this the value obtained directly
by experiment, we have :
1. Solution of copper sulphate.
The part cooled to 20 contained 17.332 per cent. 14.3
per cent, would correspond to a temperature of 80; in-
stead of this, 14.03 per cent, was found.
2. Solution of copper sulphate.
The part cooled to 20 contained 29.867 per cent. 24.8
per cent, would correspond to a temperature of 80; in-
stead of this, 23.871 per cent, was found.
It must, indeed, be added that the earlier experiments of
Soret gave less favorable results, yet, on account of the diffi-
culty of such observations, too much stress must not be laid
upon them.
4. AVOGADRO'S LAW FOR DILUTE SOLUTIONS.
While up to the present essentially only those changes have
been dealt with which the osmotic pressure in solutions under-
goes due to changes in concentration and temperature, and
while the agreement with the corresponding laws which hold
for gases manifested itself, we must now deal with the direct
comparison of the two analogous quantities, elastic pressure and
osmotic pressure of one and the same substance. It is evident
that this applies to gases which have also been investigated in
solution ; and, as a matter of fact, it will be proved that, in
case the law of Henry is satisfied, the osmotic pressure in solu-
tion is exactly equal to the elastic pressure as gas, at least at
the same temperature and concentration.
21
MEMOIRS ON
For the purpose of demonstration, we will perform a reversi-
ble cycle at constant temperature, by means of semipermeable
walls, and then employ the second law of thermodynamics,
which, in this case, as is known, leads to an extremely simple
result, that no heat is transformed into work, or work into heat,
and consequently the sum of all the work done must be equal
to zero.
The reversible cycle is performed by two similarly arranged
double cylinders, with pistons, like one already described. One
cylinder is partly filled with a gas
(A), say oxygen, in contact with a so-
lution of oxygen (5), saturated under
the conditions of the experiment ; for
example, an aqueous solution. The
wall be allows only oxygen but no
water to pass throu g h ; the wal1 ab >
on the contrary, allows water but not
oxygen to pass, and is in contact on
the outside with the liquid (E) in
question. A reversible transformation can be made with such
a cylinder; which amounts to this, that by raising the two
pistons (1) and (2) oxygen is evolved from its aqueous solution
as gas, while water is removed through ab. This transformation
can take place so that the concentrations of gas and solution
remain the same. The only difference between the two cyl-
inders is in the concentrations which are present in them.
These we will express in the following manner:
The unit of weight of the substance in question fills, in the
left vessel, as gas and as solution, the volumes v and V respec-
tively, in the right of v + dv and V+dV\ then, in order that
Henry's law be satisfied, the following relation must obtain :
v:V=(v + dv) '.(V+dV)
therefore : v : V dv : d V.
Let now the pressure and osmotic pressure of gas and solu-
tion, in case unit weight is present in unit volume, be respec-
tively P and p (values which hereafter will be shown to be
equal), the pressure in gas and solution is, then, from Boyle's
P i}
law, respectively, -- and ~.
If we now raise the pistons (1) and (2), and thus liberate a
unit weight of the gas from the solution, we increase, then,
22
THE MODERN THEORY OF SOLUTION
x ^vvafcvA"
this gas volume v by dv, in order that it may have the concen-
tration of the gas in the left vessel ; if the gas just set free is
forced into solution by lowering pistons (4) and (5), and thus
the volume of the solution F-frfFdiminished by d Fin the cyl-
inder with setnipermeable walls, the cycle is then completed.
Six amounts of work are to be taken into consideration,
whose sum, from what is stated above, must be equal to zero.
We will designate these by numbers, whose meaning is self-
evident. We have, then :
(1)4- (2) -f (3) + (4) + (5) + (6) = 0.
But (2) and (4) are of equal value and opposite sign, since
we are dealing with volume changes v and v + dv, in the op-
posite sense, which take place at pressures which are inversely
proportional to the volumes. For the same reasons the sum
of (1) and (5) is zero ; then, from the above relation :
The work done by the gas (3), in case it undergoes an in-
p
crease in volume dv at a pressure , is :
while the work done by the solution (6), in case it undergoes a
diminution in volume dV at an osmotic pressure , is :
(G)= -
We obtain, then :
.and since v : Vdv :dV, P and p must be equal, which was to
be proved.
The conclusion here reached, which will be repeatedly con-
firmed in what follows, is, in turn, a new support to the law
of Gay-Lussac applied to solutions. In case gaseous pressure
and osmotic pressure are equal at the same temperature,
changes in temperature must have also an equal influence on
both. But, on the other hand, the relation found permits of
an important extension of the law of Avogadro, which now
finds application also to all solutions, if only osmotic pressure
is considered instead of elastic pressure. At equal osmotic
pressure and equal temperature, equal volumes of the most
23
MEMOIRS ON
widely different solutions contain an equal number of mole-
cules, and, indeed, the same number which, at the same press-
ure and temperature, is contained in an equal volume of a gas.
5. GENERAL EXPRESSION OF THE LAWS OF BOYLE, GAY-
LUSSAC, AND AVOGADRO, FOR SOLUTIONS AND GASES.
The well-known formula, which expresses for gases the two
laws of Boyle and Gay-Lussac :
PV=RT,
is now, where the laws referred to are also applicable to liquids,
valid also for solutions, if we are dealing with the osmotic pres-
sure. This holds even with the same limitation which is also
to be considered with gases, that the dilution shall be sufficiently
great to allow one to disregard the reciprocal action of, and the
space taken by, the dissolved particles.
If we wish to include in the above expression, also, the third,
the law of Avogadro, this can be done in an exceedingly simple
manner, following the suggestion of Horstmann,* considering
always kilogram-molecules of the substance in question; thus,
2 k. hydrogen, 44 k. carbon dioxide, etc. Then R in the
above equation has the same value for all gases, since at the
same temperature and pressure the quantities mentioned oc-
cupy also the same volume. If this value is calculated, and
the volume taken in Mr*, the pressure in K per Mr*, and
if, for example, hydrogen at and atmospheric pressure is
chosen :
"P = 10333, F = --, ^3,^ = 845.05. .
The combined expression of the laws of Boyle, Gay-Lussac,
and Avogadro is, then :
PF=845 T,
and in this form it refers not only to gases, but to all solutions,
P being then always taken as osmotic pressure.
In order that the formula last obtained may be hereafter easily
applied, we give it finally a simpler form, by observing that the
number of calories, which is equal to a kilogram-metre, there-
fore to the equivalent of work f [A = V stands i
\ 4/w/
in a very
* Ber. deutscli. chem. GeselL, 14, 1243.
f [The reciprocal of the "mechanical equivalent of heat.'' 1 ']
24
- - / f\ 1-JsA^A- f^-* y-\ ,>/**.
' i~* ,-> <*
v *'
THE MODERN THEORY OF SOLUTION
simple relation to R, indeed, AR^, (more exactly, about one-
thousandth less).
Therefore, the following form can be chosen :
APV=2 T,
which has the great practical advantage that the work done,
of which we shall often speak hereafter, finds a very simple ex-
pression, in case it is calculated in calories.
Let us next calculate the work, expressed in calories, which
is done when a gas or a solution at constant pressure and tem-
perature expands by a volume V, a kilogram -molecule being
the mass involved. This work is evidently 2 T. We should
add that this constant pressure is preserved only if the entire
volume of gas or solution is very large in proportion to V, or
if we are dealing with vaporization at maximum tension.
The subordinate question will often arise, of the work ex-
pressed in calories, which is done by isothermal expansion,
either by a kilogram-molecule of a gas, or, if it is a solution, by
that amount which contains this quantity of the dissolved
substance. If the pressure decreases, then, by a very small
fraction AP, which therefore corresponds to an increase in vol-
ume of A V, the work done will be AP& V, or 2 A7 T .
0. FIRST CONFIRMATION OF AYOGADRO'S LAW AS APPLIED TO
SOLUTIONS. DIRECT DETERMINATION OF OSMOTIC PRESSURE.
It would be expected beforehand that the law of Avogadro,
which we developed for solutions of gases, as a consequence of
the law of Henry, would not be limited to solutions of those
substances which, perchance, are in the gaseous state under
ordinary conditions. Yet the confirmation of this conjecture
is very welcome in other cases, especially in those now to be
mentioned, since we are not dealing here with theoretical con-
clusions, but with the results of direct experiment. As a mat-
ter of fact, we will find in Pfeffer's determinations of the os-
motic pressure of solutions of sugar* a striking confirmation
of the law which we are defending.
A one-per-cent. solution of sugar was used in the experi-
ment under consideration, i.e., a solution obtained by bringing
* Osmotische UntersucJiungen, Leipsic, 1877.
25
MEMOIRS ON
together 1 part of sugar and 100 parts of water, which contain-
ed, then, 1 gram of the substance named, in 100.6 cm. 3 of the
solution. If we compare the osmotic pressure of this solution
with the pressure of a gas say hydrogen which contains the
same number of molecules in 100.6 cm. 3 , therefore, in the case
2
chosen,- grams (C 12 H 22 11 = 342), a striking agreement be-
comes manifest. Since hydrogen at one atmosphere pressure
and at weighs 0.08956 grams per litre, and the above con-
centration contains 0.0581 grams per litre, we are dealing,
ut 0, with 0.649 atmosphere, and, therefore, at /, with 0.641)
(1 + 0.003670- If we compare these with Pfeffer's data, we
have :
TEMPERATURE (t). OSMOTIC PRESSURE. 0.649(1+0.00867$).
6.8 0.664.. 0.665
13.7 0.691 0.681
14.2 0.671 0.682
15.5 0.684 0.686
22.0 0.721 0.701
32.0 0.716 0.725
36.0 0.746 0.735
The osmotic pressure of a solution of sugar, ascertained di-
rectly, is, then, at the same temperature, exactly equal to the
gas pressure of a gas which contains the same number of mole-
cules in a given volume as there are sugar molecules in the
same volume of the solution.
This relation can be extended from cane-sugar to other dis-
solved substances; as invert sugar, malic acid, tartaric acid, cit-
ric acid, malate and sulphate of magnesium, which, from the
physiological investigations* of De Vries, show the same osmot-
ic pressure for equal molecular concentration of the solutions.
7. SECOND CONFIRMATION OF THE LAW OF AVOftADRO AS
APPLIED TO SOLUTIONS. MOLECULAR LOWERING OF VAPOR-
PRESSURE.
The relation which exists between osmotic pressure and
maximum vapor-tension, and which can be easily developed on
* Eine Methode zur Messung der Turgorkraft, 512.
26
THE MODERN THEORY OF SOLUTION
thermodynamic gronnds, furnishes a suitable means of testing
the laws in question, through the experimental material re-
cently collected by Raoult.
\Ve shall then begin with a perfectly general law, which is
rentirely independent of that hitherto developed : Isotonism in
\xolutiom in the same solvent Conditions equality of maximum
I tension. This proposition can be easily demonstrated by car-
rying out a reversible cycle at constant temperature. For this
purpose two solutions are taken with the same maximum ten-
sion, and a small amount of the solvent is transported, in a re-
versible manner, from one to the other, as vapor, i. e., with pis-
ton and cylinder. This transference takes place when the
maximum tensions are equal, without doing work, therefore no
work is done in returning the solvent, since in the whole cycle
no work can be done. If we now return the solvent by means
of a semipermeable wall, which separates the two solutions, the
necessity of the isotonic state is at once evident, since otherwise
this transformation could not take place without doing work.
If we apply this principle to dilute solutions, with the aid of
the laws developed for them, we arrive at once at the simple
conclusion that equal molecular concentration of dissolved
substance conditions equal maximum tension of the solution.
But this is exactly the principle recently discovered by Raoult,*
of the constancy of molecular lowering of vapor - pressure.
This is, however, obtained by multiplying the molecular weight
of dissolved substances with the so-called relative lowering of
the vapor-pressure of a one-per-cent. solution, i. e., with the
part of the maximum tension which the solvent has thus lost.
The equality of the molecular lowering of vapor-pressure refers
then to solutions of equi-molecular concentration, on the as-
sumption of the approximate proportionality between lowering
of vapor-pressure and concentration. For example, the value
in question for ether, for the thirteen substances which were
investigated in it, fluctuated between 0.07 and 0.74, with a
mean of 0.71.
But we can carry this relation still further, and com-
pare the different solvents with one another, to arrive at the
second law which Raoult likewise found experimentally.
For this purpose, we perform, at T, with a very dilute
* Camp, rend., 87, 167; 44, 1431.
27
MEMOIRS ON
P-per-cent. solution, the following reversible cycle, consisting
of two parts :
1. That mass of the solvent is removed by means of piston
and cylinder in which a kilogram-molecule ( M ) of the dissolved
substance is contained. The mass of the solution is so large
that change in concentration is not thus produced, and the
work done amounts, therefore, to 2 T.
2. The amount of solvent just obtained, 73 kilograms, is
returned as vapor in a reversible way, therefore first obtained
from the liquid at maximum tension, then expanded until the
maximum tension of the solution is reached, and finally lique-
fied in contact with the solution. The kilogram-molecule of
the solvent (M') would require, thus, an expenditure of 2 A2 T
work, in which A represents the relative lowering of vapor-
pressure ; and therefore the kilograms in question would
require 2 JA But Mis Raoult's molecular lowering of
PM P
vapor-pressure, which we will therefore represent by the letter
K, whence the expression in question becomes simplified to
aoo TK
M'
But from the second law of thermodynamics, the sum of the
work done in this cycle, completed at constant temperature,
must again be equal to zero, therefore what is gained in the
first part is expended in the second. We have, consequently :
^00 TJ?
2 T= M or 100 K=M'.
This relation comprises all of Raoult's results. It expresses,
at once, what was obtained above, that the molecular lowering
of the vapor-pressure is independent of the nature of the dis-
solved substance. But it shows, also, what Raoult found, that
the value in question does not change with the temperature.
It contains, finally, the second proposition of Raoult, that the
molecular lowering of the vapor-pressure is proportional to the
molecular weight of the solvent, and amounts to about one one-
hundredth of it. The following figures, obtained by Raoult,
suffice to show this :
28
THE MODERN THEORY OF SOLUTION
MOI Frm AR WFTOHT MOLECULAR LOWERING
SOLVENT. OF VAPOR-PRESSURE
(K).
. Water 18 0.185
Phosphorus trichloride. .137.5 1.49
Carbon bisulphide 76 0.80
Carbon tetrachloride 154 1.62
Chloroform 119.5 1.30
Amylene 70 0.74
Benzene 78 0.83
Methyl iodide 142 1.49
Methyl bromide 109 1.18
Ether 74 0.71
Acetone 58 0.59
Methyl alcohol 32 0.33
8. THIRD CONFIRMATION OF AVOGADRO's LAW AS APPLIED
TO SOLUTIONS. MOLECULAR LOWERING OF THE FREEZING-
POINT.
There can also be stated here a perfectly general and rigid
proposition, which connects the osmotic pressure of a solution
with its freezing-point. Solutions in the same solvent, having
the same freezing-point, are isotonic at that temperature. This
proposition can be proved exactly as the preceding one, by car-
rying out a cycle at the freezing-point of the two solutions ;
only here the reversible transference of the solvent is effected
not as vapor, but as ice. It is returned again through a semi-
permeable wall, and since there can be no work done, isoto-
nism must exist.
We also apply this proposition to dilute solutions, and if we
take into account, then, the relations already developed, we ar-
rive at once at the very simple conclusion that solutions which
contain the same number of molecules in the same volume, and,
therefore, from Avogadro's law, are isotonic, have also the same
freezing-point. This was, in fact, discovered by Raoult, and
found its expression in the term introduced by him, the so-
called "normal molecular lowering of the freezing-point,"
which is shown by the large majority of dissolved substances,
and means that the freezing-point lowering of a one-per-cent.
solution, multiplied by the molecular weight, is constant. This
refers, therefore, to solutions of equal molecular concentration,
29
MEMOIRS ON
on the assumption of an approximate proportionality between
concentration and lowering of freezing-point. For example,
this value is about 18.5 for almost all organic substances dis-
solved in water.
We can, however, carry the relation still further, and derive
the above normal molecular lowering of the freezing-point from
other data, on the assumption of Avogadro's law for solutions.
This quantity bears a necessary and simple relation to the la-
tent heat of fusion of the solvent, as the following reversible
cycle shows, using the second law of thermodynamics. Let us
take a very dilute .P-per-cent. solution, which gives a freezing-
point lowering A ; the solvent freezes at T, and its latent heat
of fusion is W per kilogram.
1. The solution is deprived at T, of that amount of the sol-
vent in which a kilogram-molecule (M) of the dissolved sub-
stance is present, exactly as in the preceding case, by means of
piston arid cylinder with semipermeable wall. The amount of
the solution is here so large that change in concentration is not
thus produced, and therefore the work done is 2 T.
2. The kilograms of the solvent obtained, is allowed to
freeze at T, when -- -^ calories are set free. The solution
and solid solvent are cooled A degrees, and the latter allowed
to melt in contact with the solution, thereby taking up the heat
just set free. Finally, the temperature is again raised A degrees.
In this reversible cycle -- ^ calories are raised from T 7 A
to T, which corresponds to an amount of work --- -- , but
p- is the molecular lowering of the freezing-point, which we
will designate by the letter / ; the work done is, therefore,
1 00 W/
- , and this was shown in the first part of the above process
to be 2 T-, therefore :
or
THE MODERN THEORY OF SOLUTION
The relation thus obtained is very satisfactorily confirmed by
the facts. We give the values calculated from the formula de-
veloped, together with the molecular freezing-point lowerings
obtained by Raoult,* so that the two may be examined.
SOLVENT.
Water
FREEZING- 1
POINT (T). C
273
LATENT HEAT
)F FUSION (W).
79
. 0.02 '/' 3
W
18.9
1OLKCUI.AR
LOWERING.
18.5
Acetic acid. . .
Formic acid . .
Benzene
273 + 16.7
273 + 8.5
273+ 4.9
43.2ft
55.6ft
29.1J
38.8
28.4
53.0
38.6
27.7
50.0
Nitrobenzene .
273+ 5.3
22.3J;
69.5
70.7
Let us add, that from the lowering found for ethylene bromide,
117.9, the latent heat of fusion of this substance, unknown at
that time, was calculated to be 13, and that the determination
which Pettersson very kindly carried out at my request gave,
in fact, the value expected (mean, 12.94).
9. -- APPLICATION OF AVOGADRO'S LAW TO SOLUTIONS.
GULDBERG AND WAAGE's LAW.
Having given the physical side of the problem the greater
prominence, thus far, in order to furnish the greatest possible
support to the principles developed, it now remains to apply
it to chemistry. The most obvious application of the law of
Avogadro for solutions, as for gases, is to ascertain the molecu-
lar weight of dissolved substances. This application has, in-
deed, already been made, only it consists not in the investiga-
tion of pressures as with gases, where every determination of
molecular weight amounts to the determination of pressure,
volume, temperature, and weight. In solutions we would have
to deal in such an experimental arrangement, with the deter-
mination of the osmotic pressure, and the practical means of
determining this are still wanting. Yet this obstacle can be
overcome by determining, instead of the osmotic pressure, one of
the two values which, from what is given above, are connected
with it, i. e., the diminution of vapor-pressure or the lowering
of the freezing-point. To this end there is the proposition
* Ann. CMm. Phys., (5), 2, (6), 11.
f Berthelot, Essai de Mecanique Chimique.
j Pettersson, Journ. prakt. Chim, (2), 24, 129.
31 '
MEMOIRS ON
of Racult already made use of for determining molecular
weights viz., the relative lowering of vapor - pressure of a
one-per-cent. aqueous solution is to be divided into 0.185, or
the freezing-point lowering is to be divided into 18.5, a method
which is comparable with those used for such determinations
with gases, and the results of which, therefore, confirm Avoga-
dro's law for solutions.
It is still more remarkable that the so general law of Guld-
berg andWaage, assumed also for solutions, can, in fact, be de-
veloped as a simple conclusion from the laws adduced above for
dilute solutions. It is only necessary to complete a reversible
cycle at constant temperature, which can be done with semi-
permeable walls, as well with solutions as with gases.
Let us imagine two systems of gaseous or dissolved sub-
stances in equilibrium, and let us represent this condition, in
general, by the following symbol :
a ;M l ' + a l "M l "+ etc.^<Jf,;4<'Jf,;'+ etc.,
in which a represents the number of molecules, and M the
[chemical} formula. This equilibrium exists in two vessels, A
and B, at the same temperature, but
at different concentrations. We will
designate the latter by the partial
pressure, or the osmotic pressure
which each of the substances in
question exercises. Let these press-
ures in vessel A be, P\P" . -P'^P",
etc. : in B they are larger by
dP' l dP' l '...dP' / ,dP', f l ,Qte.
The reversible cycle, to be carried
out, consists in this : the mass of
the first system, expressed by the
above symbol, is introduced into
A in kilograms, while the second is removed in equivalent
quantity. Both have here the concentrations which exist in A.
This transformation is so carried out that every one of the
substances in question enters or leaves by means of a suitable
piston and cylinder, which is separated from the vessel A by
a wall, permeable to this substance alone. If we are dealing
with a solution, the cylinders themselves are made with a semi-
permeable wall, and are surrounded with the solvent.
If this is accomplished, every part of the second system
32
(5)
(1)
Fig. 5
THE MODERN THEORY OF SOLUTION
undergoes the change in concentration necessary to become
equal to that which exists in B. The work done, per kilo-
gram-molecule, is, as before, 2 AT 7 ; in which A is the
dP
fraction of the increase in pressure, therefore here ; for
the amounts in question the work done is then %aT .
The second system just obtained, is now conducted over into
the first by means of the vessel B, exactly as above, at the con-
centrations prevailing in B, and these are finally changed into
the original concentrations existing in A, by suitable change in
volume.
Where we are dealing with a cycle completed at constant
temperature the sum of the amounts of work in question is
zero, and this can be indicated by the following equation, which,
indeed, needs no explanation :
If we observe that (1) and (5) are transformations, in the re-
verse sense, of the same parts, with the same mass, at the same
temperature, it follows that :
and, for the same reasons :
(2)+(4)=0;
from which we conclude that :
(3) + (6)=0.
But this leads immediately to the law of Gruldberg and Waage.
The amount of work (3) is, indeed, from the foregoing,
2 2a,, T '-', and likewise (6) is equal to 2 2 / T '-, whence it
follows : L r ^_ 2a/ T dP\ =0;
-* ii * t /
On integration we obtain :
2 (a ti \og P ll a l log P t )= constant,
but in this P is proportional to the concentration or active
mass C, and the latter can therefore be introduced instead of
the former without destroying the constancy of the whole ex-
pression. Therefore :
2 (a lt log C ti a, log C t ) = constant,
c 33
MEMOIRS ON
which is nothing but the Guldberg-Waage formula in logarith-
mic form.
10. DEVIATIONS FROM AVOGADRO'S LAW IN SOLUTIONS. VARI-
ATION FROM THE GULDBERG-WAAGE LAW.
We have tried to show in the preceding portion of this paper,
the genetic connection which exists between the Guldberg-Waage
law and the known or newly established laws for solutions of
Boyle, Henry, Gay-Lussac, and Avogadro. It is the same which,
indeed, long ago, allowed the law of Guldberg and Waage to be
demonstrated for gases on thermodynamic grounds.
It is now a question of further developing the laws of chem-
ical equilibrium, and, therefore, at first, we must examine more
closely the real validity of the three principles from which the
law of Guldberg and Waage is derived.
