Thermodynamic Derivation of Nernst's Distribution Law

Thermodynamic Derivation of Nernst's Distribution Law

The thermodynamic derivation of the distribution law is based upon the principle that if there are two phases in equilibrium (i.e. two immiscible solvents containing the same solute dissolved in them), the chemical potential(μ) of a substance present in them must be same in both the phases.
From thermodynamics, we know that the chemical potential (μ) of a substance is a solution given by-
μ = μ^o + RT lna
Where μ^o is the standard chemical potential and 'a' is the activity of the solute in the solution.
Thus for the solute in liquid A, we have-
μ_A = μ^o_A + RT lna_A
Similarly for the solute in liquid B we have-
μ_B = μ^o_B + RT lna_B
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