UPSC Combined Geo-Scientist, Mains · 2024 · Mains Paper II

Q1(e). Chemical potential and its change with temperature

Question

What do you understand by chemical potential? Give an account of variation of chemical potential with temperature.

μi = (∂G/∂ni) at constant T, P, nj, the partial molar Gibbs energy; (∂μi/∂T)P = −S̄i, so μ falls as T rises, most steeply for the gas.

Meaning: the increase in G when 1 mol of i is added to a very large amount of the system at constant T, P and composition; pure substance: μ = Gm.
Escaping tendency: matter moves from high μ to low μ; at equilibrium μi is the same in every phase.
Cross-differentiation of dG gives (∂μi/∂T)P = −S̄i (pure substance: −Sm).
Sm > 0 ⇒ μ decreases as T rises; Sm(gas) ≫ Sm(liquid) > Sm(solid) ⇒ the gas line is steepest.
The phase of lowest μ is stable: the lines cross at Tf and Tb, giving melting and boiling.

The full model answer

As written for the answer booklet: the diagram carries the working, the lines stay short. Read here only; it is not offered as a download.

Coverschemical potentialpartial molar Gibbs energyphase stability(∂μ/∂T)P = −SGibbs–Helmholtz equation