Buffer Capacity Calculator (Henderson-Hasselbalch)

Buffer capacity, written beta, is the differential resistance of a solution to pH change: the number of moles of strong monoprotic acid or base that must be added to one liter to move the pH by one unit. The Van Slyke expression beta = 2.303 * C * alpha * (1 - alpha) follows directly from differentiating the acid dissociation equilibrium. C is the analytical concentration of the conjugate pair (HA plus A-), alpha is the fraction present as A-, equal to 10^(pH - pKa) / (1 + 10^(pH - pKa)), and the constant 2.303 is the natural logarithm of 10 that appears when converting from ln to log base 10. Because the product alpha * (1 - alpha) is largest at 0.25 when alpha is 0.5, capacity peaks exactly at pH = pKa, giving beta max = 0.576 * C. A 0.1 M acetate buffer at pH 4.76 therefore reaches only 0.0576 mol per liter per pH unit. Bench chemists treat pKa plus or minus 1 as the working window, where beta has already fallen to roughly a third of its maximum. Outside about pH 3 to 11 the water term 2.303 * ([H+] + [OH-]) starts to dominate and the buffer pair contributes little. The main limitations are that the equation uses concentrations rather than activities, so at ionic strengths above roughly 0.1 M the effective pKa shifts by several hundredths of a unit; polyprotic systems such as phosphate or citrate require summing a separate term for each dissociation step; and pKa values are temperature dependent, with Tris moving about -0.028 pH units per degree C of warming.

The idea that a solution has a measurable resistance to pH change emerged soon after Soren Sorensen defined the pH scale at the Carlsberg Laboratory in 1909. The word buffer itself was already in use in enzyme work by Fernbach and Hubert around 1900. In 1914 Koppel and Spiro published a quantitative treatment of what they called the buffer value, but the formulation that became standard came from Donald Dexter Van Slyke at the Rockefeller Institute, whose 1922 paper in the Journal of Biological Chemistry, On the Measurement of Buffer Values, defined beta as dn/d(pH) and derived the expression still used today. Van Slyke reached the problem through blood chemistry, where he needed to describe how plasma proteins and bicarbonate share the load of neutralizing metabolic acid. That clinical lineage continued through the mid twentieth century. In Copenhagen, Poul Astrup and Ole Siggaard-Andersen built the base excess concept of acid-base diagnosis on buffer-value reasoning, quantifying whole-blood buffering near 48 to 52 mmol per liter per pH unit. On the laboratory side, Norman Good and colleagues published their 1966 survey of zwitterionic buffers in Biochemistry, screening compounds specifically for pKa values falling in the physiological 6 to 8 range and for low metal binding, which turned buffer capacity from a descriptive quantity into a design criterion for reagents such as HEPES and MES.