Question

Some chemists at ISRO wished to prepare a saturated solution of a silver compound and they wanted it to have the highest concentration of silver ion possible. Which of the following compounds, would they use?
$K_{sp}(AgCl)=1.8\times 10^{-10}$
$K_{sp}(AgBr)=5.0\times 10^{-13}$
$K_{sp}\left(A{g}_{2}Cr{O}_4\right)=2.4\times 10^{-12}$

• A. $AgCl$
• B. $AgBr$
• C. $A{g}_{2}Cr{O}_4$
• D. None of these

Answer 1

Answer: (C)

For binary salts (like $AgCl,AgBr$ )
$s=\sqrt{K_{sp}}$
$\therefore$ Solubility of $AgCl=\sqrt{1.8\times 10^{-10}}$
$=1.35\times 10^{-7}mol/L$
Solubility of $AgBr=\sqrt{5.0\times 10^{-13}}$
$=7.1\times 10^{-7}mol/L$
For, $A{g}_{2}Cr{O}_4,K_{sp}=4s^3$
$\therefore$ Solubility of $A{g}_{2}Cr{O}_4$
$=\sqrt[3]{\frac{K_{sp}}{4}}=\sqrt[3]{\frac{2.4\times 10^{-12}}{4}}$
$=\sqrt[3]{600\times 10^{-15}}$
$=8.44\times 10^{-5}mol/L$
As $A{g}_{2}Cr{O}_4$ has maximum solubility, it will give maximum $A{g}^{+}$ions in solution. Hence, it will be used.