Henderson Hasselbalch Calculator

The equation is nothing more than the acid dissociation expression Ka = [H+][A-]/[HA] rearranged and put through a negative base-10 logarithm, which turns a multiplicative equilibrium into the additive form pH = pKa + log([A-]/[HA]). The practical value of writing it this way is that the ratio of the two buffer species, not their absolute concentrations, sets the pH, so diluting a buffer barely moves it while diluting a strong acid moves it a great deal. When the ratio is 1:1 the log term vanishes and pH equals pKa, which is also where buffer capacity peaks. Buffer value beta = 2.303*C*Ka*[H+]/(Ka + [H+])^2 reaches a maximum of 0.576*C at that point, and the conventional working window of pKa plus or minus 1 corresponds to species ratios between 1:10 and 10:1. Common pKa values at 25 degrees C are 4.76 for acetic acid, 6.35 for the first carbonic acid dissociation, 7.20 for dihydrogen phosphate, 7.55 for HEPES and 8.07 for Tris. The equation rests on approximations that fail predictably. It substitutes prepared concentrations for true equilibrium concentrations, which breaks down below roughly 1e-3 M or when the acid is not weak. It ignores activity coefficients, so at an ionic strength of 0.1 M the apparent pKa can shift by around 0.1 unit and a correction such as the Davies equation is needed. It ignores water autoionisation, which matters outside about pH 4 to 10. Temperature is a further trap: the pKa of Tris falls by roughly 0.03 units per degree C, while phosphate changes about ten times less.

Lawrence Joseph Henderson, a physiologist at Harvard, published the underlying relation in 1908 in the American Journal of Physiology while investigating how blood neutralises the acid produced by metabolism. He wrote it in linear concentration form, since the pH notation did not yet exist; Soren Sorensen introduced the pH scale at the Carlsberg Laboratory in Copenhagen the following year, 1909. Karl Albert Hasselbalch, a Danish physician also connected to the Carlsberg Laboratory, recast Henderson's expression in logarithmic form using Sorensen's notation in work published around 1916 and 1917, applying it directly to the carbon dioxide and bicarbonate system in blood. The joint name reflects that two-step origin rather than any collaboration between the men. The framework was extended in the 1920s when Donald Van Slyke, at the Rockefeller Institute, defined buffer value quantitatively and developed the manometric methods that made blood gas chemistry a clinical discipline. Acid-base measurement was transformed again during the 1952 poliomyelitis epidemic in Copenhagen, where Poul Astrup and later Ole Siggaard-Andersen built the interpretive nomograms and electrode methods behind modern blood gas analysis. Laboratory buffering changed in 1966, when Norman Good and colleagues published a set of zwitterionic buffers, including HEPES, MOPS and PIPES, deliberately designed with pKa values near physiological pH and minimal interaction with biological systems.