dissolved salt, more or less hydrolyzed. The state of the system is
going to be modified. Let us suppose that we have added acid : we
increase C A . In order that the equilibrium subsist, it is necessary
that the product C A . C B remain constant, since C AB cannot in-
crease, the solution being already saturated in reference to the salt
AB. C B must diminish then, which can be obtained only by the
combination of a certain number of molecules of B introduced with
the molecules of A; but, as the solution is already saturated with
the non-hydrolyzed salt AB, the molecules AB, thus produced, must
become precipitated from solution.
It is easily seen that the diminution of solubility of the salt AB,
resulting from this precipitation, will be more perceptible for a small
excess of reagent added in proportion as the product C A . C B is
smaller, that is, for but slightly hydrolyzed salts ; chlorides, nitrates
and sulphates of the strong bases, on condition, of course, that no
special combinations can be produced between the salt AB and the
reagent added, as in the case of sulphuric acid added to the neutral
sulphate of potassium which produces the bisulphate, more soluble
than the neutral sulphate. Hydrochloric acid, for example, added
in slight excess to saturated solutions of chlorides, precipitates in a
quantitative manner, so to speak,* chlorides of very strong bases:
potassium, sodium, barium, calcium, which are very slightly
hydrolyzed. With chlorides of medium strong bases (magnesium
group), it is only with very strong concentrations of hydrochloric
acid that the precipitation takes place (proto-chlorides of iron and
chromium) ; chlorides capable of giving oxychlorides have, on the
contrary, their solubility increased by hydrochloric acid (ZnCl 2 ,
SnQ 2 , Fe 2 Cl e ).
*Engel, C. R., civ, 433 (1892). These precipitations may be a source of
error in quantitative determinations in that they cause one to think, at times,
of the formation of salts insoluble in water.
BASED UPON CHEMICAL REACTIONS 141
One can then say that, with the exceptions due to the formation
of special combinations between the precipitate and the precipitating
reagent, the excess of the reagent favors, in general, precipitation
by making it more complete. For the same reasons, the solubility
of precipitates is diminished in the washing liquid by adding to the
wash water the acid or base of the precipitate either free or in the
form of a salt. The applications of this principle to chemical
analysis are innumerable. For example, the washing of ammonium
magnesium phosphate with ammonia water, of potassium fluoborate
with potassium acetate in the determination of boric acid by the
Stromeyer method, of ammonium phosphomolybdate with ammonium
nitrate, lead sulphate with a water slightly acidified with sulphuric
acid, mercurous chromate with a solution of mercurous nitrate,
etc. One should, of course, choose the additional substance in such
a way that it will not interfere in subsequent operations. That is
why ammonium or mercury salts are freely employed, which later
heating removes completely from the stable precipitates. In certain
cases, we can, after the use of a fixed salt, remove the latter by an-
other wash water in which the precipitate may be totally insoluble.
It is thus, that, in one of the previous examples, the potassium
acetate in the wash water is removed from the potassium fluoborate,
by means of alcohol which dissolves the acetate and in which the
fluoborate is completely insoluble.
Ostwald's Solubility Product. Ostwald gave in another form,*
the explanation of the influence of the excess of reagent, by basing
his statements upon the electrolytic theory and by laying down what
he calls the principles of the solubility product (Loslichkeit produkt).
We shall give his demonstration in detail, for we have here a par-
ticularly interesting example of the reciprocal relation of the calori-
metric and electrolytic explanations.
Let us assume, says Ostwald, a solid electrolyte in contact with
a saturated aqueous solution. The solution contains in equilibrium
the electrolyte in part undissociated and in part dissociated into its
ions. The concentration C of the undissociated part is controlled
by the ordinary law of equilibrium of solid bodies in saturated solu-
tion in contact with the solid body in excess ; it is then constant.
The concentrations a and b of the dissociated parts, ions, are,
on the contrary, variable and related to the concentration c of the
undissociated part, with which the free ions are in equilibrium by
* W. Ostwald, Wissenschaftlichen Grundlagen der anal. Chemie, p. 73.
