# Why does pH = pK when pH = 7?

Aug 20, 2016

$p H$ $=$ $p {K}_{a}$ in a buffer solution WHEN $\left[H A\right] = \left[{A}^{-}\right]$.

#### Explanation:

When weak acid, $H A$, is titrated,

$p H = p {K}_{a} + {\log}_{10} \left\{\frac{\left[{A}^{-}\right]}{\left[H A\right]}\right\}$

But if $\left[H A\right] = \left[{A}^{-}\right]$, then ${\log}_{10} \left\{\frac{\left[{A}^{-}\right]}{\left[H A\right]}\right\} = {\log}_{10} 1 = 0$ and CLEARLY $p H = p {K}_{a}$. And thus the $p H$ at half-equivalence $=$ $p {K}_{a}$.