UPSC Combined Geo-Scientist, Mains · 2023 · Mains Paper II
Q1(e). Chemical potential and its link with Gibbs energy
Question
Explain the physical significance of chemical potential. How is it related to Gibbs free energy?
Answer in brief
μᵢ = (∂G/∂nᵢ)T,P,nⱼ, the partial molar Gibbs energy: the escaping tendency of species i. Matter moves from high μ to low μ. G = ∑nᵢμᵢ; pure substance μ = Gm.
Key points
- Meaning: the change in G when 1 mol of i is added to a very large amount of the mixture at constant T, P and composition.
- Escaping tendency: matter flows from high μ to low μ, as heat flows from high T to low T.
- Equilibrium: μᵢ equal in every phase; ∑νᵢμᵢ = 0 for reaction equilibrium.
- Relation to G: G = ∑nᵢμᵢ; for a pure substance μ = Gm.
- (∂μ/∂T)P = −Sm, (∂μ/∂P)T = Vm, μᵢ = μᵢ° + RT ln aᵢ.
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 energyescaping tendencyGibbs free energyphase equilibrium
All parts of Question 1
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- 1(b) Exceptional behaviour of hydrogen and helium5 marks
- 1(c) Unit cell of solid C₆₀ and its carbon atoms5 marks
- 1(d) Planes that diffract: simple cubic, a = 5 Å5 marks
- 1(e) Chemical potential and its link with Gibbs energy5 marks
- 1(f) Debye–Hückel limiting law for γ±5 marks
- 1(g) Activation energy of 2HI → H₂ + I₂5 marks
- 1(h) Best coagulant for the Sb₂S₃ sol5 marks
- 1(i) E° of Na⁺/Na from ΔrH° and ΔrS°5 marks
- 1(j) pH from a calomel–quinhydrone cell5 marks
- 1(k) Degeneracy of the level 6h²/8mL² in a cubic box5 marks
- 1(l) Is Peⁱᵏˣ + Qe⁻ⁱᵏˣ an eigenfunction?5 marks
- 1(m) Zero-point energy in joule and in cm⁻¹5 marks
- 1(n) Microwave activity of SF₆, CO, H₂, H₂O and CO₂5 marks
- 1(o) Stark–Einstein law and the quantum yield5 marks
- 1(p) Decay routes of a photoexcited molecule5 marks