142 METHODS OF ANALYTICAL CHEMISTRY
the ordinary equation ab = kc (if it is a question of monovalent
ions), k being constant for a given temperature.* A.s c is constant
for a given temperature, so the product ab is constant. Ostwald
calls it the "solubility product," which, for any salt whatever, has
always a definite value for a given temperature. If the electrolyte
were composed of polyvalent ions in the proportion of m acid ions to
n basic ions, the product of solubility would then take the form:
a m b n = Const. From this definition, Ostwald formulates the fol-
lowing principle, which is an immediate corollary:
"Each time that in a liquid the product of solubility of a solid
substance is exceeded, the liquid is supersaturated in proportion to
its solid substance ; each time that the product of solubility is not yet
attained, the liquid acts as a solvent upon the solid."
v By means of this principle, Ostwald easily explains the role of
the excess of reagent in rendering the precipitation more complete.
Let us assume, for example, that it is a question of the determina-
tion of SO 4 in the form of BaSO 4 by means of BaCl 2 . If we add
only the quantity of barium chloride exactly the equivalent of SO 4
to be determined, there will remain in solution a proportion of SO 4
ions corresponding to the solubility product of barium sulphate, that
is to say, that the concentration a of the SO 4 ions remaining in solu-
tion, multiplied by the concentration b of the non-precipitated barium
ions, should give a product equal to the constant kc. Let us now
add a small excess of barium chloride, then the factor b of the
product ab is increased, and as this product should remain equal to
kc, the value of the factor a must diminish, which necessitates the
precipitation of a new quantity of barium sulphate. Adding again
some barium chloride, a new effect will be produced in the same
- direction ; however, the mass of the free SO 4 ions can never become
nil, because the concentration of the Ba ions cannot be rendered
infinite. t
From the solubility product, Ostwald deduces again this rule,
that the excess of reagent ought to be greater in proportion as the
precipitate is more soluble. In fact, to reduce the concentration of
the ion to be precipitated to the nth part of that which it possesses
in pure aqueous solution of the precipitate, a quantity of the other
ion n times larger must be introduced, and n should be larger in pro-
* Let us observe here that this coefficient k is not the same as in the pre-
ceding thermodynamic equation of equilibrium. It is even perceptibly the
inverse of what we have said on the reciprocity of hydrolysis and ionization.
BASED UPON CHEMICAL REACTIONS 143
portion as the solubility is itself greater. On the contrary, if the
precipitate is but slightly soluble, kc is necessarily very small and
then a small excess of the precipitating reagent suffices, in general,
to precipitate practically all of the ions to be determined.
We see that the electrolytic explanation of the influence of the
excess of reagent amounts practically to the same thing as the calori-
metric explanation which I gave above. The electrolytic explana-
tion, however, does not take into account this fact that, for example,
neutral chlorides of strong bases are much more completely pre-
cipitated by hydrochloric acid than those of weak bases, and the
solubility product tends even to a contrary conclusion, since this
product is with equal solubility smaller for a chloride of a weak
base than for a more ionized strong base, and that it would conse-
quently seem that the same excess of hydrochloric acid ought to
make this product decrease for alkali chlorides less easily than for
chlorides of the medium strong or weak bases while in fact it is
the contrary that is true.
Substitution of a Weak Acid for a Free Strong Acid in Solu-
tion. This is one of the most frequent operations in analytical
chemistry. It has for its aim to permit the formation of a precipi-
tate which would be soluble in a strong acid and consequently
would not form in presence of this free acid, while it is insoluble
in a weak acid and forms in the presence of the latter, this weaker
acid having still sufficient strength to maintain in solution other
substances which it is desirable to leave dissolved.
The process permitting the substitution of a weak acid for a
free strong acid is derived readily from the heats of neutralization
of the same base, sodium hydroxide, for example, by the series of
acids, and the stability of the salts formed in presence of water.
The simplest case is that in which two monobasic acids, and of a
single property, stand opposed, that is to say, such that each one
can form in presence of water only a single compound with an
alkaline base. In that case, as we have seen (Chapter III, Section i),
the acid capable of liberating heat by decomposing the neutral salt
of the opposed acid is the one which remains combined with the
base in a clearly complete manner when the salt which it forms is
stable in presence of water. It is thus, then, by adding sodium
acetate to a solution containing free hydrochloric or nitric acids,
the latter are combined entirely with the sodium, and there no
longer remains anything but the free acetic acid.
144 METHODS OF ANALYTICAL CHEMISTRY
With exactly equal equivalents, there would remain, of course,
a trace of free strong acid; but by adding an excess of sodium
acetate it is determined at will, conforming to the equilibrium
equation :
^ acetate ==k ^nitrate C acetic acid.
