Answer to Question #109325 in Physical Chemistry for GHOST

Question

Give the thermodynamic derivation of the distribution law

Answer 1

The thermodynamic derivation of the distribution law is based upon he principle that if there are two phases in equilibrium (i.e. two immiscible solvents containing the same solute dissolved in them), the chemical potential of a substance present in them must be same in both the phases.

The chemical potential of a substance in a solution given by

Where 'm' is the standard chemical potential and ‘a’ is the activity of the substance (solute) in the solution.

Thus for the solute in liquid A, we have

Similarly for the solute in liquid B we have

But as already stated, since the liquids A and B are in equilibrium,

Further at a given temperature, 'm_A' and 'm_B' are constant for given substance in the particular solvents. Hence at constant temperature, we have from equation

and therefore 

Which is the original form of the distribution law.