A concentration cell is set up as Ag(s) | Ag2CrO4(s) saturated in 0.010 M K2CrO4 \| Ag^+(0.10 M) | Ag(s) at 298 K. Its EMF is measured as 0.236 V.…

Both half cells are $\mathrm{Ag^+/Ag}$, so $E^\circ=0$ and $E=0.059\log\dfrac{[\mathrm{Ag^+}]_{cathode}}{[\mathrm{Ag^+}]_{anode}}$. The right electrode (0.10 M) is the cathode, so $0.236=0.059\log\dfrac{0.10}{c}$, giving $\log(0.10/c)=4$ and $c=[\mathrm{Ag^+}]=1.0\times10^{-5}\ \mathrm{M}$ in the left half cell. In that half cell the chromate concentration is fixed by the added $\mathrm{K_2CrO_4}$ (the contribution from dissolution is negligible), $[\mathrm{CrO_4^{2-}}]=0.010$ M. Hence $K_{sp}=[\mathrm{Ag^+}]^2[\mathrm{CrO_4^{2-}}]=(10^{-5})^2(10^{-2})=1.0\times10^{-12}$. Option (B) uses $K_{sp}=[\mathrm{Ag^+}]^2$ alone, (C) uses $[\mathrm{Ag^+}][\mathrm{CrO_4^{2-}}]$ (no square), and (D) wrongly doubles the silver-ion concentration, taking $[\mathrm{Ag^+}]=2\times10^{-5}$ M, which gives $(2\times10^{-5})^2(10^{-2})=4\times10^{-12}$.