It is necessary to notice that, in this case, in common practice
in analytical chemistry, a part of the acetic acid liberated by the
strong acid, can combine with the sodium acetate in excess in order
to give a triacetate. This triacetate (whose formation in the solid
state liberates 5.7 Calories) is, however, dissociated practically com-
pletely by water, so that, finally there is only free acetic acid.
The neutralization of hydrochloric and nitric acids is likewise
practically complete with the formates of the alkalies, and it is
always thus when two acids of very unequal strengths are opposed
to each other. On the other hand, it is quite different when the acids
are of comparable strength; strong monobasic acids opposed to
each other, likewise the fatty acids which are not utilized in analyt-
ical chemistry ; and one can change, for example, a nitric acid solu-
tion into a solution containing only hydrochloric acid by repeated
evaporations to dryness, after the addition each time of an excess of
hydrochloric acid, involving irreversible reactions, such as the
formation of nitrosyl chloride, which allows the elimination more
and more completely of all the free nitric acid or nitrates.
In the case of the polybasic acids, the effects may be more com-
plicated, because these acids form with the same base several combi-
nations of different stability in presence of water. If the polybasic
acid is very weak, as boric acid, it is displaced from its combination
with the alkalies completely by strong monobasic acids, as is shown
from the calorimetric measurements of Berthelot:
^Na 2 B 4 O 7 +HCl (liberates) +2.13 Calories
^B 4 O 6 +NaCl (free) +0.08 Calories.
The difference, 2.05 Calories, is, in fact, almost exactly equal to
the difference of the heats of neutralization :
13.7 Calories n.6 Calories = +2.1 Calories.
Sulphuric acid displaces acetic acid completely from sodium
acetate in a manner similar to two molecules of a strong monobasic
acid.
BASED UPON CHEMICAL REACTIONS 145
>^H 2 SO 4 +NaC 2 H 3 O 2 liberates +2.38 Calories,
^Na 2 SO 4 +HC 2 H 3 O 2 liberates 0.12 Calories.
The difference, 2.50 Calories, is almost equal to the difference of
the heat of neutralization : 2.57 Calories. A sulphuric acid solution
can be rendered exclusively acetic by an excess of sodium acetate,
exactly similar to the hydrochloric and nitric acid liquids.
Finally, hydrochloric acid displaces in a precisely complete man-
ner, the oxalic acid of sodium oxalate, but with the absorption of a
very noticeable amount of heat, as the following data show :
HCl+^Na 2 C 2 O 4 liberates 0.70 Calories,
^H 2 C 2 O 4 +NaCl liberates+o.05 Calories.
The difference, 0.65 Calories, corresponds exactly to the dif-
ference of the heat of neutralization of hydrochloric and oxalic
acids by sodium hydroxide.
13.69 Cal. 14.34 Cal. 0.65 Calories.
The last example shows that it is impossible to foresee the direc-
tion of displacement by the single consideration of heats of neutral-
izations when it is a question of acids of different basicities. Per-
haps it is the hydrolytic dissociation of normal sodium oxalate into
free oxalic acid and sodium binoxalate which would explain, in
this case, the direction of the displacement.
The applications of this general method of displacement of a
free strong acid by a weaker acid are extremely numerous in analyt-
ical chemistry: the precipitation of zinc from an acetic acid solu-
tion by hydrogen sulphide, of lead as the chromate from an acetic
acid solution, the determination of normal calcium phosphates by
the so-called "acetate" method, etc.
Decreasing the Free Weak Acid by the Addition of an Alkali
Salt of the Same Acid. The experience of chemical analysis has
shown for a long time that when the precipitation of an insoluble
compound is to be made in a solution containing a weak acid or a
medium strong one in the free state, capable of keeping the precipi-
tation from being complete, one can succeed in making it complete
by adding to the solution a greater or less excess of the normal
alkali salt of the free acid. It is in this manner that, as Rivot indi-
cated, the precipitation of nickel or cobalt by hydrogen sulphide,
which does not take place in a hydrochloric acid solution, is possible,
10
146 METHODS OF ANALYTICAL CHEMISTRY
but only partial in an exclusively acetic acid solution, and becomes
complete if we add to the solution a large excess of alkali acetate.
