The conceptions of osmotic pressure and ideal semi-permeable membranes enable us to deduce other thermodynamic relations between the different properties of solutions.
Artificial membranes are seldom or never perfectly semi-permeable - some leakage of solute nearly always occurs, but the imperfections of actual membranes need no more prevent our use of the ideal conception than the faults of real engines invalidate the theory of ideal thermodynamics founded on the conception of a perfect, reversible, frictionless, heat engine.
From this equation the osmotic pressure Po required to keep a solution in equilibrium as regards its vapour and through a semi-permeable membrane with its solvent, when that solvent is under its own vapour pressure, may be calculated from the results of observations on vapour pressure of solvent and solution at ordinary low hydrostatic pressures.
The vapourmolecules of the solvent are free to pass through the semi-permeable membrane, and will continue to condense in the solution until the hydrostatic pressure is so raised as to produce equality of vapour-pressure.
They merely show that, in the conditions of the particular experiments, the thermodynamic equilibrium value of the osmotic pressure cannot be reached - the thermodynamic or theoretical osmotic pressure (which must be independent of the nature of the membrane provided it is truly semi-permeable) is a different thing from the equilibrium pressure actually reached in a given experiment, which measures the balance of ingress and egress of solvent through an imperfect semi-permeable membrane.
The osmotic pressures of strong sugar solutions were measured successfully by a direct method with semi-permeable membranes of copper ferrocyanide by Lord Berkeley and E.
The conception of a semi-permeable membrane, permeable to the solvent only, was used by van't Hoff as a means of applying the principles of thermodynamics to the theory of solution.
On this view, the function of the solvent is to give space for the solute to diffuse, and the pressure on a semi-permeable membrane is due to the excess of solvent molecules entering over those leaving in consequence of the smaller number which impinge on the membrane from the side of the solution; the defect in the number must be proportional, roughly at any rate, to the number of solute molecules, present, that is, to the strength of the solution.
The osmotic pressure (defined as the difference in the hydrostatic pressures of the solution and solvent when their vapour pressures are equal and they are consequently in equilibrium through a perfect semi-permeable membrane) may also depend on the absolute values of the hydrostatic pressures, as may the vapour pressure of the liquids.
Solvent may be supposed to be squeezed out from the solution which has become more dilute through a semi-permeable wall, and through another such wall allowed to mix with the solution which in the electrical operation had become more concentrated.