strengths are equivalent at very high dilutions.
Heat of Neutralisation and the Law of Thermoneutrality. One
can calculate with the aid of the electrolytic theory the heat liberated
by the chemical reaction between two electrolytes, notably by the
106 METHODS OF ANALYTICAL CHEMISTRY
neutralization of acids by bases. Let us consider, for example, a
strong acid (HC1), and a strong base (NaOH), and, with Arrhenius
assume them to be completely ionized, as well as the product (NaCl)
of their reaction. We had before mixing, the free ions, H, Cl, Na
and OH, and after reaction, we have as free ions Na and Cl; the
only reaction which has been produced is the union of the ions H
and OH, to form water, H 2 O, dissociated to an infinitely small
degree. The heat liberated by this reaction is the heat of combina-
tion of the H and OH ions which Arrhenius terms the heat of dis-
sociation of water.
Since all the strong acids and bases, as well as the neutral salts
which they produce, are practically completely dissociated into their
ions, one explains likewise, that the heat of formation of the neutral
salts should be obviously the same, whatever the salt, since they
are all reduced to nearly the heat of dissociation of the water. Like-
wise, the mixture of two neutral salts produces no perceptible evo-
lution of heat (Hess' law of Thermoneutrality) because, after the
mixing as before, one has only free ions in solution.
One can take into account, moreover, the small fraction of the
electrolytes undissociated, as determined by their conductivity, for
the exact calculation of their heat of neutralization, as Arrhenius
has shown it, and notice that there is an agreement between the heats
of neutralization determined by the calorimeter and that deduced
from calculation, according to the electrolytic theory.
Another consequence which Ostwald* draws from this theory is
the instantaneousness of the double decomposition of salts, that are
highly ionized. If a reaction among electrolytes is slow, one may
be sure that one of the substances at least is very slightly ionized.
This is what takes place notably in phenomena of hydrolysis where
water intervenes molecularly in the reaction.
Direction of Transformations by Double Decomposition of
Salts. Starting with these principles, Ostwald assumes that it is in
the direction of the formation of the least ionized electrolyte that
reactions among electrolytes occur. "Two neutral salts," he says,t
"exert almost no action upon one another, because both they them-
selves and the possible resultant new salts produced by their double
decomposition are all strongly ionized and the ions remain substan-
tially in their original condition." . . . "An action takes place, how-
*Loc. cit. p. 51.
t Ibid, (zd English Ed. 1908, pp. 64-65. Editors' Note.)
BASED UPON CHEMICAL REACTIONS 107
ever, if the ions present are capable of uniting to form one or more
compounds, which are either not dissociated at all (practically
speaking) or only slightly so under the existing conditions. The
constant k has then a small value ; in the equation ab = kc, a and b
(the concentrations of the ions) must therefore become greatly re-
duced, while c (the concentration of the non-dissociated portion)
must grow correspondingly, until the equation is fulfilled."
"The reaction thus results in the more or less complete disap-
pearance of the ions of the electrolyte, which has a small constant,
k, going as they do to build up the non-ionized portion."
From this, according to Ostwald, results the neutralization of
strong acids by strong bases causing the formation of very slightly
dissociated water ; the displacement of the weak acid of a salt by a
strong acid, because the salt of a weak acid is still considerably dis-
sociated, while the free weak acid is but slightly dissociated; the
tendency to the formation of insoluble substances, because the con-
centration of the ions of insoluble bodies is necessarily very small,
etc.
CHAPTER V
OBJECTIONS TO THE ELECTROLYTIC THEORY
The electrolytic theory explains the phenomena of double de-
composition of salts with great simplicity, and is certainly very
attractive by reason of the advantageous applications which it
allows in the varied lines of experimentation, such as osmotic pres-
sures, freezing points, vapor pressures, and electrical conductivities.
The extensive studies, which have been occasioned in these later
years by the conceptions of Arrhenius, have revealed, as we shall
subsequently see, such numerous disagreements between the facts
observed and the electrolytic theory, that it seems one can no longer
consider the latter but as the expression of an ideal physical law,
resting upon too fragile a foundation to base upon it the principles
of analytical chemistry.
After having presented as impartially as possible the electrolytic
theory of double decomposition of salts, we are now going to dis-
cuss it first, from a theoretical point of view, showing that, for a
number of incontestable facts, the explanations of our calorimetric
theory are equally as satisfactory as those of the electrolytic theory,
and that, for the phenomena of hydrolysis, the deductions of the
latter are even in contradiction with the direction of the reaction.
