For the cell Zn|Zn²⁺‖Cu²⁺|Cu with $E^0_{cell} = 1.10$ V, the equilibrium constant $K$ at 298 K ($n=2$, RT/F = 0.0257) is approximately:
A$10^{74}$
B$10^{37}$
C$10^{18}$
D$10^{0.04}$
Answer & Solution
Correct answer: B. $10^{37}$
From $\Delta G^0 = -RT\ln K = -nFE^0$: $\ln K = nFE^0/RT$ = $2(96485)(1.10)/(8.314 \times 298) \approx 85.7$. $K = e^{85.7} \approx 10^{37.2}$ ≈ $10^{37}$. The huge $K$ confirms the Daniell cell reaction is essentially irreversible.
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