[225] See Chapter VIII in regard to this proof that mercuric sulphide is less soluble than mercuric oxide and in regard to the question how, by a continuous disturbance of the equilibrium conditions, all the mercury may be precipitated from the cyanide solution as the sulphide, in spite of the very slight degree of ionization of the cyanide.
[226] The chloride is, however, sufficiently ionized to make possible the precipitation of the very insoluble silver chloride, when silver nitrate is added to its solution.
CHAPTER VII PHYSICAL OR HETEROGENEOUS EQUILIBRIUM.—THE COLLOIDAL CONDITION
The law governing physical or heterogeneous equilibrium applies to all cases where, at a constant temperature, one and the same chemical substance is present in two or more physical conditions, or "phases," in contact and in equilibrium with each other. We have, for instance, the common case of a liquid, say water, in contact with its vapor, or the liquid in contact with its solid phase (ice) and its vapor; or, we may have a gas, say oxygen, in contact with its solution in some solvent like water. We may have a solid, like cane sugar, in contact with its solution. We may also have a substance like bromine, which is soluble both in chloroform and in water, present in both solutions at the same time, the two solutions being in contact but immiscible. These cases represent the most common types of systems to which the law of physical equilibrium may be applied, although the list has by no means been exhausted. The law of physical or heterogeneous equilibrium states that when one and the same chemical compound is present in two physical states or phases, as expressed in the equation S1 ⇄ S2, then when equilibrium is reached, at a given temperature, the ratio of the concentrations of the substance in the two phases is some constant number:
[S1] : [S2] = k.
The bracketed symbols denote concentrations.
It should be noted that the condition of equilibrium is independent of the total quantity[227] of substance present in either phase or in both phases; that is, provided the ratio of the concentrations is maintained constant at a given temperature, the quantity of substance present in both phases or in either phase is variable. For instance, the condition of equilibrium between water and [p119] water vapor is independent of the quantity of water or of water vapor present: in a closed liter bottle containing water and water vapor, the ratio of the concentrations is maintained, irrespective of the question whether the bottle contains 10 c.c. of water and 990 c.c. of vapor or 990 c.c. of water and 10 c.c. of vapor.
The law is one of experience; instances of its application are given below. Its probable theoretical significance may be explained mechanically with the aid of the kinetic theory of gases and solutions, as follows: If chloroform is added to a solution of bromine in water, the chloroform takes up part of the bromine and, if the mixture is vigorously shaken, a condition of equilibrium and a definite distribution of bromine between the two solvents will result (exp.[228]). Now, if one imagines a liter of the aqueous solution to contain one mole of bromine at some given temperature and to cover a liter of chloroform, the whole system being left to itself, then all the conditions affecting the migration of the bromine into the chloroform will be definite ones—the concentration of the bromine, the temperature, the surface between the two solvents—and bromine will pass from the aqueous solution into the chloroform solution at a definite speed. We may call the quantity (in moles) of bromine which would enter the chloroform in one minute, if the concentration of the bromine in the water were kept constant (one mole) throughout the minute, the velocity of migration of the bromine—this velocity, like chemical velocity, representing a quantity, not a distance. The velocity being a definite one under these conditions, we have v1 = k1. Now, if all the conditions are left unaltered, except that the concentration of the bromine is changed, say kept at one-hundredth its original value, then only one one-hundredth as many molecules of bromine as in the first case will come into contact with the chloroform surface in unit time. The chances for migration are one one-hundredth as great, and the quantity entering the chloroform in unit time—the velocity of the [p120] change—will be one one-hundredth of the original velocity. In general, the velocity will be proportional to the concentration of the bromine [Br]aq. in the water at any moment and to the characteristic constant k1.
v1 = [Br]aq. × k1.