Question

A silver chromate solution at $298K$ has its $K_{sp}$ value $=1.1\times 10^{-12}$ . Determine the solubility of the solution in ${\text{mol L}}^{-1}$

• A. $6.5\times 10^{-5}$
• B. $2.4\times 10^{-2}$
• C. $3.6\times 10^{-3}$
• D. $8.9\times 10^{-4}$

Answer 1

Answer: (A)

$\underset{\text{s}}{{\text{Ag}}_2{\text{CrO}}_4}\rightleftharpoons \underset{\text{2s}}{{\text{2Ag}}^{+}}+\underset{\text{s}}{{\text{CrO}}_4^{2-}}\text{;}{\text{K}}_{\text{sp}}=\text{1}\text{.1}\times {\text{10}}^{-\text{12}}$

${\text{K}}_{\text{sp}}={\left[{\text{Ag}}^{+}\right]}^2\cdot \left[{\text{CrO}}_4^{2-}\right]$

${\text{K}}_{\text{sp}}=[2\text{s}{]}^2.\left[\text{s}\right]=4{\text{s}}^3$

${\text{s}}^3=\frac{{\text{K}}_{\text{sp}}}{4}$

$=\frac{1.1\times 10^{-12}}{4}$

$\text{s}=\sqrt[3]{275\times 10^{-15}}$

$=6.5\times 10^{-5}\text{mol}{\text{L}}^{-1}$

$\Rightarrow \text{s}=6.53\times 10^{-5}$