of a solution is the number of moles
of solute per litre of solution, in contrast
which is the number of moles
of solute per kilogram of pure solvent. With
water as the solvent (which has a density of 1 kg per
litre) and with dilute solutions, in which the change
in volume of solvent upon adding solute is small, the
difference between molarity and molality also is small.
In the above expression, if the osmotic
pressure (P ) is measured in atmospheres, concentration
(CA) is in moles per litre, and T is the
absolute temperature in degrees Kelvin, then R is the
gas constant encountered first in Chapter 2: R = 0.0821
litre atm deg-1mol-1. (Notice
the similarity between the osmotic pressure law for
ideal dilute solutions and the gas law for ideal gases.)
Osmotic pressure is more sensitive to concentration
than is freezing point depression, and therefore is
more useful for molecular-weight determinations of large
Example. A 200-mg
sample of cytochrome c is dissolved in 10 ml of water.
The molecular weight of cytochrome c is 12,400. What
will be the osmotic pressure in the solution when diffusion
equilibrium is restored?