decomposition under consideration, which often suffices to interpret
BASED UPON CHEMICAL REACTIONS 83
a definite method of chemical analysis. The principle of Le Chatelier
in consequence of the displacement of the equilibrium under the
influence of the variation of one of the above factors or the law of
opposition of reaction to action* (which is deduced either from the
experimental study of reversible reactions, or from the preceding
general equation in varying successively each factor) is usually
sufficient in the discussions in analytical chemistry. We will recall
in view of the applications we will have to make of it that, for
double decompositions of salts, this principle can be expressed thus :
if the reaction liberates heat, an elevation of the temperature should
diminish the transformation of the first system into the second
and inversely, the increase of concentration of one of the substances
of the first system increases the transformation of this system into
the second and inversely.
Significance of the Laws of Berthollet. As a conclusion to this
calorimetric study of the double decomposition of salts and at the
same time as an immediate consequence of the Guldberg-Waage
law, we should see what is the exact role of the physical character-
istics, the insolubility and the volatility, of substances which can be
produced in a double decomposition of salts, that is to say, to
examine the scientific value of the laws of Berthollet.
Let us assume, in the equilibrium reaction
that the factors n are equal; and likewise, the coefficients z; this
does not change anything in the reasoning we are going to follow
and has for its object the simplification of the discussion.f Let us
consider the case of an isothermal transformation of two substances
constantly of the same concentration (with the same number of
equivalents). The general equilibrium equation reduces to:
GC C
c ,,. c // =C (constant) or - = k.
That is to say, the proportion of the first system transformed
into the second is the same whatever may be the initial concentra-
tion, on the condition, of course, that all the substances present
remain in the solution in the dissolved condition.
*Le Chatelier, Ann. des Mines, Series (8), Vol. 13.
t This discussion is taken from the previously cited memoir of Le Chatelier.
84 METHODS OF ANALYTICAL CHEMISTRY
But, let us now assume that one of the substances of the second
system, B t , for example, attains its limit of solubility and begins to
precipitate. From this moment, its concentration ^ becomes con-
stant. The preceding equality becomes
GC^ JC _ks_
C"-s ~ C" " C *
That is to say that, if we continue to increase simultaneously the
concentration of the substances of the first system, the ratio ^
which was constant until then, is going to diminish suddenly from
the moment the substance B t begins to precipitate, since ks is con-
stant and C increases. This signifies that C" is going to increase
proportionally more rapidly than C, consequently, the precipitation
of the substance B t correlative to the formation of the substance A 1?
is going to continue increasing and it can be practically complete if
s is sufficiently small and k is not too large.
This is the explanation of the laws of Berthollet ; the insolubility
of substances is not the reason for the reactions in double decompo-
sition of salts, but it makes them practically complete when k has a
very small value. The same is true for the 'volatility of the substance.
But, if k is very large, while s is very small, we see that the
precipitate cannot be produced, since the transformation of the first
system into the second may be very slight. This explains, for
example, the lack of action of carbon dioxide upon calcium chloride,
in spite of the insolubility of calcium carbonate, as well as the
numerous exceptions to the law of Berthollet, when it is a question
no longer of the action of salts upon salts, but of acids and bases
upon salts. This comes from the fact that in this case the coefficient
k is quite large, and, consequently, the product ks may take a large
value notwithstanding the small value of s.
What makes the Berthollet laws really applicable in many cases,
is that frequently the coefficient k, whose magnitude depends upon
that of the heat of reaction L, takes finite values approaching unity,
when L is zero, a condition realized in the simple double decompo-
sition of all salts formed by a strong acid and a strong base (alkali
and alkaline earths, salts of sulphuric, hydrochloric and nitric acids)
and which led the chemist Hess to formulate the law of thermo-
neutrality.
In the action of acids on salts, the heat of displacement of the
BASED UPON CHEMICAL REACTIONS 85
medium or weak acids by strong acids attains much more important
values. Thus, in some cases the laws of Berthollet often seem at
fault whereas they should be utilized only when the heat of neutral-
ization of the same base by two acids is practically the same; like-
wise, for the action of bases upon salts.*
From the form of the mathematical law of equilibrium in double
decompositions of salts, it is apparent that the influence of variations
of temperature upon the coefficient of partition k is small when the
heat of reaction L is very small, that is to say, in the cases where
the law of Berthollet is applicable. Temperature can, however, in
certain cases of analysis, play an important role by modifying the
solubility of the reacting substances and also of the products of the
reaction. It may happen, in fact, according as one employs a cold
or a hot solution, that it is a salt of the one or of the other system
that first reaches its limit of solubility, so that the direction which
the reaction tends to take in order to become more complete, may be
reversed by a variation of the temperature. This is one of the rea-
sons why the temperature employed in analytical chemistry at which
each precipitation should be produced, ought to be very carefully
determined.
