UPSC Civil Services (Mains), Chemistry optional · 2022 · Paper I
Q1(d). ΔG for the formation of ozone in smog
Question
Calculate ΔG at 298 K for the formation of O₃ from O₂ in urban smog, where [O₂] = 0.21 atm and [O₃] = 5 × 10⁻⁷ atm. Given: ΔG°f(O₃) = 163 kJ mol⁻¹, R = 8.314 J mol⁻¹ K⁻¹, F = 96485 C mol⁻¹.
Answer in brief
ΔG = ΔG° + RT ln Q = 163 − 30.1 = +132.9 kJ per mol of O₃; it is positive, so ozone does not form from oxygen spontaneously.
Key points
- For 3/2 O₂(g) → O₃(g), ΔG° = ΔG°f(O₃) = +163 kJ mol⁻¹ since ΔG°f(O₂) = 0.
- Reaction quotient: Q = p(O₃)/p(O₂)3/2 = 5 × 10⁻⁷/(0.21)1.5 = 5.20 × 10⁻⁶.
- RT ln Q = (8.314)(298) ln(5.20 × 10⁻⁶) = −30.1 kJ mol⁻¹.
- If written as 3 O₂ → 2 O₃, every term doubles and ΔG = +265.7 kJ.
- Ozone in smog is made by light (sunlight splits NO₂), held at a photostationary level, not an equilibrium one.
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.
Coversreaction isothermGibbs free energyreaction quotientozone formationphotochemical smog
All parts of Question 1
- 1(a) Average and most probable distance of the 1s electron10 marks
- 1(b) Non-bonding interactions between orbitals of A and B10 marks
- 1(c) F-centres: one colour by every route; effect on density10 marks
- 1(d) ΔG for the formation of ozone in smog10 marks
- 1(e) ΔG° and K for the zinc–copper cell reaction10 marks