while the presence of basic bodies retards it and makes it finally
incomplete even after boiling for several hours.
The unequal influence of these different factors allows the pro-
duction, practically at will, of these two distinct successive end-
points of the reaction for the same experiment. Starting with a
boiling solution to which we add at once 10 grams of pulverized
zinc oxide, then titrating immediately without reheating, shaking
vigorously during 30 seconds after each addition of the perman-
ganate, and allowing it to settle a moment to ascertain the tint of
the supernatant liquid, this operation lasting in all 15 to 20 min-
*A. Carnot, Methodes d'analyse des fers, f antes et atiers, p. 101, 1895.
t That is to say, a quantity of pure MnCl , equivalent to exactly 0.200
gram of MnO , was dissolved in one-half liter of water containing one cubic
centimeter of concentrated HC1. For the titration, I used six grams of pure
permanganate per liter, and according to the equation (i), theoretically it
would require 40.4 c.c. of this permanganate solution for the quantity of
MnQ 2 solution used for the test.
50 METHODS OF ANALYTICAL CHEMISTRY
utes, the quantity of permanganate introduced, until the appear-
ance of the pink tint, corresponds in a very constant manner to
95.8 per cent of the theoretical quantity (a value given by the
coefficient 0.307 of Wencelius). If we then raise the liquid to the
boiling point, it becomes decolorized, and if we continue the addition
of permanganate until the reappearance of the permanent pink tint,
by boiling one or two minutes between each addition, we obtain a
second value, less constant than the first, corresponding on an
average to 97.5 per cent of the quantity of permanganate ; the pink
tint then persists for more than twenty-four hours after cooling.
The two values of the reaction obtained, the first without reheat-
ing the liquid, the second by boiling it more or less after each
addition of permanganate, become the same whatever may be the
order of operation, but with varying coefficients. Here are ex-
amples of those that I have obtained :
1ST 2D
VALUE VALUE
HC1 neutralized by CaCO 3 in great excess (log). 94.6 98.0
HC1 neutralized by ZnO in great excess (log) 95.8 97.5
HC1 neutralized by ZnO without excess 98.5 99.3
HC1 neutralized by Sodium Acetate in large excess 97.3 100.2
HC1 not neutralized (solution to acid ^y ) 95.8 (A)
(A) With free HC1 the second value cannot be exactly obtained, the acid
by prolonged boiling decolorizing the permanganate far beyond the theoretical
quantity. In this case the precipitate assumes a gray black color of pure
MnO 2 , while in all the other methods of operation, the color of the precipitate
is more or less brown, denoting the presence of oxides lower than MnO 2 .
If we maintain the liquid constantly at 100 during the whole
test, the two values unite naturally into one (the second of the
preceding table). In particular, by exactly saturating HC1 with
ZnO without excess, which is the method of de Koninck, a coeffi-
cient of 99.5 to 100.00 is obtained, which agrees with the theoretical
value, as that author has rightfully indicated; likewise, the same
holds with sodium acetate. In these two cases, the oxide of man-
ganese formed is much more gelatinous than in the presence of
ZnO and remains longer in suspension; one understands then how
it can act much more completely upon the permanganate. But it
should not be concluded from this that, in this case, the reaction
is represented by the theoretical equation. Upon filtering the liquid
after having added 86 per cent of the theoretical amount of per-
manganate, I have employed but 7.3 per cent to finish the titration
BASED UPON CHEMICAL REACTIONS 51
upon the precipitate. The precipitate is then still at this point a
lower oxide than MnO 2 .
Finally, to insure myself that oxides lower than MnO 2 when
warm are very susceptible to reacting upon permanganate, I pre-
pared the oxide of Carnot, Mi^On, and verified the fact that at
the boiling temperature it is capable of decolorizing up to 13.5 per
cent of permanganate.
In substance, the value of the reaction depends then essentially
upon the manner of operating, which leaves more or less saline
oxide in the precipitate, depending upon the speed of the operation
and the intermediate reactions which are produced. But in spite of
the differences which the variety of coefficients proposed denote,
the method of Guyard-Volhard is, however, capable of giving exact
results, provided that the permanganate be standardized against a
standard solution of manganese chloride, and provided that the
same procedure is followed in all of the operations. According to
what we have said, the relative error, which is measured by the
coefficient adopted, then always remains the same, and the estima-
tion is still susceptible of a very acceptable precision.*
*The choice of method depends upon the kind of determination one has
in view. Upon taking into account the rapidity of settling of the precipitate,
greater with excess of ZnO than without excess, to operate with a large
excess of ZnO (iog) added to the boiling and very slightly acid solution of
MnCl 2 and titrating without reheating in 15 to 20 minutes, appears to me to
be the best method suited to all cases from the richest pyrolusite to the steels,
containing 0.4 per cent of manganese.
