Question

At ${25}^{\circ }C$, the dissociation constant of a base BOH is $1.0\times {10}^{-12}$. The

concentration of Hydroxyl ions in 0.01 M aqueous solution of the base

would be

• A. $2.0\times {10}^{-6}mol{L}^{-1}$
• B. $1.0\times {10}^{-5}mol{L}^{-1}$
• C. $1.0\times {10}^{-6}mol{L}^{-1}$
• D. $1.0\times {10}^{-7}mol{L}^{-1}$

Answer 1

The correct option is D

$1.0\times {10}^{-7}mol{L}^{-1}$

$BOH\leftrightharpoons B^{+}+O{H}^{-}$

Initially,
$BOH=C$, $B^{+}$ = $0$ and $O{H}^{-}$ = $0$

At Equilibrium
$BOH=C-C\alpha$, $B^{+}$ = $C$$\alpha$ and $O{H}^{-}$ = $C$$\alpha$

$K_b=\frac{C^2{\alpha }^2}{C(1-\alpha )}$ = $C$${\alpha }^2$ assuming $\alpha$$<<1$; $1-\alpha$ $\sim$ $1$
${10}^{-12}$ = ${10}^{-2}\times {\alpha }^2$; ${\alpha }^2$ = ${10}^{-10}$; $\alpha$ = ${10}^{-5}$
$O{H}^{-}$ = $C$$\alpha$ = $0.01\times {10}^{-5}={10}^{-7}$