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. C^n.
The number of collisions of n1 molecules of A1, n2 molecules of A2 ...
is accordingly proportional to C1^{n1}C2^{n2} ..., and the
reaction-velocity corresponding to it is therefore
v = kC1^{n1}C2^{n2} ...,
and similarly the opposed reaction-velocity is
v' = k'C'1^{n'1}C'2^{n'2} ...;
the resultant reaction-velocity, being the difference of these two
partial velocities, is therefore