If we are still considering "ideal solutions," a class of phe-
nomena must be dealt with which, from the now clearly demon-
strated analogy between solutions and gases, are to be classed
with the earlier so-called deviations of gases from Avogadro's
law. As the pressure of the vapor of ammonium chloride, for
example, was too great in terms of this law, so, also, in a large
number of cases the osmotic pressure is abnormally large ; and
as was afterwards shown, in the first case there is a breaking
down into hydrochloric acid and ammonia, so also with solu-
tions we would naturally conjecture that, in such cases, a
similar decomposition had taken place. Yet it must be con-
ceded that anomalies of this kind, existing in solutions, are
much more numerous, and appear with substances which, it is
difficult to assume, break down in the usual way. Examples in
aqueous solutions are most of the salts, the strong acids, and
the strong bases ; and, therefore, the existence of the so-called
normal molecular lowering of the freezing-point and diminution
of the vapor -pressure were not discovered until Raoult em-
ployed the organic compounds. These substances, almost
without exception, behave normally. It may, then, have ap-
peared daring to give Avogadro's law for solutions such a
prominent place, and I should not have done so had not
Arrhenius pointed out to me, by letter, the probability that
salts and analogous substances, when in solution, break down
into ions. As a matter of fact, as far as investigation has
34
THE MODERN THEORY OF SOLUTION
been carried, the solutions which obey the law of Avogadro
are non-conductors, which indicates that they are not broken
down into ions ; and a further experimental examination of the
other solutions is possible, since, from the assumption made
by Arrhenins, the deviation from Avogadro's law can be cal-
culated from the conductivity.
However this may be, the attempt will now be made to take
into account these so-called deviations from Avogadro's law,
and, retaining the laws of Boyle and Gay-Lussac for solutions,
to give the development, thus made possible, of Guldberg and
Waage's formula. The change which the expressions hitherto
developed undergo, can be made easily and briefly when what
is stated above is taken into account.
The combined expression of the laws of Boyle, Gay-Lussac,
and Avogadro developed on page 25 :
APV=2T,
is changed into :
APV=2iT,
where the pressure is in general i times the value presupposed
in the above expression.
Therefore, the work done by reversible change in solutions
will be i times the former value, and this sums up the entire
transformation to be introduced, which is then easily applied
to the development of the Guldberg and Waage formula just
given.
If we return to the relation obtained at the end of the com-
pleted cycle, page 33 :
(3) + (6)=0,
the amounts of work done, (3) and (6), which were formerly
represented by 220,, T- ^and 2 2a t T ', are now expressed
by i times these respective values. The result is consequently :
After integration we have :
S (a^i,, log P u ai, log P,)= constant,
and by introducing the concentration or active mass C, instead
of the pressure which is proportional to it :
2 (a ll i ll \QgC n ai t log C t )= constant.
This is, then, the logarithmic statement of the Guldberg-
Waage formula in its new form, which differs from the earlier
35
MEMOIRS ON
form only in that it contains the quantity i. It now remains to
show that the newly obtained relation agrees very much better
with the facts than the original expression. It is, therefore,
necessary to know exactly the values of i, in question, and in
this we are limited to aqueous solutions, since only here is
there sufficient experimental data at hand to make the exami-
nation desired.
11. DETERMINATION OF I FOR AQUEOUS SOLUTIONS.
Since we have succeeded in establishing Avogadro's law for
solutions in four different ways, there are also four ways of
studying the deviations referred to, therefore of determining i.
But of these, that which depends upon the lowering of the
freezing-point so far surpasses the others, due to the extended
and careful investigations in this field, that we can limit our-
selves entirely to this method.
Let us then return to the cycle which, on the basis of freez-
ing-point determinations, led us to Avogadro's law. This gave
the relation :
loom
rp * * >
in which the second term represents the work done by revers-
ibly removing that amount of the solvent which contains a
kilogram-molecule dissolved in it. This must then be multi-
plied by i :
100JFZ
~yr-=^iT.
From this there appears at once a very simple way of deter-
mining i. This value, from the above equation, seems to be
proportional to t, i. e., to the molecular lowering of the freez-
ing-point, since all other values (T, absolute temperature of
fusion W, latent heat of fusion of solvent) are constant. But
18.5 is the molecular lowering of the freezing-point for cane-
sugar, which, from page 25, rigidly obeys the law of Avogadro,
and for which, therefore, i = l. The value of i for other sub-
stances is, therefore, the lowering produced by them, divided
by 18.5. Almost exactly the same result is obtained if, in the
above equation, for J'and W the corresponding values for ice,
273 and 79, respectively, are introduced. They will, therefore,
be used in the following calculations.
36
THE MODERN THEORY OF SOLUTION
12. PROOF OF THE MODIFIED GULDBERG-WAAGE LAW.
In using the relation now proposed, and in the comparison
with the results of the Guldberg -Waage formula to be made
by the reader, it is necessary to mention briefly the differ-
ent forms which the latter has taken in the course of time.
We will first represent our relation by a simple formula,
in which also Guldberg and Waage's conceptions can be ex-
pressed, viz. :
2ailogC=K. (1)
It differs from the expression on page 35 only in this, the
terms referring to the constituent parts of the two systems
are regarded with inverse signs. The original expression of
the Swedish* investigators f is, then, very similar to the above:
2klogC=:, (2)
only that here k is to be determined for each constituent in
question by observing the equilibrium of the system.
But when Guldberg and Waage repeatedly found the coef-
ficient in question k, to be equal to 1, in the observations!
which they had made bearing upon this point, they gave their
law the simplified form:
SlogC^JT. (3)
In their last communication, however, the change is intro-
duced which takes into account also the number of molecules
#, and therefore the following relation obtains, corresponding
to the formula since developed for gases on thermodynamic
grounds :
2a\ogC=K. (4)
We have, therefore, designated this above as the Guldberg-
Waage formula.
Although this simplified expression, with coefficients which
are whole numbers, was defended for solutions by the Swedish
Investigators, Lemoine,|| on the basis of Schloesing's experi-
ments on the solubility of calcium carbonate in water contain-
ing carbon dioxide, returned, not long ago, to the original
* [Guldberg and Waage are Professors in the University of Christiania.]
f Christiania Videnskabs SelsJcabs Forhandlingar, 1864.
\ fitudes sur les affinity chimiques, 1867.
Journ. prakt. Chem., 19, 69.
H Etudes sur les equilibres c/iimiques, 266.
37
MEMOIRS ON
formula (2), with coefficients which remain to be more accu-
rately determined, but which were, in general, not whole num-
bers; and, indeed, if whole numbers were employed, there was
not an agreement between fact and theory.
In view of this uncertainty, the formula which we have intro-
duced has the advantage that the coefficients which appear in
it are completely determined at the outset, and therefore their
correctness can be decided at once by experiment. It will, in
fact, become apparent that in the cases studied by Guldberg
and Waage, through the peculiar values of i, the simple form
brought forward by these investigators as of general appli-
cability, is completely verified, and the fact that such simplifi-
cation is in most cases permissible is in accordance with what
we have laid stress upon above viz., the validity of Avo-
gadro's law for solutions. On the other hand, the investiga-
tion of Schloesing, brought prominently forward by Lemoine,
would show that the simplification in question is not allowable,
since with it the same fractional coefficients appeared which
Schloesing obtained.
Before we can proceed to examine our relation more closely,
it is necessary to adapt it also to the case where, in part, undis-
solved substances are present. This is very simply done, and
leads to the same result for all of the above-mentioned formulas ;
if we consider that such substances are present in the solu-
tion, even to saturation, therefore at constant concentration.
All such concentrations can then be transferred from the first
term of the above equation to the second, without destroying
the constancy of the latter. All remains, then, exactly the same,
only that the dissolved substances are to be considered exclu-
sively in the first term.
1. We will first examine the observations of Guldberg and
Waage. These investigators studied chiefly the equilibrium
expressed by the following symbol :
Ba CO^+K 2 SO, ^zb Ba S0,+ K 2 C0 3 ,
and found, corresponding to their simplified formula :
log Cx.soi log Cs; 2 co 3 = K.
But from our equation almost exactly the same relation re-
sults, since for JT 2 $0 4 , a = l and i=%.ll ; for K 2 CO& a I and
i'=2.26; therefore:
log CK.SO. 1.07 log CK^CO^K.
The same agreement exists between the two results, in case we
38
THE MODERN THEORY OF SOLUTION
are dealing with the sodium salts, since where i for Na 2 80+
and 3?< 2 C0 3 is 1.91 and 2.18 respectively, we obtain the follow-
ing relation :
1 og C N a* so,. 1 1 4 log C NO* co 3 = K.
2. But in the above-mentioned experiments of Schloesing*
we do not expect these nearly integral numbers. It was a
question there of the solubility of calcium carbonate in water
containing carbon dioxide, therefore of an equilibrium which
can be expressed by the following symbol :
Ca C0 3 +H 2 C0 3 ^T Ca (HC0 3 ) 2 .
We expect, then, since i=I for carbon dioxide, and {=2.56 for
acid calcium carbonate:
0.39 log Cif,c0 3 log C C a(HCO^ = K,
while Schloesing found the following relation :
0.37866 log <7tf 2 co 3 -log C C a(HCo 3 ) 2 =K.
The agreement is also very satisfactory for the corresponding
phenomenon with barium, since i for acid barium carbonate
being 2.66, we obtain:
0.376 log Cn 2 co 3 log
while experiment gave .
0.38045 log Cn 2 co 3 log
3. Let us now turn to Thomson's experiments f on the action
of sulphuric acid on sodium nitrate in solution. This investi-
gator arrived at the result that the state of the case as foreseen
by Guldberg and Waage actually obtains. But this is, indeed,
another one of the cases where our relation and Guldberg-
Waage's formula lead to the same result.
If we express the equilibrium in question by the following
smbol :
Guldberg-Waage's relation requires:
log (?Aa 8 Sr04 + log C H N0 3 ~ log CyaHSO^ log
But:
iNoy. 504 = 1 .91, /^ i V0 3 = l'94, iA r aff5O 4 = l-8
and we obtain then :
1.05 log Cya>sOi+ 1-06 log CW jfoj-l.03 log C Na nso.
which amounts to almost the same thing.
* Compt. rend., 74, 1552 ; 75, 70.
f Thermocliemiscli Untersuchungen, 1.
39
MEMOIRS ON
If, on the other hand, we express the equilibrium by the fol-
lowing symbol :
Guldberg and Waage would have :
logCVoa^+Blog CW0 3 log C H ,SOi
while we obtain :
log CV^o 4 + 2.03 log CW 3 -1.07 log CH.SO.
thus, again, an almost perfect agreement.
4. The investigations of Ostwald* on the action of hydro-
chloric acid on zinc sulphide, which relate to the equilibrium
expressed by the following symbol :
Zn S+2H Cl ^ H 2 S+Zn C1 2 ,
leads us, by taking into account the fact that :
to the relation :
3.96 log <7#cz 1.04 log Cn 2 s-2.53 log
Where at the beginning only hydrochloric acid and zinc sul-
phide were present, the concentrations of hydrogen sulphide
and zinc chloride in this series of experiments are evidently
equal. The result would then be so expressed that the orig-
inal concentration of the hydrochloric acid would be given by
the volume ( F), in which a known amount of this substance
was present, while the fraction (x) denoted that portion which,
by contact with zinc sulphide, had been finally transformed into
zinc chloride. We obtain accordingly :
3. 96 logi^- 3. 57 log -^constant;
and therefore also :
--F - n = constant.
This function appears, in fact, to be nearly constant :
VOLUME (7).
1
UNTRANSFORMED
PART (X).
0.0411
2
0.0380
4..
. 0.0345
0.0430
0.0428
0.0418
8 0.0317 0.0413
* Journ. prakt. Chem., (2), 19, 480.
40
THE MODERN THEORY OF SOLUTION
The analogous experiments with sulphuric acid, where i for
H 2 SOt and Zn 80^ is 2.06 and 0.98 respectively, gave, simi-
larly :
x
(l-z)
]7- a constant,
which amounts, therefore, to nearly a constant value for x.
This is also, in fact, the experimental result, as is shown by
the following table :
. Tr% UNTRANSFORMED
VOLUME (7). PART(*).
2 .......................... 0.0238
4 .......................... 0.0237
8 ............ .............. 0.0240
16 .......................... 0.0241
5. The experiments of Engel* also merit consideration. In
these, the question is as to the solubility of magnesium car-
bonate in water containing carbon dioxide, therefore of the
following equilibrium :
Mg C0 3 +H 2 C0 3 ^: Mg (HC0 3 ) 2 .
Since i for magnesium dicarbonate is 2.64, our formula leads
here to the following relation :
0.379 log <7tf 2 o> 3 -log
while that observed was :
0.37 log CWaCOa log
6. The experiments of the same author, f on the simulta-
neous solubility of ammonium and copper sulphates, should
also be mentioned here, in -which we have to deal essentially
with the equilibrium :
Cu S0 4 + (NH 4 ) 2 SO, ^ (NHJ 2 Cu (S0 4 ) 2 .
Since the double salt was always present partially undissolved,
and since i for Cu S0 4 and (NH) 2 S0 is 0.98 and 2, respective-
ly, we obtain here the relation :
0.49 log C cu so, -flog C
while that found was :
0.438 log C
* Compt. rend., 1OO, 352, 444.
\lbid., 102,113.
41
MEMOIRS ON
7. Finally, we mention the experiments of Le Ohatelier* on
the equilibrium between basic mercury sulphate and sulphuric
acid, which is expressed by the following symbol :
ffffs ##6 + 2 H 2 S0 4 ^ 3 Hg #0 4 + 2 H 2 0.
In this case, where i for H 2 S0 4 and Hg S0 4 is 2.06 and 0.98, re-
spectively, we expect the following relation :
1 . 4 log C H2 sot log Cog so^ K,
while that observed was :
1.58 log <7tf a so 4 log C Hg so t = K.
A very satisfactory agreement, in general, is thus indicated.
AMSTERDAM, September, 1887.
JACOBUS HENDRICUS VAN'T HOFF was born August 30,
1852, at Rotterdam. He received the degree of Doctor of
Philosophy from Utrecht in 1874, having studied at the Poly-
technic Institute in Delft from 1869 to 1871, at the University
of Leyden in 1871, at Bonn with Kekule in 1872, with Wiirtz
in Paris in 1873, and with Mulder in Utrecht in 1874.
He was made privat- decent at the veterinary college in
Utrecht in 1876, and in 1878 professor of chemistry, mineral-
ogy, and geology at the university in Amsterdam. The latter
position he held until about two years ago, when he was called
to a chair created for him in the University of Berlin.
Probably the best known work of Van't Hoff is La Chimie
dans VEspace, which was the origin of that branch of chemistry
which has come to be. known as stereochemistry. He pointed
out here that whenever a compound is optically active, it al-
ways contains at least one "asymmetric" carbon atom, i.e.,
a carbon atom in combination with four different elements or
groups. This book appeared first in Dutch in 1874, a year
later in French, and has recently been enlarged and translated
into English. Other books by Van't Hoff which should be
mentioned are : Views on Organic Chemistry, Ten Years in the
History of a Theory, Studies in Chemical Dynamics, revised
and enlarged by Cohen, and translated into English by Ewan
one of Van't HofFs most valuable contributions to science ;
Lectures on the Formation and Decomposition of Double Salts,
and Lectures on Theoretical and Physical Chemistry, which is
just appearing.
* Compt. rend., 97, 1555.
42
THE MODERN THEORY OF SOLUTION
The number of papers published by Yan't Hoff is not very
large, indeed, unusually small, for one who is so well known.
That on Solid Solutions and the Determination of the Molec-
ular Weight of Solids,* opened up a field in which a number
have subsequently worked.
* Ztichr. Fhys. Chem., 5, 322.
ON THE DISSOCIATION OF SUBSTANCES
DISSOLVED IN WATER
BY
SVANTE ARRHENIUS
Professor of Physics in the Stockholm High School
Zeitschrift fur Phynkalische CJiemie, 1, 631, 1887
45
CONTENTS
PAGE
Van't Hoffs Law 47
Exceptions to Van't Hoff's Law 48
Two Methods of Calculating the Van't Hoff Constant "i" 49
Comparison of Results by the Two Methods 50
Additive Nature of Dilute Solutions of Salts 57
Heats of Neutralization 59
Specific Volume and Specific Gravity of Dilute Solutions of Salts 61
Specific Refmctimty of Solutions 62
Conductivity 63
Lowering of Freezing -Point 65
ON THE DISSOCIATION OF SUBSTANCES
DISSOLVED IN WATEE*
BY
SVAXTE AREHENIUS
\y>v*
IN a paper submitted to the Swedish Academy of Sciences,
on the 14th of October, 1805, Van't Hoff proved experimen-
tally, as well as theoretically, the following unusually significant
generalization of Avogadro's law:f
"The pressure which a gas exerts at a given temperature, if
a definite number of molecules is contained in a definite vol-
ume, is equal to the osmotic pressure which is produced by
most substances under the same conditions, if they are dis-
solved in any given liquid."
Van't Hoff has proved this law in a manner which scarcely
leaves any doubt as to its absolute correctness. But a diffi-
culty which still remains to be overcome, is that the law in
question holds only for "most substances"; a very consider-
able number of the aqueous solutions investigated furnishing
exceptions, and in the sense that they exert a much greater
osmotic pressure than would be required from the law re-
ferred to.
If a gas shows such a deviation from the law of Avogadro,
it is explained by assuming that the gas is in a state of dis-
sociation. The conduct of chlorine, bromine, and iodine, at
higher temperatures is a very well-known example. We re-
gard these substances under such conditions as broken down
into simple atoms.
* Ztschr. Phys. CJiem., 1, 631, 1887.
f Van't Hoff, Une propriete generate de la matidre diluee, p. 43 ; Sv.
Vet-Ak-s Handlingar, 21, Nr. 17, 1886. [Also in Archives Neerlandaises
for 1885.]
47
MEMOIRS ON
The same expedient may, of course, be -marie use of to explain
the exceptions to Van't Hoff's law ; but it has not been put for-
ward up to the present, probably on account of the newness of
the subject, the many exceptions known, and the vigorous objec-
tions which would be raised from the chemical side, to such an
explanation. The purpose of the following lines is to show that
such an assumption, of the dissociation of certain substances
dissolved in water, is strongly supported by the conclusions
drawn from the electrical properties of the same substances, and
that also the objections to it from the chemical side are dimin-
ished on more careful examination.
In order to explain the electrical phenomena we must assume
with Clausius* that some of the molecules of an electrolyte are
dissociated into their ions, which move independently of one
another. But since the "osmotic pressure " which a substance
dissolved in a liquid exerts against the walls of the confining
vessel, must be regarded, in accordance with the modern ki-
netic view, as produced by the impacts of the smallest parts of
this substance, as they move, against the walls of the vessel,
we must, therefore, assume, in accordance with this view, that
a molecule dissociated in the manner given above, exercises as
great a pressure against the walls of the vessel as its ions
would do in the free condition. If, then, we could calculate
what fraction of the molecules of an electrolyte is dissociated
into ions, we should be able to calculate the osmotic pressure
from Van't Hoff's law.
In a former communication " On the Electrical Conductivity
of Electrolytes," I have designated those molecules whose ions
are independent of one another in their movements, as active ;
the remaining molecules, whose ions are firmly combined with
one another, as inactive. I have also maintained it as probable,
that in extreme dilution all the inactive molecules of an elec-
trolyte are transformed into active.f This assumption I will
make the basis of the calculations now to be carried out. I
have designated the relation between the number of active
molecules and the sum of the active and inactive molecules,
as the activity coefficient. J The activity coefficient of an
* Clansius, Pong. Ann., 1O1, 347 (1857); Wied. Elektr., 2, 941.
f Bihang der Stockholmer Akademie, 8, Nr. 13 and 14, 2 Tl. pp. 5 and 13 ;
1 Tl., p. 61.
tt..,2Tl.,p.5.
48
THE MODERN THEORY OF SOLUTION
electrolyte at infinite dilution is therefore taken as unity. For
smaller dilution it is less than one, and from the principles
established in my work already cited, it can be regarded as
equal to the ratio of the actual molecular conductivity of the
solution to the maximum limiting value which the molecular
conductivity of the same solution approaches with increasing
dilution. This obtains for solutions which are not too concen-
trated (i.e., for solutions in which disturbing conditions, such
as internal friction, etc., can be disregarded).
If this activity coefficient (a) is known, we can calculate as
follows the values of the coefficient i tabulated by Yan't Hoff.
i is the relation between the osmotic pressure actually exerted
by a substance and the osmotic pressure which it would exert
if it consisted only of inactive (undissociated) molecules, i is
evidently equal to the sum of the number of inactive mole-
cules, plus the number of ions, divided by the sum of the inac-
tive and active molecules. If, then, m represents the number
of inactive, and n the number of active molecules, and k the
number of ions into which every active molecule dissociates
(e.g., k=2 for K Cl, i. e., K and Cl; k=3 for Ba Cl z and
K 2 SO i, i. e., Ba, Cl, Cl, and K, K, 4 ), then we have :
._m+kn
m + n
But since the activity coefficient (a) can, evidently, be written
n
m-\-ri
Part of the figures given below (those in the last column),
were calculated from this formula.
On the other hand, i can be calculated as follows from the
results of Raoult's experiments on the freezing-point of solu-
tions, making use of the principles stated by Yan't Hoff. The
lowering (t) of the freezing-point of water (in degrees Celsius),
produced by dissolving a gram-molecule of the given substance
in one litre of water, is divided by 18.5. The values of i thus
calculated, i = ', are recorded in next to the last column.
18.5
All the figures given below are calculated on the assumption
that one gram of the substance to be investigated was dissolved
in one litre of water (as was done in the experiments of
Raoult).
D 49
MEMOIRS ON
In the following table the name and chemical formula of the
substance investigated are given in the first two columns, the
value of the activity coefficient in the third (Lodge's dissocia-
tion ratio*), and in the last two the values of i calculated by the
two methods: i= and i ! + (& l)a.
18.5
The substances investigated are grouped together under four
chief divisions : 1, non-conductors ; 2, bases ; 3, acids ; and 4,
salts.
NON-CONDUCTORS.
SUBSTANCE. FORMULA. a i=-. 1
18.5 i-r(Ki)a.
Methyl alcohol CH 3 OH 0.00 0.94 1.00
Ethyl alcohol C 2 H 5 OH -0.00 0.94 1.00
Butyl alcohol C' 4 H 9 OH 0.00 0.93 1.00
Glycerin C 3 H 5 (OH) 3 0.00 0.92 1.00
Mannite 6 H U 6 0.00 0.97 1.00
Invert sugar 6 H 12 6 0.00 1.04 1.00
Cane-sugar }2 H 22 U 0.00 1.00 1.00
Phenol C 6 H 5 OH 0.00 0.84 1.00
Acetone 3 H 6 0.00 0.92 1.00
Ethyl ether (C 2 H 5 ) 2 0.00 0.90 1.00
Ethyl acetate O^H Q 2 0.00 0.96 1.00
Acetamide C 2 H 3 ONH 2 0.00 0.96 1.00
BASES.
t i
SUBSTANCE. FORMULA. a ^=^~^- i i(t~ 1\
18.5 l~r (A I) a.
Barium hydroxide Ba(OH) 2 0.84 2.69 2.67
Strontium hydroxide. .. Sr (OH) 2 0.86 2.61 2.72
Calcium hydroxide .... Ca(OH) 2 0.80 2,59 2.59
Lithium hydroxide Li OH 0.83 2.02 1.83
Sodium hydroxide Na OH 0.88 1.96 1.88
Potassium hydroxide .. K OH 0.93 1.91 1.93
Thallium hydroxide ... Tl OH 0.90 1.79 1.90
Tetramethylammonium
hydrate (CH^NOH 1.99
* Lodge, On Electrolysis, Report of British Association, Aberdeen, 1885,
p. 756 (London, 1886).
