The Elements of Qualitative Chemical Analysis, vol. 1, parts 1 and 2. / With Special Consideration of the Application of the Laws of Equilibrium and of the Modern Theories of Solution.

by Julius Stieglitz

v₁ = k₁ × [A] × [B].

Hence, if by the symbols [A] and [B] the concentrations at any given moment are represented, we may say that the velocity of the formation of C and D at that moment[169] is proportional to the product of the concentrations of A and B, and to some constant, which is characteristic of the interaction of A and B.

The validity of this conclusion has been fully verified by experiment.[170] The case is an instance of the law of mass action, which states that in chemical changes the velocity of the action is proportional at any moment to the molecular concentrations[171] of the reacting components, and to a constant, which is characteristic of the chemical nature of the reacting components (and of the temperature).

If we start with the reversed action

A + B ← C + D,

the relation may be developed in the same way. Thus the two substances C and D will react upon each other, at the given temperature, with a velocity proportional to a constant, k₂, and, at any given moment, proportional also to their respective concentrations at that moment:

v₂ = k₂ × [C] × [D].

Equilibrium will be reached when the substances A and B are formed at any moment from C and D just as rapidly as they are used up to produce C and D, and vice versa. Such is the case, [p094] when the velocities of the two opposite reactions are equal to each other. For the condition of equilibrium, then, v₁ must be equal to v₂ and therefore

k₁ × [A] × [B] = k₂ × [C] × [D]

or