Question

Why does the buffer capacity reach a maximum when $\mathbf{pH}\mathbf{=}{\mathbf{pK}}_{\mathbf{a}}$?

Short answer

If an acid or a base is added it would have a least effect on the$\left[{\mathrm{A}}^{-}\right]/\left[\mathrm{HA}\right]$ ratio because these concentrations are initially equal.

Step-by-step solution

 Define pH and  pKa

pH stands for Potential hydrogen. It is the symbol for the logarithm of the reciprocal of hydrogen ion concentration in gram atoms per litre, used to express the acidity and alkalinity of a solution on a scale of 0 to 14

${\mathrm{pK}}_{\mathrm{a}}$is the number that describes the acidity of a particular molecule. The formula to find the is

${\mathrm{pK}}_{\mathrm{a}}\mathrm{is}$

role="math" localid="1663410028653" ${\mathrm{pK}}_{\mathrm{a}}=-{\mathrm{logK}}_{\mathrm{a}}$

 If pH and pKa are equal

When pH =${\mathrm{pK}}_{\mathrm{a}}$ the ratio of conjugate base and conjugate acid are equal to each otherand ratio of$\left[{\mathrm{A}}^{-}\right]/\left[\mathrm{HA}\right]$ is unity.

 Reason why buffer capacity is maximum

If an acid or a base is added it would have a least effect on the$\left[{\mathrm{A}}^{-}\right]/\left[\mathrm{HA}\right]$ ratio because these concentrations are initially equal.