UPSC Civil Services (Mains), Chemistry optional · 2022 · Paper I
Q1(e). ΔG° and K for the zinc–copper cell reaction
Question
For a cell reaction Cu²⁺(aq) + Zn(s) → Cu(s) + Zn²⁺(aq), the standard electrode potential for Zn/Zn²⁺ = 0.339 V and for Cu²⁺/Cu = 0.762 V at 25 °C. Calculate standard change in free energy ΔG° and equilibrium constant K for the reaction. [R = 8.314 J mol⁻¹ K⁻¹]
Answer in brief
E°cell = 1.101 V; ΔG° = −nFE°cell = −212.5 kJ mol⁻¹; K = 1.7 × 10³⁷.
Key points
- Anode: Zn → Zn²⁺ + 2e⁻; cathode: Cu²⁺ + 2e⁻ → Cu; two electrons pass, so n = 2.
- E°cell = oxidation potential of anode + reduction potential of cathode = 0.339 + 0.762 = 1.101 V.
- ΔG° = −(2)(96485)(1.101) = −212 460 J = −212.5 kJ mol⁻¹.
- ln K = nFE°cell/RT = 85.75, so log K = 37.24 and K = 1.7 × 10³⁷; cross-check log K = nE°/0.0591 = 37.26.
- ΔG° is large and negative and K enormous, so zinc displaces copper completely (Daniell cell).
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.
CoversDaniell cellstandard EMFΔG° = −nFE°equilibrium constant from EMFNernst equation
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