CHAPTER III
STUDY OF DOUBLE DECOMPOSITION BY THE
CALORIMETRIC METHOD
Reversible Reactions in Analysis. The most frequent case of
operations to be accomplished in analysis is that of a homogeneous
liquid containing, in an aqueous solution, the different elements to
be determined, in the form of saline substances. We seek then by
adding to the solution a suitable reagent, acid, base or salt, to form
with one of the elements contained in solution, a gaseous body or
an insoluble precipitate which is itself an acid, a base or a salt, pro-
duced by double decomposition among the elements of the solution
and the reagent introduced. The separation of the elements under
consideration ought to be practically complete, that is to say, that
the gas or the precipitate which is eliminated ought to contain the
totality of the element with a degree of approximation of the order
of sensibility of the apparatus employed in measuring the same.
The point of view which should be adopted in analytical chem-
istry is the one which guided Berthollet in his investigations of the
"Chemical Statics" of double decompositions and whose results
may be summed up in the following statement, "The decomposition
of a salt by an acid, a base or a salt is more complete in proportion
as there results, from the exchange of the acid group and metal,
a less soluble or more volatile compound than the reacting bodies
under the conditions of the experiment.
In fact, upon this empirical law have been founded almost all
of the methods of analysis based upon the chemical precipitation of
definite compounds whose weight permits one to calculate the
weights of the elements thus separated in the insoluble state in the
midst of a liquid easy to separate by filtering the precipitate or
separating themselves by volatilization in the gaseous state. But
there is no acid, base or salt strictly insoluble in water, and the pre-
cipitates considered in analytical chemistry as the most insoluble,
ammonium magnesium phosphate, barium sulphate, etc., have in
reality a solubility of the order of one millionth in pure water, that
is, one liter of pure water contains from one to two milligrams when
saturated, a weight which exceeds considerably the accuracy of our
./. 52
BASED UPON CHEMICAL REACTIONS 53
apparatus. From this point of view, it is apparent that small vol-
umes must be employed in analytical chemistry. Precipitation is,
then, never absolutely complete, owing to the slight solubility of
the precipitates in pure water, and the experiments show that this
solubility is frequently increased by the presence of the reagents
already introduced, or of the products of the double decomposition
that gave the desired precipitate. It is thus that the solubility of
silver chloride in water, which is practically zero when the water is
pure or only acid with nitric acid, becomes very appreciable in the
presence of the sodium nitrate which is necessarily produced in
the precipitation of silver by the method of Gay-Lussac in which the
precipitate of silver chloride is formed by double decomposition
between silver nitrate and sodium chloride.
In a general way, double decompositions or reciprocal actions of
acids, bases and salts, yield incomplete reactions, limited by the
reverse reaction, or chemical equilibria, even when there is pro-
duced a precipitate insoluble in water or a volatile body ; and the al-
most exclusive object of inorganic analysis ought to be the research
for conditions in which the equilibria of these reversible reactions
can be displaced in the direction of practically complete reaction.
The same study imposes itself more strongly upon the volumetric
methods, so numerous to-day, utilizing the double decomposition,
no longer to obtain a definite insoluble compound, but a reaction in
the solution without precipitation, the end of the reaction being
simply indicated by a change of color due to an excess of the
reagent added.
The study of these conditions may be carried on by two differ-
ent methods :
i. A method which I shall call Calorimetric, consisting in con-
sidering exclusively the reacting masses and the heat change in the
double decompositions, and in utilizing the data of the calorimeter
in order to interpret the direction of the displacement of the equi-
librium by the aid of the principles of thermodynamics. This 1
method will permit us to explain the processes of analysis based
upon double decompositions without forming any hypotheses upon
the constitution of the salt molecules in aqueous solutions. It
admits the fact alone that heat is the only mode of energy capable
of variation in the system in which the chemical reaction is pro-
duced, realized in the calorimeter at an obviously constant tempera-
ture. The energies corresponding to the electric state, luminous
54 METHODS OF ANALYTICAL CHEMISTRY
state, etc., of the system, are then supposed to be constant or, at
least, to occasion variations of a magnitude negligible in comparison
to the calorific effects, which represent well the conditions realized
in the practice of inorganic analysis.
