# A weak base, B has basicity constant, $K_b = 2 \times 10^{-5}$. The $pH$ of any solution in which $[B] = [BH^+]$ is

(a) 4.7

(b) 7.9

(c) 9.3

(d) 9.7

$B + H_2O \rightleftharpoons BH^+ + OH^-$

$K_b = \frac{[BH^+][OH^-]}{[B]}$
Given, $[BH^+] = [B]$
$\therefore K_b = [OH^-]$ = $2 \times 10^{-5}$

$[H^+] = \frac{K_w}{[OH^-]} = \frac{10^{-14}}{2 \times 10^{-5}} = \frac{10^{-9}}{2}$

$pH = - log [H^+] = - log \frac{10^{-9}}{2} = 9 + log 2 = 9 + 0.3010 = 9.3010$