Question

Derive Henderson - Hasselbalch equation and mention its significance.

Answer 1

$HA\rightleftharpoons H^{+}+A^{-}........\left(1\right)$

$\therefore$ The dissociation constant, $K_a=\frac{\left[H^{+}\right]\left[A^{-}\right]}{\left[HA\right]}......\left(2\right)$

$\therefore \left[H^{+}\right]=K_a\frac{\left[HA\right]}{\left[A\right]}$

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

$\Rightarrow pH=p{K}_a-\log \frac{\left[HA\right]}{\left[A^{-}\right]}$

$\Rightarrow pH=p{K}_a+\log \frac{\left[A^{-}\right]}{\left[HA\right]}$

$\therefore pH=p{K}_a+\log \frac{\left[protonacceptor\right]}{\left[protondonor\right]}$

This equation is called the Henderson-Hasselbalch equation.

Significance.

• The pH of the buffer solution can be calculated by the initial concentration of weak acid and the salt if $K_a$ is given.
• The dissociation constant of the weak acid can be determined.