Thermodynamic Derivation Of The Distribution Law
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Thermodynamic Derivation of the Distribution Law
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.From thermodynamics, we know that the chemical potential


Where

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,



and therefore

This is the exact expression of the distribution law. However, if the solutions are dilute, the activates are equal o the concentrations so that the expression (3.3.6) is modified to

Which is the original form of the distribution law.
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