Limitations and applications of the laws.
These formulae hold for gases and for dilute solutions, but assume the
system to be homogeneous, i.e. to be either a homogeneous gas-mixture or
a homogeneous dilute solution. The case in which other states of matter
share in the equilibrium permits of simple treatment when the substances
in question may be regarded as pure, and consequently as possessing
definite vapour-pressures or solubilities at a given temperature. In
this case the molecular species in question, which is, at the same time,
present in excess and is hence usually, called a _Bodenkorper_, must
possess a constant concentration in the gas-space or solution. But since
the left-hand side of the last equation contains only variable
quantities, it is simplest and most convenient to absorb these constant
concentrations into the equilibrium-constant; whence we have the rule:
leave the molecular species present as _Bodenkorper_ out of account,
when determining the concentration-product. Guldberg and Waage expressed
this in the form "the active mass of a solid substance is constant." The
same is true of liquids when these participate in the pure state in the
equilibrium, and possess therefore a definite vapour-pressure or
solubility. When, finally, we are not dealing with a dilute solution but
with any kind of mixture whatever, it is simplest to apply the law of
mass-action to the gaseous mixture in equilibrium with this. The
composition of the liquid mixture is then determinable when the
vapour-pressures of the separate components are known. This, however, is
not often the case; but in principle this consideration is important,
since it involves the possibility of extending the law of chemical
mass-action from ideal gas-mixtures and dilute solutions, for which it
primarily holds, to any other system whatever.
The more recent development of theoretical chemistry, as well as the
detailed study of many chemical processes which have found technical
application, leads more and more convincingly to the recognition that in
the law of chemical mass-action we have a law of as fundamental
significance as the law of constant and multiple proportions. It is
therefore not without interest to briefly touch upon the development of
the doctrine of chemical affinity.
_Historical Development of the Law of Mass-action._--The theory
developed by Torbern Olof Bergman in 1775 must be regarded as the first
attempt of importance to account for the mode of action of chemical
forces. The essential principle of this may be stated as follows:--The
magnitude of chemical affinity may be expressed by a definite number; if
the affinity of the substance A is greater for the substance B than for
the substance C, then the latter (C) will be completely expelled by B
from its compound with A, in the sense of the equation A.C + B = A.B +
C. This theory fails, however, to take account of the influence of the
relative masses of the reacting substances, and had to be abandoned as
soon as such an influence was noticed. An attempt to consider this
factor was made by Claude Louis Berthollet (1801), who introduced the
conception of chemical equilibrium. The views of this French chemist may
be summed up in the following sentence:--Different substances have
different affinities for each other, which only come into play on
immediate contact. The condition of equilibrium depends not only upon
the chemical affinity, but also essentially upon the relative masses of
the reacting substances.
Essentially, Berthollet's idea is to-day the guiding principle of the
doctrine of affinity. This is especially true of our conceptions of many
reactions which, in the sense of Bergman's idea, proceed to completion,
i.e. until the reacting substances are all used up; but only for this
reason, viz. that one or more of the products of the reaction is removed
from the reaction mixture (either by crystallization, evaporation or
some other process), and hence the reverse reaction becomes impossible.
Following Berthollet's idea, two Norwegian investigators, C.M. Guldberg
and Peter Waage, succeeded in formulating the influence of the reacting
masses in a simple law--the law of chemical mass-action already defined.
The results of their theoretical and experimental studies were published
at Christiania in 1867 (_Etudes sur les affinites chimiques_); this work
marks a new epoch in the history of chemistry. Even before this,
formulae to describe the progress of certain chemical reactions, which
must be regarded as applications of the law of mass-action, had been put
forward by Ludwig Wilhelmy (1850), and by A.G. Vernon-Harcourt and
William Esson (1856), but the service of Guldberg and Waage in having
grasped the law in its full significance and logically applied it in all
directions, remains of course undiminished. Their treatise remained
quite unknown; and so it happened that John Hewitt Jellett (1873), J.H.
van't Hoff (1877), and others independently developed the same law. The
thermodynamic basis of the law of mass-action is primarily due to
Horstmann, J. Willard Gibbs and van't Hoff.
_Applications._--Let us consider, as an example of the application of
the law of mass-action, the case of the dissociation of water-vapour,
which takes place at high temperatures in the sense of the equation 2H2O
= 2H2 + O2. Representing the concentrations of the corresponding
molecular species by [H2], &c., the expression [H2]^2 [O2] / [H2O]^2 must
be constant at any given temperature. This shows that the dissociation
is set back by increasing the pressure; for if the concentrations of all
three kinds of molecules be increased by strong compression, say to ten
times the former amounts, then the numerator is increased one thousand,
the denominator only one hundred times. Hence if the original
equilibrium-constant is to hold, the dissociation must go back, and,
what is more, by an exactly determinable amount. At 2000 deg. C.
water-vapour is only dissociated to the extent of a few per cent;
therefore, even when only a small excess of oxygen or hydrogen be
present, the numerator in the foregoing expression is much increased,
and it is obvious that in order to restore the equilibrium state, the
concentration of the other component, hydrogen or oxygen as the case may
be, must diminish. In the case of slightly dissociated substances,
therefore, even a relatively small excess of one component is sufficient
to set back the dissociation substantially.
_Chemical Kinetics._--It has been already mentioned that the law of
chemical mass-action not only defines the conditions for chemical
equilibrium, but contains at the same time the principles of chemical
kinetics. The previous considerations show indeed that the actual
progress of the reaction is determined by the difference of the
reaction-velocities in the one and the other (opposed) direction, in the
sense of the corresponding reaction-equation. Since the
reaction-velocity is given by the amount of chemical change in a small
interval of time, the law of chemical mass-action supplies a
differential equation, which, when integrated, provides formulae which,
as numerous experiments have shown, very happily summarize the course of
the reaction. For the simplest case, in which a single species of
molecule undergoes almost complete decomposition, so that the
reaction-velocity in the reverse direction may be neglected, we have the
simple equation
dx/dt = k(a-x)
and if x = 0 when t = 0 we have by integration
k = t^{-1}log{a/(a-x)}.