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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. Limitations and applications of the laws.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 Bodenkörper, 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 Bodenkörper 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 (Études sur les affinités 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° 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(ax),

and if x = 0 when t = 0 we have by integration

k = t−1 log |a / (ax)|.

We will now apply these conclusions to the theory of the ignition of an explosive gas-mixture, and in particular to the combustion of “knallgas” (a mixture of hydrogen Theory of explosive combustion.and oxygen) to water-vapour. At ordinary temperatures knallgas undergoes practically no change, and it might be supposed that the two gases, oxygen and hydrogen, have no affinity for each other. This conclusion, however, is shown to be incorrect by the observation that it is only necessary to add some suitable catalyst such as platinum-black in order to immediately start the reaction. We must therefore conclude that even at ordinary temperatures strong chemical affinity is exerted between oxygen and hydrogen, but that at low temperatures this encounters great frictional resistances, or in other words that the reaction-velocity is very small. It is a matter of general experience that the resistances which the chemical forces have to overcome diminish with rising temperature, i.e. the reaction-velocity increases with temperature. Therefore, when we warm the knallgas, the number of collisions of oxygen and hydrogen molecules favourable to the formation