Buffer pH Calculator

A buffer holds pH steady because it contains appreciable amounts of a weak acid HA and its conjugate base A- at the same time. Rearranging the dissociation constant Ka = [H+][A-]/[HA] and taking negative logarithms gives the Henderson-Hasselbalch equation, pH = pKa + log([A-]/[HA]). The striking consequence is that pH depends on the ratio of the two species, not on their absolute amounts, so diluting a buffer two-fold barely moves the pH even though it halves the capacity. When the two are equal the log term is zero and pH equals pKa exactly; a ten-to-one ratio shifts pH by only one unit in either direction. Working with volumes, the moles of each component are computed first (molarity times liters) and the ratio taken, since both species end up in the same final volume. Common systems and their 25 degrees C pKa values are acetate at 4.76, useful over roughly pH 3.8 to 5.8; carbonic acid at 6.35; dihydrogen phosphate at 7.20, covering pH 6.2 to 8.2; HEPES at 7.5; and Tris at 8.06, covering pH 7.1 to 9.1. The equation carries real limitations. It substitutes concentrations for activities, so it degrades above about 0.1 M ionic strength; it assumes dissociation of HA and hydrolysis of A- are negligible, which fails in very dilute buffers or more than about two units from pKa; and it ignores temperature, a serious issue for Tris, whose pH drops roughly 0.028 units for every degree C of warming, so a buffer titrated at 4 degrees C reads noticeably lower when warmed to 37 degrees C.

Lawrence Joseph Henderson, a physiologist at Harvard, published the underlying relationship in 1908 while investigating how blood maintains near-neutral reaction despite continuous production of carbon dioxide and organic acids. His equation was written in terms of hydrogen ion concentration rather than a logarithm, because the logarithmic pH scale did not yet exist; Soren Sorensen introduced pH at the Carlsberg Laboratory in Copenhagen in 1909. The Danish physician Karl Albert Hasselbalch recast Henderson's expression in logarithmic form in 1916, specifically to make the bicarbonate buffering of blood easier to evaluate from measured carbon dioxide tension, and the combined name has been attached to it ever since. The equation spread from respiratory physiology into general chemistry and then into industrial and pharmaceutical practice as pH measurement became routine, particularly after Arnold Beckman commercialized a rugged vacuum-tube pH meter in 1935 that let anyone read pH to about 0.01 units. Buffer choice was transformed again in 1966 when Norman Good and coworkers published a systematic screen in Biochemistry for zwitterionic buffers with pKa values in the physiological range and minimal interaction with metal ions and enzymes, yielding MES, HEPES, MOPS and their relatives. Those reagents are still specified by pKa precisely because the Henderson-Hasselbalch relation makes pKa the single number that predicts a buffer's useful range.