In the second place, from an experimental point of view, which
brings out the fact that, in the very field which Arrhenius has inves-
tigated, there are numerous disagreements between the facts and the
theory of ionization. We will close this critical examination by indi-
cating how the recent conceptions of the state of polymerization of
the solvents and of the solutes can account for the anomalies which
necessitate the use of the coefficient * for solutions of salts.
i. Objections of a Theoretical Character
Additive Properties, Speed of Reactions, etc. We will call
attention first to the fact that the additive properties of salt solutions,
explained upon the basis of the ionization of electrolytes, can be
equally well explained upon the basis of the hydrolysis of salts into
free acid and base. It suffices, in fact, to assume the dissociation of
1 08
BASED UPON CHEMICAL REACTIONS 109
the dissolved substance into any two parts whatever, the acid and
base as well as into the ions, each one endowed with specific proper-
ties, in order to arrive at the same conclusions.
As to the agreement between the speed of reaction and the con-
ductivity of the electrolytes which produce it, it can depend, in our
opinion, upon a much more general cause than the electrolytic dis-
sociation. This agreement is explained, in fact, quite as well, by
assuming that the speed of reaction considered by Ostwald, the
inversion of cane sugar by acids, is expressed by an equation of the
same form for all acids. The speed of this reaction which belongs
to the category of homogeneous systems with unlimited reaction,
ought to obey a law similar to the one applied to the irreversible
reactions of the same kind: (Chapter II, 2),
log (i-j) = -kt
in which p is the initial quantity of sugar, y, the quantity trans-
formed in the time t, and k, a function of the temperature, depend-
ing upon the strength of the. acid employed.
It is, in fact, this law which was verified by the experiments per-
formed in 1850 by Wilhelmy upon the inversion of cane sugar by
acids.*
Now, at a constant temperature, and for the same acid, k is a
function only of the concentration of the acid, or of a property, a
function, itself, of this concentration, such as the degree of hydroly-
sis, the heat of dilution, the electrolytic dissociation, etc. If, then,
we assume k = /(#), x being one of these properties taken as an
independent variable, we see that the comparison made by Ostwald
between the energy of different acids in the inversion of sugar
(see p. 99) is equivalent to comparing the values of t, correspond-
ing to y = , that is to say,
- lQ g ( * ^ _ A
t - ' /. / v *
A being a constant which has the same value, whatever may be the
acid. If the property x, taken as an independent variable, is con-
nected with the concentration of the acid by the same law for all
*W. Ostwald, Abrege de Chimie generate, p. 335, of the French edition.
no METHODS OF ANALYTICAL CHEMISTRY
acids studied, which is not at all impossible, we see then that one
ought to find necessarily a perfect agreement between the results of
the experiments and those of calculation.
Likewise, it is natural that the study of equilibria between an
electrolyte and its ions and between two electrolytes (see page 99).
should have given excellent agreement between the experimental
and the calculated results, since it is a question here of clearly re-
versible phenomena, whose state of equilibrium depends exclusively
on the concentration of the solute present.
In what concerns the decrease of the activity of an acid by a
salt of this acid (addition of an electrolyte having a common ion,
page 100) which plays a principal role in many important methods
of inorganic analysis, it is very simply explained by phenomena of
hydration. We shall have occasion, subsequently, to show it in
detail in one of the following chapters, apropos of one of these
methods (precipitation of metals of the iron group by H 2 S in an
acetic acid solution). In the example chosen by Arrhenius for his
verification (the retarding action of NH 4 C1 in the saponification of
ethyl acetate by NH 3 ) the reaction is easily understood, by recalling
the fact that NH 4 C1 is slightly hydrolyzed into NH 3 and HC1 (see
page 59). The addition of increasing proportions of NH 4 C1 to the
ammoniacal system + ethyl acetate, increases the concentration of
free HC1 proportionally to this addition without changing appreci-
ably that of the free ammonia. And, as we know, from the work of
Berthelot and Pean de Saint-Gilles, that the quantity of ester pro-
duced in the action of an acid upon an alcohol is proportional to
the quantity of acid for a constant quantity of alcohol (see page 70)
we see that one can retard the saponification of acetic ester almost
proportionally to the quantity of NH 4 C1 introduced.
