Q2(a). Variation of the Gibbs energy with temperature and pressure
Using the Gibbs equation for a closed system in the absence of non-expansion work at constant composition, answer the following: (i) Deduce the thermodynamic relations for the variation of G with T, and with P. (ii) What are the implications of the above relations? (iii) Draw the G versus T graph and identify the phase transition temperatures, if any. (iv) Explain how the presence of (1) attractive and (2) repulsive molecular interactions affects the molar Gibbs free energy of a gas relative to its normal value.
Answer in brief
dG = V dP − S dT, so (∂G/∂T)ₚ = −S and (∂G/∂P)ₜ = V; attractions lower Gₘ of a gas below the perfect-gas value, repulsions raise it.
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CoversGibbs energyGibbs–Helmholtz equationMaxwell relationfugacityphase transitionClapeyron equation
All parts of Question 2
- 2(a) Variation of the Gibbs energy with temperature and pressure20 marks
- 2(b) Continuous energy of a free particle, quantised energy in a box10 marks
- 2(c) Primitive cubic lattice: points, voids and the sphere at the centre10 marks
- 2(d) Dissociation equilibrium A₂(g) ⇌ 2A(g)10 marks