Question 20.11: Calculating the Equilibrium Constant from Cell emf The stand...
Calculating the Equilibrium Constant from Cell emf
The standard emf for the following voltaic cell is 1.10 \mathrm{~V} :
\mathrm{Zn}(s)\left|\mathrm{Zn}^{2+}(a q) \| \mathrm{Cu}^{2+}(a q)\right| \mathrm{Cu}(s)
Calculate the equilibrium constant K_{c} for the reaction
\mathrm{Zn}(s)+\mathrm{Cu}^{2+}(a q) \rightleftharpoons \mathrm{Zn}^{2+}(a q)+\mathrm{Cu}(s)
PROBLEM STRATEGY
Substitute the standard emf into the equation relating this quantity to the thermodynamic equilibrium constant, K. Solve for K. Note that K=K_{c}.
The reaction corresponds to the one for the voltaic cell. Note that n=2. Substituting into the equation relating E_{\text {cell }}^{\circ} and K gives
1.10=\frac{0.0592}{2} \log K_{c}
Solving for \log K_{c}, you find
\log K_{c}=37.2
Now take the antilog of both sides:
K_{c}=\operatorname{antilog}(37.2)=1.6 \times 10^{37}
The number of significant figures in the answer equals the number of decimal places in 37.2 (one). Thus
K=2 \times 10^{37}