# Henderson’s Equation

Henderson derived an equation to calculate the pH value of a buffer solution.

Let any weak acid HA have dissociation constant $K_a$, it strong salt is NaA which ionises completely.

The ionisation of HA may be given as:

$HA \leftrightharpoons H^+ + A^+$

$\text{At equilibrium} \hspace{3mm} K_a = \dfrac{[H^+][A^-]}{[HA]}$

$or \hspace{2mm} [H^+] = \dfrac{K_a[HA]}{A^-]}$

$or \hspace{2mm} \log [H^+] = \log K_a + \log_{10} \dfrac{[HA]}{[A^-]}$

$or \hspace{2mm} -\log [H^+] = - \log K_a + \log_{10} \dfrac{[A^-]}{[HA]}$

$or \hspace{2mm} pH = pK_a + \log_{10} \dfrac{[A^-]}{[HA]}$

$or \hspace{2mm} pH = pK_a + \log_{10} \dfrac{[salt]}{[acid]}$

Because $[A^-]$ is due to concentration of salt as it ionises completely and [HA] is the concentration of acid as it ionises upto small extent.

Similarly, we can prove that:

$pOH = pK_b + \log_{10} \dfrac{[Salt]}{[Base]}$

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