Question

A certain buffer solution contains equal concentration of $X^{-}$ and $HX$. $K_b$ for $X^{-}$ is ${10}^{-10}$. The $pH$ of the buffer will be:

Answer 1

Given, $K_b$ for $X^{-}$ is ${10}^{-10}$
Also for conjugate acid - base pair
$K_a\left(HX\right)\times K_b\left(X^{-1}\right)={10}^{-14}\Rightarrow K_{a\left(HX\right)}={10}^{-4}$
Now $\underset{\left(acid\right)}{\left[HX\right]}=\underset{\left(salt\right)}{\left[X^{-}\right]}$
According to Henderson Hasselbalch equation,
$pH=-\log K_a+\log \frac{\left[Salt\right]}{\left[Acid\right]}\Rightarrow pH=-\log {10}^{-4}\Rightarrow pH=4$