2. A method which we can call Electrolytic, which attributes to
salt solutions a hypothetical molecular constitution based upon the
manner in which they act under the influence of an electric current
produced by a source outside of the solution and dividing the dis-
solved molecules into two elements or groups of elements called
ions, set free at the electrodes : H and Cl for HC1, 2K and SO 4 for
K 2 SO 4 , Na and OH for NaOH, etc. In this method, we admit,
(and this is what constitutes the hypothesis), that, in salt solutions
not subjected to an electric current, and whose electric charge is
consequently constant, the molecules are more or less dissociated
into free ions which alone play the active role in double decomposi-
tions. We extend, moreover, to the masses of the ions and the
undissociated molecules, the laws of equilibrium drawn from the
principles of thermodynamics, but without specifically incorporating
the heat effect of the reactions, which, in this method, is replaced
by the electrical conductivity, corresponding to the degree of dis-
sociation of the chemical molecules into free ions. The electrolytic
method, which is that adopted by Ostwald in his Scientific Founda-
tions of Analytical Chemistry, is certainly more attractive, a priori,
than the calorimetric method, in that it is attached to the general
theory of Arrhenius, permitting coordination of a large group of
phenomena, abnormal in appearance, in the most varied domains;
osmotic pressures, freezing points, boiling points, electrical con-
ductivities, etc. But, as we will see later, numerous facts have
been established in these later years, notably by Professor Kahlen-
berg of the University of Wisconsin, which cast a certain doubt
upon the legitimacy of the extension of the electrolytic theory to
the concentrated salt solutions which are commonly employed in
inorganic analysis, and under these conditions, it appears to us
preferable in order to explain the processes of analysis, to have
recourse to the calorimetric method, which is surely free from
hypotheses and appeals only to the reaction taking place. Moreover,
the two methods will be successively described and, in the theories
which I will present in the course of this work upon a few of the
operations of inorganic analysis founded upon double decomposi-
tion, I will take care to indicate the electrolytic explanation of
BASED UPON CHEMICAL REACTIONS
55
Ostwald beside the calorimetric explanation, giving the reasons
which seem to me to militate in favor of the latter.
The study of double decomposition made from the calorimetric
point of view with which we shall begin, will be divided into three
parts : in the first it will be shown how we can follow the
processes of double decomposition by means of the calorimeter; in
the second, we will present the successive developments which the
notion of chemical equilibrium has taken in double decompositions,
studied from a purely experimental point of view ; finally, in the
third, we will indicate the mathematical expression of the law con-
trolling these equilibria established by means of the principles of
thermodynamics, and we shall see in what measure it is in accord
with the facts established by experiment.
i. Thermal Changes in Double Decompositions
The immense work of thermochemistry produced by Berthelot
conveniently furnishes all the data necessary for the study of
double decompositions, from the point of view of inorganic analysis,
Neutralization of Acids by Bases. The point of departure in
order to understand the reactions which are produced in the mutual
reaction of two salts in solution, is the calorimetric study of the
neutralization of acids by bases. On one hand the same acid dis-
solved in water sets free very different quantities of heat with
different bases, and on the other hand the same base sets free very
different quantities of heat with different acids. This is shown by
the following table for the principal acids employed in inorganic anal-
ysis and for a few bases chosen as types in each family of metals.
The table giving the heat of formation of salts at 15 obtained in
a dissolved or precipitated state, by neutralization of the base and
of the acid dissolved generally as one half equivalents per liter.
BASES
%H 2 S0 4
HC1
HN0 3
HC 2 H 3 2
/ 2 co 2
%H 2 S
Cal.
Cal.
Cal.
Cal.
Cal.
Cal.