50
THE MODERN THEORY OF SOLUTION
BASES (continued).
t i=
8DBSTANCE. FORMULA. fit * = 18~5* 1+ (& !)
Tetraethylammonium
hydrate (^#5)4 &OH 0.92 1.92
Ammonia " XH 3 0.01 1.03 1.01
Metliylamine Cff 3 NH 2 0.03 1.00 1.03
Trimethylamiiie (ON 3 ) 3 N 0.03 1.09 1.03
Ethylamhie C 2 H 5 XH 2 0.04 1.00 1.04
Propylamine C 3 H,^H 2 0.04 1.00 1.04
Aniline C & H,NH 2 0.00 0.83 1.00
ACIDS.
t i=
SUBSTANCE. FORMULA. a * = j"tt~ = ' !+(& I) a
Hydrochloric acid H Cl 0.90 1.98 1.90
Hydrobromic acid H Br 0.94 2.03 1.94
Hydroiodicacid HI 0.96 2.03 1.96
Hydrofluosilicic acid... H 2 SiF 6 0.75 2.46 1.75
Nitric acid H N0 3 0.92 1.94 1.92
Chloric acid HCW 3 0.91 1.97 1.91
Perchloric acid HCIO 0.94 2.09 1.94
Sulphuric acid H 2 80 0.60 2,06 2.19
Selenic acid H 2 SeO, 0.66 2.10 2.31
Phosphoric acid H^PO^ 0.08 2.32 1.24
Sulphurous acid H 2 SO^ 0.14 1.03 1.28
Hydrogen sulphide .... H 2 8 0.00 1.04 1.00
lodic acid HI0 3 0.73 1.30 1.73
Phosphorous acid P (Off) 3 0.46 1.29 1.46
Boric acid B(OH) 3 0.00 1.11 1.00
Hydrocyanic acid H CN ' 0.00 1.05 1.00
Formic acid HCOOH 0.03 1.04 1.03
Acetic acid Cff 3 CO OH 0.01 1.03 1.01
Butyric acid C 3 H,COOH 0.01 1.01 1.01
Oxalic acid (CO OH) 2 0.25 1.25 1.49
Tartaricacid C\ff B 6 0.06 1.05 1.11
Malic acid O 4 H 6 5 0.04 1.08 1.07
Lactic acid C 3 H 6 3 0.03 1.01 1.03
MEMOIRS ON
SALTS.
SUBSTANCE. FORMULA. a i^ l + (j fcI 1)a .
Potassium chloride KCl 0.86 1.82 1.86
Sodium chloride NaCl 0.82 1.90 1.82
Lithium chloride Li Cl 0.75 1.99 1.75
Ammonium chloride. . . NH^ Cl 0.84 1.88 1.84
Potassium iodide KI 0.92 1.90 1.92
Potassium bromide K Br 0.92 1.90 1.92
Potassium cyanide KCN 0.88 1.74 1.88
Potassium nitrate K N0 3 0.81 1.67 1.81
Sodium nitrate Na N0 3 0.82 1.82 1.82
Ammonium nitrate Nff 4 N0 3 0.81 1.73 1.81
Potassium acetate CH^COOK 0.83 1.86 1.83
Sodium acetate CH 3 COONa 0.79 1.73 1.79
Potassium formate HCOOK 0.83 1.90 1.83
Silver nitrate Ag N0 3 0.86 1.60 1.86
Potassium chlorate K Cl 3 0.83 1.78 1.83
Potassium carbonate... K 2 C0 3 0.69 2.26 2.38
Sodium carbonate Na 2 C0 3 0.61 2.18 2.22
Potassium sulphate K 2 4 0.67 2.11 2.33
Sodium sulphate. Na 2 S0 4 0.62 1.91 2.24
Ammonium sulphate... (NffJ 2 S0 4 0.59 2.00 2.17
Potassium oxalate K 2 C 2 0.66 2.43 2.32
Barium chloride Ba C1 2 0.77 2.63 2.54
Strontium chloride Sr C1 2 0.75 2.76 2.50
Calcium chloride Ca C1 2 0.75 2.70 2.50
Cupric chloride Cu C1 2 2.58
Zinc chloride ZnCl* 0.70 2.40
Barium nitrate Ba(N0 3 ) 2 0.57 2.19 2.13
Strontium nitrate Sr N0 3 ) 2 0.62 2.23 2.23
Calcium nitrate Ca(N0 3 \ 0.67 2,02 2.33
Lead nitrate PI (N0 3 ) 2 0.54 2.02 2,08
Magnesium sulphate.. . Mg S0 0.40 1.04 1.40
Ferrous sulphate Fe 80^ 0.35 1.00 1.35
Copper sulphate Cu SO* 0.35 0.97 1.35
Zinc sulphate Zn S0 4 0.38 0.98 1.38
Cupric acetate (C 2 H 3 2 ) 2 Cu 0.33 1.68 1.66
Magnesium chloride... Mg C1 2 0.70 2.64 2.40
Mercuric chloride Hg C1 2 0.03 1.11 1.05
Cadmium iodide Cd I 2 0.28 0.94 1.56
Cadmium nitrate..... . Cd(N0 3 ) 2 0.73 2.32 2.46
Cadmium sulphate.... Cd SO. 0.35 0.75 1.35
52
THE MODERN THEORY OF
The last three numbers in next to the last column are not
taken, like all the others, from the work of Raoult,* but from
the older data of Riidorff,t who employed in his experiments
very large quantities of the substance investigated, therefore
no very great accuracy can be claimed for these three numbers.
The value of a is calculated from the results of Kohlrausch,J
Ostwald (for acids and bases), and some few from those of
Grotrian|| and Klein. ^[ The values of a, calculated from the
results of Ostwald, are by far the most certain, since the two
quantities which give a can, in this case, be easily determined
with a fair degree of accuracy. The errors in the values of i,
calculated from such values of a, cannot be more than 5 per
cent. The values of a and i, calculated from the data of Kohl-
rausch, are somewhat uncertain, mainly because it is difficult
to calculate accurately the maximum value of the molecular
conducting power. This applies, to a still greater extent, to the
values of a and i calculated from the experimental data of
Grotrian and Klein. The latter may contain errors of from 10
to 15 per cent, in unfavorable cases. It is difficult to estimate
the degree of accuracy of Rao ult's results. From the results
themselves, for very nearly related substances, errors of 5 per
cent., or even somewhat more, do not appear to be improbable.
It should be observed that, for the sake of completeness, all
substances are given in the above table for which even a fairly
accurate calculation of i by the two methods was possible. If
now and then data are wanting for the conductivity of a sub-
stance (cupric chloride and tetramethylammonium hydrate),
such are calculated, for the sake of comparison, from data for
a very nearly related substance (zinc chloride and tetraethylam-
monium hydrate), whose electrical properties cannot differ ap-
preciably from those of the substance in question.
Among the values of i which show a very large difference
from one another, those for hydrofluosilicic acid must be
* Raoult, Ann. Chim. Phys., [5], 28, 133 (1883) ; [6], 2, 66, 99, 115
(1884); [6]. 4, 401 (1885). [This volume, p. 52.]
t Riidorff, Ostwald's Lehrb. all. Chem., L, 414.
j Kohlrausch, Wied. Ann., 6, 1 and 145 (1879); 26, 161 (1885).
Ostwald, Journ. prakt. Chem., [2], 32, 300(1885) ; [2], 33, 352 (1886) ;
Ztschr. PJiys. Chem., 1, 74 and 97 (1887).
fl Grotrian. Wied. Ann., 18. 177 (1883).
1 Klein, Wied. Ann., 27, 151 (1886).
53
MEMOIRS ON
especially mentioned. But Ostwald has, indeed, shown that
in all probability, this acid is partly broken down in aqueous
solution into HF and Si0 2 , which would explain the large
value of i given by the Raoult method.
There is one condition which interferes, possibly very seri-
ously, with directly comparing the figures in the last two col-
umns namely, that the values really hold for different temper-
atures. All the figures in next to the last column hold, indeed,
for temperatures only a very little below 0C., since they were
obtained from experiments on inconsiderable lowerings of the
freezing-point of water. On the other hand, the figures of the
last column for acids and bases (Ostwald's experiments) hold at
25, the others at 18. The figures of the last column for non-
conductors hold, of course, also at 0C., since these substances
at this temperature do not consist, to any appreciable extent,
of dissociated (active) molecules.
An especially marked parallelism appears,* beyond doubt,
on comparing the figures in the last two columns. This shows,
a posteriori, that in all probability the assumptions on which I
have based the calculation of these figures are, in the main,
correct. These assumptions were :
1. That Van't HoflPs law holds not only for most, but for all
substances, even for those which have hitherto been regarded as
exceptions (electrolytes in aqueous solution).
2. That every electrolyte (in aqueous solution), consists partly
of active (in electrical and chemical relation), and partly of
inactive molecules, the latter passing into active molecules on
increasing the dilution, so that in infinitely dilute solutions
only active molecules exist.
The objections which can probably be raised from the chemi-
cal side are essentially the same which have been brought for-
ward against the hypothesis of Clausius, and which I have
earlier sought to show, were completely untenable. f A repe-
tition of these objections would, then, be almost superfluous. I
will call attention to only one point. Although the dissolved
substance exercises an osmotic pressure against the wall of the
vessel, just as if it were partly dissociated into its ions, yet
* In reference to some salts which are distinctly exceptions, compare
below, p. 55.
f 1. c., 2 Tl., pp. 6 and 31.
54
THE MODERN THEORY OF SOLUTION
the dissociation with which we are here dealing is not exactly
the same as that which exists when, e.g., an ammonium salt
is decomposed at a higher temperature. The products of
dissociation in the first case (the ions) are charged with very
large quantities of electricity of opposite kind, whence cer-
tain conditions appear (the incompressibility of electricity),
from which, it follows that the ions cannot be separated from
one another to any great extent, without a large expenditure
of energy.* On the contrary, in ordinary dissociation where no
such conditions exist, the products of dissociation can, in gen-
eral, be separated from one another.
The above two assumptions are of the very widest significance,
not only in their theoretical relation, of which more hereafter,
but also, to the highest degree, in a practical sense. If it could,
for instance, be shown that the law of Van't Hoff is generally
applicable which I have tried to show is highly probable the
chemist would have at his disposal an extraordinarily conven-
ient means of determining the molecular weight of every sub-
stance soluble in a liquid. f
At the same time, I wish to call attention to the fact
that the above equation (1) shows a connection between the
two values i and a, which play the chief roles in the two
chemical theories developed very recently by Van't Hoff and
myself.
I have tacitly assumed in the calculation of ?, carried out
above, that the inactive molecules exist in the solution as sim-
ple molecules and not united into larger molecular complexes.
The result of this calculation (i. e., the figures in the last col-
umn), compared with the results of direct observation (the fig-
ures in next to the last column), shows that, in general, this
supposition is perfectly justified. If this were not true the
figures in next to the last column would, of course, prove to
be smaller than in the last. An exception, where the latter
undoubtedly takes place, is found in the group of sulphates
of the magnesium series (Mg SO^ Fe S0, Cu #0 4 , Zn 80^ and
Cd 50 4 ), also in cadmium iodide. We can assume, to explain
this, that the inactive molecules of these salts are, in part,
*l.c, 2Tl.,p. 8.
f This means has already been employed. Compare Ruoult, Ann.
Chim. Phys. t [6], 8, 317 (1886) ; Pateru6 and Nasini, Ber. deutsctt. chem.
Gesell, 1886, 2527.
55
MEMOIRS ON
combined with one another. Hittorf,* as is well known, was led
to this assumption for cadmium iodide, through the large change
in the migration number. And if we examine his tables more
closely we will find, also, an unusually large change of this num-
ber for the three of the above-named sulphates (Mg $0 4 , Cu S0 4 ,
and Zn jSO) which he investigated. It is then very probable
that this explanation holds for the salts referred to. But we
must assume that double molecules exist only to a very slight
extent in the other, salts. It still remains, however, to indicate
briefly the reasons which have led earlier authors to the assump-
tion of the general existence of complex molecules in solution.
Since, in general, substances in the gaseous state consist of sim-
ple molecules (from Avogadro's law), and since a slight increase in
the density of gases often occurs near the point of condensation,
indicating a union of the molecules, we are inclined to see in
the change of the state of aggregation, such combinations tak-
ing place to a much greater extent. That is, we assume that
the liquid molecules in general are not simple. I will not com-
bat the correctness of this conclusion here. But a great differ-
ence arises if this liquid is dissolved in another (e.g., H Cl in
water). For if we assume that by dilution the molecules which
were inactive at the beginning become active, the ions being sep-
arated to a certain extent from one another, which of course re-
quires a large expenditure of energy, it is not difficult to assume,
also, that the molecular complexes break down, for the most part,
on mixing with water, which in any case does not require very
much work. The consumption of heat on diluting solutions
has been interpreted as a proof of the existence of molecular
complexes.f But, as stated, this can also be ascribed to the
conversion of inactive into active molecules. Further, some
chemists, to support the idea of constant valence, would as-
sume 1 molecular complexes, in which the unsaturated bonds
could become saturated. But the doctrine of constant valence
is so much disputed that we are scarcely justified in basing any
conclusions upon it. The conclusions thus arrived at, that, e.g.,
potassium chloride would have the formula (KCl) 3 , L. Meyer
* Hittorf, Pogg. Ann., 1O6, 547 and 551 (1859) ; Wied. Elektr., 2, 584.
f Ostwald, Lebrb. all. Chem., I., 811; L. Meyer, Moderne Theorien der
Chemie, p. 319 (1880).
\ L. Meyer, 1. c. p. 360.
56
THE MODERN THEORY OF SOLUTION
sought to support by the fact that potassium chloride is much
less volatile than mercuric chloride, although the former has a
much smaller molecular weight than the latter. Independent
of the theoretical weakness of such an argument, this conclu-
sion could, of course, hold only for the pure substances, not for
solutions. Several other reasons have been brought forward by
L. Meyer for the existence of molecular complexes, e.g., the
fact that sodium chloride diffuses more slowly than hydrochloric
acid,* but this is probably to be referred to the greater friction
(according to electrical determinations), of sodium against water,
than of hydrogen. But it suffices to cite L. Meyer's own words :
"Although all of these different points of departure for ascer-
taining molecular weights in the liquid condition are still so
incomplete and uncertain, nevertheless they permit us to hope
that it will be possible in the future to ascertain the size of
molecules, "f But the law of Van't Hoff gives entirely reliable
points of departure, and these show that in almost all cases the
number of molecular complexes in solutions can be disregarded,
while they confirm the existence of such in some few cases, and,
indeed, in those in which there were formerly reasons for as-
suming the existence of such complexes.]; Let us, then, not
deny the possibility that such molecular complexes also exist
in solutions of other salts and especially in concentrated solu-
tions ; but in solutions of such dilution as was investigated
by Raoult, they are, in general, present in such small quantity
that they can be disregarded without appreciable error in the
above calculations.
Most of the properties of dilute solutions of salts are of a
so-called additive nature. In other words, these properties
(expressed in figures) can be regarded as a sum of the proper-
ties of the parts of the solution (of the solvent, and of the parts
of the molecules, which are, indeed, the ions). As an example,
the conductivity of a solution of a salt can be regarded as the
sum of the conductivities of the solvent (which in most cases
is zero), of the positive ion, and of the negative ion. In
most cases this is controlled by comparing two salts of one
* L. Meyer, 1. c. p. 316.
f L. Meyer, L c. p. 321. The law of Van't Hoff makes this possible, as
is shown above.
\ Hittorf, I. c. Ostwald's Lelirb. all. Cliern., p. 816.
Kohlrausch, Wied. Ann., 167 (1879).
57
MEMOIRS ON
acid (e.g., potassium and sodium chlorides) with two corre-
sponding salts of the same metals with another acid (e. g., potas-
sium and sodium nitrates). Then the property of the first salt
(K CT), minus the property of the second (Na Cl), is equal to
the property of the third (KN0 3 ), minus the property of the
fourth (NaN0 3 ). This holds in most cases for several proper-
ties, such as conductivity, lowering of freezing-point, refrac-
tion equivalent, heat of neutralization, etc., which we will treat
briefly, later on. It finds its explanation in the nearly com-
plete dissociation of most salts into their ions, which was shown
above to be true. If a salt (in aqueous solution) is completely
broken down into its ions, most of the properties of this salt
can, of course, be expressed as the sum of the properties of
the ions, since the ions are independent of one another in most
cases, and since every ion has, therefore, a characteristic prop-
erty, independent of the nature of the opposite ion with which
it occurs. The solutions which we, in fact, investigate are
never completely dissociated, so that the above statement
does not hold rigidly. But if we consider such salts as are
80 to 90 per cent, dissociated (salts of the strong bases with the
strong acids, almost without exception), we will, in general, not
make very large errors if we calculate the properties on the
assumption that the salts are completely broken down into
their ions. From the above table this evidently holds also
for the strong bases and acids : Ba (OH) 2 , Sr (OH) 2 , Ca (OH) 2 ,
Li OH, Na OH, K OH, Tl OH, and H Cl, H Br, HI, H NO.,,
HC10 3 , and #C70 4 .
But there is another group of substances which, for the most
part, have played a subordinate role in the investigations up to
the present, and which are far from completely dissociated, even
in dilute solutions. Examples taken from the above table are,
the salts, Hg C1 2 (and other salts of mercury), Cd T 2 , Cd S0 4 ,
Fe S0 4 , Mg S0, Zn S0, Cu S0, and Cu (C 2 H 3 2 ) 2 ; the weak
bases and acids, as NH 3 , and the different amines, H 3 P0 4 , H 2 8,
B (OH) 3 , H CN, formic, acetic, butyric, tartaric, malic, and lac-
tic acids. The properties of these substances will not, in gen-
eral, be of the same (additive) nature as those of the former
class, a fact which is completely confirmed, as we will show
later. There are, of course, a number of substances lying
between these two groups, as is also shown by the above
table. Let attention be here called to the fact that several
58
THE MODERN THEORY OF SOLUTION
investigators have been led to the assumption of a certain kind
of complete dissociation of salts into their ions, by considering
that the properties of substances of the first group, which have
been investigated far more frequently than those of the second,
are almost always of an additive nature.* But since no reason
could be discovered from the chemical side why salt molecules
should break down (into their ions) in a perfectly definite
manner, and, moreover, since chemists, for certain reasons not
to be more fully considered here, have fought as long as pos-
sible against the existence of so-called unsaturated radicals
(under which head the ions must be placed), and since, in
addition, it cannot be denied that the grounds for such an as-
sumption were somewhat uncertain,! the assumption of com-
plete dissociation has not met with any hearty approval up to
the present. The above table shows, also, that the aversion of
the chemist to the idea advanced, of complete dissociation, has
not been without a certain justification, since at the dilutions
actually employed, the dissociation is never complete, and even
for a large number of electrolytes, (the second group) is rela-
tively inconsiderable.
After these observations we now pass to the special cases in
which additive properties occur.
1. The Heat of Neutralization in Dilute Solutions. When
an acid is neutralized with a base, the energies of these two
substances are set free in the form of heat; on the other hand,
a certain amount of heat disappears as such, equivalent to the
energies of the water and salt (ions) formed. We designate
with ( ) the energies for those substances, for which it is unim-
portant for the deduction whether they exist as ions or not,
and with [ ] the energies of the ions, which always means the
energies in dilute solution. To take an example, the follow-
ing amounts of heat are set free on neutralizing Na OH with
| H, S0 4 (1), and with H Cl (2), and on neutralizing K OH with
\ H. 2 S0 4 (3), and with H Cl (4) (all in equivalent quantities,
and on the previous assumption of a complete dissociation of
the salts) :
*Valson, Compt. rend., 73, 441 (1871); 74, 103 (1872); Favre and
Valson, Compt. rend., 75, 1033 (1872); Raoult, Ann. Chim. Phys., [6],
4, 426.
f In reference to the different hypotheses of Raoult, compare, I. c.,
p. 401.
59
MEMOIRS ON
(Na OH) + (H 01) - (H, 0) - [ Aa] - [ Cl] .
. (I)
(2)
(3)
(K OH) + (H Cl) -(H,0)- [AH - [ Cl]. (4)
(1) (2) is, of course, equal to (3) (4), on the assumption of
a complete dissociation of the salts. This holds, approximately,
as above indicated, in the cases which actually occur. This is
all the more true, since the salts which are farthest removed
from complete dissociation in this case JV# 8 $0 4 and JT S $0 4
are dissociated to approximately the same extent, therefore
the errors in the two members of the last equation are approxi-
mately of equal value, a condition which, in consequence of
the additive properties, exists more frequently than we could
otherwise expect. The small table given below shows that the
additive properties distinctly appear on neutralizing strong bases
with strong acids. This is no longer the case with the salts of
weak bases with weak acids, because they are, in all probability,
partly decomposed by the water.
HEATS OF FORMATION OF SOME SALTS IN DILUTE SOLUTION, ACCORDING
TO THOMSEN AND BERTHELOT.
HCl
H Br
HI
HN0 3
C 2 /A 2
CH 2 2
i- (CO OH) 2
Na OH. .
KOH
NH,
iCa(OH),.
Ba(OH),
k8r(OH) t .
13.7
13.7
124
14.0
13.8
14.1
13.7 (0.0)
13.8 ( + 0.1)
12.5(+0.1)
13.9 (-0.1)
18.9 (+0.1)
13.9 (-0.2)
13.3 (-0.4)
13.3 (-0.4)
12.0 (-0.4)
13.4 (-0.6)
13.4(-04)
13. 3 (-0.8)
13.4 (-0.3)
13.4(-0.3)
11.9(-0.5)
13.5 (-0.5)
13.5 (-0.3)
13.5 (-0.6)
14.3 (+0.6)
14.3 (+0.6)
12.7 (+0.3)
t #2 SOi
in s s
HCN
* C0 2
Na OH
15 8 (+2 1)
3 8 ( 99)
2 9 ( 108)
i o 2 { 3 ^\
KOH
15 7 ( + 2 0)
3 8 (9 9)
3 ( 10 7)
10 1 ( 36)
NH 3
14 5 (+2 0)
3 1 ( 9 3)
1 3( 11 1)
5 3 ( 71)
| Ca(OH)*. .
$ Ba(OI-f) 9 . .
i Sr(Off)
3.9 (-10.1)
As can be seen from the figures inclosed in brackets (which
represent the difference between the heat tone in question and
the corresponding heat tone of the chloride), they are approxi-
60
THE MODERN THEORY OF SOLUTION
mately constant in every vertical column. This fact is very
closely connected with the so-called thermo-neutrality of salts ;
but since I have previously treated this subject more directly,
and have emphasized its close connection with the Williamson-
Clausius* hypothesis, I do not now need to give a detailed
analysis of it.
2. Specific Volume and Specific Gravity of Dilute Salt Solu-
tions. If a small amount of salt, whose ions can be regarded as
completely independent of one another in the solution, is added
to a litre of water, the volume of this is changed. Let x be the
quantity of the one ion added, and y that of the other, the vol-
ume will be approximately equal to (\+ax + by) litres, a and b
being constants. But since the ions are dissociated from one
another, the constant a of the one ion will, of course, be inde-
pendent of the nature of the other ion. The weight is, similar-
ly, (\ + cx+dy) kilograms, in which c and d are two other con-
stants characteristic for the ions. The specific gravity will
then, for small amounts of x and y, be represented by the
formula :
l + (c-a)x+(b-d)y,
where, of course, (c a) and (b d) are also characteristic con-
stants for the two ions. The specific gravity is, then, an addi-
tive property for dilute solutions, as Valsonf has also found.
