# Henderson-Hasselbalch Equation

## Why do we need Henderson hasselbalch equation

It is easy to calculate the ionization constants of strong acids and strong bases as we have direct methods for them. In case of weak bases and weak acids, the calculations are rather difficult to be made as weak acids or weak bases hardly ionize. Hence, we use approximation to predict the pH of such solutions. Henderson-Hasselbalch equation is generally used for such predictions.

### Henderson hasselbalch equation example

Let us take an example of ionization of weak acid HA:

$HA~ +~ H_{2}O~ ⇋ ~H^{+}~ +~ A^{−}$

Acid dissociation constant, K a can be given as:

K a = $\frac{[H^+][A^-]}{[HA]}$

Taking, negative log of RHS and LHS:

$-log~K_a$ = $-log~\frac{[H^+][A^-]}{[HA]}$

$\Rightarrow -log~K_a$ = $-log~[H^+] ~ – ~log~\frac{[A^-]}{[HA]}$

As we know, $-log~[H^+]$ = $pH$ and $-log~K_a$ = $pKa$,

Above equation can be written as,

$pK_a$ = $pH~ -~ log~\frac{[A^-]}{[HA]}$

Rearranging the equation,

$\Rightarrow pH$ = $pK_a ~+ ~log\frac{[A^-]}{[HA]}$

The above equation is known as Henderson-Hasselbalch equation, popularly known as Henderson equation. It is very useful for estimating the pH of a buffer solution and finding the equilibrium pH in acid-base reactions. From the equation we can infer when $pH$ = $pK_a$

$log~\frac{[A^-]}{[HA]}$ = $0$

$[A^-]$ = $[HA]$

That is, when $pH$ = $pK_a$, concentration of both the species are same or in other words, acid will be half dissociated.

Similarly, for a weak base B:

$B~ +~ H_2O~ ⇋ ~ OH^− ~+~ HB^+$

Base dissociation constant, Kb, of the base can be given as,

$K_b$ = $\frac{[BH^+][OH^-]}{[B]}$

Taking negative log of RHS and LHS

$-logK_b$ = $-log \frac{[BH^+][OH^-]}{[B]}$

$\Rightarrow -logK_b$ = $-log~[OH^-]-log\frac{[BH^+]}{[B]}$

As we know, $-log~[OH^-]$ = $pOH$ and $-logK_b$ = $pKb$,

Above equation can be written as,

$pK_b$ = $pOH ~- ~log\frac{[BH^+]}{[B]}$

Rearranging the equation,

$\Rightarrow pOH$ = $pK_b + log~\frac{[BH^+]}{[B]}$

### Limitations of Henderson-Hasselbalch equation:

The Henderson – Hasselbalch equation makes correct predictions for weak acids and bases but fails to predict accurate values for the strong acids and strong bases as it assumes that the concentration of the acid and its conjugate base at chemical equilibrium will remain the same as the formal concentration.

For details discussions on Henderson equation and the calculations involving buffer solutions, please visit Byju’s.

#### Practise This Question

When an excess of a very dilute aqueous solution of KI is added to a very dilute aqueous solution of silver nitrate, the colloidal particles of silver iodide are associated with which of the following Helmholtz double layer?