The buffer capacity () for a weak acid (A) – conjugate base (B) buffer is defined as the number of m — Ionic Equilibrium Chemistry Question
Question
The buffer capacity ($\beta$) 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 $\beta = \frac{2.303(C_A + C_B) K_a [\text{H}^+]}{([\text{H}^+] + K_a)^2}$. Under what condition will a buffer best resist a change in pH?
💡 Solution & Explanation
The buffer capacity ($\beta$) defines how effectively a buffer resists changes in pH upon addition of an acid or base. Mathematically, the function $\beta = \frac{k [\text{H}^+]}{([\text{H}^+] + K_a)^2}$ reaches its absolute maximum when the derivative with respect to $[\text{H}^+]$ is zero, which occurs exactly when $[\text{H}^+] = K_a$. Taking the negative logarithm of both sides yields $\text{pH} = pK_a$. Therefore, correct answer is C.