Indian Forest Service (Mains), Chemistry optional · 2025 · Paper I
Q1(d). Pressure dependence of solid Gibbs energy
Question
Choose the correct molar Gibbs energy versus pressure curve at fixed temperature for a single solid component: (i) increasing, concave downward; (ii) decreasing, concave downward; (iii) decreasing, concave upward; (iv) increasing, concave upward. Explain.
Answer in brief
Curve (i) is correct: molar Gibbs energy increases with pressure, with a weak downward curvature for a mechanically stable compressible solid.
Key points
- For a pure phase, dGₘ = −Sₘ dT + Vₘ dP; thus (∂Gₘ/∂P)T = Vₘ > 0.
- The isothermal compressibility κ_T = −(1/Vₘ)(∂Vₘ/∂P)T > 0 for a stable solid.
- Hence (∂²Gₘ/∂P²)T = (∂Vₘ/∂P)T = −κ_T Vₘ < 0; the slope stays positive but decreases as the solid compresses.
- Since solids are only weakly compressible, the curve is nearly straight: Gₘ(P) ≃ Gₘ(P₀) + Vₘ(P − P₀).
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.
CoversGibbs energy vs pressure(∂G/∂P)_T = Visothermal compressibilitysolid phase stabilityMaxwell relations
All parts of Question 1
- 1(a) Equivalent bonds in nitrate8 marks
- 1(b) Formula from occupied crystal voids8 marks
- 1(c) Formation free energy of uranium hydride8 marks
- 1(d) Pressure dependence of solid Gibbs energy8 marks
- 1(e) Fast and slow electrode systems8 marks