A special difficulty presents itself in this respect, which at times
is impossible to overcome. Since most all salts are more soluble in
hot than in cold water it is, in general, preferable to carry on the
double decompositions in the cold, so that they may be more com-
plete. Hut, on the other hand, many precipitates obtained in the cold
are too fine or colloidal to be washed and filtered with convenience,
and it is of advantage to produce the precipitation from hot solu-
tions in order to increase the size of the grain or to render the pre-
cipitate less gelatinous. This is the method by which one may
avoid this particular difficulty.
Precipitates, the solubility of which in hot solutions is even very
slight, should be produced in hot solutions and then heated near the
boiling temperature for some time before filtering (silver chloride,
calcium oxalate, barium sulphate, etc.).
Those precipitates are produced in the cold and filtered cold
* Berthollet understood this perfectly and he, himself, indicated the fact
that estimates drawn from the physical properties of substances apply only
when they are in double decompositions between neutral salts (salts with
strong acids and bases), or in the neutral displacement of the acids and
bases of the same strength.
86 METHODS OF ANALYTICAL CHEMISTRY
whose solubility is excessive when hot, and which are susceptible
of assuming rather large crystalline grains when digested in the
cold mother liquor (magnesium ammonium phosphate, potassium
fluosilicate, potassium chlorplatinate, separation of alkaline earth
metals by the insolubility of the nitrates of barium and of calcium in
absolute alcohol, etc.).
Finally, in cases in which the grains become rather large only
when warmed and where the solubility of the precipitate is too
great, heat to incipient boiling and produce the precipitation while
hot. Although it is incomplete, rather large crystalline grains are
formed and the precipitation is then allowed to finish slowly in the
cold. The texture of the precipitate thus formed in the cold is
always less fine than when the whole operation is carried out in the
cold (precipitation of ammonium phosphomolybdate, of numerous
metallic sulphides by hydrogen sulphide, etc.)-
CHAPTER IV
THE ELECTROLYTIC THEORY OF DOUBLE
DECOMPOSITION OF SALTS
i. Law of Osmotic Pressure
The basis of the electrolytic theory of salt solutions applied by
Ostwald to the methods of analytical chemistry is, in the first place,
the discovery by Van't Hoff in 1885, of the law of osmotic pressure,
and, in the second place, the explanation which Arrhenius gave in
1887-1888, of the anomalies, presented by salts in comparison to
organic substances, in the values of the osmotic pressures, freezing
points and boiling point measurements.
We will recall briefly the experimental work upon which the
electrolytic theory rests before we explain the applications made
of it by Arrhenius and Ostwald to double decomposition of salts.
Experiments of Pfeffer and of De Fries: Van't Hoff's Law:
The walls of vegetable cells and certain colloidal substances such as
copper ferrocyanide, have the property of being penetrated by pure
water, but not by the substances dissolved in the water. We can
obtain artificially semipermeable membranes like those of vegetable
cells, by producing, as the German botanist Pfeffer* did in 1877, a
precipitate of copper ferrocyanide within the walls of a porous cup.
If, in such a cup, furnished with a mercury manometer, any aque-
ous solution whatever is placed, of sugar for example, and if the
jar be sealed hermetically and placed in pure water, the mercury of
the manometer is slowly pressed back by the pure water entering
the cup through the semipermeable membrane and finally attains a
certain height P, which remains constant.
The water being able to circulate freely through the walls of
the jar in both directions, this pressure P can be attributed only to
the presence of the dissolved substance. Pfeffer called it the
osmotic pressure of the solution.
Van't Hoff collected the results obtained by Pfeffer, who ex-
perimented at a constant temperature with solutions of different
* Pfeffer, Osmotische Untersuchungen, Leipzig, 1877.
87
88
METHODS OF ANALYTICAL CHEMISTRY
concentrations, and at different temperatures, upon solutions of the
same concentration, and ascertained that at a constant temperature,
the osmotic pressure is proportional to the concentration C and that
with equal concentrations, the osmotic pressure is proportional to
the absolute temperature T. This is clearly shown by the following
table for solutions of cane sugar and of sodium tartrate in water,
according to the results obtained by Pfeffer.
