Question

At ${25}^{o}C$, the dissociation constant of a base $BOH$ is $1\times {10}^{-12}$. The concentration of hydroxly ions in $0.01M$ aqueous solution of the base would be:

• A. ${10}^{-5}mol{L}^{-1}$
• B. ${10}^{-6}mol{L}^{-1}$
• C. ${2\times 10}^{-6}mol{L}^{-1}$
• D. ${10}^{-7}mol{L}^{-1}$

Answer 1

The correct option is D ${10}^{-7}mol{L}^{-1}$

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

$C$

$C(1-\alpha )$ $C\alpha$ $C\alpha$

$K_b=\frac{\left[B^{+}\right]\left[{OH}^{-}\right]}{\left[BOH\right]}=\frac{\left(C\alpha \right)\left(C\alpha \right)}{C(1-\alpha )}$

Assume '$\alpha$'<<1 so

$K_b=C{\alpha }^2$

$\alpha ={10}^{-5}$

$\left[O{H}^{-}\right]=C\alpha ={10}^{-7}mol{L}^{-1}$