96 THE THEORY OF IONIZATION
- When 4.88 grams of a certain other substance are dis-
solved in 50 grams of benzene the solution freezes at 2.85°.
What is the molecular weight of the substance?
Osmotic Pressure. From a consideration of the nature of osmotic
pressure (page 83) one would wonder how it could ever be meas-
ured. The pressure of a pure gas against a mercury surface or a
piston is readily determined. The total pressure of a gas mixture
is also just as readily determined, but the partial pressures of the
individual gases in the mixture cannot be separately measured.
Although osmotic pressure resembles the partial pressure of one
gas in a mixture, the problem is much more complicated than with
gases because of the enormous cohesion of liquids. If water, for
example, did not possess cohesion the expansive force of liquid
water at room temperature would be about 1,000 atmospheres.
Thus the cohesive force of water, or of a solution, is more than
1,000 atmospheres, and this force would apply to the molecules
of solute as well as of solvent to prevent them from escaping from
the bounding surface. Osmotic pressure does not exert its force
against a bounding surface such as a beaker or the air. Within
the solution the cohesive force acting upon the molecules of
solute is the same in every direction, and hence the net effect is
zero. Thus the solute resembles a gas, the cohesion between its
own molecules is negligible, and it expands until it has filled
the whole solution at a uniform concentration.
If a solution of sugar is placed in the bottom of a tall cylindrical
jar and pure water is carefully run in on top of it, so as to avoid
mixing the layers, and the whole is left undisturbed, the sugar by
virtue of its osmotic pressure diffuses upward until it has filled
the whole solution. The diffusion is of course slow because of the
friction between the sugar molecules and the water. If now we
could imagine a movable membrane impermeable to sugar,
the pores of which were filled with water, and if this membrane
were placed above the layer of sugar solution, and the cylinder
above the membrane were filled with pure water, then if the sugar
diffused upward it would have to push the membrane before it and
water would pass through the membrane as the latter moved
upward. Such a membrane is called a semipermeable membrane.
The pressure which would have to be applied to the membrane
to prevent its being pushed upward would be equal to the osmotic
pressure of the sugar.