Electrodes involving sparingly soluble salts (Electrodes of the second kind)


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> Consider the sparingly soluble salt, $\ce{AgI}$ ($K\_\text{sp} = 8.52\times10^{-17}$) and a silver electrode (Standard Reduction Potential = $\pu{0.799V}$). $\pu{0.02L}$ of $\pu{0.001M}~\ce{KI}$ solution is added to a silver nitrate solution with a silver electrode immersed. After connecting to SHE, the reading is $\ce{0.068V}$. Hence, what is the concentration of silver nitrate added at 298K?
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Clearly, we should start off by writing the relevant Nernst equation, as follows
$$E = \pu{0.799V} - \frac{8.314 \times 298}{1 \times 96485}\ln\left(\frac{1}{[\ce{Ag+}]}\right) $$


From here we can substitute $E = \pu{0.068V}$ and obtain a result of $[\ce{Ag+}] = 4.331 \times 10^{-4}$


However, I am not sure how to proceed from here. An unknown amount of $\ce{AgI}$ precipitated and so we cannot calculate the initial amount of silver nitrate added. Although we know the amount of $\ce{KI}$ added, most of it presumably precipated due to low [$\ce{I-}$] from $K\_\text{sp}$, suggesting excess silver nitrate. However, the still low concentration of silver nitrate presents problems when we use approximations.


