Q. In a saturated solution of the sparingly soluble strong electrolyte ${AgIO}_{3}$ (molecular mass=283) the equilibrium which sets in is $AgIO_{3}(s) \rightleftharpoons Ag^{+}(aq) + IO_{3}^{-}(aq)$ If the solubility product constant $K_{sp}of\ AgIO_{3}\ at\ a\ given\ temprature\ is\ 1.0 \times 10^{- 8}$ , what is the mass of $AgIO_{3}$ contained in 100 mL of its saturated solution?
A) $28.3 \times 10^{- 2}$ g
B) $2.83 \times 10^{- 3}$ g
C) $1.0 \times 10^{- 7}$ g
D) $1.0 \times 10^{- 4}$ g
Explanation
(b)
$AgIO_{3}(s) \rightleftharpoons Ag^{+}(aq) + IO_{3}^{-}(aq)$
Let solubility of $AgIO_{3}$ be $S$
$K_{sp} = \left\lbrack Ag^{+} \right\rbrack\left\lbrack IO_{3}^{-} \right\rbrack$
$1.0 \times 10^{- 8} = S^{2}\ \ \ \ or\ \ \ \ \ \ \ \ \ \ S = 1 \times 10^{- 4}$ mol/L
In 1000 mL of mol of $AgIO_{3}$ dissolved = $1 \times 10^{- 4}\ mol$
In 100 mL of mol of $AgIO_{3}$ dissolved = $1 \times 10^{- 5}\ mol$
Mass of $AgIO_{3}$in 100 mL =$1 \times 10^{- 5} \times 283$
$= 2.83 \times 10^{- 3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.