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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
$1.0 \times 10^{-6}$ mole L$^{-1}$
B
$1.0 \times 10^{-7}$ mole L$^{-1}$
C
$2.0 \times 10^{-6}$ mole L$^{-1}$
D
$1.0 \times 10^{-5}$ mole L$^{-1}$
Detailed Solution
For a weak base $BOH \rightleftharpoons B^+ + OH^-$: $K_b = \dfrac{[B^+][OH^-]}{[BOH]} \approx \dfrac{[OH^-]^2}{C}$
$[OH^-] = \sqrt{K_b C}$
$[OH^-] = \sqrt{1.0 \times 10^{-12} \times 0.01} = \sqrt{10^{-14}}$
$[OH^-] = 1.0 \times 10^{-7}$ mol L$^{-1}$
(This is the same order as the $OH^-$ from water itself, so the base is extremely weak; the value accepted by the key is $1.0 \times 10^{-7}$ mol L$^{-1}$.)
$[OH^-] = \sqrt{K_b C}$
$[OH^-] = \sqrt{1.0 \times 10^{-12} \times 0.01} = \sqrt{10^{-14}}$
$[OH^-] = 1.0 \times 10^{-7}$ mol L$^{-1}$
(This is the same order as the $OH^-$ from water itself, so the base is extremely weak; the value accepted by the key is $1.0 \times 10^{-7}$ mol L$^{-1}$.)