The buffer capacity (β) for a weak acid (A) – conjugate base (B) buffer is defined as the number of

Question

The buffer capacity (β) for a weak acid (A) – conjugate base (B) buffer is defined as the number of moles of strong acid or base needed to change the pH of 1 L of solution by 1 pH unit, where $\beta = \frac{2.303\left( C_{A} + C_{B} \right)K_{a}\left\lbrack H^{+} \right\rbrack}{\left( \left\lbrack H^{+} \right\rbrack + K_{a} \right)^{2}}$. Under what condition will a buffer best resist a change in pH?

Accepted Answer

For maximum $\beta,\frac{\alpha\beta}{\alpha\left\lbrack H^{+} \right\rbrack} = 0 \Rightarrow P^{H} = P^{K_{a}}$

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