Q.The hydrogen ion concentration of a buffer solution consisting of a weak acid and its salt is given by

A buffer is a solution of a weak acid and its conjugate base (an acidic buffer, e.g. $CH_3COOH$/$CH_3COONa$) or a weak base and its conjugate acid (a basic buffer, e.g. $NH_4OH$/$NH_4Cl$) that resists drastic pH changes when small amounts of acid or base are added -- buffer action. Blood's carbonic-acid/bicarbonate buffer ($H_2CO_3$/$HCO_3^-$) is a physiological example.

Mechanism. In a $CH_3COOH$/$CH_3COONa$ buffer, both the acidic and basic components are present together and don't consume each other: if acid is added, the extra $H^+$ is absorbed by $CH_3COO^-$ (re-forming $CH_3COOH$); if base is added, the extra $OH^-$ is neutralised by the dissociating acid's $H^+$, which is continually replenished. So the pH barely moves either way.

Buffer capacity/index. $\beta=\dfrac{dB}{d(pH)}$, the gram-equivalents of acid/base added per litre of buffer needed to shift its pH by one unit -- a quantitative measure of how resistant the buffer is. …