C. CONSTANT
T. CONSTANT
T. VARIABLE
C. -VARIABLE
OSMOTIC PRESSURE
M tt tff M
H < *""
I
1
i
o
^ p^ ^!
w ^~*
J
M
&H r ^
fe H ^
pq
S
CJ
^ K>
Q c/2 ^ fa
o
CO
M
W M O
Qj ^
RATIO
P
H
(X
^
O "
H 5 5
( S
P
C/5
H
k^
W p O
w w
C
8
H W
g > <n
g S
K
(6
W
i
5 H
, S 5 g
O p v^> (JJ
P M
W >J /-^
CO hJ >H
1 s g
PH ^ - U
<
g
c^
z i
O
I
u 5
i.
535
535
Sugar
32.
544
542
2.
i 016
508
14. 15
510
512
2.74
i 518
554
Sodium
37-30
983
984
4.00
2 082
521
Tartrate
I3-30
908
007
6.00
3 075
513
The agreement is very satisfactory considering the extreme
difficulty of obtaining Pfeffer's cups perfectly semipermeable.
It follows then from this that the concentration C, of a solution,
its osmotic pressure P and its absolute temperature T are related
by an equation of the form P = A-GT, where A is a constant.
If we consider the molecular weight m of the substance dis-
solved in a volume V of the solvent, we will have C =-y-, and the
above equation becomes:
(1) PV = AwT
an equation of the same form as the Mariotte-Gay Lussac law :
(2) PV = RT.
Van't Hoff conceived the idea of comparing the value Am of
equation (i) obtained for sugar (m = 342) with that of the con-
BASED UPON CHEMICAL REACTIONS 89
stant R of the Mariotte-Gay Lussac law and ascertained that the
value of Am, equal to 842 (expressing m in kilograms and P in
kilograms per square meter), is practically the same as that of the
constant P of the Mariotte-Gay Lussac law, equal to 846, expressed
in the same units. He believed this at first to be a purely accidental
coincidence* but, on pursuing the same verification with other data
obtained by Pfeffer, and by another botanist, de Vries, he always
obtained the same value for the product Am, and was thus led to
conclude the identity of equations (i) and (2) and that a molecule
of a substance transformed into a vapor under the volume V, or dis-
solved in a volume V of the solvent, has exactly the same vapor
pressure and osmotic pressure.
The great difficulty of obtaining Pfeffer porous cups, really
semipermeable, has not permitted much repetition and verification
of these experiments. However, the experiments of Ponsotf may
be cited, who obtained the following results with very dilute solu-
tions of cane sugar placed in different Pfeffer cups :
t = 11.8, C 1.235 g- per liter, P = 861 to 890 mm. of liquid
t = 11.8, C = 0.6175 g- P er liter > P = 433 to 444 mm - * liquid.
With the same cells and solutions of 1.235 grams per liter,
t= 11.8, P 890
t= 0.8, P = 846, (P calculated = 855).
The agreement is less satisfactory than with Pfeffer's data, es-
pecially at a variable temperature, but it is still, however, acceptable.
The constant Am is then equal to R for the dilute solutions of
organic substances. But, for the metallic salts dissolved in water,
the constant of the law of osmotic pressure is not the same, and we
must replace the preceding equation (i) by an expression of the
form:
(3) PV = iRT
* being a constant >i, which depends on the nature of the solution.
This anomaly has been shown by means of the isotonic coeffi-
cients, obtained by de Vries in the following manner. Fresh
cells of certain plants present the semipermeable characteristics to
a very high degree. Placed in water they swell, while if they are
* Lecture given by Van't Hoff before the Chemical Society at Paris,
(Revue Scientifique, First Semester, 1894, page 580).
t Ponsot, C. R., cxxv, 867 (1897).
METHODS OF ANALYTICAL CHEMISTRY
placed in concentrated salt solutions the protoplasm which fills the
cell contracts while losing water, which passes through the wall of
the cells. By varying the concentration of the dissolved substance,
one can obtain solutions in which the protoplasm neither expands
nor contracts, and the limit is very clearly defined for a very small
variation of concentration.