As to the classification of acids and bases, the one Ostwald de-
duced from their degree of ionization is exactly the same as the one
we established from the respective heats of neutralization. The
anomalies presented by certain salts are explained just as well by
one theory as by the other. We can say, for example, that HgO
functions as a strong base and displaces the potassium in its halogen
compounds by reason of its heat of neutralization with the halogens,
being greater in the case of HgO than with the KOH. The elec-
trolytic theory explains this abnormal displacement by saying that
the reaction is produced because there results from it mercury salts
which are very slightly ionized.
BASED UPON CHEMICAL REACTIONS in
Finally, the equality of strength of the acids in the state of infinite
dilution, deduced by Ostwald from the complete ionization in this
state, results in our calorimetric theory, from this fact that in the
state of infinite dilution, all salts ought to be entirely hydrolyzed,
and their acids set wholly free.
The Law of Thermoneutrality. Hess' law of thermoneutrality,
which has been brought forward as a decisive argument in favor of
the electrolytic theory, can equally in our opinion, find an explana-
tion in two very general cases.
i. The first is that every reversible reaction ought to cause some
small thermal change. This is confirmed both by theory and
experiment. We saw (see Chapter II, 2) that from the two
principles of thermodynamics, there can be deduced that the heat Q
liberated by any reaction whatever carried out at the absolute tem-
perature T, is the sum of two terms; one the compensated heat
T(S A SB) corresponding to the variation of the entropy S in
the initial and final state (a term which may be positive or negative),
the other term, the noncompensated heat TP, a term always positive
and which represents the fraction of the heat of reaction susceptible
of being transformed into mechanical work :
Q = T(S A -S B )+TP.
In reversible reactions (system in equilibrium) the term TP is
zero, since any initial modification in a system in equilibrium can
produce no noncompensated heat, without which the system would
be out of equilibrium and would tend to approach the system giving
the term TP = zero. In double decompositions of salts, which are
reactions of equilibrium, we have, then,
Q = T(S A -S B ).
Now, experiment shows that in reactions, even the most ener-
getic, the compensated heat is reduced to a few hundredths of the
total heat liberated, in all cases, where the compensated and non-
compensated heat can be estimated separately for example, combus-
tion of carbon monoxide, and reactions employed in electrical
batteries.
As the heat of neutralization of acids by the strongest bases does
not exceed about fifteen Calories, it is understood that the heat liber-
ated in a double decomposition of salts such as
H2 METHODS OF ANALYTICAL CHEMISTRY
represents only a relatively small fraction of the fifteen Calories;
in fact, it is still two Calories or a little more than a tenth of
the heat of neutralization of potassium hydroxide by a strong acid
(13.7 Cal. with HC1, 15.7 Cal. with ^H 2 SOJ.
The same conclusions can be verified in the reversible reactions
in which ionization certainly plays no role. Let us take, for ex-
ample, the action at high temperature of oxygen on anhydrous
metallic chlorides and, inversely, of chlorine on oxides. The reac-
tions are not generally reversible, but, however, there exists a well-
known case in which a metallic chloride can be decomposed at will
by a current of oxygen and the oxide of the same metal by a current
of chlorine. This is the reaction used in the preparation of chlorine
by the Weldon-Pechiney process:
MgCl 2 +O ** 2Cl+MgO.
If the preceding reasoning is correct, the heats of combination
of magnesium and chlorine and magnesium and oxygen ought to
differ but slightly, so that this reaction liberates but little heat. This
is, indeed, what has been found by experiment: Mg-j-O liberates
143.4 Calories and Mg+Cl 2 gives 151.2 Calories. The difference,
7.8 Calories, which represents the heat liberated in the previously
mentioned reaction, is even proportionately much greater than the
difference between the heats of neutralization of potassium hydrox-
ide by hydrochloric and by sulphuric acids.
We have practically the same thing for the following reaction
which is reversible at a high temperature (red heat) :
Fe 2 O 3 +6H <- 3H 2 O+2Fe.
2Fe+3O liberates, in fact, 65.2X3 Calories and 6H-J-3O,
58.7X3 Calories. The difference scarcely exceeds one tenth of the
heat of combustion of iron in oxygen. By taking, one by one, all of
the known reversible reactions, one would, likewise, arrive at this
conclusion, that in these reactions the heats of combination of the
two opposed systems are but slightly different, that is to say, the
same law in reality, as that of the thermoneutrality of salts.