But since "specific gravity is not applicable to the representation
of stoichiometric laws," as Ostwald ]; maintains, we will refrain
from a more detailed discussion of these results. The deter-
mination of the constants a and b, etc., promises much of value,
but thus far has not been carried out.
The changes in volume in neutralization are closely related to
these phenomena. It can be shown that the change in volume
in neutralization is an additive property, from considerations
very similar to those above for heat of neutralization. All
the salts investigated (K^ Na- NH^) are almost completely
dissociated in dilute solutions, as is clear from the above table
(and is even clearer from the subsequent work of Ostvvald),
so that a very satisfactory agreement for these salts can be
expected. The differences of the change in volume in the
*l. c.,2Tl., p. 67.
f Valson, Compt. rend., 73, 441 (1871) ; Ostwald, Lehrb. all Chem., I., 384.
\ Ostwald, ibid., I., 386.
61
MEMOIRS ON
formation of the salts in question, from nineteen different acids,
are also found to be nearly constant numbers.* Since bases
which form salts of the second group have not been investi-
gated, there are no exceptions known.
3. Specific Refr activity of Solutions. If we represent by n
the index of refraction, by d the density, and by P the weight
n ^
of a substance, P is, as is well known, a value which, when
added for the different parts of mixtures of several substances,
gives the corresponding value for the mixture. Consequently,
this value must make the refraction equivalent an additive
property also for the dissociated salts. The investigations of
Gladstone have shown distinctly that this is true. The potas-
sium and sodium salts have been investigated in this case just
as the acids themselves. We take the following short table
on molecular refraction equivalents from the Lelirbuch of Ost-
wald : f
POTASSIUM. SODIUM. HYDROGEN. K~Na. KH.
Chloride 18.44 15.11 14.44 3.3 4.0
Bromide 25.34 21.70 20.63 3.6 4.7
Iodide 35.33 31.59 31.17 3.7 4.2
Nitrate 21.80 18.66 17.24 3.1 4.5
Sulphate 30.55 22.45 2x4.1
Hydrate 12.82 9.21 5.95 3.6 6.8
Formate 19.93 16.03 13.40 3.9 6.5
Acetate 27.65 24.05 21.20* 3.6 6.5
Tartrate 57.60 50.39 45.18 2x3.6 2x6.2
The difference KNa is, as is seen, almost constant through-
out, which was also to be expected from the knowledge of the
extent of dissociation of the potassium and sodium salts. The
same holds also for the difference KH, as long as we are
dealing with the strong (dissociated) acids. On the contrary,
the substances of the second group (the slightly dissociated
acids), behave very differently, the difference KH being much
greater than for the first group.
4. ValsonJ believed that he also found additive properties
* Ostwald, Lefirb. all. Chem., I., 388.
f Ostwald, I. c.,p. 443.
i Valson, Compt. rend,, 74, 103(1872) ; Ostwald, 1. c. p. 492.
62
THE MODERN THEORY OF SOLUTION
of salt solutions in C&pillary Phenomena. But since this can be
traced back to the fact that the specific gravity is an additive
property, as above stated, we need not stop to consider it.
5. Conductivity. F. Kohlrausch, as is well known, has done
a very great service for the development of the science of elec-
trolysis, by showing that conductivity is an additive property.*
Since we have already pointed out how this is to be understood,
we pass at once to the data obtained. Kohlransch gives in his
work already cited, the following values for dilute solutions :
Li=21, J#=40, #=278, C2=49,
= 46, Cl 3 =4D,
But these values hold only for the most strongly dissociated
substances (salts of the monobasic acids and the strong acids
and bases). For the somewhat less strongly dissociated sul-
phates and carbonates of the univalent metals (compare above
table), he obtained, indeed, much smaller values: JT = 40,
NHt = 31, Na = 22, Li = 11, Ag=32, #=166, i#0 4 = 40,
(70 3 =36; and for the least dissociated sulphates (the metals
of the magnesium series), he obtained the following still smaller
values : i Mg = 14= f $Zn=12, Cu = 12, %SO=22.
It appears, then, that the law of Kohlrausch holds only
for the most strongly dissociated salts, the less strongly disso-
ciated giving very different values. But since the number of
active molecules also increases with increase in dilution, so
that at extreme dilution all salts break down completely into
active (dissociated) molecules, it would be expected that, at
higher dilutions, the salts would behave more regularly. I
showed, also, from some examples that " we must not lay too
much stress upon the anomalous behavior of salts (acetates and
sulphates) of the magnesium series, since these anomalies dis-
appear at greater dilutions. "f I also believed I could establish
the view that conductivity is an additive property, J and I as-
cribed to the conductivity of hydrogen in all acids (even in the
poorest conducting, whose behavior was not at all compatible
with this view), a value which was entirely independent of the
* Kohlrausch, Wied. Ann., 6, 167 (1879); Wied. Elek., 1, 610 ; 2, 955.
1 1. c., 1 Tl., p. 41.
\l.c., 2Tl.,p. 12.
MEMOIRS ON
nature of the acid. This, again, was accomplished only with the
aid of the conception of activity. The correctness of this view
appears still more clearly from the later work of Kohlrausch,*
and of Ostwald. f Ostwald attempts to show in his last work
upon this subject, that the view that conductivity is additive
is tenable without the aid of the activity conception, and he
succeeds very well for the salts which he employed (potassium,
sodium, and lithium), because these are, in general, very nearly
completely dissociated, and especially at very great dilutions.
This result receives further support from the fact that anal-
ogous salts of the univalent metals, if they are very closely re-
lated to one another, are dissociated to approximately the same
extent at the same concentrations. But if we were dealing
with salts of less closely related metals we should obtain very
different results, as is shown distinctly by previous investi-
gations. As Ostwald I himself says, the law of Kohlrausch
does not hold for the acids, but we must add to it the con-
ception of activity if we would have it hold true. But this
law does not apply to all salts. A closer investigation of cop-
per acetate would, indeed, lead to considerable difficulties.
This would be still more pronounced if we took into account
the mercury salts, since it appears from the investigations of
Grotrian,|| as if these gave only a very small fraction of the
conductivity derived from this law, even in extreme dilutions.
It is apparent that not all of the salts of the univalent metals
conform to this law, since, according to Bouty,^[ potassium
antimonyl tartrate, in 0.001 normal solution, conducts only
about one-fifth as well as potassium chloride. From the law
of Kohlrausch it must conduct at least half as well as potas-
sium chloride. But if we make use of the activity conception,
the law of Kohlrausch holds very satisfactorily, as is shown
by the values of i in the above table for weak bases and acids,
calculated on the basis of this law, and also for Hg C1 2 and
Cu(C 2 Hz O.^)^- They agree very well with the values of i de-
rived from the experiments of E-aoult.
* Kohlrausch, Wied. Ann., 26, 215 and 216 (1885).
f Ostwald, Ztschr. Phys. Chem., 1, 74 and 97 (1887).
j Ostwald, 1. c. p. 79.
My work, already cited. 1 Tl., p. 39.
|| Grotrian, Wied. Ann., 18, 177 (1883).
-If Bouty, Ann. Chim. Phys., [6], 3, 472 (1884;.
64
THE MODERN THEORY OF SOLUTION
G. Lowering of the Freezing-Point. Raoult* shows, in one of
his investigations, that the lowering of the freezing-point of
water by salts can be regarded as an additive property, as
would be expected, in accordance with our views for the most
strongly dissociated salts in dilute solutions. The following
values were obtained for the activities of the ions :
GROUP.
1 st. Univalent (electro) negative ions (radicals) . . 20 (Cl. Br, OH, N0 3 , etc.)
2d. Bivalent 11(S0 4 . Cr 4 , etc.)
3d. Univalent (electro) positive " " 15(H, K, Na,NIJ t , etc.)
4th. f Bivalent or polyvalent " 8(Ba, Mg, Al^ etc.)
But there are very many exceptions which appear because of
unusually small dissociation even in the most dilute solutions,
as is seen from the following table :
Calculated. Observed.
Weak acids. 35 19
Cu(C 2 H 3 2 ) 2 48 31.1
Potassium antimonyl tar-
trate 41 18.4
Mercuric chloride.. . 48 20.4
Calculated. Observed.
Lead acetate 48 22.2
Aluminium acetate 128 84.0
Ferric acetate 128 58.1
Platinic chloride. . . 88 29.0
We know, from experiments on the electrical conductivity of
those substances which are given in the first column, that their
* Raoult, Ann. Chim. Phys., [6], 4, 416 (1885).
f All ions have the same value 18.5, according to the views already ex-
plained. Raoult has, evidently, ingeniously forced these substances under
the general law of the additivity of freezing-point lowering, by assigning
to the ions of the less dissociated substances, as Mg 80 t , much smaller values
(8 and 11 respectively). The possibility of ascribing smaller values to the
polyvalent ions is based upon the fact that, in general, the dissociation of
salts is smaller the greater the valence of their ions, as I have previously
maintained (1. c., I Tl., p. 69 ; 2 Tl., p. 5). "The inactivity (complexity)
of a salt solution is greater, the more easily the constituents of the
salt (acid and base) form double compounds." This result is, moreover,
completely confirmed through subsequent work by Ostwald (Ztschr. Phys.
Chem.,\, 105 to 109). It is evident that if we were to give the correct value.
18.5, to the polyvalent ions, the salts obtained from them would form
very distinct exceptions. (Probably a similar view in reference to other addi-
tive properties could be correctly brought forward.) Although Raoult has,
then, artificially forced these less strongly dissociated salts to conform to
his law, he has not succeeded in doing so with all of the salts, as is pointed
out above.
E 65
MEMOIRS ON
molecules are very slightly dissociated. The remaining sub-
stances are closely related to these, so that we can expect them
to behave similarly, although they have not been investigated,
electrically, up to the present. But if we accept the point of
view which I have brought forward, all of these substances,
the latter as well as the cases previously cited, are not to be
regarded as exceptions ; on. the contrary, they obey exactly the
same laws as the other substances hitherto regarded as normal.
Several other properties of salt solutions are closely connect-
ed with the lowering of the freezing-point, as Goldberg* and
Van't Hofff have shown. These properties are proportional
to the lowering of the freezing-point. All of these properties
- lowering of the vapor -pressure, osmotic pressure, isotonic
coefficients, are, therefore, to be regarded as additive. De
VriesJ has also shown this for isotonic coefficients. But since
all of these properties can be traced back to the lowering of the
freezing-point, I do not think it necessary to enter into the
details of them here.
SVAKTE ARRHE^IUS was born February 19, 1859, near
tlpsala, Sweden. After leaving the Gymnasium in 1876, he
studied in the University of Upsala until 1881. From 1881 to
1883 he worked at the Physical Institute of the Academy of
Sciences in Stockholm. Having received the Degree of Doctor
of Philosophy from the University of Upsala in 1878, he was
appointed privat-docent in that institution in 1884.
A little later, the Stockholm Academy of Sciences granted
Arrhenius an allowance that he might visit foreign universities.
In 1888 he worked with Van't Hoff in Amsterdam, in 1889 with
Ostwald in Leipsic, and in J890 with Boltzmann in Gratz.
In 1891 he was called to Stockholm as a teacher of physics,
in what is termed the Stockholm High School, but which, in
reality, corresponds favorably with many of the smaller univer-
sities abroad. In 1895 he was appointed to the full professor-
ship of physics in Stockholm, a position which he now holds.
Some of his more important pieces of work, in addition to
* Guldberg, Compt. Tend., 7O, 1349 (1870).
f Van't Hoff, I. c. p. 20.
j De Vries, Erne Metlwde zur Analyse der Turgorkraft, PrinffsheinVs Jahr-
biichcr, 14, 519 (1883) ; Van't Hoff, /. c. p. 26.
66
THE MODERN THEORY OF SOLUTION
that included in this volume, are : The Conductivity of Very
Dilute Aqueous Solutions (Dissertation); Theory of Isohydric
Solutions ; Effect of the Solar Radiation on the Electrical Phe-
nomena in the Earth's Atmosphere; Effect of the Amount of
Carbon Dioxide in the Air on the Temperature of the Earth's
Surface.
Arrhenius is also a member of a number of learned societies
and academies.
THE GENERAL LAW OF THE FREEZING
OF SOLVENTS
BY
F. M. RAOULT
Professor of Chemistry in Grenoble.
(Annales de Chimie et de Physique, [6], 2, 66, 1884.)
CONTENTS
PAGE
Effect of Dissolved Substances on Freezing-Points 71
Solutions in Acetic Acid 73
Solutions in Formic Acid 77
Solutions in Benzene 78
Solutions in Nitrobenzene 80
Solutions in Ethylene Bromide 82
Solutions in Water 83
Conclusions. . . 88
THE GENERAL LAW OF THE FREEZING
OF SOLVENTS *
BY
F. M. RAOULT
IF we represent by A the coefficient of lowering of a substance,
i.e., the lowering of the freezing-point produced by one gram
of the substance dissolved in one hundred grams of the sol-
vent ; by J/ the molecular weight of the compound dissolved,
calculated by making in the atomic formula of this compound
supposing it to be an anhydride H=l, 0=16, etc.; by T
the molecular lowering of freezing i.e., the lowering of the
freezing-point produced by one moleculef of the substance
dissolved in 100 molecules of the solvent, we have :
MA = T.
I have found that if the solutions are dilute, and do not con-
tain more than one equivalent]; of substance to a kilogram of
water, all the organic substances in aqueous solution produce
a molecular lowering which is nearly constant, always lying
between 17 and 20, and which usually approaches the mean
T=IS.5; and I have shown (Ann. C/iim. Phys., January, 1883)
what use could be made of this fact for determining the molec-
ular weights of organic compounds soluble in water. I will
now show that analogous results are obtained with all solvents
which can be readily solidified, and that a very important gen-
eral law is connected with them.
In the researches which I shall discuss here, I have gener-
ally employed very dilute solutions, containing less than one
molecule of substance in two kilograms of water.
* Ann. Chim. Phys., [6], 2, 66.
f [By " one molecule >: is meant a number of grams of the substance equal
to the number expressing its ''molecular iceight."]
\ [By " equivalent " i* meant the same as " molecule." See above.]
71
MEMOIRS ON
The use of very dilute solutions oilers several advantages.
First, it makes it possible to avoid, for the most part, the er-
rors resulting from the more or less arbitrary opinions as to
the state of the substance in the solutions, and which result in
assigning to the solvent some molecules which, in most cases,
belong really to the dissolved substance. An example will
make this clear.
If I dissolve 6 grams of anhydrous magnesium sulphate
(Mg SO^=120) } i.e., -fa of a molecular weight, in 100 grams of
water, I produce a lowering of the freezing-point of 0.958.
But if we admit that 6.3 grams of the water are united with
the dissolved salt to form a hydrate with 7 H 2 (which appears
to me not very probable), the weight of the water acting as sol-
vent is reduced to 93.7 grams. We have, then, for the molecular
lowering of the salt :
T _ 0.958 x 120 x93.7 = 1? 95
GxlOO
If, on the contrary, we suppose that the dissolved salt exists in
the anhydrous state, we find :
y_0.958xl20_ 19 16
6
The digression is relatively only -fa ; and if the first value was
correct, this digression would still diminish with the more di-
lute solutions, until it almost completely disappeared. An-
other advantage, equally important, which results from using
very dilute solutions, is that a sufficient quantity of ice can be
produced during the experiment, without greatly changing the
concentration of the solution. The result is, the thermometer
remains stationary for a long time, usually for several minutes,
and the temperature indicated can be determined with the-
greatest precision.
Without compelling myself to make all of the solutions of the
same dilution (which would have unnecessarily increased the
difficulties), I have, as far as possible, made their dilution such,
that the lowering of the freezing-point should be between 1
and 2. This lowering is, indeed, quite sufficient, since it can
be determined to about -g-J-g- of a degree, as I have already ex-
plained. (Ibid.)
The solvents which I have employed in these researches
are :
72
THE MODERN THEORY OF SOLUTION
FREEZING-
POINT.
Water ............................... 0.00
Benzene ............................. 4,96
Nitrobenzene ......................... 5.28
Ethylene bromide. .................... 7.92
Formic acid .......................... 8. 52
Acetic acid ............... : . . . . ....... 16.75
Since in the experiments on the freezing-point the cooling is
sloiv, and since the liquid is constantly agitated, that portion
which solidifies appears in the form of glistening plates, or of
very small crystalline grains which float in the liquid. It is al-
ways the pure solvent which separates, at least at the beginning
of the freezing and under the conditions which I employed.
The freezing-point can thus be obtained by the process indicated,
with a very great degree of accuracy, as well when the solvent
is pure as wheli it contains a substance dissolved in it.
The lowering of the freezing-point due to the presence of a
foreign substance in one of these solvents, is always obtained
by taking the difference between the freezing-point of the solu-
tion and that of the pure solvent, determined in the same way,
and with only a short interval between the determinations. If
P is the weight of the solvent, P' that of the dissolved substance,
and K the lowering of the freezing-point as obtained experi-
mentally, we have for the coefficient of lowering A, (i. e., the
lowering produced by 1 gram of the substance in 100 grams of
the solvent) :
P' X 100
for all of the solutions of the dilution which I employed, thus
following the law of Blagden, at least approximately. The sub-
stances to be dissolved are used in as pure condition as possible,
and weighed with the usual precautions. If they are volatile
they are weighed in bulbs, which are afterwards broken by
shaking in the closed flasks containing a known weight of the
solvent.
SOLUTIONS IN ACETIC ACID.
Although acetic acid undergoes very marked undercooling, it
always freezes exactly at the same temperature when in contact
73
MEMOIRS ON
with a portion of the acid previously solidified. The crystals
formed, although heavier than the liquid, float in it during the
stirring, in the form of glistening plates. A bath of water con-
taining ice suffices to cool the acid, and it must be used in all
of the experiments.
Acetic acid can dissolve a large number of substances, partic-
ularly those of an organic nature. It is absolutely necessary
to use this acid completely dehydrated, i. e., without any water,
for those experiments which have to do with hygroscopic sub-
stances. But for other substances an acid such as is found
in commerce, containing from one to two per cent, of w^ater,
can be used without any inconvenience. The compounds to
be dissolved in the acid ought always to be dry and freed from
water of crystallization. Otherwise the water which they would
introduce into the solvent would complicate the results. We
can avoid the difficulty cf obtaining acetic acid absolutely
free from water by making several determinations, after having
added to the same liquid, in succession, new quantities of the
substance to be investigated. If the substance is very hygro-
scopic, the quantity first added generally takes up the water
dissolved in the acid, and gives a very small lowering. The
quantities next added find no more water present, and give a
constant lowering. It is the latter which is adopted. The fol-
lowing table contains a summary of my results :
TABLE L*
Freezing -Point Lowerings of Solutions in Acetic Acid.
SUBSTANCES DISSOLVED MOLECULAR
IN ACETIC ACID. FORMULAS. LOWERINGS.
Methyl iodide CH 3 1 38.8
Chloroform Off C1 3 38.6
Carbon tetrachloride C Cl 38.9
Carbon bisulphide OS 2 38.4
Hexane C 6 ff u 40.1
Ethylene chloride C 2 ff 4 C1 2 40.0
Oil of turpentine O lo ff ]6 39.2
* The molecular weights, M, and the lowering coefficients, A, are omitted
in this and the following tables ; their product, T, which is the value of im-
portance, being given.
74
THE MODERN THEORY OF SOLUTION
TABLE I. (Continued.)
Nitrobenzene .................. C 6 H 5 X0 2 41.0
Naphthalene .................. O 10 ff 8 39.2
Methyl nitrate ................. Cff 3 N0 3 38. 7
Methyl salicylate .............. C 8 H 8 3 39.1
Ether ........................ C\H W O 39.4
Ethyl sulphide ................ C\H 10 M 38.5
Ethyl cyanide ................. C 3 ff 5 N 37.6
Ethyl formate ................. O 3 H 6 2 37.2
Ethyl valerate ................. C \ H^ 2 39.6
Allyl snlphocyanate ............ <7 4 H 5 .>S' 38.2
Aldehyde ..................... C 2 H, 38.4
Chloral ....................... C' 2 HOC1 3 39.2
Benzaldehyde ................. 6' 7 H % * 39.7
Camphor ...................... O W R 16 39.0
Acetone ...................... C 3 H 6 38.1
Acetic anhydride ............... C^H 6 3 36.6
Formic acid ................... CH 2 2 36.5
Butyric acid ................... CH 8 2 37.3
Valeric acid ................... C 5 H }0 6 2 39.2
Benzoic acid .................. C,H 6 2 43.0
Camphoric acid ....... .- ........ C\ H 16 4 40.0
Salicylic acid .................. C,H 6 3 40.5
Picric acid .................... O 6 II 3 N 3 0, 39.8
Water ......................... H 2 33.0
Methyl alcohol ................. CH^ 35.7
Ethyl alcohol ................. C 2 R 6 36.4
Butyl alcohol .................. C\H IQ 38.7
Amyl alcohol .................. 5 H 12 39.4
Allyl alcohol ................... C 3 H 6 39.1
Glycerin ....................... C 3 ff 8 3 36.2
Salicin ........................ C 13 H 18 0, 37.9
Santonin ...................... C\ 5 H 18 3 38.1
Phenol ........................ C 6 ff 6 36.2
Pyrogallol ..................... O 6 H 6 3 37.3
Hydrocyanic acid ............... If ON 36.6
Acetamide ..................... C 2 H 5 NO 36.1
75
MEMOIRS ON
TABLE I. (Concluded.}
SUBSTANCES DISSOLVED
IN ACETIC ACID.
MOLECULAR
FORMULAS. LOWERINGS.
T=MA.
Ammonium acetate C 2 H^ N0 2 35.0
Aniline acetate C Q H U N0 2 36.2
Quinine acetate (7 24 N 32 N 2 6 41.0
Strychnine acetate C 23 H 2Q N 2 4 41.6
Brucine acetate C 25 H^ N 2 6 40.0
Codeine acetate (7 20 H 2r , N0 5 38.3
Morphine acetate C 38 H^ & N 2 }0 43.0
Potassium acetate C 2 H 3 K0 2 39.0
Sulphur monochloride S 2 01 2 38.7
Arsenic trichloride As CI 3 41.5
Tin tetrachloride Sn C1 4 41.3
Hydrogen sulphide H 2 S 35.6
Sulphur dioxide S0 2 38.5
ABNORMAL
LOWERINGS.
Sulphuric acid H 2 SO^ 18.6
Hydrochloric acid . . . II Cl 17.2
Magnesium acetate CH 6 Mg 18.2
An examination of the preceding table gives rise to two im-
portant remarks :
1. For substances dissolved in acetic acid there is a maxi-
mum molecular lowering, wliicli is 39. A few substances like
benzoic acid and morphine acetate, have, it is true, a low-
ering as great as 43 ; but everything points to the conclusion
that this extraordinary amount of lowering is only apparent,
and that it results from some chemical action, such, for exam-
ple, as the combination of the dissolved substance with some
molecules of the solvent.
