A saturated solution \(AgCl\) was found to have a concentration of \(1.30 \times 10^{-5} moldm ^{-3}\). The solubility product of \(AgCl\) therefore is
A. \(1.30 \times 10^{-5} mol ^{2} dm ^{-6}\) B. \(2.60 \times 10^{-12} mol ^{2} dm ^{-6}\) C. \(1.30 \times 10^{-7} mol ^{2} dm ^{-6}\) D. \(1.69 \times 10^{-10} mol ^{2} dm ^{-6}\)
Correct Answer: D
Explanation
\(AgCl _{(s)} \rightarrow Ag _{(\text {(aq) }}^{+}+ Cl _{(\text {(qq) })}^{-}\) Solubility of \(AgCl =\left[ Ag ^{+}\right]=\left[ Cl ^{-}\right]\) \(\left[ Ag ^{+}\right]=\left[ Cl ^{-}\right]= S\) Solubility(s) product, \begin{aligned} & K _{\phi p}=\left[ Ag ^{+}\right]\left[ Cl ^{-}\right] \\ & K _{\phi p}=S \times S=S^{2} \\ &S=1.30 \times 10^{-5} moldm ^{-3} \\ & K _{\phi p}=\left(1.30 \times 10^{-5}\right)^{2} \\ &=1.65 \times 10^{-10} mol ^{2} dm ^{-6} \end{aligned}