NaOH
15-85
13.70
13.70
13.30
I0.2O
3.85
%Ca(OH) 2
15.60
14.00
13.90
1340
10.50
3.oo
NH 3
14.50
12.45
12.00
12.00
5-35
3-io
%Zn(OH) 2
11.15
9.85
9.80
8.90
5-50
9.60
(solid)
(solid)
y 6 Fe 2 (OH) 6
570
5-90
5-90
4.50
%Cu(OH) 2
9-35
7-50
7-50
6.2O
2.40
15-80
(solid)
(solid)
^Ag 2
7-25
2.06
5-20
4.70
6.00
27-9
(solid)
(solid)
(solid)
56 METHODS OF ANALYTICAL CHEMISTRY
From this table we can classify the acids into strong, medium,
and "weak, and likewise the bases into strong, medium, and weak,
according to the quantities of heat liberated in the process of
neutralization; 13.50 Calories at least for strong acids and bases,
13.50 to 12 for the medium, and below 12 for the weak. The
determinations made by Berthelot have shown that the reciprocal
displacement of acids or of bases in salts is more complete in pro-
portion as the difference of the heat of neutralization of the same
base by two acids is greater, and conversely. The displacement is
practically complete if the difference is very large, partial if it is
small, as is shown by the following two typical examples* of these
reciprocal displacements :
Displacement of a medium base by a strong base :
NH 4 Cl+NaOH = NH a +NaCl+H 2 O+i.o7 Cal.
The total displacement would correspond to 1.25 Cal.
NH 3 -f-NaCl sets free only 0.05 Cal. which shows that the
displacement of NaOH, a strong base by NH 3 , a medium base, is
extremely small.
Displacement of a medium acid by a strong acid :
NaC 2 H 3 O 2 +HNO 3 = HC 2 H 3 O 2 +NaNO 3 +o.45 Cal.
The thermal change is obviously equal to the difference of the
heat of neutralization of sodium hydroxide by the nitric acid and by
acetic acid; the reaction is almost complete. The inverse reaction
of acetic acid upon sodium nitrate liberates only 0.06 Cal. ; the
action is very weak, but not null, however. It is known, in fact,
that traces of hydrochloric or nitric acids can be easily liberated by
boiling an alkaline chloride or nitrate with an excess of acetic acid.
Action of Water upon Salts in Solution; Phenomena of Hydroly-
sis. If we measure the quantities of heat evolved in the neutraliza-
tion of acids by bases in solution in volumes of water more or less
large, we ascertain that the heat of neutralization diminishes in
general when the dilution increases. It decreases very little when
it is a question of strong acids acting upon strong bases, notably
with weak acids and strong bases and reciprocally, finally, in a con-
* Berthelot, Essai de mecanique fondee sur la thermochinvie, II. 689-593
BASED UPON CHEMICAL REACTIONS 57
siderable proportion with weak acids and bases. This is shown by
the following examples.*
VOLUME
DIFFERENCES OF
CALORIES LIBERATED
4 LITERS 24
LITERS
KOH + HNO 3
H 3 BO 3 -f-NaOH
H 3 B0 3 +NH 3
13-83
11.74
9-44
13.76
10.91
7.27
0.07
0.83
2.17
Of course the values obtained from the calorimeter are cor-
rected for the thermal effect produced by the increased quantity of
water acting separately upon the acid and the base, a very marked
effect when the base forms hydrates with evolution of heat.
The difference between the numbers in the first two columns of
the preceding table, or heat absorbed on dilution, can be equally well
obtained by beginning with the salt completely formed, dissolved in
four liters and adding water, which gives the same results conform-
ing to the principle of the initial and final states.
The thermal effect of the dilution is produced completely in a
few seconds, as, moreover, is that of the neutralization of the bases
by acids.
The heat absorbed by dilution can be explained only by an
interaction less and less complete, of acid and base in proportion as
they are diluted by a larger volume of water, or reciprocally, by
the dissociation of the dissolved salt into free acid and free base,
the greater in proportion as the salt is diluted. Following the prin-
ciple of thermochemistry, the degree of dissociation when one passes
from a given concentration to a weaker concentration, is equal to
the ratio of the heat of dilution to the heat of formation of the salt
in the initial concentration. It is this decomposition of the salt
molecules by water into free acid and free base that is termed
hydrolysis.
One could be tempted to attribute the thermal effect of the dilu-
tion to an action of water upon the dissolved body, other than the
separation of the salt into its two components which have become
partially free; but a great number of well-known reactions place
the phenomena of hydrolysis beyond doubt and an uninterrupted
chain of intermediate reactions can be easily established between the
*Ibid., II. p. 216.
