On the other hand, if a solution of bromine in chloroform is covered with water, bromine enters the water (exp.).[229] We would find, by the method of analysis used before, and for the same conditions, that the velocity of migration, v2, of the bromine into the water is also proportional to a characteristic constant, k2, and to the concentration of the bromine in the chloroform [Br]ch.. We have, therefore v2 = [Br]ch. × k2.
Equilibrium between the two solutions will be reached when
v1 = v2 or [Br]aq. × k1 = [Br]ch. × k2,
from which follows that[230] for the condition of equilibrium
[Br]aq. / [Br]ch. = k2 / k1 = k.
Applications of the Law of Physical Equilibrium.
Now, at a fixed temperature, a pure liquid has a fixed concentration, its specific gravity being a definite one. Hence, for a fixed temperature, the second term of the constant ratio being definite, the first term, [CHCl3]vap., representing the concentration of the vapor, must also have a fixed, constant value for the condition of equilibrium, i.e. when the space above the liquid is saturated with its vapor. This is in agreement with well-known facts. The concentration of the vapor is usually expressed in terms of its [p121] pressure, and is called the vapor pressure or vapor tension of the liquid at the temperature in question. Tables giving the definite vapor pressures of important liquids at the various fixed temperatures are in common use.
(2) For oxygen in equilibrium with its saturated solution, say in water, at a fixed temperature, we have, according to the law, [O2]gas : [O2]solut. = k.
If the oxygen is under a given pressure at a definite temperature, its concentration [O2]gas is fixed, and consequently the second term, [O2]solut., of the ratio, the concentration of the dissolved oxygen, or its solubility, must also be definite, i.e. oxygen must have a definite solubility in water at a given temperature under a given pressure. If the pressure on the gas is doubled, its concentration is doubled and, to maintain the constant ratio, its solubility must also be doubled—which is in agreement with the facts (Henry's law). If air of the same pressure is taken, in place of pure oxygen, then the concentration of the oxygen (first term of the above ratio) is only about one-fifth as great as for the pure gas, and the water must be saturated with oxygen when it has taken up only one-fifth (second term of the ratio) as much as it would from the pure gas (Dalton's law): Each gas in a mixture is soluble in proportion to its own partial pressure or concentration.
(3) For sugar in equilibrium with its solution in water, i.e. in contact with its saturated solution, at a given temperature, we should have