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17. The solubility product () of can be found using the concentration cell . If the EMF is 0.164 V aElectrochemistry Chemistry Question

Question

17. The solubility product ($K_{sp}$) of $Ag_2CrO_4$ can be found using the concentration cell $Ag / Ag^+(sat. Ag_2CrO_4) // Ag^+(0.1 M) / Ag$. If the EMF is 0.164 V at 298 K, find $K_{sp}$. (Use 2.303RT/F = 0.059 V)

Answer: A

💡 Solution & Explanation

$E = -0.059 \log([Ag^+]_{anode} / [Ag^+]_{cathode})$. $0.164 = 0.059 \log(0.1 / x) \implies \log(0.1/x) = 2.78 \implies 0.1/x = 602.5 \implies x = [Ag^+]_{anode} = 1.66 \times 10^{-4} M$. $K_{sp} = [Ag^+]^2[CrO_4^{2-}] = (2S)^2(S)$. Since $[Ag^+]=2S$, $S = 0.83 \times 10^{-4}$. $K_{sp} = 4(0.83 \times 10^{-4})^3 = 2.28 \times 10^{-12}$.

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