The change in the quantity of water brought about the difference in result—the quantitative relations were altered thereby. In order to follow intelligently this and the other actions referred to, the study of reactions in solutions must be taken up from the quantitative side—the development heretofore has been essentially qualitative in character. On several occasions we have found that all electrolytes do not ionize equally well, and that the intensity of their action, demonstrated, for instance, for potassium and ammonium hydroxides, varies accordingly. We shall now have to study these relations in greater detail.
For our purpose, the study of two of the fundamental quantitative laws governing action in solution and of their application to analytical phenomena, will be sufficient: these are, the law of chemical or homogeneous equilibrium, in which the law of mass action is included, and the law of physical or heterogeneous equilibrium.
The Law of Chemical Equilibrium.
A + B ⇄ C + D,
in which A, B, C and D represent four different substances reacting in the molecular proportions indicated by their symbols, which as usual represent molecular weights. And the condition for equilibrium may be expressed in the mathematical equation
[A] × [B] / ([C] × [D]) = k.
[A], [B], [C] and [D] are used to represent the concentrations[166] of [p092] the four reacting substances and k is some definite number, called the equilibrium constant.
The law was discovered by Guldberg and Waage in 1867, and, with certain limiting conditions (see below) it has been fully established by extensive experimental work.[167] The significance of the law may be interpreted on the basis of the following considerations. If we start with the two substances A and B alone and have one mole of each in one liter (as gas or in solution) at a given temperature, then, all the conditions being given,—the temperature, the concentrations, and the nature of the substances,—the reaction A + B → C + D, leading to the formation of C and D, will proceed with a perfectly definite velocity. The molecules of A and of B move in all directions (kinetic theory of gases and solutions), and molecules of A will collide with molecules of B a definite number of times in unit time and will form a definite number[168] of molecules of C and D per minute. The velocity of chemical change of a given substance (chemical velocity) is also measured in terms of moles, and is represented by the number of moles or the fraction of a mole changed per minute. If v′1 stands for the velocity of the action between A and B, under the given conditions, then
v′1 = k1,
where k1 is some number. Now, if the concentration of one of the components, e.g. A, should be doubled, then the chances for collision and for action between molecules of A and B will be twice as great as before and the velocity of the action will be doubled. If only one-tenth of the concentration of A (one-tenth mole) is used, the velocity will only be one-tenth as great as originally, and, in general terms, if [A] moles of A are used per liter, the velocity of the change will be proportional to [A], and equal to k1 × [A]. If the concentration of the other reacting component, B, is now doubled, the chances for action are again doubled, and, in general, the velocity of the action will be proportional also to the concentration [p093] [B] of the second reacting substance. For the velocity, v1 of the action for any concentrations, [A] and [B], of A and B at any moment at a given temperature, we have