Question

A silver chromate solution at $298 \, K$ 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{​} \, $

$\text{K}_{\text{sp}} = \left[\text{Ag}^{+}\right]^{2} \cdot \left[\text{CrO}_{4}^{2 -}\right]$

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

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

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

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

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

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