Chemistry - Electrochemistry Question with Solution | TestHub

${\mathrm{K}}_{sp}(AgX)=[A{g}^{+}]\times [X^{-}]=(S_1+S_2)\times S_1$

$$\begin{array}{rl}& {\mathrm{K}}_{sp}(AgY)=[A{g}^{+}]\times [Y^{-}]=(S_1+S_2)\times S_2\\ & \therefore S_1+S_2=\sqrt{{\mathrm{K}}_{sp}(AgX)+{\mathrm{K}}_{sp}(AgY)}=\sqrt{3\times 10^{-12}+10^{-12}}=2\times 10^{-6}M\\ & \therefore [A{g}^{+}]=2\times 10^{-6}M,[X^{-}]=\frac{3\times 10^{-12}}{2\times 10^{-6}}=1.5\times 10^{-6}M\\ & \therefore [Y^{-}]=\frac{10^{-12}}{2\times 10^{-6}}=0.5\times 10^{-6}M\\ & \mathrm{K}[A{g}^{+}]=\frac{{\lambda }_{[A{g}^{+}]}^0\times M_{(A{g}^{+})}}{1000}=\frac{60\times 2\times 10^{-6}}{1000}=1.2\times 10^{-7}Sc{m}^{-1}\\ & \mathrm{K}[X^{-}]=\frac{90\times 1.5\times 10^{-6}}{1000}=1.35\times 10^{-7}Sc{m}^{-1}\\ & \therefore \mathrm{K}[A{g}^{+}]+\mathrm{K}[X^{-}]+\mathrm{K}[Y^{-}]=0.4\times 10^{-6}\\ & \therefore \mathrm{K}[Y^{-}]=4\times 10^{-7}-(1.2+1.35)10^{-7}=1.45\times 10^{-7}{\Omega }^{-1}c{m}^{-1}\end{array}$$