A buffer's job is to resist pH change, but not all buffers resist equally well — and even a single buffer resists better at some pH values than others. Buffer capacity (β) puts a number on that resistance, and the Van Slyke equation is the standard tool chemists use to calculate it from a buffer's concentration, pKa, and current pH.

What buffer capacity actually measures

Buffer capacity is defined as the moles of strong acid or base, per liter of solution, required to change the pH by exactly one unit. A buffer with β = 0.1 mol/L per pH resists twice as hard as one with β = 0.05: it takes twice as much added acid or base to move its pH the same amount. Unlike pH itself, which only tells you the current state of a solution, β tells you how the solution will respond to a disturbance — the property that actually matters when designing a buffer for a real application.

Why capacity peaks exactly at pH = pKa

The Van Slyke equation, β = ln(10)·C·(Ka·[H⁺])/(Ka+[H⁺])², is maximized when the denominator (Ka+[H⁺])² is smallest relative to the numerator Ka·[H⁺] — which happens precisely when Ka equals [H⁺], i.e. when pH equals pKa. At that point the weak acid and its conjugate base are present in equal concentrations, so there is equally as much of each species available to neutralize incoming acid or base. Move away from pH = pKa in either direction and one species runs relatively short, so the buffer's resistance weakens — even though the total concentration hasn't changed.

The practical pKa ± 1 rule, and why it's ~33%, not zero

Chemists conventionally treat a buffer as "effective" within about one pH unit of its pKa — a base:acid ratio between 1:10 and 10:1. This isn't an arbitrary cutoff: at those edges, β has fallen to roughly 33% of its maximum, a large enough drop that the buffer starts allowing noticeably bigger pH swings per unit of acid or base added. It is not zero, though — the buffer still provides real resistance outside pKa ± 1, just meaningfully less. Choosing a weak acid whose pKa sits close to the pH you actually need to maintain is the single biggest lever over how well a buffer performs in practice.

Using buffer capacity in lab and formulation work

Buffer capacity calculations answer a very practical question: will this buffer hold its pH against the acid or base load my process is going to generate? Biological buffers (like phosphate-buffered saline) are formulated with enough capacity to absorb the CO₂ and metabolic acids a cell culture produces; industrial and pharmaceutical buffers are sized the same way against known process loads. Because β scales linearly with total concentration, the two levers formulators actually control are (1) picking a pKa close to the target pH and (2) choosing a concentration high enough to survive the expected acid/base load — both of which this calculator lets you check directly.