The role of the alkali acetate added to the hydrochloric acid solu-
tion is not limited then, as in the previously examined cases, to the
substitution of acetic acid for free hydrochloric acid. There is in
addition, an apparent decrease of the acetic acid by the addition of
the excess of alkali acetate.
Ostwald gave an explanation of this phenomenon which is cer-
tainly one of the most attractive deductions of the electrolytic
theory. We will briefly summarize it before giving the calorimetric
explanation which we have deduced from the experimental study
of these reactions.
Let us assume, says Ostwald,* that we mix in the same solution
two electrolytes having a common ion, the acid ion, for example.
If the two electrolytes are highly ionized, no notable reaction will
be produced by reason of their being mixed. It will be the same if
we mix a slightly dissociated electrolyte, a weak acid, for example,
with a normal salt of this acid, which itself is highly ionized. In
this case, however, there is a forcing back of the ionization of the
acid, which is thus weakened, its strength being proportional to the
free H ions. This follows from the equilibrium equation ab = kc
between the concentrations a and b of the free cations and anions
of the acid and the concentration c of the non-dissociated part of
the acid. The acid being weak, c is very large in comparison to
a and b : if then, we add to the solution a normal salt of the same
acid, a is greatly increased, and b (the concentration of the hydrogen
ions) ought from that moment to decrease almost in the same pro-
portion, c being able to increase but very little, since the larger part
of the acid exists already in a non-dissociated state in the solution.
The free acid is then greatly weakened by the addition of the neutral
salt, and this weakening will be the more noticeable as the acid is
itself weaker, and by the addition of a larger amount of the normal
salt.
In support of this theory, Ostwald refers to the following experi-
ments. He shows first the parallelism between electrical conduct-
ivity (degree of ionization) and the strength of acids by determin-
ing that sheets of zinc of the same size liberate much more hydrogen
in unit time, directly after they are introduced into hydrochloric
* W. Ostwald, Wissensch. Grundlagen der anal Ch. p. 63 (3d Eng. Ed.,
p. fy. Editors' Note}.
BASED UPON CHEMICAL REACTIONS 147
acid than into acetic acid of the same molecular concentration.
Then he shows the decrease in the strength of the acetic acid by
sodium acetate, by demonstrating that of two solutions of acetic
acid of the same concentration, the one formed with pure water, the
other with a solution of sodium acetate, this latter produces with
the same sized piece of zinc a much less rapid evolution of hydrogen.
The following series of experiments which I have undertaken
with the view of verifying Ostwald's theory, has permitted me to
establish the fact that, in the case which concerns us here, namely,
the production of a precipitate in the presence of a free weak acid,
the apparent weakening of the latter by a neutral salt of the same
acid is explained quite simply by the phenomena of chemical
equilibrium.*
i. I have first verified if, as Ostwald indicates it, the decrease in
the rate of the evolution of hydrogen by the addition of an acetate,
in the action of acetic acid on zinc, is indeed in proportion to the
ionization of the acetate. With this object I tried successively the
action upon the same sheet of zinc, 17 square centimeters area,
carefully cleaned before each trial, of normal solutions of different
acetates of the same concentration, mixed with the same propor-
tion of pure acetic acid (20 to 40 per cent of acid) and of five drops
of the saturated solution of copper acetate to one hundred cubic
centimeters of the solution, to allow the continuous evolution of
hydrogen. The decomposing apparatus, furnished with a capillary
delivery tube, was kept at a constant temperature by immersion in a
rapid current of water. Upon each new test, we waited until the
liberation of hydrogen became constant, which occurred at the end
of five to ten minutes, and estimated from the number of bubbles
produced under a constant water pressure above the delivery tube
one bubble = 0.036 cc. in the apparatus employed).
Acetic acid dissolved alone in pure water gives at temperatures
between 7.5 and 10.1 very concordant results: 9 to 9.5 bubbles of
hydrogen per minute. With different acetates added to the acetic
acid the results are as follows :
Sodium acetate 4 bubbles (2 experiments)
Manganese acetate 3.9 to 5.5 bubbles
Zinc acetate 0.7 bubble
Nickel acetate 56.0 bubbles
*G. Chesneau, C. R., cxxxviii, 968 (1904).
