this is a special case of the general equation
n1A1 + n2A2 + ... <--> n'1A'1 + n'2A'2 + ...,
in which only one molecule of each substance takes part in the reaction.
The reacting substances may be either gaseous or form a liquid mixture,
or be dissolved in some selected solvent; but in each case we may state
the following considerations regarding the course of the reaction. For a
transformation to take place from left to right in the sense of the
reaction equation, all the molecules A1, A2, ... must clearly collide at
one point; otherwise no reaction is possible, since we shall not
consider side-reactions. Such a collision need not of course bring about
that transposition of the atoms of the single molecules which
constitutes the above reaction. Much rather must it be of such a kind as
is favourable to that loosening of the bonds that bind the atoms in the
separate molecules, which must precede this transposition. Of a large
number of such collisions, therefore, only a certain smaller number will
involve a transposition from left to right in the sense of the equation.
But this number will be the same under the same external conditions, and
the greater the more numerous the collisions; in fact a direct ratio
must exist between the two. Bearing in mind now, that the number of
collisions must be proportional to each of the concentrations of the
bodies A1, A2, ..., and therefore, on the whole, to the product of all
these concentrations, we arrive at the conclusion that the velocity v of
the transposition from left to right in the sense of the reaction
equation is v = kc1c2 ..., in which c1, c2, ... represent the spatial
concentrations, i.e. the number of gram-molecules of the substances A1,
A2, ... present in one litre, and k is, at a given temperature, a
constant which may be called the velocity-coefficient.
Exactly the same consideration applies to the molecules A'1, A'2.... Here
the velocity of the change from right to left in the sense of the
reaction-equation increases with the number of collisions of all these
molecules at one point, and this is proportional to the product of all the
concentrations. If k' denotes the corresponding proportionality-factor,
then the velocity v' of the change from right to left in the sense of the
reaction-equation is v' = k'c'1c'2.... These spatial concentrations are
often called the "active masses" of the reacting components. Hence the
reaction-velocity in the sense of the reaction-equation from left to
right, or the reverse, is proportional to the product of the
"active-masses" of the left-hand or right-hand components respectively.
Law of chemical statics.
Neither v nor v' can be separately investigated, and the measurements of
the course of a reaction always furnish only the difference of these two
quantities. The reaction-velocity actually observed represents the
difference of these two partial reaction-velocities, whilst the amount
of change observed during any period of time is equal to the change in
the one direction, minus the change in the opposite direction. It must
not be assumed, however, that on the attainment of equilibrium all
action has ceased, but rather that the velocity of change in one
direction has become equal to that in the opposite direction, with the
result that no further total change can be observed, i.e. the system has
reached equilibrium, for which the relation v - v' = 0 must therefore
hold, or what is the same thing
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.
Law of chemical kinetics.
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 equilibrium state, is given by the equation