Q. 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? $K_{sp}(AgCl) = 1.8 \times 10^{- 10}$ $K_{sp}(AgBr) = 5.0 \times 10^{- 13}$ $K_{sp}\left( Ag_{2}CrO_{4} \right) = 2.4 \times 10^{- 12}$
Explanation
(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, $Ag_{2}CrO_{4},\ K_{sp} = 4s^{3}$
$\therefore$ Solubility of $Ag_{2}CrO_{4}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = \sqrt[3]{\frac{K_{sp}}{4}} = \sqrt[3]{\frac{2.4 \times 10^{- 12}}{4}}$
$= \sqrt[3]{600 \times 10^{- 15}}$
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ = 8.44 \times 10^{- 5}$ mol/L
As $Ag_{2}CrO_{4}$ has maximum solubility, it will give maximum $Ag^{+}$ ions in solution. Hence, it will be used.
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.