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The solubility product of $AB_2$ is $8\times 10^{-5}\,M^3$ . If the salt is $80\,\%$ dissociated in saturated solution, find the solubility of the salt.
Given [Molar mass $(AB_2) = 360$ ]
$0.050$
$0.065$
$0.034$
$0.074$
Solution
$A{B_2}\overset {80\% } \longleftrightarrow \mathop {{A^{ + 2}}}\limits_{0.8S} + \mathop {2{B^ – }}\limits_{2 \times 0.8S} $
${{\text{K}}_{{\text{sp}}}} = (0.8 \times {\text{S}}){(2 \times 0.8{\text{S}})^2}$
$8 \times {10^{ – 5}} = 2.048{{\text{S}}^3}\left( { = 2{{\text{S}}^3}} \right)$
${{\text{S}}^3} = \frac{{8 \times {{10}^{ – 5}}}}{2}$
${{\text{S}}^3} = 40 \times {10^{ – 6}}$
$S = \sqrt[3]{{40 \times {{10}^{ – 6}}}}$
$ = 3.4 \times {10^{ – 2}}\,{\text{M}}$
$ = 0.034\,{\text{M}}$
Similar Questions
The solubility product $(K_{sp})$ of the following compounds are given at $25\,^oC$
| Compound | $K_{sp}$ |
| $AgCl$ | $1.1\times10^{-10}$ |
| $AgI$ | $1.0\times10^{-16}$ |
| $PbCrO_4$ | $4.0\times10^{-14}$ |
| $Ag_2CO_3$ | $8.0\times10^{-12}$ |
The most soluble and least soluble compounds are respectively.