2. The second reason for this law can be deduced from a very
general empirical law well known in organic chemistry in which it
BASED UPON CHEMICAL REACTIONS
has been established by numerous examples, namely, that the sub-
stitution of one radical for another in respect to bodies endowed
with analogous properties, liberates the same quantity of heat.
The inorganic compounds conform to it equally well and in-
numerable cases can be cited in confirmation of this. Thus, in the
substitution of hydrochloric acid for ^2H 2 SO 4 when in combination
with sodium, 2.1 Calories are absorbed, and when in combination
with ammonia, 2.05 Calories. That is to say, the same quantity,
although the heats of neutralization differ by more than one Calorie :
HC1
^H 2 S0 4
NaOH dissolved
NH 3
13.7 Cal.
12.45 "
15.85 Cal.
14-50 "
This alone suffices to explain the fact that the action of am-
monium sulphate upon sodium chloride liberates no heat even if
the reaction is complete, because the algebraic sum of the heats of
formation of the two opposed systems ought necessarily to be zero.
These examples could be easily multiplied by cases of double decom-
position of salts, but it seems to us of more interest to show it is the
same for reactions among molten anhydrous salts, having very dif-
ferent heats of formation.
Let us take, for example, the chlorides, bromides, chlorates and
nitrates of potassium, sodium and ammonium (strong monobasic
acids, in combination with analogous metals) and let us calculate
from the heats of formation of the salts in the solid state, starting
with the elements, what will be the heats liberated by the substitu-
tion of Br, (C1O 3 ) or (NO 3 ) for chlorine.
ELEMENT
OR
RADICALS
HEAT OF COMBINATION OF
METALS WITH THE ELE-
MENTS IN COLUMN I
(ANHYDROUS SALT)
HEAT LIBERATED BY THE SUBSTITU-
TION OF THE GROUP IN COLUMN I
FOR CL IN THE ANHYDROUS SALT
K
Na
NH 4
K
Na
NH 4
Cl
Br
C10 3
N0 3
1057
99-3
93-8
1 1 9.0
97-9
89.8
84.8
1107
76.8
70.1
88.6
-6.4
i 1.9
+ 13-3
8.1
13-1
+ 12.8
-67
+ 11.8
From this table we see that the substitution of monovalent ele-
ments or groups of elements for a monovalent element, when com-
ii 4 METHODS OF ANALYTICAL CHEMISTRY
i
bined with the alkali metals, liberates exactly the same amount of
heat ; the differences do not reach two per cent of the total heat of
combination. So if we consider the mutual actions of any two salts
whatever in the preceding table, the heat liberated will be just as
small relatively as in the double decomposition of those salts in
aqueous solution, although it is a question here of salts whose heats
of formation vary within wide limits (from 70.1 Calories to 119).
lonization, properly speaking, moreover, cannot be assumed, since
these facts are absolutely independent of electrical conductivity and
are verified in the same manner in the homologous organic series of
nonelectrolytes.
Disagreement Between the Phenomena of Hydrolysis and the
Deductions of the Electrolytic Theory. One of the phenomena
which contradict most clearly the electrolytic theory is the hydrolysis
of salts in aqueous solutions. In the hydrolysis of ferric chloride,
Fe 2 Q 6 +6H 2 O ^ Fe 2 (OH) 6 +6HCl,
the electrolytic theory requires the dissociation of water into its
hydrogen (H) and hydroxyl (OH) ions, to produce ferric hydroxide
and hydrochloric acid. Now, the second system is much richer in
free ions than the first, since according to the electrolytic theory,
HC1 is almost completely ionized, while Fe 2 Q 6 is much less ionized
than HC1 (in the ratio of about three to five) and water and ferric
hydroxide, Fe 2 (OH) 6 , are not ionized at all. It is then, not in the
direction of the least ionized system that the reaction tends to be
produced, but on the contrary, in the direction of the most ionized
system, that is, in the inverse direction to the rule given by Ostwald
to predict double decomposition of salts. In fact, the hydrolysis of
Fe 2 Cl 6 and of most salts, absorbs heat, while the rule formulated by
Ostwald has, for its basis, the tendency to form water with the
liberation of 13.5 Calories.
In his Wissenschaftlichen Grundlagen der analytischen Chemie,
Ostwald tries, nevertheless, to connect the phenomena of hydrolysis
with electrolytic dissociation. This is the method which he employs.*
"Water," says Ostwald, "is a substance very slightly dissociated.