2. Of the fifty-nine substances in this table, fifty-six have
a molecular lowering between 37 and 41, and always close to
39, which I take as the normal lowering. Only three give an
abnormal lowering, which is close to 18, and is nearly half the
preceding value. These three substances, which appear at the
end of the list, are of mineral nature, and it is to be observed
that they are very hygroscopic. Thus : The molecular lowering s
76
THE MODERN THEORY OF SOLUTION
produced by the different compounds in acetic acid approach two
numbers, 39 and 18, of which the one, produced in the great ma-
jority of cases, is obviously double the other.
SOLUTIONS IN FORMIC ACID.
The formic acid which I employed froze at 8. 52, present-
ing the same phenomena as acetic acid. The solvent power of
this acid appears to be just as great as that of acetic acid. It
seems to be even greater for the compounds soluble in water.
But its high price and the difficulty of obtaining it again from
the solutions have prevented me from making very extensive
experiments with it. Table II. gives a resume of the results
obtained.
TABLE II.
Freezing- Point Lowerings of Solutions in Formic Acid.
Chloroform CHC1 3 26.5 '
Benzene C G H 6 29.4
Ether C^H 10 28.2
Aldehyde O 2 ff,0 26.1
Acetone C^H 6 27.8
Acetic acid C 2 H 2 26.5
Brucine formate C u H 28 N 2 G 29.7
Potassium formate CH K0 2 28.9
Arsenic trichloride As C1 3 26.6
ABNORMAL
LOWERING.*
Magnesium formate C 2 H0 4 Mg 13.9
The above table gives rise to two remarks already made for
acetic acid :
1. There is a maximum of molecular lowering of the freezing-
point for substances dissolved in formic acid, which is about 29.
2. The molecular loiverings of the freezing-point produced
by the different compounds in formic acid approach the two
numbers 28 and 14, the one being twice the other.
* [Unimportant note omitted.]
77
MEMOIRS ON
SOLUTIONS IN BENZENE.
The benzene sold under the name of crystallizable benzene, and
which freezes at about 5, is nearly chemically pure, and very
well adapted for use. The results which it gives do not differ
from those obtained with the purest benzene made from benzoic
acid. The undercooling which is always produced, as in the
preceding liquids, is removed by contact with a particle of solid
benzene, and small opaque crystals of benzene are seen to in-
crease in number immediately, which, although more dense than
the liquid, float in it during the stirring.
The results obtained are summarized in the following table :
TABLE III.
Freezing -Point Lowerings of Solutions in Benzene.
SUBSTANCES DISSOLVED LOWKMNG?
IN BENZENE. FORMULAS. p-WA
Methyl iodide ...../.. Cff 3 1 50.4
Chloroform , CH C1 3 51.1
Carbon tetrachloride C7 4 51.2
Carbon bisulphide C 8 2 49.7
Ethyl iodide 2 H 5 I 51.0
Ethyl bromide C 2 H 5 Br 50.2
Hexane O 6 H U 51.3
Ethylene chloride C 2 H 4 C1 2 48.6
Oil of turpentine O ]Q H 16 49.8
Nitrobenzene C 6 H 5 N0 2 48.0
Naphthalene C\ Q H Q %Q.O
Anthracene C u H ]n 51.2
Methyl nitrate C H 3 N0 3 49.3
Methyl oxalate O,H 6 0^ 49.2
Methyl salicylate C B H B 3 51.5
Ether " C\H 10 49.7
Ethyl sulphide O^H^S 51.8
Ethyl cyanide C 3 ff 5 N 51.6
Ethyl formate O 3 H 6 2 49.3
Ethyl valerate C^H^0 2 50.0
Oil of mustard C\H 5 N8 51.4
Nitroglycerin O 3 N 3 H 5 9 49.9
78
THE MODERN THEORY OF SOLUTION
TABLE III. (Continued.)
SUBSTANCES DISSOLVED
IN BENZENE.
FORMULAS.
Tributyrin C }5 H 26 6
Triolein C 51 # ]04 6
Aldehyde C, H 4
Chloral C 2 HOC1 3
Benzaldehyde C\ H 6
Camphor C w H }6
Acetone C 3 H 6
Valerone C 9 H^
Acetic anhydride C 4 H 6 3
Santonin. C\ 5 ff^ 8 3
Picric acid C 6 H 3 N 3 0,
Aniline C B H^N
Narcotine C 22 H 23 JV r 7
Codeine C lB H 2l ^0 3
Thebaine C 19 H 2l N0 3
Sulphur monochloride S 2 C1 2
Arsenic trichloride. . . As C1 3
Phosphorus trichloride P C1 3
Phosphorus pentachloride P C1 5
Stannic chloride Sn Cl
Methyl alcohol CH,
Ethyl alcohol, C 2 H 6
Butyl alcohol O^ff lo O
Amyl alcohol C 5 H 12
Phenol C 6 H 6
Formic acid CH 2 2
Acetic acid C 2 H0 2
Valeric acid C 5 H w 2
Benzoic acid C- H Q 2
MOLECULAR
LOWERINGS.
T=MA.
48.7
49.8
48.7
50.3
50.1
51.4
49.3
51.0
47.0
50.2
49.9
46.3
52.1
48.7
48.0
51.1
49.6
47.2
51.6
48.8
ABNORMAL
LOWERINGS.
25.3
28.2
43.2
39.7
32.4
23.2
25.3
27.1
25.4
This table gives rise to the same remarks as the preced-
ing.
1. For substances dissolved in benzene there is a maximum
lowering of the freezing-point. This maximum lowering appears
79
MEMOIRS ON
to be about 50. Some lowerings, it is true, are a little above
this figure, but the difference seems to me to be due either to
impurities or to some action exerted upon the solvent.
2. For the hydrocarbons and their derivatives, the ethers,
aldehydes, acetones, acid anhydrides, glucosides, alcaloids,
and chlorides of the metalloids, the molecular lowering of the
freezing-point in benzene lies between 48 and 51, and always
approaches 49, a number which ought to be considered the
mean normal molecular lowering in benzene. As to the alco-
hols, phenol, and the acids (that is, the compounds which con-
tain hydroxyl), their molecular lowering in benzene generally
lies between 23 and 27, and approaches the mean 25, a number
which is obviously half the mean of the normal lowering.
The only hydroxyl compound which produces the normal low-
ering in benzene is picric acid ; but we know that this acid
forms a definite compound with the benzene, thus making it
an exceptional substance. Two or three alcohols give an in-
termediate lowering. We thus see that in benzene, as in the
preceding solvents, the molecular loiverings of the freezing-point
of the different compounds are grouped around two values, 49
and 25, the one being, obviously, twice the other.
It should be observed that the smaller of these two values,
which appears, only exceptionally with acetic and formic acids,
occurs more frequently when benzene is used as solvent.
SOLUTIONS IN KITKOBENZENE.
It is difficult to find commercial nitrobenzene sufficiently
pure for these experiments. I prepared the specimen which
I used. For this purpose I treated pure benzene with nitric
acid, at only a slightly elevated temperature, so as to entirely
avoid the production of dinitrobenzene. The product, washed
with sodium carbonate and water, was separated by fractional
distillation from the excess of benzene and other impurities.
The nitrobenzene thus obtained distils completely at 205,
and freezes at 5. 28. Nitrobenzene, like the preceding sol-
vents, undergoes undercooling, and in contact with a solidified
particle of the same substance it freezes in the form of small
crystals, which, notwithstanding their great density, float in
the liquid during the stirring.
The law relating to the molecular lowerings produced by the
80
THE MODERN THEORY OF SOLUTION
different substances in a given solvent being clearly estab-
lished by the preceding experiments, I limited myself to ascer-
tain whether it is verified with nitrobenzene. I obtained the
following results :
TABLE IV.
Freezing- Point Lowerings of Solutions in Nitrobenzene.
MOLECULAR
SUBSTANCES DISSOLVED FORMULAS. LOWERING*.
IN NITROBENZENE. T MA
Chloroform C H C1 3 69.9
Carbon bisulphide CS 2 70.2
Oil of turpentine C\ Q H IB 69.8
Benzene C 6 H 6 70.6
Naphthalene C\ ff 8 73.6
Ether C\H W 67.4
Ethyl valerate C~,H U 2 73.2
Ethyl acetate CH Q 2 72.2
Beuzaldehyde O, H 6 70.3
Acetone. C 3 H 6 69.2
Codeine C\ B H 2} ^0 3 73.5
Arsenic trichloride As C1 3 67.5
Stannic chloride Sn Cl 71.4
ABNORMAL
LOWERINGS.
Methyl alcohol CHJ) 35.4
Ethyl alcohol C, H 6 35.6
Acetic acid C 2 H0 2 36.1
Valeric acid C S H W 2 42.4
Benzoic acid C-H 6 2 37.7
\Ve see that the effects produced in nitrobenzene by com-
pounds of the different chemical types, are exactly analogous
to those which the same substances produce in benzene.
There is a maximum of the molecular lowering, which appears to
be close to 73, for the substances which do not act chemically upon
the solvent.
The hydrocarbons and their substitution products, the
ethers, aldehydes, and acetones, and the chlorides of the
metalloids, produce in nitrobenzene lowerings which always
lie between 67 and 73, in general about 72.
F 81
MEMOIRS ON
The alcohols and the acids (i. e., the hydroxyl compounds)
give molecular lowerings in nitrobenzene between 35.5 and
2.2, and generally about 36, which is equal to half the preced-
ing number.
SOLUTION'S IN ETHYLEN"E BROMIDE.
The ethylene bromide which I used froze at 7. 92, giving
crystalline opaque plates heavier than the liquid. Like all the
other solvents which can be frozen, it always undergoes under-
cooling, but to a less extent. Its solvent power is, as it ap-
peared to me, exactly analogous to that of benzene and chloro-
form. It undergoes a slow change, which in two or three days
lowers its freezing-point to an appreciable extent. The solu-
tions ought, therefore, to be always made just before they are
used. I limited myself to proving by some experiments that
the laws observed in the preceding cases are applicable here.
The following results were obtained :
TABLE V.
SUBSTANCES DISSOLVED MOLECULAR
IN ETHYLENE BROMIDE. FORMULAS. LOWEHING8.
_/ At A .
Carbon bisulphide ,...,,.. CS 2 116.6
Chloroform CH C1 3 118.4
Benzene O 6 H 6 119.2
Ether C\ff w O 117.5
Arsenic trichloride , As C1 3 118.1
ABNORMAL
LOWERINGS.
Aceticacid C 2 H^0 2 57.7
Alcohol C 2 H 6 56.8
Therefore :
1. There is a maximum of molecular lowering in ethylene
bromide, which is approximately 119.
2. The molecular lowerings produced by different compounds
in this solvent, approach the two values 118 and 58, the one being
double the other; a result similar to those which we have ob-
served with all the preceding solvents.
THE MODERN THEORY OF SOLUTION
AQUEOUS SOLUTIONS.
As I have observed elsewhere, water is the only solvent
which was employed by my predecessors, and the metallic
salts the only substances which were dissolved in it. The re-
sults obtained, although numerous and remarkable, especially
from the point of view of the existence of saline hydrates in
the solutions, do not admit of general conclusions. It is right
to recall, however, that De Coppet has recognized that the salts
of the same chemical constitution have nearly the same molecular
lowering ; an important result which is the first clew to the great
law to which the phenomenon conforms. (Ann. Chim. Phys.,
[4], 25.) After this remark De Coppet divided salts into
five groups, as follows, having nearly the same molecular low-
ering :
MOLECULAK
LOWE1UNGS.
(1) Chlorides and hydrates of potassium and sodium. 34
(2) Chlorides of barium and of strontium 45
(3) Nitrates of potassium, sodium, and ammonium. . . 27
(4) Chromate, sulphate, carbonate of potassium; sul-
phate of ammonium 38
(5) Sulphates of zinc, magnesium, iron, copper 17
The results pertaining to salts in aqueous solution present,
therefore, a peculiar complication, which we have not met with
in the other solvents. However, the lowerings produced in wa-
ter appear discordant only when they are examined closely and
separately. As soon as we consider all of the effects produced,
not only by the salts (which behave in a very special manner),
but also by the soluble oxides, by the mineral acids, and
especially by the organic substances, we recognize also here
the manifestation of the general law. This will be seen from
the following table. I have not introduced the salts of the
metals whose atomicity is greater than 2, because they all ap-
pear to undergo more or less decomposition in water :
MEMOIRS ON
TABLE VI.
Lowering of the Freezing -Point of Aqueous Solutions.
IN . _
Hydrochloric acid . , . ....... . . . // Cl 39.1
Hydrobromic acid ..... .... ---- H Br 39.6
Nitric acid ................... H N0 3 35.8
Perchloric acid ........ ....... H Cl <9 4 38.7
Arsenic acid (?) ............... H 3 As 4 42.6
Phosphoric acid ..... .... ..... ff 3 P0 4 42.9
Sulphuric acid ---- . . .......... H 2 S0 38.2
Selenious acid ............. . . . Se 2 42.9
Hydrofluosilicic acid . . ........ H 2 SiF Q 46.6
Potassium hydrate ...... ,,.... KOH 35.3
Sodium hydrate ............... Na OH 36.2
Lithium hydrate .............. Li OH 37.4
Potassium chloride ............ K Cl 33.6
Sodium chloride .............. Na Cl 35.1
Lithium chloride .............. Li Cl 36.8
Ammonium chloride . . . . ....... NH 4 Cl 34.8
Potassium iodide .............. KI 35.2
Potassium bromide ............ K Br 35.1
Potassium cyanide ............. K CN 32.2
Potassium ferrocyanide ........ KFe (CN) 6 46.3
Potassium ferricyanide ........ K^Fe (CN) 6 47.3
Sodium nitroprussiate ......... Na Fe(CN) 5 NO 46.8
Potassium sulphocyanate . . . ---- K CNS 33.2
Potassium nitrate ............. K N0% 30.8
Sodium nitrate ............... Na N0 3 34.0
Ammonium nitrate ............ Nff 4 N0 3 32.0
Potassium formate ............ K C H 2 35.2
Potassium acetate ............. K C 2 H 3 2 34. 5
Sodium acetate ............... Na C 2 H 3 2 32.0
Potassium carbonate ........... K 2 C0 3 41.8
Sodium carbonate ............. Na z CO^ 40.3
Potassium sulphate ............ K 2 S0 39.0
Acid potassium sulphate ....... KHSO 34.8
Sodium sulphate .............. Na 2 S0 4 35.4
Ammonium sulphate .......... (NH} 2 S0 4 37.0
84
THE MODERN THEORY OF SOLUTION
SUBSTANCES DISSOLVED
IN WATER.
TAIJLE VI. (Continued.}
FORMULAS.
MOLECULAR
LOWERING S.
Sodium tetraborate (borax) .... Xa 2 B 4 7 66.0
Potassium chromate ........... K 2 Or 38.1
Potassium bichromate ..... .... K 2 Cr 2 T 43.7
Disodium phosphate .......... Xa 2 H PO^ 37.9
Sodium pyrophosphate ........ Xa 4 P 2 0- 45.8
Potassium oxalate ............. K 2 C 2 46.8
Sodium oxalate ............... Xa 2 C 2 4 43.2
Potassium tartrate ............ K 2 C\H 6 36.3
Sodium tartrate ............... Xa 2 C\ H 6 44.2
Acid sodium tartrate .......... XaH C\ H 4 6 31.2
Barium hydroxide ............. Ba(OH) 2 49.7
Strontium hydroxide .......... Sr(OH) 2 48.2
Calcium hydroxide ............ Ca (OH) 2 48.0
Barium chloride .............. Ba C1 2 48.6
Strontium chloride ............ Sr CI 2 51.1
Calcium chloride .............. CaCl 2 49.9
Cupric chloride ............... Cu CI 2 47.8
Barium nitrate ................ Ba (X0 3 ) 2 40.5
Strontium nitrate ............. Sr (X0 3 ) 2 41.2
Calcium nitrate ............... Ca (X0 3 } 2 37.4
Lead nitrate .................. Pl> (NO^) 2 37.4
Barium formate ............... BaC 2 H 2 0^ 48.2
Barium acetate ............... BaC^H^O^ 48.0
Magnesium acetate ............ Mg C 4 H 6 47.8
ABNORMAL
LOWERINGS.
Sulphurous acid .............. S0 2 20.0
Hydrogen sulphide ........ ____ H 2 S 19.2
Arsenious acid ................ H 3 As 3 20.3
Metaphosphoric (?) acid ....... HP 3 21.7
Boric acid .................... H 3 B0 3 20.5
Potassium antimonyl tartrate. .. KSbG\H. f Ot 18.4
Mercuric cyanide .............. Hg (CX) 2 17.5
Magnesium sulphate ........... Mg 80^ 19.2
Ferrous sulphate .............. Fe S0 18.4
Zinc sulphate ........ ......... Zn S0 4 18.2
Copper sulphate.. ............. CuSO^ 18.0
85
MEMOIRS ON
TABLE VI. (Concluded.)
Organic Compounds*
T=MA.
Methyl alcohol ..... ........... CII.O 17.3
Ethyl alcohol ................. C 2 H 6 O 17.3
Butyl alcohol ................. O 4 H W O 17.2
Glycerin ..................... C 3 ff 8 3 17.1
Mannite ...................... O 6 H U O 6 18.0
Dextrose ..................... C 6 H 12 6 19.3
Milk sugar ................... C 12 H 22 O u 18.1
Salicin ....................... 6' 13 // 18 0, 17.2
Phenol ....................... C 6 H 6 15.5
Pyrogallol .................... O 6 H 6 O, 16.3
Chloral hydrate ............... C 2 C1 3 H 3 2 18.9
Acetone ...................... O 3 H 6 O 17.1
Formic acid .................. H,C0 2 19.3
Acetic acid ................... C 2 ff^0 2 19.0
Butyric acid .................. O,H Q O 2 18.7
Oxalic acid. . . ................ C Z H 2 22.9
Lactic acid ................... C 3 H 6 O L 19.2
Malic acid . . . . ................ C\H 6 5 18.7
Tartaric acid ................. QH 6 6 19.5
Citric acid .................... C G H Q 0~, 19.3
Ether ........................ C 4 H }0 O 16.6
Ethyl acetate ................. V 4 H 8 2 17.8
Hydrocyanic acid ............. H CN 19.4
Acetamide ................... C 2 H 5 NO 17.8
Urea .......................... CON 2 H, 17.2
Ammonia ..................... A 7 /T 3 19.9
Ethylamine .................. C 2 NH 7 18.5
Propylamine .................. C 3 NH 9 18.4
Aniline ...................... C 6 NH 7 15.3
Notwithstanding the variations which are much larger than
with the other solvents, we find here also the laws previously
observed.
* [This table is taken from Ann. Cliim. Pliys., (5), 28, 137 (1883).]
86
THE MODERN THEORY OF SOLUTION
For the compounds which are not dissociated in water there is
a maximum of the molecular lowering, which is about 47.*
The molecular lowerings of some salts which are not decom-
posable by water are, it is true, larger than this value. But
this arises, in a great measure, from the fact that they are
referred to substances which we suppose to be anhydrous,
while these really exist as hydrates in the solutions. As an
example, the molecular lowering of barium chloride is 48.6
when we suppose this salt to be anhydrous in the solutions,
but falls to 46.9 when we suppose it to exist in the solutions as
the hydrate Ba C7 2 4-2 H 2 O, as Rlidorff thinks it does. Some
deviations ought also to be attributed to impurities.
Two compounds are exceptions to this law, if we adopt for
them molecular weights which are double the equivalents, as
most modern chemists are inclined to do. These are : potas-
sium ferricyanide and sodium nitroprussiate. As a matter of
fact, with the formulas K 6 Fe 2 (CN) l2 and Na 4 (NO) 2 Fe 2 (C^V) lQ
we find for the molecular lowering of each of these sub-
stances a value which is exactly double the maximum, 47.
But these formulas do not appear to be necessary for the
explanation of the chemical properties of these substances, and
nothing is opposed, as far as I know, to assigning to them,
at least in solution, the formulas K-^Fe (CN) 6 and Na 2 NO-
Fe (CN) 5 , which correspond to the maximum molecular lower-
ing. The only serious objection resulting from the formula
/i" 3 Fe ((Ly) 6 is that potassium ferricyanide appears to be a sub-
stance containing an odd number of unsaturated bonds. But
this anomaly is found in some other compounds e. g., in alu-
minium ethyl and it alone is not a sufficient reason for con-
demning a formula which agrees so well with the physical facts.
I have, therefore, adopted for these substances molecular
weights equal to the equivalents.
A glance at the figures in the last column of the preceding
table shows that the molecular lowerings of the freezing-point of
icater are grouped around the two numbers 37 and 18.5, the one
being double the other; so that the law observed with acetic
* Borax, which decomposes in water, as Berthelot has shown (Median.
Chim., II., 224), appears in the table with a molecular lowering of 66. But
this number is, in reality, the sum of the molecular lowerings of the acid
and base into which the original salt decomposes, and each of these ap-
pears in the law enunciated.
87
MEMOIRS ON
acid, formic acid, benzene, nitrobenzene, and ethylene bromide,
still manifests itself, although less clearty, when water is used
as a solvent.
One fact shows clearly the simple relation which exists, even
in water, between the normal and abnormal lowerings. The
solution of anhydrous phosphoric acid in water, made in the
cold, has, for more than an hour, a molecular lowering of 21.7.
If it is boiled and the liquid brought to the original volume by
adding water, we find that the molecular lowering is about
44.2, that is, it is doubled.
The molecular lowerings of all the salts of the alkalies and
alkaline earths, of all the strong acids and bases, are grouped
around the mean normal lowering 37. The abnormal molec-
ular lowering 18.5 belongs to some salts of the bivalent metals,
to all the weak acids and bases, and, without exception, to all
of the organic compounds which are non-saline.
CONCLUSIONS.
Several important propositions follow from the mass of facts
recorded in this paper:
1. Every substance, solid, liquid, or gaseous, when dissolved
in a definite liquid compound capable of solidifying, lowers its
freezing-point. This fact, which it was impossible to foresee,
and of which it will be very interesting to know the cause, is ab-
solutely general. The exceptions which arc observed are only
apparent and are easily explained. Thus, when we dissolve
anhydrous stannic chloride in acetic acid containing a little
water, each molecule of the chloride combines with two mole-
cules of water forming only one molecule of the hydrate. In-
stead of two molecules in solution, there is, therefore, only one,
and an elevation of the freezing-point necessarily results ; for,
as we shall see later, the amount of lowering depends only upon
the relation between tlie number of molecules of the dissolved
substance and of the solvent.
But such an effect is due entirely to the reciprocal action of
the dissolved substances. It is never produced when the solv-
ent is a definite compound, free from impurities. It results
lfrom the above principle that : of two specimens of a substance,
that one is purer which solidifies or melts at the higher tem-
perature.
88
THE MODERN THEORY OF SOLUTION
This furnishes an excellent means, unfortunately limited in
its applicability, of examining the purity of substances.
2. There is in each solvent a maximum molecular lowering of
the freezing-point. This maximum lowering is about 47 in
water, 36 in acetic acid, 29 in formic acid, 50 in benzene, 73 in
nitrobenzene, 119 in ethylene bromide.
This fact can be applied directly to the determination of a
certain number of molecular weights. Given a compound whose
molecular weight it is desired to know ; we determine its co-
efficient of lowering, A, in one of the. preceding solvents, then
divide the maximum molecular lowering of the solvent em-
ployed by A, and we obtain the maximum of the molecular
weight. We know, besides, that the molecular weight corre-
sponds to the simplest atomic formula of the compound ex-
amined, or to a whole multiple of this formula. Whenever,
then, the maximum found is not twice the molecular weight
corresponding to the simplest atomic formula, the latter ought
to be adopted.
