The Henderson-Hasselbalch Equation and Buffer Solutions

A buffer solution is one that resists an appreciable change in pH when a small amount of a strong

acid or a strong base is added to it, or when it is moderately diluted. The most common type — an

acidic buffer — is prepared by mixing a weak acid with a salt of its conjugate base (for example,

$\text{CH}_3\text{COOH}$ with $\text{CH}_3\text{COONa}$); a basic buffer is the analogous mixture

of a weak base with a salt of its conjugate acid (for example, $\text{NH}_4\text{OH}$ with

$\text{NH}_4\text{Cl}$).

Deriving the Henderson-Hasselbalch equation. Starting from the ionization equilibrium of the weak

acid, $\text{HA} \rightleftharpoons \text{H}^+ + \text{A}^-$, the equilibrium expression is

$K_a = [\text{H}^+][\text{A}^-]/[\text{HA}]$. Solving for $[\text{H}^+]$,

$[\text{H}^+] = K_a \times [\text{HA}]/[\text{A}^-]$. Taking $-\log_{10}$ of both sides and using the

definitions $\text{pH} = -\log[\text{H}^+]$ and $\text{p}K_a = -\log K_a$,

This is the Henderson-Hasselbalch equation. Its derivation relies on one simplifying assumption:

because the buffer already contains a substantial, deliberately-added concentration of the salt (the

conjugate base $\text{A}^-$), the weak acid's own, otherwise-small ionization is suppressed by the

common ion effect, so the equilibrium concentrations $[\text{HA}]$ and $[\text{A}^-]$ can safely be

taken as equal to the initial, as-mixed concentrations of the acid and the salt, without needing to

solve an ICE table.

Why a buffer resists pH change. The buffer contains a large reservoir of both the weak acid (which

can neutralize any added $\text{OH}^-$) and its conjugate base (which can neutralize any added

$\text{H}^+$). Adding a small amount of strong acid converts a small amount of $\text{A}^-$ into

$\text{HA}$; adding a small amount of strong base converts a small amount of $\text{HA}$ into

$\text{A}^-$. In either case, only the ratio $[\text{A}^-]/[\text{HA}]$ changes, and only slightly,

so by the Henderson-Hasselbalch equation the pH — which depends on the logarithm of that ratio — …