Question

Solubility product $K_{sp}$ of a sparingly soluble salt $Zn(CN{)}_2$ is $8\times {10}^{-12}.$ Its solubility value in $\left(mol{L}^{-1}\right)$ is:
(Take $\sqrt[3]{32}=1.26$)

• A. $1.26\times {10}^{-4}$
• B. $1.26\times {10}^{-5}$
• C. $1.26\times {10}^{-6}$
• D. $1.26\times {10}^{-12}$

Answer 1

The correct option is A $1.26\times {10}^{-4}$

Given $K_{sp}=8\times {10}^{-12}$
The equilibrium between the undissolved solid and the ions in a saturated solution can be represented by the equation: $Zn\left(CN{)}_2\right(s)\rightleftharpoons Z{n}^{2+}(aq)+2C{N}^{-}(aq)Initial:C00Equilibrium:C-ss2s$

$K_{sp}=\left[Z{n}^{2+}\right][C{N}^{-}{]}^2$
$K_{sp}=s\times (2s{)}^2=4s^3$
$K_{sp}=4s^3=8\times {10}^{-12}$
$\therefore 4s^3=8\times {10}^{-12}$
$s^3=2\times {10}^{-12}$
$s=1.26\times {10}^{-4}M$