Chemistry
Buffer Capacity: Dependence on pKa and Concentration
Quick fact
The buffer capacity is maximum when pH = pKa, and it halves when the pH is one unit away from the pKa—a simple but powerful rule.
Why this is interesting
Why can a buffer with a certain pH suddenly fail when you add just a bit more acid? The answer lies in two hidden levers: concentration and distance from pKa.
Read the full explanation
Understanding Buffer Capacity: Dependence on pKa and Concentration
Think of a buffer as a sponge for H+ ions. The sponge is made of a weak acid (HA) and its conjugate base (A-). When you add acid (H+), the base A- soaks it up: A- + H+ → HA. When you add base (OH-), the acid HA neutralizes it: HA + OH- → A- + H2O. The buffer works until one component runs out. Now, imagine the amounts of HA and A- in the solution. The pH of the buffer is determined by the ratio of these two, as described by the Henderson-Hasselbalch equation: pH = pKa + log([A-]/[HA]). This means the buffer's pH is set by the pKa and the ratio of base to acid. Buffer capacity is about how much acid or base the buffer can handle before the pH changes significantly. There are two factors that control this capacity: 1. Concentration: A buffer with more HA and A- (higher total concentration) has more 'sponge' to absorb H+ or OH-. So, a 0.1 M buffer can neutralize more added acid than a 0.01 M buffer of the same pH. 2. Proximity to pKa: The buffer is most effective when [HA] ≈ [A-], which happens when pH ≈ pKa. If the ratio is far from 1 (pH far from pKa), one component is in low supply, and the buffer quickly exhausts its capacity. In summary, buffer capacity (β) is defined as the moles of strong acid or base needed to cause a unit pH change. It directly rises with total buffer concentration and falls as the pH moves away from pKa.
A deeper explanation
We can quantify buffer capacity mathematically to see why these factors matter. The buffer capacity β is often expressed as: β = 2.303 × ( [H+] + [OH-] + (Cacid × Ka × [H+]) / ([H+] + Ka)^2 ) where Cacid is the total concentration of weak acid species (HA + A-). For practical purposes, when pH is near pKa (within 1 unit), the third term dominates. In this region, the formula simplifies to: β ≈ 2.303 × (Cacid × Ka × [H+]) / ([H+] + Ka)^2 Substituting [H+] = 10^(-pH) and using the Henderson-Hasselbalch ratio, we can derive a simpler expression: β ≈ 2.303 × (Cacid × [A-] × [HA]) / ([A-] + [HA])^2 This equation clearly shows: - Concentration: β is proportional to the total concentration (Cacid = [HA]+[A-]). Double the concentration, and you double the buffer capacity. - Proximity to pKa: The term [A-][HA] is maximized when [A-] = [HA], i.e., when pH = pKa. At pH = pKa ± 1, the capacity is only about a third of the maximum, and at pH = pKa ± 2, it drops to a tiny fraction. Therefore, effective buffers are designed with a pKa close to the desired pH (typically within 1 unit), and with adequate concentration to handle the expected acid/base load. This principle guides buffer selection in biochemistry (e.g., using HEPES for pH 7.5) and in industrial processes.