Mixtures at low compositions

Consider adding a small amount of A molecules to a liquid of B molecules (0 1). The free energy of mixing per site 

The free energy of mixing per site can then be rewritten for small 

Imagine a semipermeable membrane that prevents passage of A molecules, but allows passage of B molecules. The difference of pressure across this membrane is called the osmotic pressure of A molecules (see Section 1.7.1). The osmotic pressure is defined as the rate of change of the total free energy of the system ATmix = nAFmix with respect to volume at constant number of A molecules  

The volume fraction (j) of molecules each with monomers is the ratio of their volume to the volume V of the system  

The derivative with respect to volume V can be expressed in terms of the derivative with respect to composition 4 at constant number of. -molecules Ha- 

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