58 METHODS OF ANALYTICAL CHEMISTRY
cases where hydrolysis is manifested by a tangible phenomenon and
those where it is explained, as in the cases examined above, only by
a thermal effect. The great importance of the phenomena, of the
comprehension of the double decompositions, and the explanation
of the methods of analysis which are derived from it, require us to
enter upon the subject in considerable detail.
In a certain number of cases, the decomposing action of water
upon salts is shown by the formation of an insoluble or volatile
product, as in the action of water :
1. Upon chlorides of antimony and of bismuth, giving insoluble
oxychlorides with a marked evolution of heat :
BiCl 3 +H 2 O = BiOCl+2HCl+7.8 Cal.
2. Upon mercuric sulphate with the formation of a precipitate
of the basic sulphate :
3 HgS0 4 +2H 2 = H 2 S0 4 +HgS0 4 -2HgO.
3. Upon ferric chloride which gives, especially in warm dilute
solution, a precipitate of ferric hydrate or oxychloride:
Fe 2 Cl 6 +6H 2 O == Fe 2 (OH) 6 +6HCl.
The same is true in the case of ferric acetate, which is still more
easily hydrolyzed and more completely than the ferric chloride, and
with stannic salts, titanium salts, etc.
As examples of the production of volatile bodies ; bicarbonate of
sodium is decomposed in dilute solutions into the neutral normal
carbonate and free carbon dioxide which remains dissolved but
which one can readily show is present by passing through the solu-
tion an inert gas, hydrogen, for example, and bubbling this current
of gas through lime water. In many cases it is sufficient to evapo-
rate a solution and condense the vapors when a little acid of the salt
is found. Thus, the distillation of a solution of zinc acetate gives
acetic acid, that of ferric nitrate, nitric acid, etc. The hydrolysis of
solutions of ammonium salts, even of strong acids, can be rendered
manifest as Berthelot* has shown by distilling dilute solutions of
these salts; ammonia, freed by hydrolysis, and very volatile, is
released, while the acid, which forms with the water a much more
* Ibid., II. 219.
BASED UPON CHEMICAL REACTIONS 59
stable combination, remains in the distilling flask and makes the
liquid more and more acid. An alkaline test of the distillate and an
acid test of the residue show the presence of free acid and free base,
and enable the estimation of the proportion of salts decomposed.
By employing 10 grams of salts dissolved in 250 c.c. and by collect-
ing the distillate until about one half of the volume is distilled off,
Berthelot found that the following decomposition was produced
under these circumstances :
For the chloride i thousandth part
For the nitrate 2 thousandth part
For the sulphate 5 thousandth part.
This proportion is greater for salts of organic acids, which are much
more strongly hydrolyzed than the preceding salts of strong acids.*
Finally, in certain cases, we can produce hydrolysis by the indi-
rect reaction of the acid or the free base of the hydrolyzed salt; if,
for example, to a concentrated solution of sodium borate, colored
blue by litmus, acetic acid is added until the red tint just begins to
appear, and if it is then diluted with a large quantity of water, the
blue color will reappear, demonstrating the liberation of alkali. We
can equally well prove the production of free sodium hydroxide in
the dilute sodium borate by adding silver nitrate to a concentrated
solution of this salt which precipitates white silver borate, then to a
very dilute solution which precipitates brown oxide of silver (Rose).
The hydrolysis of ammonium chloride can be demonstrated by
adding phenolphthalein to a concentrated solution of this salt and
then enough ammonium hydroxide to make the solution distinctly
pink; by then diluting the solution with water, the pink coloration
disappears by reason of the liberation of a little hydrochloric acid
(Ostwald).
In the saponification of esters by water, which is related to the
phenomenon of hydrolysis, the liberation of acid is manifest likewise
by the increasing acidity of the water up to a certain limit.
* This decomposition of ammonium salts by water at the boiling tempera-
ture ought always to be considered, in the precipitations made by the addition
of ammonium hydroxide to boiling acid solutions of salts of iron (ferric),
aluminium, etc. In many cases, in order to obtain a more complete precipi-
tation there is a tendency to add a slight excess only of ammonium hydroxide
and to heat a long time in order to expel this excess and collect the precipi-
tate; but it is necessary to be very careful to verify at the end that the
liquid has not become acid, in which case the precipitation is necessarily
incomplete.
60 METHODS OF ANALYTICAL CHEMISTRY
Dialysis can reveal the production of the acid liberated in