Electrochemistry 2 Question 46
45. The standard reduction potential of the $\mathrm{Ag}^{+} / \mathrm{Ag}$ electrode at $298 \mathrm{~K}$ is $0.799 \mathrm{~V}$. Given that for $\mathrm{AgI}, K_{\mathrm{sp}}=8.7 \times 10^{-17}$, evaluate the potential of the $\mathrm{Ag}^{+} / \mathrm{Ag}$ electrode in a saturated solution of AgI. Also calculate the standard reduction potential of the $\mathrm{\Gamma} / \mathrm{AgI} / \mathrm{Ag}$ electrode.
(1994, 3M)
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Solution:
- In a saturated $\mathrm{AgI}$ solution;
$$ \begin{aligned} {\left[\mathrm{Ag}^{+}\right] } & =\sqrt{8.7 \times 10^{-17}} \mathrm{M} \ & =9.32 \times 10^{-9} \mathrm{M} \ \Rightarrow \quad E_{\mathrm{Ag}^{+} / \mathrm{Ag}} & =E^{\circ}-0.0592 \log \frac{1}{\left[\mathrm{Ag}^{+}\right]} \ & =0.799-0.0592 \log \frac{1}{9.32 \times 10^{-9}} \ & =0.324 \mathrm{~V} \end{aligned} $$
Also, for $\mathrm{AgI} \rightleftharpoons \mathrm{Ag}^{+}+\mathrm{I}^{-} ; \quad E^{\circ}=0.0592 \log K_{\text {sp }}$
$$ \begin{aligned} & =-0.95 \mathrm{~V} \ \mathrm{Ag} \longrightarrow \mathrm{Ag}^{+}+e^{-} ; E^{\circ} & =-0.799 \mathrm{~V} \ \mathrm{AgI}+e^{-} \longrightarrow \mathrm{Ag}+\mathrm{I}^{-} & E^{\circ}=x \end{aligned} $$
$$ \begin{aligned} \hline \text { Adding }: & \mathrm{AgI} \longrightarrow \mathrm{Ag}^{+}+\mathrm{I}^{-} ; E^{\circ} & =-0.95 \mathrm{~V} \ & & =x-0.799 \ \Rightarrow & & x=-0.151 \mathrm{~V} \end{aligned} $$
