# Why is the pH of a buffer close to the pK_a of the acid used to make the buffer...?

Aug 23, 2016

The $p H$ of a buffer is tolerably close to the $p {K}_{a}$ of the acid because this gives the greatest buffer capacity.

#### Explanation:

Buffers are formed from a mixture of appreciable quantities of a weak acid and its conjugate base. The $p H$ of the solution is tolerably close to the $p {K}_{a}$ of the acid, which of course will be somewhat below $7$.

The buffer equation gives us:

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

Of course when $\left[{A}^{-}\right] = \left[H A\right]$ (at the point of half equivalence in a titration), $p H = p {K}_{a}$, because ${\log}_{10} 1 = 0$.