The expression which represents the chemical potential of the ith sp species (μi) in a mixture (i ≠ j) is · ABC26PH0576

Subject: Physical Chemistry · Chapter: Thermodynamics · Topic: Partial Molar Quantities · Exam: GATE 2005-2021 · Marks: 2 · Difficulty: Medium

The expression which represents the chemical potential of the $\mathrm{i}^{\text {th }}$ sp species $\left(\mu_{\mathrm{i}}\right)$ in a mixture $(\mathrm{i} \neq \mathrm{j})$ is
(a)$\left(\dfrac{\partial \mathrm{E}}{\partial \mathrm{n}_{\mathrm{i}}}\right)_{\mathrm{S}, \mathrm{V}, \mathrm{n}_{\mathrm{j}}}$
(b)$\left(\dfrac{\partial \mathrm{H}}{\partial \mathrm{n}_{\mathrm{i}}}\right)_{\mathrm{S}, \mathrm{V}, \mathrm{n}_{\mathrm{j}}}$
(c)$\left(\dfrac{\partial \mathrm{A}}{\partial \mathrm{n}_{\mathrm{i}}}\right)_{\mathrm{S}, \mathrm{V}, \mathrm{n}_{\mathrm{j}}}$
(d)$\left(\dfrac{\partial \mathrm{G}}{\partial \mathrm{n}_{\mathrm{i}}}\right)_{\mathrm{S}, \mathrm{V}, \mathrm{n}_{\mathrm{j}}}$
Answer
Answer: A ✓ checked by 4AB · confidence high

The source book printed no answer; this one was worked out and checked — see the explanation.

Explanation
With S, V and n_j held constant the natural function is U (here written E): μ_i = (∂U/∂n_i)_{S,V,n_j}. The H, A and G derivatives give μ_i only at their own natural variables (S,P), (T,V), (T,P).

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