3. The molecular lowerings of the freezing-point of all the
solvents, produced by the different confounds dissolved in them,
approach two mean values, wliicli vary with the nature of the solv-
ent, the one being twice the other. These mean values are 117
and 58 for ethylene bromide, 72 and 36 for nitrobenzene, 49
and 24 for benzene, 39 and 19 for acetic acid, 28 and 14 for
formic acid, 37 and 18.5 for water. The larger of the two
lowerings, which I call normal lowering, is produced much more
frequently than the smaller, and in all the solvents studied,
with the exception of water, it is obviously identical with the
maximum molecular lowering. In formic and acetic acids it
appears almost constantly. In benzene, nitrobenzene, and
ethylene bromide, it is produced by all substances which do
not contain hydroxyl, and consequently by all substances which
have a constitution analogous to that of the solvents. In water
it is produced by the strong acids, and by the salts whose acid
or base is monatomic.
The substances which produce normal or abnormal lowering
in a given solvent belong to well-defined groups, and this fact
can also be utilized for the determination of MOLECULAR
WEIGHTS. All the salts of the alkalies in solution in water
give a molecular lowering which is approximately 37. If, then,
we have to choose between several numbers which are multiples
MEMOIRS ON
of one another, for the molecular weight of a salt of an alkali,
we choose that one which, multiplied by the coefficient of
lowering of the salt in water, gives the number nearest to 37.
Similarly, with respect to the organic substances soluble in
water, that molecular weight is to be adopted which, multi-
plied by the coefficient of lowering in water, gives the num-
ber nearest to 18.5 (Ann. Chim. Phys., January, 1883). All
organic substances in solution in acetic acid give a molecular
lowering of about 39. The formula which must be adopted for
an organic compound soluble in this solvent is, then, that
which corresponds to the molecular weight the closest to the
number obtained by dividing 39 by the coefficient of lowering
of this substance in acetic acid. As most of the compounds
are soluble either in water or in acetic acid, this method fur-
nishes the means of establishing the molecular weights in a large
number of cases. If necessary, the coefficients of lowering in
benzene, or in other solvents, can be turned to account. There
are, then, but few compounds, whatever their nature, whose
molecular weight cannot be established by the method of freez-
ing the solvents. But I must not enlarge further upon this
subject here, and shall return to it in a special work. It suf-
fices to have indicated this important application.
Returning to the experimental facts already stated, we can
explain them by admitting that : In a constant weight of a given
solvent, all the physical molecules, whatever their nature, produce
the same lowering of the freezing-point. According to this hypoth-
esis, when the dissolved substances are completely disintegrated,
as they would be in a perfect vapor, and when each physical
molecule contains only one chemical molecule, the molecular
lowering is a maximum, and the same for all. When the chemi-
cal molecules are united in pairs, to a greater or less extent, form-
ing a certain number of double physical molecules, the lowering
produced is less than if the condensation had not taken place,
since each of these double molecules produces the same effect
as one simple molecule. If all of the chemical molecules
are united in pairs, the lowering is half the maximum. The
abnormal lowerings in almost all of the solvents correspond to
this condition. When water is employed as solvent, we observe
certain number of abnormal lowerings, which are considerably
less than half the maximum lowering. This shows that the
condensation can proceed still further. The exceptionally small
90
THE MODERN THEORY
lowering of phenol and pyrogollol in water can be explained by
assuming that the molecules of these substances are united in
groups of three. To explain all of the facts observed, it there-
fore suffices to apply to the constitution of dissolved substances
the hypotheses admitted by all for the constitution of vapors.
The preceding considerations explain the effects produced
by different compounds in a given solvent; but they indicate
nothing as to the value of the lowering produced by a given
compound in different solvents.
In order to bring out the law relating to the nature of the
solvents, it is necessary to reduce the .results by calculation
to the case of 1 molecule of each substance dissolved in 100
molecules of the solvent This is accomplished by dividing
the molecular lowering of each substance, T, by the molecular
weight of the solvent, M'. Indeed, the molecular lowerings
are those produced by 1 molecule of a foreign substance in 100
i < K )
grams, or iuj -^-, molecules of the solvent. Moreover, from the
' Jj
law of Bla^en, the lowerings are, ceteris paribus, inversely
proportional to the quantities of solvent which contain 1. mole-
cule dissolved in them. We have then, calling T' the lowering
produced by 1 molecule dissolved in 100 molecules :
from which : 77
T' __ .
~M'
If, then, we divide the molecular lowerings indicated above by
the molecular weights of the solvents to which they refer, we
reduce the results to the case of 1 molecule of the dissolved
substance in 100 molecules of the solvent. Below are the re-
sults obtained by introducing into the calculation the values
of 7* corresponding to a maximum molecular lowering :
Maximum Molecular Lower-
Molecular Maximum Molecular ing Divided by the Molec-
Weights towering Produced ular Weight of the Solvent,
Solventa of by 1 Molecule iu 100 or Lowering Produced by 1
Solvents. Grams. Molecule in 100 Molecules.
Water .......... 18 47 2.61
Formic acid ..... 46 29 0.63
Acetic acid ...... 60 39 0.6o
Benzene ......... - 78 50 0.64
Nitrobenzene ---- 123 73 0.59
Ethylene bromide 188 119 0.63
91
MEMOIRS ON
Leaving out of the question for the moment water, which be-
haves in a peculiar manner, we see that the maximum lowering
of the freezing-point, which results from the action of 1 mole-
cule dissolved in 100 molecules of solvents, varies only from
0.59 to 0.65, mean 0.63, and is consequently nearly the same
in all of the solvents. This fact is the more remarkable since
the molecular lowerings which enter into the calculation vary
considerably namely, in the ratio of 1 to 4. It is, moreover,
reasonable. In fact, whatever is the nature of the action ex-
erted between the molecules of the solvent and those of the
dissolved substance, it seems that it ought to be mutual ; and
if the effect is independent of the nature of the dissolved sub-
stance, it ought probably to be independent also of the nature
of the solvent.
Water is the only exception ; but it is not astonishing on the
part of a liquid which presents so many other peculiarities. To
explain the anomaly, it is allowable to suppose that each of the
physical molecules of which water is composed, is formed of
several chemical molecules united with one another. At the
time when I had found only a few molecular lowerings in
aqueous solutions larger than the mean lowering 37, I believed
that the physical molecules of water were formed of 3 chemical
molecules. Indeed, by dividing 37 by 18x3, we obtain 0.685,
which is not very far removed from the mean value 0.63 obtained
with other solvents. This I have observed in a previous pub-
lication {Compt. rend., November 27th, 1882). But, in the
light of new determinations, it is no longer possible to consider
as doubtful the molecular lowerings which are much larger
than 37, and I am compelled to recognize that the molecular
lowerings in water can be even as great as 47, a maximum
value in most cases where the dissolved substances do not
decompose. Such a lowering can be explained by admitting
that the molecules of water are united in groups of four, at least
in the neighborhood of zero. Then, indeed, 47 divided by
18x4 is 0.65, which is remarkably near the mean 0.63 obtained
with other solvents.
The anomalies relating to solvents, like those relating to dis-
solved substances, can then be explained by the condensation
of the molecules, and they do not prevent us from expressing
the GENERAL LAW OF THE FREEZING OF SOLVENTS, as follows :
molecule of any substance, is dissolved in 100 molecules of
92
THE MODERN THEORY OF SOLUTION
any liquid of a different nature, the lowering of the freezing-
point of this liquid is always nearly the same, and approxi-
mately 0.G3.
Consequently, the lowering of the freezing-point of a dilute
solution of any strength whatever is, obviously, equal to the prod-
uct obtained by multiplying 63 by the ratio between the number
of molecules of the dissolved substance and that of the solvent.
Let us recall, iu conclusion, that the molecules with which
we are here dealing are physical molecules, which, in certain
cases, can be formed by two or several chemical molecules
united with one another.
r
.* ,
^
V
<*
A/ ._
/ I \t
' ^
AW IV
<&
UNIVE RSITT
ON THE VAPOR-PRESSURE OF ETHEREAL
SOLUTIONS
BY
F. M. RAOULT
Professor of Chemistry in Grenoble
(Annales de Chimie et de Physique, [6], 15, 375, 1888)
CONTENTS
PACK
Method of Work 97
Influence of Concentration on the Vapor- Pressure of Ethereal Solutions. 105
General Results 110
Laws Pertaining to Dilute Solutions 112
Particular Expression of the Law Pertaining to Dilute Solutions 113
Influence of Temperature on the Vapor- Pressure of Ethereal Solutions. . 114
Influence of the Nature of the Dissolved Substance on the Vapor- Pressure
of Ethereal Solutions 116
Another Expression of the Law 119
ON THE VAPOR-PRESSURE OF ETHEREAL
SOLUTIONS*
BY
F. M. RAOULT
I DISCOVERED some time ago (Compt. rend., July 22, 1878) that
a close relation exists between the lowering of the vapor-press-
ures of aqueous solutions, the lowering of their freezing-points,
and the molecular weights of the dissolved substances. This
observation was the starting-point for my researches on the
freezing-point of solutions (Compt. rend., 94 to 1O1), and it
is this which now leads me to undertake a similar piece of
work on their vapor-pressures.
I employed, first, ethereal solutions, since they lend them-
selves easily to this kind of study. To simplify the question
I shall consider here only the case where the vapor-pressure of
the dissolved substances is very small, and is negligible with
respect to that of the ether. In a subsequent investigation I
shall examine the more general case, where the dissolved sub-
stances themselves have a considerable vapor-pressure.
I determined the vapor-pressures of these kinds of solutions
by the method of Dalton. I measured with the cathetometer
the heights to which the mercury is raised in the barometric
tubes, the one containing only mercury, the other, in addition,
a small quantity either of pure ether or of ether in which were
dissolved different substances which are nearly non-volatile.
Before making the measurements I shook all of the solutions,
moistening well the walls, and not until ten minutes later did
I proceed with the measurements, the temperature remaining
constant. In the calculation of the results I have taken care
to add to the pressure of the mercury in each tube the pressure
* Ann. Chim. Phys., [6], 15, 375 (1888) ; Ztschr. Phys. Chem., 2, 353(1888).
G 97
MEMOIRS ON
which arises from the small column of ether, or of ethereal
solution, which is placed upon it. I have even taken the pre-
caution to correct the concentration of the solutions for the
small quantity of ether separated as vapor.
The quantities upon which all of the comparisons are based,
and which are to be determined, are : the vapor-pressure of the
pure ether,/, and the vapor -pressure of the ether containing
the dissolved substance, /', the temperature remaining the
same. To determine these quantities as accurately as possi-
ble, I worked as follows :
Preparation of the Ether. Pure commercial ether was taken,
and after washing it with water it was shaken several times
with a concentrated aqueous solution of caustic potash. It
was digested over calcium chloride and distilled in a Le Bel
and Henninger apparatus with eight bulbs. The portion
which distils at a constant temperature was left in contact with
thin fragments of sodium for forty-eight hours, in a balloon
flask provided with a condenser with eight bulbs. It was then
distilled a second time. Nearly all of it distilled at 34. 7 under
760 millimetres pressure. Regnault gave 34. 97 as the boiling-
point of ether.
Regnault says that he had considerable trouble in obtaining
an ether which was always exactly the same. He observed this
substance undergo change by prolonged boiling under slight
pressure. He observed it undergo change even at the ordi-
nary temperature, in a flask hermetically closed and freed
from air. The change was manifested only by a change in
the vapor -pressure (Mem. de I'Acad. des Sciences, 26, 1862).
Perhaps this change resulted from the fact that the ether
used by Regnault, which had not been distilled from sodium,
contained traces of water or of ethyl peroxide. Lieben (Ann.
CJiem. Pharm., 165) was not able to prove the presence of any
trace of alcohol, even after a year, in ether distilled from sodium
and preserved in a closed vessel. For my part, I found that
pure ether, preserved for five months in a barometric tube at
ordinary temperatures, had, at 15, exactly the same vapor-
pressure as at the beginning. It is not certain but that ether,
even when very pure, undergoes a more or less rapid change in
the flasks in which it is preserved, and into which the air always
penetrates a little. This lowers its vapor-pressure and gives it
the property of soiling mercury. It is, therefore, necessary to
THE MODERN THEORY OF SOLUTION
use it immediately after it has been distilled from sodium. I
have always done this. I do not, however, think that the
ether which I employed was absolutely pure. It contained,
indeed, a small quantity of a gas which appeared to me to be
a hydrocarbon, and from which I never succeeded in completely
freeing it. This compelled me to employ very long tubes, as
will be seen later.
Preparation of the Solutions. The substances which I dis-
solved in ether were chosen from those whose boiling-points are
above 160, and their vapor-pressure at the ordinary tempera-
ture was scarcely 6 millimetres of mercury. It is therefore
a simple matter to work with them. To make solutions of
known strength, a certain quantity of the substance is weighed
in flasks of 20 centimetres capacity, provided with good corks.
A sufficient quantity of ether is then poured into each of these
flasks, which are now closed and reweighed. The increase in
weight is the weight of the ether. In preparing dilute solu-
tions i. e., solutions containing only a small quantity of non-
volatile substance this is weighed in thin-walled bulbs, which
are afterwards broken by shaking in the flasks containing a
known quantity of ether, which is large with respect to the
amount of substance.
Choice of Barometric Tubes. I employ tubes of colorless
glass, and of about 1 centimetre internal diameter. The capil-
lary effect in such tubes is not zero, but we endeavor to make it
constant throughout the entire length of the tube by choosing
the tubes as nearly cylindrical as possible. This does not pre-
vent the determination of its exact value and correcting the re-
sults accordingly, as we will see later. After having cleansed
and dried the interior of the tubes, they are drawn out at 90
centimetres from the end to a long tube, which is bent about
the middle in the form of a hook. An elliptic ring of not
very stout platinum wire is shoved clear up to the top of each
of these, and remains there by virtue of its elasticity. This is
used to stir the interior liquid.
Filling the Tubes. To fill one of these tubes it is thrust into
a deep mercury bath, the drawn-out end being kept above the
bath. When it is almost entirely immersed in the mercury,
the descending limb of the bent tube is inserted in a small flask
containing the ethereal solution which it is desired to introduce
into the tube. The tube and flask are carefully raised and the
99
MEMOIRS ON
solution is quickly drawn into the tube. When this liquid has
reached a depth of about 3 centimetres in the cylindrical por-
tion of the tube, the flask is removed, and without raising the
tube farther the point is closed with a burner a few millimetres
from the ethereal solution. It is now necessary to expel the
gases adhering to the walls,
or dissolved in the liquid,
without losing any trace of
ether by evaporation.
To accomplish this the
barometric tube is raised
nearly out of the deep bath,
leaving the end only 1 to
2 centimetres under the
mercury. By means of two
hot irons placed against the
tube the solution is boiled
with sufficient rapidity, and
long enough to drive the
mercury down to the bot-
tom. The heating is then
discontinued, and the tube
again thrust into the deep
bath. When the mercury in the interior is on the same plane
as that on the exterior, the end of the fine point is cut off with
scissors, and then the tube is slowly thrust farther into the
bath. The ethereal solution enters the capillary portion, and,
when it is only a few millimetres from the end, this is closed
with a blow-pipe. The same operation is begun again, then a
third time, when there remains in the tube only a trace of gas,
which, under atmospheric pressure, generally occupies not more
than 3 to 4 millimetres. The influence which this small quan-
tity of gas exerts on the heights of the mercurial columns is
negligible in my experiments. Finally, the tube thus pre-
pared was removed to a special mercury bath, wide, and shal-
low, where it could be observed.
Arrangement for Stirring the Contents of the Tubes. In the
barometric tubes thus prepared, the ethereal solutions, and
ether itself if not absolutely pure, tend constantly to lose
their homogeneity, due to changes in temperature and to the
atmospheric pressure. If the volume of the vapor diminishes,
100
Fig. i
THE MODERN THEORY OF SOLUTION
due to these variations, a certain quantity of ether vapor con-
denses in each tube, which results in a dilution of the upper
portions of the liquid layers in contact with the vapor. The
opposite effect is produced if the volume of the vapor increases.
If, therefore, care is not taken, the vapor-pressures observed cor-
respond to solutions whose concentration is uncertain, and more
or less different from that of the original liquids. To avoid this
source of error, not pointed out up to the present, I have always
been careful to shake the liquids several minutes before deter-
mining their vapor-pressure. At first I seized each tube in suc-
cession with wooden forceps, and inclined it until the ether came
in contact with the top. I then righted it again, and repeated
this several times. I use now the following arrangement, which
gives the same result more rapidly and more conveniently :
The mercury bath, in which the barometric tubes rest, is of
cast-iron, wide and shallow, and firmly supported on a column
of masonry. On its upper edge is a screw-nut in which a screw
10 centimetres long is held vertically, its lower point just
touching the surface of the mercury. The barometric tubes,
generally six in number, rest upright on a narrow shelf im-
mersed in the mercury of the bath, and which forms the lower
part of an iron frame, to which they are fastened by iron wire.
The frame can rock with all the tubes which it carries, turning
on its base as a hinge, without the end of the tubes coming out
of the bath. We are thus able, by inclining the frame and
righting it several times, to shake, simultaneously, the solutions
contained in all the tubes which it carries, and to wet the walls
quite up to the top. The small rings of platinum wire, which
are placed up in the top of the tubes, facilitate the stirring very
much. The tubes, having been restored to the vertical position,
are left to rest for about ten minutes, when the heights are
measured.
The necessity of agitation can be easily demonstrated by
experiment. Two tubes, the one containing pure ether, the
other an ethereal solution, having been placed side by side,
are not disturbed for a day or two. The difference between
the heights of the mercurial columns is then measured. The
tubes are then shaken, and fifteen minutes after the shak-
ing we almost always find considerable increase in this differ-
ence, even when the temperature has remained absolutely the
same. The increase in the difference is sometimes fa.
101
MEMOIRS ON
On the other hand, I have convinced myself many times that
the difference of vapor-pressure in two given tubes is exactly
the same at the same temperature, provided the measurement
is made after agitation and in the manner just described.
Regulation of the Temperature. We always work at the tem-
perature of the laboratory, but this is so arranged that the
temperature can vary between certain limits or remain almost
completely stationary. The laboratory is small, is on the north
side, and the sun never shines into it. It is heated by a gas-
stove, provided with a thermo-regulator whose reservoir con-
tains 50 litres of air. The air of the laboratory is constantly
stirred by the swinging of the door of a closet, which acts as a
fan. Thermometers placed to the right, and left, above, and
below the barometric tabes constantly indicate the same tem-
perature, and this often remains constant for hours to nearly
fy of a degree.
Measurement of the Heights of the Mercurial Columns. The
heights of the mercury in the different tubes are measured
by means of an excellent cathetometer, of 1.50 millimetres
range, giving fiftieths of a millimetre. This instrument rests
firmly on a column of masonry covered with an iron plate. The
tubes to be observed are placed between the cathetometer and
a well-lighted glass door, so that the tops of the mercury col-
umns stand out clearly in black against a light background.
The end of the screw in contact with the mercury in the bath
can be as easily seen, and we are able without difficulty to de-
termine the vertical distance between the upper point of this
screw and the level of the mercury in each tube. A normal
barometer placed in the same room gives the atmospheric
pressure.
Method of Observation. We choose a moment for the obser-
vation when the temperature and atmospheric pressure are as
constant as possible. The tubes containing the solutions are
shaken, and after ten minutes the observations are begun. The
temperature never being exactly constant, the levels are never
absolutely stationary. Notwithstanding all this, to obtain very
accurate results, recourse is had to the method of alternate ob-
servations. Two tubes are observed alternately from minute
to minute, the one containing pure ether, the other an ethereal
solution, until the heights in two successive observations do not
differ more than 0.2 millimetre. If the heights found, in three
102
THE MODERN THEORY OF SOLUTION
consecutive observations on each tube, are in arithmetical pro-
gression, the observations are regarded as satisfactory, and the
mean of them is taken. A single observation, made at the end,
gives the height of the mercury in the tube containing the pure
ether. Another gives the height of the barometer.
These quantities being determined, it only remains to know
the depressions of the mercury due to capillary action, and to
the weight of the liquid added, in order to calculate the vapor-
pressures, /and /', of pure ether, and of the solution under
consideration.
Correction for the Depression of the Mercury Due to the
Liquid Placed Above It and to Capillarity. After having
made all the observations desired on a tube, it is transferred
to a deep bath whose upper walls are of glass. It is lowered
to 1% its length, and held in this position by means of a stand
and clamp. Finally, the slender drawn-out end is cut. The
air enters the tube and the mercury within descends below
the level in the bath. Enough water is then carefully poured
on the mercury of the bath to bring the top of the column of
mercury in the tube exactly to the same plane as the mercury
in the bath. The height of water added is a measure of the
sum of the pressures, due to the weight of liquid placed over
the mercury, and to capillarity. It is easy to estimate it in
terms of height of mercury column.
Let H be the height of the barometer, *Ji the height of the
mercury in the tube containing pure ether, and a the column
of mercury equivalent to the weight of liquid placed above
it, and to capillarity ; h f and a' the corresponding quantities
for the tube containing the ethereal solution ; t) the difference
between the heights of mercury in the two tubes, so that
c lili, all the heights being reduced to zero.
We have, for the vapor-pressure of pure ether, / :
/ H h a-,
and for the vapor-pressure of the ethereal solution examined,
Error Produced by the Gaseous Residue. I have stated that
ether purified as was indicated contains a small quantity of gas
in solution, from which it is very difficult to free it completely.
To eliminate as much as possible the influence of this trace
of gas on the heights of the mercurial columns, I have found
103
MEMOIRS ON
nothing better than to allow the vapor formed to occupy a
large volume. This is the reason why I ^employ very long
tubes, in which the vapor formed occupies always a volume of
at least 20 centimetres. Even under these conditions the in-
fluence of the gaseous residue is not zero. If, for example, this
residue occupies a volume of 5 cubic millimetres under atmos-
pheric pressure, it will produce a pressure of 0.19 millimetre
in a volume of 20 centimetres ; and the resulting error in the
measurement of vapor-pressure is nearly T 2 ^ of a millimetre,
which is still appreciable. However, as all of the tubes are pre-
pared in the same manner, and since they contain nearly equal
quantities of the same ether, the volume of the gaseous residue
is everywhere nearly the same. The influence exerted by this
residue on the heights of the mercurial columns, therefore, dis-
appears for the most part in the differences, or even in the ratios.
Error Arising from the Solutions Becoming More Concen-
trated, Due to the Formation of Vapor. The weight of ether
which separates from the solution as vapor, to saturate the rela-
tively large empty space presented to it, is often sufficient to
appreciably change the concentration. But it is possible to
calculate the amount with sufficient accuracy, and, notwith-
standing this, to know the true concentration of the solution in
contact with the vapor.
If we represent by n and ri the weights of non-volatile sub-
stance dissolved in 100 grams of ether, before and after the
production of vapor, we have :
) 76000000'
in which I is the length in centimetres which the ether-vapor
occupies in the tube ; I', the length occupied by the solution ;
d, the density of ether-vapor referred to air (d 2.57) ; d', the
density of the solution ; /', the elastic force of the vapor of the
solution ; t, the temperature ; a=0.00367.
In the exact calculations n' ought to be substituted for n ;
but if the temperature is not high, and if the solutions are
dilute, the correction is reduced to a mere trifle.
If, for example, we have approximately :
n=I5, 1=30, f =300, * = 16, 7=3, d'=O.SO,
it becomes :
w'=1.01 + w.