De Vries* studied, in this manner, the aqueous solutions of a
large number of different substances and called those which were in
equilibrium with the liquid of the protoplasm isotonic. By experi-
menting with cellular tissues offering different osmotic forces, it
is clear that one can obtain several series of isotonic liquids.
De Vries found the same ratio of concentration in the different
series, as is shown in the following table giving for potassium
nitrate, sugar and potassium sulphate, on the one hand, (A) the
absolute concentration expressed in gram-molecules per liter, on the
other hand (B), the ratio between the concentrations by taking
that of potassium nitrate as unity in the different series :
A
B
oERIES
KN0 8
SUGAR
K 2 S0 4
o 3
SUGAR
K 2 S0 4
i
0.12
O.I2
O.09
i
I
0-75
ii
0.13
O.2O
O.IO
i
1-54
0.77
in
0.195
0.30
0.15
i
i-54
0.77
IV
O.26O
0.40
0.15
i
1-54
0.77
These numbers confirm in an almost exact manner the law of
proportionality between the concentrations and the osmotic pres-
sures at constant temperature. We see from the preceding table
that the isotonic solutions of potassium nitrate, sugar and potassium
sulphate, which have the same osmotic pressure, are more concen-
trated for sugar than for the salts of potassium. If we admit that
the pressure is proportional to the concentration, it follows that one
molecule of potassium nitrate, for example, dissolved in a volume
V of water, gives an osmotic pressure 1.54 times as great as one
molecule of sugar dissolved in the same volume V. If, then, the
osmotic pressure of sugar is related to the volume V and to the
temperature T by the equation PV = RT, that of potassium nitrate
will be represented by PV = I.54RT; the coefficient , in the equa-
*De Vries, Eine Methode zur Analyse der Turgorkraft (Pringsheim's
Jahrbilcher), Vol. 14.
BASED UPON CHEMICAL REACTIONS 91
tion (3), is then equal to 1.54 for potassium nitrate. It is sufficient,
in short, to divide the molecular concentrations of sugar and of the
saline substances, giving isotonic solutions, the one by the other, in
order to obtain the coefficient i, to be introduced into the equation
PV = i'RT for these saline substances. The table given hereafter
(page 96) gives a certain number of coefficients. It is to be noted
that the values of * are quite different, according to the experi-
menters.
Molecular Lowering of the Freezing Point and Vapor Pres-
sure: Raoult' s Laws. The law of osmotic pressure which, on the
whole, has been established directly by only a rather small number
of concordant experiments, has especially gained in value and forced
itself upon physical chemists as the expression of a general phe-
nomenon through the advantageous explanation which it afforded
of the data previously determined in freezing point and boiling
point measurements, at the time when Van't Hoff discovered this
law.
By studying the freezing points of a large number of solutions
so diluted that the first crystals formed by the gradual lowering of
the temperature, are formed of the pure solvent, Raoult arrived at
the following results : For organic substances, the lowering of the
freezing point is independent of the nature of the substance dis-
solved and of the solvent ; it is proportional to the concentration and
equal to 0.63 for one molecule dissolved in 100 molecules of the
solvent. For saline substances in dilute aqueous solutions, the
lowering is proportional to the concentration, but has not the same
value as cane sugar taken as the unit. Raoult compiled Cryoscopic
tables, giving for a large number of substances the proportional
lowering i compared to that of sugar. The assumed molecular
weights of all of the substances were taken and dissolved in 100
grams of water. If we call A the lowering produced by a solution
of a salt, we have
A
18.3 being the lowering produced by sugar. Now, the coefficients i,
thus obtained, are practically equal to those that we deduced from
isotonic coefficients, as is shown by the following table :
METHODS OF ANALYTICAL CHEMISTRY
i OBTAINED FROM THE ISOTONIC
OBTAINED FROM
SUBSTANCE
DISSOLVED
COEFFICIENTS
THE LOWERING
OF THE FREEZ-
OBSERVED BY
OBSERVED BY
DE VRIES
OTHERS
ING POINT
Cane Sugar
1. 00
....
1. 00
Citric Acid
1.07
....
1.04
NaCl
1.60
....
1.89
KN0 3
1-54
1.76
1.66
K 2 S0 4
MgCl 2
CuCl 2
Potassium Acetate
2.08
2.30
2.30
1.60
2.73
2.24
1.66
2.1 1
2.64
2.52
1.86
It is the same for similar coefficients deduced from the molecu-
lar lowering of the vapor tension (boiling point measurements or
tonometry). Wiillner, in 1858, established the fact that the boiling
point of solutions under atmospheric pressure is higher than that of
the pure solvent, and the higher the concentration, the greater the
rise. Wiillner concluded from his experiments that the lowering
of the vapor pressure is proportional to the quantity of the dissolved
substance in the same weight of the solvent.
