kc1c2 ... = k’c’1c’2 ...,
this is the fundamental law of chemical statics.
The conception that the equilibrium is not to be attributed to absolute indifference between the reacting bodies, but that these continue to exert their mutual actions undiminished and the opposing changes now balance, is of fundamental significance in the interpretation of changes of matter in general. This is generally expressed in the form: the equilibrium in this and other analogous cases is not static but dynamic. This conception was a direct result of the kinetic-molecular considerations, and was applied with special success to the development of the kinetic theory of gases. Thus with Clausius, we conceive the equilibrium of water-vapour with water, not as if neither water vaporized nor vapour condensed, but rather as though the two processes went on unhindered in the equilibrium state, i.e. during contact of saturated vapour with water, in a given time, as many water molecules passed through the water surface in one direction as in the opposite direction. This view, as applied to chemical changes, was first advanced by A.W. Williamson (1851), and further developed by C.M. Guldberg and P. Waage and others.
From the previous considerations it follows that the reaction-velocity at every moment, i.e. the velocity with which the chemical process advances towards the Law of chemical kinetics. equilibrium state, is given by the equation
V = v - v′ = kc1c2 ... - k′c′1c′2 ...;
this states the fundamental law of chemical kinetics.
The equilibrium equation is simply a special case of this more general one, and results when the total velocity is written zero, just as in analytical mechanics the equilibrium conditions follow at once by specialization of the general equations of motion.
No difficulty presents itself in the generalization of the previous equations for the reaction which proceeds after the scheme
n1A1 + n2A2 + ... = n′1A′1 + n′2A′2 + ...,
where n1, n2, ..., n′1, n′2, ... denote the numbers of molecules of the separate substances which take part in the reaction, and are therefore whole, mostly small, numbers (generally one or two, seldom three or more). Here as before, v and v′ are to be regarded as proportional to the number of collisions at one point of all molecules necessary to the respective reaction, but now n1 molecules of A1, n2 molecules of A2, &c., must collide for the reaction to advance from left to right in the sense of the equation; and similarly n′1 molecules of A′1, n′2 molecules of A′2, &c., must collide for the reaction to proceed in the opposite direction. If we consider the path of a single, arbitrarily chosen molecule over a certain time, then the number of its collisions with other similar molecules will be proportional to the concentration C of that kind of molecule to which it belongs. The number of encounters between two molecules of the kind in question, during the same time, will be in general C times as many, i.e. the number of encounters of two of the same molecules is proportional to the square of the concentration C; and generally, the number of encounters of n molecules of one kind must be regarded as proportional to the nth power of C, i.e. Cn.