Osmotic pressure for incompressible solutions

When solutions are incompressible, the partial molecular volumes 

The function F /V can easily be interpreted it is related to the Helmholtz free energy (V, N ) by the equality 

However, let us note that here F, fV ) is a function which varies very rapidly with V and which is not of interest for us. 

The function F A itself can be expressed as a function of the solute concentrations 

Let us now calculate the osmotic pressure of a solution made of (m + 1) constituents. The species with s/ = 0,. .., 1 can cross the membrane and are present in cells I and II. On the contrary, the species with si = / + 1,. . . , m cannot cross the membrane and are found only in cell I. The osmotic equilibrium is defined by the conditions 

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