Question

$M(OH{)}_x$ on dissolving produce $M^{x+}$ and $O{H}^{-}$ ions has $K_{sp}=4\times {10}^{-12}$ and solubility, S = ${10}^{-4}$ M. The value of $x$ is:

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$M(OH{)}_x\rightleftharpoons M_x^{+}{+}_{x}O{H}^{-}$

${10}^{-4}$ $x{10}^{-4}$

$K_{sp}=\left[M{x}^{+}\right][O{H}^{-}{]}^x$

$K_{sp}={10}^{-4}(x\times {10}^{-4}{)}^x=4\times {10}^{-12}$

By inspection this relation will hold good when $x=2$ :

$\left[{10}^{-4}\right({10}^{-4x})x^x=4\times {10}^{-12}$

$x^x=4$ when $x=2$

${10}^{-4}{.10}^{-4x}={10}^{-12}$

$\Rightarrow -4-4x=-12$

$\Rightarrow x=2$