Question

In a sautrated solution of the sparingly soluble strong electrolyte $AgI{O}_3$ (Molecular mass $=283$) the equilibrium which sets in is
$AgI{O}_{3(s)}\rightleftharpoons A{g}_{(aq)}^{+}+I{O}_{3(aq)}^{-}$
If the solubility product constant $K_{sp}$ of $AgI{O}_3$ at a given temperature is $1.0\times 10^{-8}$, what is the mass of $AgI{O}_3$ contained in $100ml$ of its saturated solution?

• A. $28.3\times 10^{-2}g$
• B. $28.3\times 10^{-3}g$
• C. $1.0\times 10^{-7}g$
• D. $1.0\times 10^{-4}g$

Answer 1

Answer: (B)

$AgI{O}_{3(s)}\rightleftharpoons A{g}_{(aq)}^{+}+I{O}_{3(aq)}^{-}$
Let the solubility of $AgI{O}_3$ be s
$K_{sp}=\left[A{g}^{+}\right]\left[I{O}_3^{-}\right]$
$1.0\times 10^{-8}=S^2$
$S=10^{-4}mol/litre$
$=\frac{10^{-4}\times 283}{1000}\times 100$
$=283\times 10^{-5}$
$=2.83\times 10^{-3}g/100ml$
Hence, (2) is correct.