148 METHODS OF ANALYTICAL CHEMISTRY
In the last case a heavy deposit of nickel is formed upon the
zinc. With the exception of this last experiment, in which the
zinc-nickel couple produced by the zinc deposit enters into considera-
tion, the addition of acetate has clearly decreased the rate of libera-
tion of hydrogen, but not at all in the direction anticipated from the
ionization, for manganese acetate, which is certainly less ionized than
sodium acetate, produces the same effect as the latter, and zinc
acetate, which ought to have about the same ionization as that of
manganese acetate,* much more than the latter, and sodium acetate,
to the extent of stopping the liberation of hydrogen almost com-
pletely. I have, besides, verified the fact that the strength of acetic
acid is equally diminished in a very large proportion by acetone,
whose ionization is absolutely nil, and which, substituted for water
to the extent of 50 per cent in the aqueous solution of acetic acid,
has reduced the liberation of hydrogen to 0.9 bubble.
This first series of experiments show already at least that it is
very difficult to establish a correlation between the roles played by
acetic acid in its action on zinc and in the precipitation of metals of
the iron group by hydrogen sulphide.
2. I have afterwards systematically studied the influence of
sodium acetate upon the precipitation by hydrogen sulphide, of the
metals of the iron group in an acetic acid solution. Ferrous acetate
was not tested because of the difficulties caused by the inevitable
oxidation of the salt during the experiment. All of the tests were
made at the laboratory temperature (on an average of 15) with
the pure acetates of zinc, manganese and nickel in dilute solution.
Ten cubic centimeters of a normal or decinormal solution were
placed into a conical half liter flask with the addition of definite
volumes of pure 40 per cent acetic acid, then, of normal solution of
sodium acetate. This was then made up to 250 cubic centimeters
with pure water, then 250 cubic centimeters of a saturated solution
of hydrogen sulphide were quickly introduced and the flask was
* I have been unable to find any measurements of the electrical conduc-
tivity of the acetates of manganese and zinc in the works of the authors who
have occupied themselves with determining the coefficients oc = of the
Poo
different salts. The great analogy of the coefficients found for the salts of
zinc, iron and copper, permit me to assume that the acetates of zinc and
manganese have a coefficient close to 0.33 which is that of copper acetate,
that of sodium acetate being 0.79.
BASED UPON CHEMICAL REACTIONS 149
immediately stoppered with a cork stopper previously coated with
paraffine, which was covered to a depth of from 5 to 10 millimeters
by melted paraffine so as to insure it being hermetically sealed.
I have ascertained first that the precipitation of zinc acetate (10
cubic centimeters of normal solution) is complete by the next day,
even in very strongly acetic acid solutions (up to 25 cubic centi-
meters) without the addition of sodium acetate. It was then useless
to study the influence of this.
With manganese acetate (10 cubic centimeters of normal solu-
tion) the precipitation is practically nil even at the end of ten days,
under the previously mentioned conditions in the presence of pure
water alone. It is still very slight when all the liquid is saturated
with hydrogen sulphide ; it becomes very abundant, although incom-
plete, by the addition of one hundred cubic centimeters of a normal
solution of sodium acetate saturated with hydrogen sulphide; but
the least addition of acetic acid (less than 5 cubic centimeters) in
this last mixture prevents completely any precipitation. The 'action
of the sodium acetate is then real, but it can counterbalance partially,
however, only the very small quantity of acetic acid coming from
the manganese acetate. Under these conditions, the effect produced
by the sodium acetate is not susceptible of being accurately measured.
It is with nickel acetate that the decrease of acetic acid by sodium
acetate is most easily studied, especially by employing under the
above-mentioned conditions, only ten cubic centimeters of a deci-
normal solution (representing consequently a very dilute solution).
In the presence of pure water without acetic acid or acetate, hydro-
gen sulphide gives an immediate black coloration, but the nickel
sulphide formed remains indefinitely in the colloidal solution, pass-
ing completely through the filter. With five cubic centimeters of
acetic acid at first there is no coloration, but at the end of twenty-
four hours a slight precipitate is noticed. The precipitate is no
longer produced with 25 cubic centimeters of acetic acid, even by
doubling the concentration of nickel acetate.
With the addition of 75 cubic centimeters of normal sodium ace-
tate, the precipitate of nickel sulphide is complete not only in the
aqueous solution of nickel acetate, but also in the presence of acetic
acid in increasing quantities up to 50 cubic centimeters of acetic
acid. It is only with 75 cubic centimeters of acetic acid that the