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JEE Advanced 2018 Paper 1 · Chemistry · Electrochemistry · medium

A galvanic cell is Zn(s) | Zn^2+(0.01 M) || Cu^2+(1.0 M) | Cu(s) at 298 K with E^°cell=1.10 V. Take F=96500 C mol^-1 and 2.303RT/F=0.059 V.

One or more options correct

A galvanic cell is Zn(s) ∣ Zn2+(0.01 M) ∣∣ Cu2+(1.0 M) ∣ Cu(s)\mathrm{Zn(s)\,|\,Zn^{2+}(0.01\ M)\,||\,Cu^{2+}(1.0\ M)\,|\,Cu(s)} at 298 K with Ecell∘=1.10E^\circ_{cell}=1.10 V. Take F=96500 C mol−1F=96500\ \mathrm{C\,mol^{-1}} and 2.303RT/F=0.0592.303RT/F=0.059 V. Select the correct statement(s).
  1. A. The emf of the cell is 1.161.16 V.
  2. B. ΔG\Delta G for the cell reaction (per mole of Zn) is −212-212 kJ.
  3. C. The equilibrium constant of the cell reaction is about 1018.610^{18.6}.
  4. D. If the Cu2+\mathrm{Cu^{2+}} concentration is also reduced to 0.010.01 M, the emf stays at 1.161.16 V.
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Answer: A

Nernst equation for n=2n=2: E=E∘−0.0592log⁡[Zn2+][Cu2+]=1.10−0.0295log⁡(0.01)=1.10+0.059=1.159E=E^\circ-\frac{0.059}{2}\log\frac{[\mathrm{Zn^{2+}}]}{[\mathrm{Cu^{2+}}]}=1.10-0.0295\log(0.01)=1.10+0.059=1.159 V, so A is correct. Then ΔG=−nFE=−2(96500)(1.159)=−223.7\Delta G=-nFE=-2(96500)(1.159)=-223.7 kJ; the value −212-212 kJ is ΔG∘\Delta G^\circ, so B is wrong. At equilibrium log⁡K=nE∘/0.059=2.2/0.059=37.3\log K=nE^\circ/0.059=2.2/0.059=37.3, so K≈1037K\approx10^{37} and C (which halves the exponent by forgetting nn) is wrong. If both concentrations are 0.01 M the ratio is 1, the log term vanishes and E=E∘=1.10E=E^\circ=1.10 V, not 1.16 V, so D is wrong. Each option therefore tests a different slip: ignoring the concentration term, mixing standard and actual free energy, dropping n in the equilibrium constant, or mishandling the reaction quotient.
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