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_{s p}( AgCl )=1.8 \times 10^{-10} $
$K_{s p}( AgBr )=5.0 \times 10^{-13} $
$K_{s p}\left( Ag _{2} CrO _{4}\right)=2.4 \times 10^{-12}$

• 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_{s p}} $
$\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, $ Ag _{2} CrO _{4}, K_{s p} =4 s^{3}$
$\therefore $ Solubility of $Ag _{2} CrO _{4}$
$=\sqrt[3]{\frac{K_{s p}}{4}}=\sqrt[3]{\frac{2.4 \times 10^{-12}}{4}} $
$=\sqrt[3]{600 \times 10^{-15}}$
$=8.44 \times 10^{-5} mol / L$
As $Ag _{2} CrO _{4}$ has maximum solubility, it will give maximum $Ag ^{+}$ions in solution. Hence, it will be used.