The relation between the osmotic pressure and the vapour pressure in a concentrated solution

Abstract

1. The relation between the vapour pressure and the osmotic pressure of a solution is often investigated by considering the equilibrium of a column of solution separated at the bottom from the pure solvent by a semi-permeable membrane, and placed in an atmosphere of vapour from the solvent. Now the hydrostatic equilibrium of the vapour column gives δp = gs -1 δh , where p is the vapour pressure of the pure solvent, g the acceleration due to gravity, h the height above the surface of the pure solvent, and s the specific volume of the vapour. Hence considering the equilibrium of the liquid column we get P + p - p' = ρhg = ρ ∫ p p' sdp , when P is the osmotic pressure, p' the vapour pressure of the solution, p that of the pure solvent, and where ρ is the effective mean density of the column of liquid.