104
THE MODERN THEORY OF SOLUTION
That is, the formation of the vapor in this case increases the
concentration about y^-. The correction would be greater
if the temperature were higher and the solution more concen-
trated. I estimate that, all corrections made, the vapor-press-
ures, /and /', of the ether and of the ethereal solution, can be
obtained to 0.2 of a millimetre.
Influence of Concentration on the Vapor- Pressure of Ethereal
Solutions. I could have wished, for the sake of greater sim-
plicity, to have been able to experiment on solutions obtained
by mixing absolutely non-volatile substances with the ether.
Unfortunately, nearly all of the substances soluble in all pro-
portions in ether have an appreciable vapor -pressure at the
ordinary temperature, and the best I could do was to select for
my experiments those substances whose vapor-pressure was the
smallest.
These are :
BOILING-POINTS.
o
Oil of turpentine 160
Nitrobenzene 205
Aniline 182
Methyl salicylate 222
Ethyl benzoate 213
At a given temperature the vapor-pressures of the last four
substances are less than that of the oil of turpentine, which is
known from the experiments of Regnault, and which, in the
neighborhood of 15, is not one-ninetieth of that of the ether.
Besides, as I shall show later, they are considerably diminished
in the ethereal solutions, and they do not prevent the manifes-
tation of the general laws which govern the phenomena.
In the following tables :
The first column gives the weight, Q, of substance dis-
solved in 100 grams of solution. This is equal to - ,, in
which p' is the weight of substance mixed with a weight p of
ether.
The second column gives the number, n, of molecules of
substance existing in 100 molecules of the solution. This is
equal to *^ , in which 74 is the molecular weight of
p X 74 x pm
ether, and m that of the dissolved substance.
105
MEMOIRS ON
The third column indicates the experimental value of the
ratio
f
, between the vapor-pressure of the solution/' and that
of pure ether /at the same temperature. This ratio has been
multiplied by'lOO.
The fourth column gives the values of ^j x 100, calculated
from the formula :
in which the coefficient Ovaries with the nature of the sub-
stance dissolved in the ether.
Mixtures of Oil of Turpentine and Ether.
Number of Molecules
of Oil in 100 Mole-
cules of Mixture.
Temperature of the experiments 16. 2
Vapor-pressure of the oil of turpentine at the tem-
perature of the experiments 4 mm.
Vapor-pressure of pure ether at the same temperature 377 mm.
Ratio her ween the Vapor-Press-
ure of the Mixture and that
of Pure Ether, Multiplied
by 100, or t- x 100.
N Observed. Calculated.
(2) (3) (4)
5.9 94.0..
12.1 88.1..
23.4 78.1 78.9
50.3 35.5 67.6 68.0
62.8 47.9 56.2 56.9
64.5.. ..42,1.. ..42.0
Weights of Oil in
100 Grams of
Mixture.
Q
(i)
10.2
20.2
35.9..
94.7
..89.1
The values of ^-x 100, in the last column, were calculated by
means of the formula :
4 X 100 = 100- 0.90 x^V.
This is the equation of a straight line having = x 100 for ordi-
nates, and N for abscissae, i. e., the number of molecules of
substance contained in 100 molecules of the mixture.
106
THE MODERN THEORY OF SOLUTION
The agreement between the results observed and calculated
is as satisfactory as could be desired.
Remark. The oil of turpentine after it has been distilled
for some time soils mercury very badly. To have it in proper
condition I pour a certain quantity of mercury in the flask in
which it is contained, and after closing the flask I expose it to
the sun, and shake from time to time. After eight days I dis-
til over magnesium, in a condenser with two bulbs, and I use
the product which passes over at 159 as soon as it is obtained.
Mixtures of Nitrobenzene and Ether.
Temperature of experiment ....................... 16
Vapor-pressure of nitrobenzene at the temperature of
experiment .................................. 2 mm.
Vapor-pressure of pure ether at the same temperature 374 mm.
Nitrobenzene, prepared from pure benzene, was purified at
first by distillation. A few days before using it it was re-
purified by repeated crystallizations. It was nearly colorless.
Weights of Nitro-
benzene in
100 Grams .of
Mixture.
Q
(i)
9.6
Number of Molecules Ratio between the Vapor-Press-
of Nitrobenzene in ure of the Mixture and that
100 Molecules of of Pure Ether, Multiplied
Mixture - by 100 or /x 100
y , f ,
N Observed. Calculated.
(2) (3) (4)
6.0 94.5 95.6
26.7
17.9....
85.8
86.8
47.2
35.5.. .
. 74.4
..73.7
65.4
53.2
62.0
60.6
80.9..
..75.9..
. 44.4. .
..43.8
88.5 84.0 35.5 37.8
f
The calculated values of '? xlOO, in the fourth column of
this table, were obtained by means of the formula :
^-x 100 = 100-0. 74 xN.
They evidently agree closely with those furnished by obser-
vation.
107
MEMOIRS ON
Mixtures of Aniline and EtJier.
Temperature of the experiments ................... 15. 3
Vapor-pressure of aniline at this temperature ....... 3 mm.
Vapor-pressure of ether at this temperature ........ 364 mm.
The aniline was prepared from pure nitrobenzene and puri-
fied by distillation. It was colorless.
Ratio between the Vapor-Press-
Weights of Ani- Number of Molecules ur e of the Mixture and that
line in 100 Grams of Aniline in 100 <> f P ur e Ether, Multiplied
of Mixture. Molecules of Mixture. by 100, or f- x 100.
Q
(i)
4.8..
N
(2)
3.85..
Observed.
(3)
96.0
Calculate
(4)
96.6
9.5..
18.1..
7.7 ..
14.8 ..
91.9
84.5
93.1
86 7
24.5..
55.3..
73.4..
20.5 ..
49.6 ..
..68.7 .
80.3
57.6
40.4..
81.6
55.4
..38.2
f
The calculated values of ^ x 100, in the fourth column, were
obtained by means of the formula :
^-x 100=100-0.90 xN.
They agree fairly well with the results of observation.
Mixtures of Methyl Salicylate and Ether.
Temperature of the experiments 14. 1
Vapor-pressure of methyl salicylate at this tempera-
ture 2 mm.
Vapor-pressure of ether at the same temperature. . . . 346 mm.
108
THE MODERN THEORY OF SOLUTION
Weights of Sali-
Number of Molecules
nauo oeiwee
Tivfni*i oir1 +Voi-
cylate in
100 Grams of
of Salicylate in 100
Molecules of
of Pure Ether, Multiplied
Mixture.
Mixture.
by 100,
or-L_x 100.
Q
N
Observed.
Calculated.
(1)
(2)
(3)
(4)
2 256
1.1 .
99.6. . .
99.1
4 20
. . 2.1. .
.. . 99.3...
98.3
9 4
.. 4.8
.. . 96.0...
96.1
17.3
. .. 9.2
91.4...
92.5
26.8 . .
15.1
. . . . 87.0. . .
87.6
38 6
.23.2
81.1...
81.0
66.4 . .
49.0
.... 60.0...
59.8
87.3 . .
77.0
.... 36.1...
36.9
91.4
..85.0
.... 29.2...
30.3
The
f
values of ^ X 100,
fourth column, were
obtained by means of the formula:
-Cx 100 =100 0.82
The agreement between the calculated and the observed re-
sults is quite remarkable.
Mixtures of Ethyl Benzoate and Ether.
C 9 ffio 2 = 150.
Temperature of the experiments 11. 7
Vapor-pressure of ethyl benzoate at this temperature. 3 mm.
Vapor-pressure of pure ether at the same temperature 313 mm.
The ethyl benzoate was purified by the ordinary method. It
nearly all distilled over at 213.
Weights of Ethyl Number of Molecules
ienzoaie in
Grams of
100 Molecules of of Pure Ether,Multiplied
Mixture.
Mixture.
by 100, or
'x 100.
Q
N
Observed.
Calculated.
(1)
(2)
(3;
(4)
9.4....
4.9..
94.9
95.6
17.7....
9.6..
90.9
91.4
43.0....
27.1..
75.2
75.6
69.6....
53.0..
52.9
52.3
86.2....
75.5..
30.0
32.1
97.1....
94.4..
12.4
15.0
109
MEMOIRS ON
f
The calculated values of ~ x 100, in the last column, were
obtained with the aid of the formula :
fj x 100 = 100-0.90 x N-,
and here, also, they agree satisfactorily with the values found
by experiment.
General Results. We see that for the different mixtures
studied the results obtained agree pretty well, as a whole,
with the results calculated by means of the formula :
(1) x 100=100-
in which N is the number of molecules of non-volatile sub-
stance existing in 100 molecules of the mixture, and K a co-
efficient which depends only upon the nature of the substance
mixed with the ether.
It should be observed that the coefficient ./T generally varies
but little with the nature of the dissolved substance, and it is
usually very nearly unity. Its values for the following sub-
stances are :
Oil of turpentine in ether ............ K 0.90
Aniline in ether ..................... K ' 0.90
Ethyl benzoate in ether .............. K= 0.90
Methyl salicylate in ether ............ K '= 0.82
Nitrobenzene in ether ................ K = 0.70
I made similar experiments on mixtures of carbon bisulphide
with different substances as slightly volatile as the above.
These experiments, an account of which will be given later,
f
prove that the ratio ~ varies, in this case, with the concentra-
tion, according to the same laws as in the ethereal solutions ;
and that in formula (1), which sums them up, the coefficient
K is also a little less than unity. This formula ought, there-
fore, until the contrary is proven, to be considered as applica-
ble to the calculation of the vapor -pressures of all volatile
liquids employed as solvents.
We will now avail ourselves of it to determine to what extent
the preceding results are modified by the vapor-pressure of the
substances mixed with the ether.
Influence of the Vapor- Pressure of the Substances Mixed witli
110
THE MODERN THEORY OF
the Ether. Let ^ be the vapor-pressure which the dissolved
substance possessed when pure; ^', the vapor -pressure of the
same substance when mixed with the ether ; N' t the number
of molecules of ether in 100 molecules of the mixture.
The vapor-pressure /' of an ethereal solution, being the sum
of the partial pressures of the ether and of the dissolved sub-
stance, the partial pressure of the ether vapor in the mixture
is /*'_ 0. But from formula (1), which finds here a legitimate
application :
From this we have :
or in dividing by/, the tension of pure ether:
(3)
f -f f 100
fl _ ,'
the exact value of the ratio J f , which exists between the
vapor - pressures of the ether in the mixture, and when pure,
is obtained, therefore, by cutting off the term y(l
f
from the crude ratio y
But in all of the preceding experiments the ratio ~ between
the tension of the dissolved substance and that of the ether,
both considered as pure, is less than ^. The correction term
~ 1 1 -) is, therefore, always less than ^, and it becomes
/ \ 100 /
less than jfa for the values of N' which are greater than 50.
It is, consequently, always negligible in comparison with the
experimental errors. The influence of the vapor - pressure of
the substances mixed with the ether is, therefore, too slight to
be introduced as a correction into the results obtained.
Causes of Error in Concentrated Solutions. There are some
differences between the results observed and those calculated
by formula (1), and these appear especially with very concen-
trated or very dilute solutions.
As far as the very concentrated solutions are concerned, in
111
MEMOIRS ON
which Nis greater than 70 i. e. 9 in which there are more than
70 molecules of non-volatile substance to 100 molecules of
mixture the differences are perhaps due only to errors of ex-
periment. The determinations then become very difficult in-
deed. In such mixtures the proportion of ether is very slight,
and however little ether is lost by evaporation during the trans-
fer, a loss which is inevitable, the solutions become more con-
centrated and their vapor-pressures too small. Moreover, it may
happen that the liquid layers in contact with the vapor in the
barometric tubes, become more concentrated than the deeper
layers, notwithstanding the shaking ; and in this case, again,
their vapor-pressure would be too slight.
Laws delating to Dilute Solutions. For solutions which are
dilute and in which N is less than 15, the differences disappear
for the most part if in formula (1) K is made equal to 1.
Indeed, in this case the results of experiment agree nearly al-
ways to -g-J-g- with those given by the formula :
(4) ^-'xioo=ioo-jv.
To show this important fact, I give in the following table the
results calculated by means of this formula (4), together with
the results observed with different dilute solutions, for which
15 :
SUBSTANCE DIS- MOLECULAK CON- J_
100.
SOLVED IN CENTRATION. /
DIFFER-
ETHER.
A~.
CALCULATED.
OBSERVED.
ENCE.
Oil of turpentine.
j 5.9
(12.1
94.1
87.9
94.0
88.1
sir
sir
Nitrobenzene
6.0
94.0
94.5
Th
Aniline
j 3.85
( 7.7
96.2
92.3
96.0
92.3
T*F
r 1.1
98.9
99.6
T!T
Methyl salicylate.
97.9
95.2
99.3
96.0
iWr
I 9.2
90.8
91.4
6
Ethyl benzoate. ..
{ t:l
95.1
90.4
94.9
90.9
~-Q-$
We see that the difference between the results observed and
calculated seldom exceeds -^ of their value. There is an
112
THE MODERN THEORY OF SOLUTION
exception only for extremely dilute solutions i. e., those in
which N is less than 2, which seem to follow a more compli-
cated law. But it appears to me to be hardly possible to make
any assertion regarding them ; determinations of this kind be-
coming more and more difficult and uncertain as the dilution
increases.
Formula (4) is, therefore, in accord with experiment, as far
as could be desired, as long as the values of N are between
2 and 15.
Comparison with the Law of Wtillner. Different physicists,
and particularly Von Babo and Wiillner, have shown that for
certain solutions of salt in water the relative diminution of
ff
pressure is practically proportional to the weight of salt
dissolved in a constant weight of water. This can be expressed
by the formula :
(5) xlOO = 100-JTJrx-^,
K being a constant coefficient for each substance.
This expression differs considerably from formula (4) ; but
it should be observed that the latter applies especially to
ethereal solutions, for which N>3. Often when _Y<3, for-
mula (4) applied to aqueous solutions gives results which are too
large, and then formula (5) advantageously replaces it. Besides
this special case, formula (5) gives, even for aqueous solutions,
information which is more and more erroneous as N becomes
f
greater. In addition, it leads to negative values for J when
wx. 10
TV >^ -, which is absurd.
These variations very probably result from the fact that the
condition of the substance in the solutions changes with the
concentration ; and we ought to be astonished that, notwith-
standing all this, we can express the vapor-pressure f of the
ethereal solutions by means of two relations which are also sim-
ple ; the one, (1), giving the values of /' at least to about ^,
for all the values of A^from to 70 ; the other, (4), giving them
to about y^j- for all the values of N between 3 and 15.
Particular Expression of the Law relating to Dilute Solu-
tions. Formula (4), relating to dilute solutions, acquires an
interesting form if were place ^Vby 100 JV', the quantity N
H 113
MEMOIRS ON
being the number of molecules of ether contained in 100 mole-
cules of the mixture. This formula then becomes transformed
into the following :
(6) xlOO = JV',
which is to say that, in ethereal solutions of medium concentra-
tions, the partial pressure of the ether vapor is proportional to the
number N', of molecules of ether existing in 100 molecules of the
mixture, and is independent of the nature of the dissolved sub-
stance. I shall return again to the last point.
Influence of Temperature on the Vapor - Pressure of Ethereal
Solutions. To study the influence of temperature I placed
four barometric tubes, containing the dilute solutions obtained
by mixing different high-boiling substances with the ether, in
the same mercury bath for several months. I then measured
the vapor-pressure very carefully whenever the circumstances
were favorable. Although in this interval the temperature
varied from to 22, I always found approximately the same
f
value for the ratio
Some of the results obtained are collected in the following
tables, t is the temperature,/ the vapor-pressure of pure ether,
and/' the vapor-pressure of the solution.
Mixture of 16.482 Grams of Oil of Turpentine and 100 Grams of Ether.
t f f ^XlOO
l.l 199.0 188.1 '.91.5
3.6 224.0 204.7 91.4
18.2 408.5 368.7 91.0
21.8 ,.472.3 430.7 91.2
Mixture of 10.442 Grams of Aniline with 100 Grams of Ether,
t f f ^xlOO
l.l 199.5 183.3 91.9
3.6 223.2 204.5 91.6
9.9 289.1 264.0 91.3
21.8 472,9 432.7 91.5
114
THE MODERN THEORY OF SOLUTION
Mixture of 27.601 Grams of Hexachlorethane with 100 Grams of Ether.
t f f xlOO
1.0 197.0 181.3 92,0
3.7 224.2 205.4 91.6
18.8 418.6 280.9 91.0
21.0 457.3 417.8 91.4
Mixture of 12.744 Grams of Benzoic Acid and 100 Grams of Ether.
t f f xlOO
j j f
3.8 224.1 209.5 93.5
18.4 412.6 382.0 92.6
21.7 470.2 431.2 91.7
These tables show that for the solutions of oil of turpentine,
of aniline, of hexachlorethane, the value of the ratio ^ does
not vary more than 0.5 in 100, when the temperature changes
from to 21. This variation is very slight and scarcely ex-
ceeds that often observed in two consecutive experiments, made
on the same solution under the same conditions.
The variation for the solution of benzoic acid is a little
greater, but this, perhaps, depends upon a chemical reaction
which takes place in time between the substances mixed with
one another.
It is worth observing that the influences of the vapor-press-
ure of the substances mixed with the ether is, even here, en-
f
tirely incapable of appreciably modifying the ratio, ~. The
f
quantity by which '- is increased is, indeed, as indicated by
formula (3) :
* L KN'\
( IST/'
But for the oil of turpentine, which is the most volatile of
all, we have :
115
MEMOIRS ON
Moreover, in all of these solutions we have JV> 90 and K is
approximately 1. The result is that the quantity, (q), to be
f
subtracted from - is :
s
< 0.00108 at
< 0.00106 at 20 ;
that is, it is completely negligible in comparison with this ratio,
which is here almost unity. It can all the more be rejected for
the other solutions.
Finally, the preceding experiments show that the ratio
f
' is independent of the temperature between and 21.
Influence of the Nature of the Dissolved Substance on the
Vapor-Pressure of Ethereal Solutions. The vapor-pressure,/',
of a solution of a non-volatile substance in ether, the vapor-
pressure of the pure ether,/, at the same temperature, and the
number, N, of molecules of non-volatile substance existing in
100 molecules of the mixture, are, as we have already seen,
united by the equation :
(1) =yx 100=100-.
We can give to this expression the following form :
(7) = *?.
/ 100
The ratio , being what is called the relative diminution of
vapor-pressure of the solution in question, formula (7) can be
translated into ordinary language thus :
For all of the ethereal solutions of the same nature, the relative
diminution of vapor-pressure is proportional to the number of
molecules of non-volatile substance dissolved in 100 molecules of
the mixture.
We have seen, also, that where the solutions are dilute, and
where N is less than 15, the coefficient K is unity, and we
have :
That is, if we divide the relative diminution of pressure : ^~
of a dilute ethereal solution by the number, N, of molecules of
116
THE MODERN THEORY OF SOLUTION
non-volatile substance existing in 100 molecules of the mixture, we
obtain as a quotient 0.01, whatever the nature of this substance.
With a view to ascertain whether this remarkable law is gen-
eral, I dissolved in ether compounds taken from the different
chemical groups, and chosen from those whose boiling-points
are the highest ; the compounds having molecular weights
which are very widely different from one another; and I meas-
ured the vapor-pressures of the solutions obtained. In every
ff
case I found, as we will see, that the ratio ' ' is very nearly
0.01, as is required by formula (8).
The substances which I employed are, for the most part, well
known to chemists, and it would be uninteresting to state here
how they were prepared and purified. I shall, therefore, limit
myself to giving some particular information in reference to the
rarest of them, which are methyl nitrocuminate and cyanic acid.
The methyl nitrocuminate, C 22 H 26 N 2 4 =382, was prepared
from a beautiful sample of very pure nitrocuminic acid, ob-
tained by M. Alexeyeff. This acid was introduced into pure
methyl alcohol, and a current of hydrochloric -acid gas was
passed through the alcohol. When the reaction was over, the
liquid was evaporated to dryness. Finally, the product ob-
tained was purified by several crystallizations from methyl
alcohol. This is a beautifully crystallized substance, of an
orange-red color, giving with ether a nearly red solution. Its
molecular weight, established with certainty by the cryoscopic
method, is very high, and this is the reason which led me to
use it.
Cyanic acid, HOCN=4=3, was prepared in the open air when
it was very cold, by distilling dry and pure cyanuric acid. After
nitration, it was introduced at 3 into a tared vessel with
thin walls which had been previously exhausted. This vessel
was weighed, then broken in a known weight of very cold
ether. The solution obtained was introduced into a baro-
metric tube, and the air and gases dissolved in it were care-
fully extracted, always in the cold. The vapor-pressure of the
solution was measured first at 1. To my great surprise the
ethereal solution contained in the barometric tube was not
changed, even after two days, at the temperature of +6, and
I was able 'to make several determinations at this temperature
which confirmed the results of the first.
117
MEMOIRS ON
Some substances, particularly those containing chlorine, not-
withstanding the most careful purifications, still have the very
inconvenient property of soiling mercury. To deprive them
of this property it is only necessary to expose them to the sun
in contact with mercury, in completely filled bottles, shaking
them from time to time. Exposure for a few days generally
suffices, if the light is intense.
The following table summarizes the results which were ob-
tained at about 15, with solutions containing from 4 to 12
molecules of non-volatile substance to 100 molecules of mixt-
ure. In this table :
Column (1) contains the names of the slightly volatile sub-
stances dissolved in the ether ;
Column (2) gives the chemical formula and the molecular
weight, M, of these substances ;
Column (3) shows the number of molecules of substance dis-
solved in 100 molecules of mixture ;
ff
Column (4) contains the values of the ratio, , i. e., the
relative lowerings of vapor-pressure ;
ff
Column (5) gives the values of the quotient, ^
(1) (2)
Hexachlorethane C Z C1 6 = 237
Oil of turpentine. C lo H 16 = 136
Nitrobenzene <7 6 U 5 N0 2 = 123
Methyl salicylate <? 8 ff s 3 = 152
Methyl nitrocuminate. . . C.^ H^ JV 2 4 = 382
Ethyl benzoate C 9 H 10 O a = 150
Cyanic acid CNOH=4S
Benzoic acid C 7 H 6 2 = 122
Trichloracetic acid <7 2 Cl a 2 II 163.5
Benzoic aldehyde C, H 6 = 106
Caprylic alcohol C s H 19 = 130
Aniline C 6 H,N=m
Mercury ethyl C^H to ffg=25S
Antimony chloride Sb C1 3 = 228.5
A'
-~
~f-
(3)
(4)
(S)
7.93
0.00288
0.0100
8.95
0.0885
0.0099
600
0.1424
0.0084
9.20
0.086
00094
2.91
0.026
0.0089
9.60
0.091
0.0095
4.52
0.041
0.0091
7.175
0.070
0.0097
11.41
0.120
0.0105
12.98
0.132
0.0102
6.27
0.070
0.0110
7.66
0.081
0.0106
9.75
0.089
0.0091
4.27
0.037
0.0087
Mean
0.0098
I have given, intentionally, the results relating to solutions
118
THE MODERN THEORY OF SOLUTION
which were of very different concentrations, and in which N
varied from 3 to 13. Notwithstanding this, the values of . '
deviate relatively little from the mean 0.0098, and this mean is
itself remarkably near to the theoretical value, which is 0.0100.
This suffices to show that formula (8) expresses, with as much
accuracy as we could expect, the law of vapor-pressures of ethe-
real solutions, within the limits of concentration indicated.