However, it contains a certain quantity of free H and OH ions which
has been estimated from recent researches at one gram molecule
of dissociated ions, in about ten million liters. . . . "
* Pages 64, 65, 3d German Edition (pages 69-70, 3d English Edition.
Editors' Note).
BASED UPON CHEMICAL REACTIONS 115
"In consequence of this in the process of neutralization of acids
and bases, there should remain in reality as many hydrogen and
hydroxyl ions as there are normally present in water, this residue
being extremely small and negligible in most cases. However, cases
may arise in which this small residue of free hydrogen and hydroxyl
ions exercises a measurable influence, and these conditions are real-
ized when the acid or base or even both of these are but slightly dis-
sociated, that is, are very weak. The presence of hydrogen ions in
the solution of a neutral salt, ought then to give, according to the
laws of chemical equilibrium, in combination with the free anions
of the salt, a certain quantity of undissociated acid, according to
the following equation, ab = kc. If k has a large value, as in the
case of strong acids, then c is very small, because b (the concentra-
tion of the hydrogen ions) is, itself, very small. But, if the value
of k is small, then c (the concentration of the undissociated part of
the acid) increases correspondingly, and if k approaches in its
numerical value to the constant of dissociation of water, then c be-
comes measurable, and we can recognize in the solution of neutral
salt of a similar acid, the presence of this non-ionized acid. Potas-
sium cyanide may be taken as an example of this ; hydrocyanic acid
has an extremely small constant of ionization, and an aqueous solu-
tion of potassium cyanide, therefore, contains a measurable quantity
of the undissociated acid, recognizable by its odor."
The explanation of Ostwald is admissible for the salts of ex-
tremely weak acids, but it is inapplicable to salts of strong acids
like ferric chloride and in a general way to most of the phenomena
of hydrolysis.
It is worth while to call attention here to the fact that in many
cases the explanations based upon the ionization of salts are exactly
the reverse of those that can be deduced from hydrolysis, because
the two phenomena are exactly the inverse of each other.
It is, in fact, those salts that are the least decomposed by water
into free acid and base (NaCl, K 2 SO 4 , etc.), that is, with a zero
heat of dilution, which are, according to the electrolytic theory, the
most strongly ionized, a fact that is shown by a very large molecular
electrical conductivity.
Inversely, the most poorly ionized salts, according to the electro-
lytic theory, i.e., those which yield poorly conducting solutions, are
those which are most decomposed in water into free acid and base,
that is to say, those whose heat of dilution is large, such as am-
n6 METHODS OF ANALYTICAL CHEMISTRY
monium borate, ferric chloride, ferric acetate, and, in general, the
salts formed from weak acids and bases.
It is, moreover, in conformity with the electrolytic theory that
this should be so. Weak acids and bases being much less ionized
than the neutral salts which they form, the more a neutral salt of
these acids and bases will be decomposed by water into free acid
and base, the fewer free ions will it give. Hydrolysis and ionization
are, then, complementary of each other, for salts of weak acids and
bases, and it is for this reason that the tables of classification of acids
and bases according to the order of strength, is the same whether
one depends upon the heats of neutralization or the degree of
ionization.
The uniform result is, then, that one may transpose without
difficulty an explanation based on the phenomena of hydrolysis into
an explanation founded on the electrolytic theory and inversely, as
we shall see subsequently.
2. Objections of an Experimental Character
At the time when Arrhenius proposed his electrolytic theory of
dissociation for salt solutions, there had been studied, from the points
of view of osmotic pressures, freezing points, boiling points, and elec-
trical conductivity, generally only very dilute aqueous solutions, and
the disagreement between the data obtained and the conceptions of
Arrhenius were so few that they could be passed over in the presence
of the magnificent generalizations allowed by the law of Van't Hoff
and the theory of ions, among phenomena so different in appearance.
In fact, the numerous researches inspired by the publications of
Arrhenius have all been directed with the aim of confirming his
theory. Notably, concentrated solutions or solutions in non-aqueous
solvents were left out of consideration for a long time. It is thus
that it is admitted, little by little, especially in Germany, thanks to
the authority of the illustrious promoters of the electrolytic theory,
that aqueous solutions of salts are alone endowed with electrical con-
ductivity, and that the dissolved substances possess abnormal weights,