Raoult verified the fact, as in the case of freezing points, that
the lowering of the vapor tension depends, in general, only on the
ratio of the number of dissolved molecules to the number of
molecules of the solvent. With aqueous solutions, that is only true
for organic substances. For solutions of inorganic salts in water,
we find molecular lowering A deviating from the law for the lower-
ing of the freezing points, and it is shown that
i 5.6mA,
A being the diminution of the tension of a one per cent solution of
a substance of molecular weight m. We find thus for NaCl, i = 1.98,
for KNO 8 , i= 1.59, for K 2 SO 4 , i= 1.97, etc., coefficients agreeing
in a satisfactory manner with the values of i obtained from cryo-
scopic measurements.
Identity of the Coefficients i Deduced from Osmotic, Cryoscopic,
and Boiling Point Measurements. The law of osmotic pressure
presents this remarkable peculiarity that not only does it agree with
the cryoscopic and boiling point anomalies of salt solutions, but it
also permits the determination of the same coefficient t, in the three
series of phenomena. This has been demonstrated by Van't Hoff,
BASED UPON CHEMICAL REACTIONS 93
who supports his proof upon the fact that isotonic solutions have
necessarily the same vapor tension, and, inversely, two solutions,
having the same freezing point, must have the same osmotic pres-
sure, since they both have as vapor pressure that of ice at the same
temperature. It is sufficient to consider cyclic reversible transfor-
mations of solutions by means of semipermeable membranes and to
apply to them the principles of thermodynamics.*
But, if this reasoning shows that one can obtain the same
coefficient i, for a definite salt solution, by the three different
methods of osmotic pressure, lowering of the freezing point and of
the vapor pressure, they do not explain why, for example, a solu-
tion of one molecule of sodium chloride in water produces the same
effect as about two molecules of cane sugar in the same solvent. It
is this gap which the hypothesis of Arrhenius filled, and, at the same
time, correlated the electrical conductivity of salt solutions to the
coefficients i, obtained by the preceding methods.
2. Electrolytic Dissociation of Salt Solutions.
Hypothesis of Arrhenius, lonization of Electrolytes.^ Arrhenius
suggests that the molecules existing in solutions that conduct elec-
tricity (aqueous solutions of salts, acids and bases or electrolytes)
are not physical molecules such as CuSO 4 for copper sulphate, NaCl
for sodium chloride, etc., but more simple molecules resulting from
the dissociation of these primary ones into different groups, those
which Faraday called electric ions and into which electricity decom-
poses the metallic salts, that is to say, SO 4 , Cu, Cl, Na, etc. If, then,
we take a certain number, N, of molecules of sodium chloride, for
example, and dissolve them in water, the total number of molecules
present in the solution is not equal to N, but to the number of undis-
sociated molecules plus the number of free molecules. If there are
m undissociated molecules and n molecules, each dissociated into
(a+&) ions, there will then be m+n(a+&) distinct molecules,
and the number of these is necessarily greater than N. Conse-
*J. H. Van't Hoff, Lois de I'equilibre chimique dans I'etat dilue, gazeux
ou dissous.
t Arrhenius presented the different points of this theory in a great many
papers published in the Zeitschrift phys. Chem. He summarized them in a
very complete manner in a memoir published in the French journal, the
Lumiere electrique, of August 31, 1889, and entitled La theorie moderne de
la constitution des solutions electrolytiques, to which we will refer later.
94 METHODS OF ANALYTICAL CHEMISTRY
quently, it is to the number m-\-n(a-\-b) , of molecules and not to
the number N (and it is in this that the hypothesis of Arrhenius
consists) that the law of osmotic pressure should be applied. If,
for example, all of the molecules of sodium chloride were disso-
ciated into Na and Cl ions, there would be in solution twice as many
ions as there were molecules introduced into the solvent, and this
would give the equation PV = 2RT, which would be absolutely the
exact form of the law of osmotic pressures for sodium chloride.
As Arrhenius indicated, this is similar to the application of the law
of Mariotte to the dissociation of ammonium chloride, at high tem-
perature, into ammonia and hydrochloric acid. If we consider a