Another Expression of the Laiv. This law can be presented
in still another way :
If R is the number of molecules of non-volatile substance
dissolved in 100 molecules of ether, we have :
100 x R
~
Substituting this value for JVin (8), it becomes :
/ /' 1
TTT "loo+TT
As R decreases i. e., as the solution becomes more dilute
ff
the ratio' ..; tends, therefore, towards 0.01, just as the ratio
ff
' . ' ; and experiment shows that it generally reaches this value
as soon as R=.\. We can therefore say:
If we dissolve 1 molecule of any non-volatile substance in 100
molecules of ether, the vapor-pressure of the ether is diminished
by a fraction of its value which is nearly constant, and approx-
imately equal to 0.01.
It is, indeed, in this form that I at first stated the law relat-
ing to the vapor -pressures of the ethereal solutions (Compt.
rend., December 6, 1886). But the statement corresponding
to formula (8) is more exact and more general.
Determination of Molecular Weights. It is possible to turn
to account the preceding results in order to determine the
molecular weights of only slightly volatile substances which
are soluble in ether.
Let P be the weight of a relatively non- volatile substance
dissolved in 100 grams of ether ; 74, the molecular weight of
ether; M, the molecular weight of the dissolved substance; N,
the number of molecules of non-volatile substance dissolved in
100 molecules of mixture.
119
MEMOIRS ON
We have :
N 74xP
100 lOOx Jf+74xP
N
Substituting this value of -^ in (4), it becomes, when finally
1UU
transformed :
(10) Jf=
for the molecular weight, M, of the substance dissolved in the
ether.
It is clear that the value of M, thus calculated, can be only
approximate. But if the boiling - point of the dissolved sub-
stance is higher than 140, this value is always sufficiently
close to the true value to determine the choice between sev-
eral possible molecular weights. It is not even necessary for
this purpose that the solutions be very dilute ; and we always
obtain results which are sufficiently exact, observing only this
condition, that the weight, P, of substance dissolved in 100
grams of ether is not greater than 20 grams.
Below are some examples, taken at random, which give an idea
of the degree of approximation usually reached by this process :
Oil of Turpentine.
In one experiment I had :
Weight, P, of oil (100 grams of ether) ........... 11.346 gr.
Vapor-pressure of the solution/' ................ 360.1 mm.
Difference between the vapor-pressure of ether and
that of the solution//' ................... 22.9 mm.
These values introduced into formula (10) gave :
M=132.
But we know that the true value of M for oil of turpentine is
136. The difference is only 1 in 34.
Aniline.
Weight, P, of aniline in 100 grams of ether ...... 10.442 gr.
Vapor-pressure of the solution /' ................ 210.8 mm.
Difference between the vapor-pressure of ether and
that of the solution / /' ................... 18.8 mm.
from which: Jf=87,
a value which is nearer to the true molecular weight, 93, than
to any other possible value.
120
THE MODERN THEORY OF SOLUTION
Ethyl Benzoate.
Results of experiment :
P= 21.517 gr.
/'=284.5 mm.
/-/'= 28.6 mm.
Result: . Jf=159.2,
which differs from the true molecular weight, 150, by 1 part
in 15.
Benzole Acid.
Results of experiment :
p= 12.744gr.
/'-382.0 mm.
/-/'= 28.9 mm.
from which : Jf=124.6,
instead of 122, which is the exact molecular weight.
We see from these examples, that by observing the vapor-
pressure of an ethereal solution, we can easily ascertain which
of several possible values is the true molecular weight of a sub-
stance.
I do not believe, however, that it is often advantageous to
have recourse to this new means of determining molecular
weights. It is, indeed, rather delicate to carry out, and is suc-
cessfully applicable only to substances which boil above 140.
Besides, the cryoscopic* method, based on the observation of the
freezing-point of solutions in water, in acetic acid, or in ben-
zene, furnishes a means of arriving at the same result, which is
incomparably.easier, more exact, and more general. It is, there-
fore, only in the exceptional case that the substance under con-
sideration is insoluble in acetic acid and soluble in ether that
it is, perhaps, expedient to make use of the method based on
the measurement of the vapor-pressure of ethereal solutions.
I shall show in a subsequent paper that the same laws apply
to the vapor -pressure of all volatile liquids, whatsoever, em-
ployed as solvents, also to the volatility of the dissolved sub-
stance itself, and I shall deduce from them the particular laws
relating to the vapor - pressures of mixtures of two volatile
liquids.
* Compt. rend., Nov. 23, 1885; Ann. Chim. Phys., [6], 8 (July,
121
THE GENERAL LAW OF THE VAPOR-
PRESSURE OF SOLVENTS
BY
F. M. RAOULT
Professor of Chemistry in Grenoble
(Comptes rendus, 1O4, 1430, 1887)
THE GENERAL LAW OF THE VAPOR-
PRESSURE OP SOLVENTS*
BY
F. M. KAOULT
THE molecular lowering, K, of the vapor-pressnre of a solu-
tion i. e., the relative diminution of pressure produced by one
molecule of non-volatile substance in 100 grams of a volatile
liquid can be calculated from the following formula :
in. which / is the vapor-pressure of the pure solvent, f that of
the solution, M the molecular weight of the dissolved sub-
stance, P the weight of this substance dissolved in 100 grams
of the solvent ; on the assumption that the relative diminution
/ f
of pressure, ' , is proportional to the concentration. Since
this proportionality is seldom rigid, even when the solutions are
very dilute, I have endeavored in these comparative studies to
always work on solutions having nearly the same molecular con-
centration, and containing from 4 to 5 molecules of non-volatile
substance to 100 molecules of volatile solvent. A greater dilu-
tion would not permit of measurements which are sufficiently
exact. All of the experiments were carried out by the baro-
metric method, and conducted like those which I made on
ethereal solutions. (Compt. rend., 16 Dec., 1886.) The tubes
were dipped into a water -bath with parallel glass sides, con-
stantly stirred, and heated at will.
In each case the temperature was so chosen that the vapor-
pressure of the pure solvent was about 400 millimetres of mer-
cury. The measurements were completed in from fifteen to
* Compt. rend., 1O4, 1430 (1887)
125
MEMOIRS ON
forty-five minutes after stirring the contents of each tube, the
temperature being constant.
I employed as solvents twelve volatile liquids water,
phosphorus trichloride, carbon bisulphide, tetrachlormethane,
chloroform, amylene, benzene, methyl iodide, ethyl bromide,
ether, acetone, and methyl alcohol.
I dissolved in water the following organic substances : Cane-
sugar, glucose, tartaric acid, citric acid, and urea. All of these
substances produced nearly the same molecular lowering of
the vapor - pressure : JT=0.185. I have omitted here the
mineral compounds ; the action of these substances has, in-
deed, been determined by experiments which are sufficiently
numerous and conclusive, carried out by Wiillner (Pogg. Ann.,
103 to 110, 1858-1860), by myself (Compt. rend., 87, 1878),
and, very recently, by M. Tammann ( Wied. Ann., 24, 1885).
In solvents other than water I have dissolved substances as
slightly volatile as possible, and have generally chosen them
from the following : oil of turpentine, naphthalene, anthracene,
hexachlorethane (C 2 C1 6 ), methyl salicylate, ethyl benzoate,
antimony trichloride, mercury ethyl, benzoic, valeric, trichlor-
acetic acids, thymole, nitrobenzene, and aniline. The error
due to the vapor - pressure of these compounds can often be
neglected. The vapor-pressure of dissolved substances is, in-
deed, considerably reduced by mixing them with a large excess
of solvent ; and if, at the temperature of the experiment, the
vapor-pressure does not exceed 5 to 6 millimetres, it does not
exert any perceptible influence on the results.
The molecular lowerings of vapor - pressure, produced by
these different substances in a given solvent, are grouped
about two values, of which the one, which I call normal, is
twice the other. This normal lowering is always produced by
the simple hydrocarbons, and chlorides, and by the ethers ;
the abnormal lowering almost always by the acids. There are,
however, solvents in which all of the dissolved substances pro-
duce the same molecular lowering of vapor-pressure; such, for
example, as ether (loc. cit.) and acetone.
Of the volatile solvents examined, I have studied carefully
the lowering of the freezing-point of two water and benzene
(Compt. rend., 95 to 1O1, and Ann. Chim. Phys., [5], 28,
[6], 2 and 8). A comparison of the results obtained shows
that for all of the solutions in a given solvent there is nearly a
126
THE MODERN THEORY OF SOLUTION
constant ratio between the molecular lowering of the freezing-
point and the molecular lowering of the vapor-tension. This
ratio in water is 100, in benzene 60 within -fa.
If we divide the molecular lowering of vapor - pressure, K,
produced in a given volatile liquid, by the molecular weight of
J
this liquid, M', the quotient, ^ n represents the relative lower-
ing of pressure which will be produced by 1 molecule of non-
volatile substance in 100 molecules of volatile solvent. I have
obtained the following results by making this calculation for
the normal values of K, produced in the different solvents by
organic compounds % and non-saline metallic compounds :
Solvent.
Water
Molecular
weight
of solvent.
M'
. 18
Normal molec-
ular lower-
ing of press-
ure.
K
0.185
Lowering of
pressure
produced
bylmol.in
100 mols.
K
M'
0.0102
Phosphorus trichloride .
Carbon bisulphide
... 137.5
... 76
1.49
0.80
0.0108
0.0105
Tetrachlormethane
154
1.62
0.0105
Chloroform
. 119.5
1.30
0.0109
Amylene
... 70.0
0.74
0.0106
. . 78.0
0.83
0.0106
Methyl iodide
... 142.0
1.49
0.0105
Ethyl bromide
. 109.0
1.18
0.0109
Ether
. . 74.0
0.71
0.0096
Acetone
. 58.0
0.59
0.0101
Methvl alcohol. .
32.0
0.33
0.0103
The values of K and of M', recorded in this table, vary in the
j
ratio of 1 to 9 ; notwithstanding this, the values of , vary
but little, and always remain close to the mean, 0.0105.
We can therefore say that 1 molecule of a non-saline, non-
volatile substance, dissolved in 100 molecules of any volatile
liquid, lowers the vapor-pressure of this liquid by a nearly con-
stant fraction of its value approximately 0.0105.
This law is strictly analogous to that which I stated in 1882,
relative to the lowering of the freezing-point of solvents. The
127
THE MODERN THEORY OF SOLUTION
anomalies presented are explained, for the most part, by assum-
ing that in certain liquids the dissolved molecules are formed
of two chemical molecules.
FRANCOIS MAKIE RAOULT was born May 10, 1830, at Four-
nes, Nord. He was for a time professor of chemistry at the
Lyceum at Sens, but was called to the professorship of chem-
istry at Grenoble in 1867 a position which he still holds.
His best-known work is that which has to do with the de-
pression of the freezing-points of solvents by dissolved sub-
stances, and the lowering of the vapor-tension of solvents by
substances dissolved in them. In addition to the papers given
in this volume, the following may be mentioned as among his
more important contributions to science :
The Law of the Freezing -Point Lowering of Water produced
~by Organic Substances (Ann. Chim. Phys., [5], 28, 133, 1883);
On the Freezing -Point of Salt Solutions (Ann. Chim. Phys.,
[6], 4, 401, 1885; On the Vapor -Tension and Freezing - Point
of Salt Solutions (Compt. rend., 87, 167, 1878) ; Law of the
Freezing -Point Lowering of Benzene produced by Neutral Sub-
stances (Compt. rend., 95, 188, 1882); General Law of the
Freezing of Solvents (Compt. rend., 95, 1030, 1882); Deter-
mination of Molecular Weights by the Freezing - Point Method
(Compt. rend., 1O1, 1058, 1885); On an Accurate Freezing-
Point Method, with Some Applications to Aqueous Solutions
(Ztschr. Phys. Chem., 27, 617).
Our knowledge of the depression of the freezing-point and
of the vapor-tension of solvents by dissolved substances, was
fragmentary before the time of Raoult. He was the first to dis-
cover the general laws to which these phenomena conform laws
which have an important bearing on chemistry and physics,
and which are especially significant for the physical chemist.
BIBLIOGRAPHY*
OSMOTIC PRESSURE.
W. Pfeffer. Osmotische Untersuchungen, Leipzig, 1877.
H. de Vries. Osmotische Versuche mit lebenden Membranen.
Zlschr. Phys. Chem., 2, 415.
Isotonische Koeffizieuten einiger Salze.
Ztschr. Phys. Chem., 3, 103.
H. J. Hamburger. Die Isotonischen Koeffizienten und die roten Blutkor-
perchen.
Ztschr. Phys. Chem., 6, 319.
J. H. Poynting. Osmotic Pressure.
Phil. Mag., 42, 1896.
Nature, 55, 33.
A. Wladimiroff. Osmotische Versuche an lebenden Bakterien.
Ztschr. Phys. Chem., 7, 529.
G. Tammann. Uber Osmose durch Niederschlagsmembranen.
Wied. Ann., 34, 299.
Zur Messung osmotischcr Drucke.
Ztschr. Phys. Chem., 9, 97.
W. Lob. Uber Molekulargewichtsbestimmuug von in Wasser
loslichen Substanzen mittels der roten Blutkorper-
chen.
Ztschr. Phys. Chem., 14, 424.
S. G. Hedin. Uber die Bestimmung isosmotischer Konzentrationen
durch Zentrifugieren von Blutmischungen.
Ztschr. Phys. Chem., 17, 164.
A. A. Noyes and C. G. Abbot. Bestimmung des osmotischen Druckes
mittels Dampfdruck-Messungen.
Ztschr. Phys. Chem., 23, 56.
Lord Kelvin. Osmotic Pressure.
Nature, 55, 273.
W. C. Dampier Whetham. Osmotic Pressure.
Nature, 54, 571.
H. M. Goodwin and G. K. Burgess. The Osmotic Pressure of Certain
Ether Solutions and its Relation to Boyle's-Van't
Hoff Law.
Phys. Rev., 7, 171.
* No attempt is made to give a complete bibliography of the subjects dealt with. Only
the more important papers are cited.
I 129
MEMOIRS ON
THEOHY OF SOLUTION.
M. Planck. Uber die molekulare Koustitution verdunnter Losun-
gen.
Ztschr.Phys. Chem., 1, 577.
Chemiscb.es Gleichgewicht in verdiinnten Losungen.
Wied. Aim., 34, 147.
S. Arrhenius. Uber den Gefrierpunkt verdiinnter wasseriger Losun-
gen.
Ztschr. Phys. Chem., 2, 491.
Uber die Dissociationswarme und den Einfluss der
Temperatur auf den Dissociationsgrad der Elek-
trolyte.
Ztschr. Phys. Chem., 4, 96.
J. H. van't Hoff und L. Th. Reicher. Uber die Dissociationstheorie der
Elektrolyte.
Ztschr. Phys. Chem., 2, 777.
Beziehung zwischen osmotischen Druck, Gcfrier-
punktserniedrigung, und elektrischer Leitfahigkeit.
Ztschr. Phys. Chem., 3, 198.
Pickering, Walker, Ramsay, Ostwald, Van't Hoff, and others. Verhand-
lungeu liber die Theorie der Losungen.
Ztschr. Phys. Chem., 7, 378.
W. Ostwald. Zur Theorie der Losungen.
Ztschr. Phys. Chem., 2, 36.
Uber die Dissociationstheorie der Elektrolyte.
Ztschr. Phys. Chem., 2, 270.
Zur Dissociationstheorie der Elektrolyte.
Ztschr. Phys. Chem., 3, 588.
Uber die Affinitatgrossen organischer Sauren, und ihre
Beziehungen zur Zusammensetzung und Konstitu-
tion derselben.
Ztschr. Phys. Chem., 3, 170, 240, 369.
Lord Rayleigh. Theory of Solutions.
Nature, 55, 253.
G. F. Fitzgerald. Helmholtz Memorial Lecture.
Journ. CJiem. Soc., 69, 885, 1896.
LOWERING OP FREEZING-POINTS OP SOLVENTS BY DISSOLVED
SUBSTANCES.
E. Beckmann. Uber die Methode der Molekulargewichtsbestimmung
durch Gefrierpunktserniedrigung.
Ztschr. Phys. Chem., 2, 638.
Uber die Methode der Molekulargewichtsbestimmung
durch Gefrierpunktserniedrigung.
Ztschr. Phys. Chem., 2, 715.
Zur Praxis der Gefriermethode.
Ztschr. Phys. Chem., 7, 323.
130
THE MODERN THEORY OF SOLUTION
II. C. Jones. liber die Bestimmung des Gefrierpunktes sehr ver-
diinnter Salzlosungen.
Ztschr. Phys. Chem , 11 110, and 529.
liber die Bestimmung des Gefrierpunktes von verdiinn-
ten Losungen eiuiger Sauren, Alkalien, Salze, und
organischen Verbindungen.
Ztschr. Phys. Chem., 12, 623.
tiber die Gefrierpunktserniedrigung verdlinnter was-
seriger Losungen von Nichtelektrolyten.
Ztschr. Phys. Chem., 18, 283.
E. H. Loomis. liber ein exakteres Verfahreu bei der Bestimmung von
Gefrierpuuktserniedrigungen.
Wied. Ann., 51, 500.
Tiber den Gefrierpunkt verdunnter wasseriger Losun-
gen.
Wied. Ann., 57, 495.
Der Gefrierpunkt verdilnnter wasseriger Losungen.
Wied. Ann., 6O, 523.
M. Wildermann. Der experimentelle Beweis der van't Hoffschen Kon-
stante, des Arrheniusschen Satzes,desOstwaldschen-
Verdilnuungsgesetzes in sehr verdiinnten Losun-
gen.
Ztschr. Phys. Chem., 15, 337.
P. B. Lewis. Methode zur Bestimmung der Gefrierpunkte von sehr
verdunnten Losungen.
Ztschr. Phys. Chem., 15, 365.
R. Abegg. Gefrierpunktserniedrigungen sehr verdiinnter Losun-
gen.
Ztschr. Phys. Chem., 2O, 207.
J. A. Harker. On the Determination of Freezing-Points.
Proc. R. S., 6O, No. 360, 154.
W. Nernst und R. Abegg. tiber den Gefrierpunkt verdiinnter Losungen.
Ztschr. Phys. Chem., 15, 681.
A. Ponsot. Recherches sur la Congelation des Solutions Aqueuses
Etendues. Paris, 1896.
Ann. Chim. Phys., [7], 1C, 79.
F. M. Raoult. Uber Prazisionskryoskopie, sowie einige Anwendungen
derselben auf wasserige Losungen. 9
Ztschr. Phys. Chem., 27, 617.
RISE IN BOILING-POINTS OF SOLVENTS PRODUCED BY DISSOLVED
SUBSTANCES.
E. Beckmann. Studien zur Praxis der Bestimmung des Molekular-
gewichtes aus Dampfdruckerniedrigung.
Ztschr. Phys. Chem., 4, 532.
Bestimmung von Molekulargewichten nach der Siede-
methode.
Ztschr. Phys. Chem., 6, 437.
131
THE MODERN THEORY OF SOLUTION
E. Beckmann. Zur Praxis der Bestimmung von Molekulargewicbten
nach der Siedemethode.
Ztsclir. Phys. Chem., 8, 223.
Beitrage zur Bestimmung von Molekulargrossen.
Ztschr. Phys. Ghem., 15, 656.
Ibid., 17, 107.
Ibid., 18, 473.
Ibid., 21, 239.
J. Sakurai. Modification of Beckmann's Boiling-Point Method of
Determining Molecular Weights of Substances in
Solution.
Journ. Chem. Soc., 61, 989.
B. H. Hite. A New Apparatus for Determining Molecular Weights
by the Boiling-Point Method.
Amer. Chem. Journ., 17, 507.
H. C. Jones. A Simple and Efficient Boiling-Point Apparatus for
Use with Low and with High Boiling Solvents.
Amer. Chem. Journ., 19, 581.
W. Landsberger. Ein neues Verfahren der Molekelgewichtsbestimmung
nach der Siedemethode.
Ber. deutsch. chem. Gesell., 31, 458.
J. Walker and J. S. Lumsden. Determination of Molecular Weights. Modi-
fication of Landsberger's Boiling-Point Method.
Journ. Chem. Soc. , 1898, p. 502.
INDEX
Arrhenius, Biographical Sketch of,
66.
Avogadro's Law : for Dilute Solu-
tions, 21; Applied to Dilute So-
lutions: First Confirmation, Di-
rect Determination of Osmotic
Pressure, 25 ; Second Confirma-
tion, Molecular Lowering of Va-
por-Pressure, 26; Third Confirma-
tion, Molecular Lowering of Freez-
ing- Point, 29 ; as applied to Solu-
tions. Gu Id berg and Waage's Law,
31 ; in Solutions, Deviations from
Guldberg and Waage's Law, 34.
B
Bibliography, 129.
Boyle's Law for Dilute Solutions, 15.
Capillary Phenomena, 63.
Conclusions from Freezing - Point
Lowering*. 88.
Conductivity, 63.
D
Dissociation, Two Kinds of, 55.
Dissociation of Substances Dissolved
in Water, 47.
E
Ethereal Solutions : Lowering of
Vapor-Pressure, General Results,
110; Influence of Temperature on
the Vapor-Pressure of, 114; Influ-
ence of the Nature of the Dissolved
Substance on the Vapor-Pressure
of, 116.
Freezing of Solvents, the General
Law of the, 69.
Freezing-Point, Lowering of the, 65.
Freezing-Points, Effect of Dissolved
Substances on, 71.
G
Gay-Lussac's Law for Dilute Solu-
tions, 17.
General Expression of Laws of Boyle,
Gay-Lussac, and Avogadro, for So-
lutions and Gases, 24.
H
Heat of Neutralization in Dilute So-
lutions, 59.
I
"t," Comparison of Results from the
Two Methods of Calculating, 50;
Determination of, for Aqueous So-
lutions. 36; Methods of Calculating
the Values of, 49.
Law Relating to Dilute Solutions,
112 ; Particular Expression of the,
113.
Law of the Lowering of the Vapor-
Tension of Ether, Another Ex-
pression of the, 119.
O
Osmotic Pressure : Apparatus. 5 ;
Apparatus and Method of Meas-
uring, 3 ; Cells, Preparation of, 3 ;
Kind of Analogy which Arises
133
INDEX
through this Conception, 13; Meas-
urement of, 7 ; Results of Meas-
urement of, 9, 10 ; Role of, in the
Analogy between Solutions and
Gases, 13.
Pfeffer, Biographical Sketch of, 10 ;
Osmotic Investigations of, 3.
Properties of Dilute Solutions Addi-
tive, 57.
R
Raoult, Biographical Sketch of, 128.
S
Solutions: in Acetic Acid, 73 ; in Ben-
zene, 78 ; in Ethylene Bromide, 82 ;
in Formic Acid, 77 ; in Nitroben-
zene, 80 ; in Water, 83.
Specific Refractivity of Solutions, 62.
Specific Volume and Specific Grav-
ity of Dilute Salt Solutions, 61.
Van't Hoff , Biographical Sketch of,
42.
Van't Hoff' s Law, 47 ; Exceptions
to, 48.
Vapor-Pressure : Method of Work in
Determining. 97; of Solvents, Gen-
eral Law of, 125.
Vapor -Pressure of Ethereal Solu-
tions, 95 : Effect of Dissolved Sub-
stance on the, 105; Influence of
Concentration on the, 105; Influ-
ence of the Nature of the Dis-
solved Substance on the, 116; In-
fluence of Temperature on the, 114.
W
Wullner, Comparison with the Law
of, 113.
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