Question

When equal volumes of the following solutions are mixed, precipitation of $AgCl$ ($K_{sp}=1.8\times {10}^{-10}$) will occur only with:

• A. ${10}^{-4}MA{g}^{+}$ and ${10}^{-4}MC{l}^{-}$
• B. ${10}^{-5}MA{g}^{+}$ and ${10}^{-5}MC{l}^{-}$
• C. ${10}^{-6}MA{g}^{+}$ and ${10}^{-6}MC{l}^{-}$
• D. ${10}^{-10}MA{g}^{+}$ and ${10}^{-10}MC{l}^{-}$

Answer 1

The correct option is A ${10}^{-4}MA{g}^{+}$ and ${10}^{-4}MC{l}^{-}$

Precipitation of $AgCl$ will occur only when ionic product exceeds the solubility product.
a) The ionic product of the solution obtained by mixing ${10}^{-4}MA{g}^{+}$ and ${10}^{-4}MC{l}^{-}$ is ${10}^{-8}{M}^2$
b) The ionic product of the solution obtained by mixing ${10}^{-5}MA{g}^{+}$ and ${10}^{-5}MC{l}^{-}$ is ${10}^{-10}{M}^2$
c) The ionic product of the solution obtained by mixing ${10}^{-6}MA{g}^{+}$ and ${10}^{-6}MC{l}^{-}$ is ${10}^{-12}{M}^2$
d) The ionic product of the solution obtained by mixing ${10}^{-10}MA{g}^{+}$ and ${10}^{-10}MC{l}^{-}$ is ${10}^{-20}{M}^2$

Since ${10}^{-8}{M}^2>1.8\times {10}^{-10}$, hence option (a) is correct.