pH is defined as −log10[H+], and d(pH) is an infinitesimal change in pH. With either definition the buffer capacity for a weak acid HA with dissociation constant Ka can be expressed as where [H+] is the concentration of hydrogen ions, and is the total concentration of added acid. Kw is the equilibrium constant for self-ionization of water, equal to 1.0. Note that in solution H+ exists as the hydronium ion H3O+, and further aquation of the hydronium ion has negligible effect on the dissociation equilibrium, except at very high acid concentration. This equation shows that there are three regions of raised buffer capacity (see figure 2). In the central region of the curve (coloured green on the plot), the second term is dominant, and Buffer capacity rises to a local maximum at pH = pKa. The height of this peak depends on the value of pKa. Buffer capacity is negligible when the concentration [HA] of buffering agent is very small and increases with increasing concentration of the buffering agent. Some authors show only this region in graphs of buffer capacity. Buffer capacity falls to 33% of the maximum value at pH = pKa ± 1, to 10% at pH = pKa ± 1.5 and to 1% at pH = pKa ± 2. For this reason the most useful range is approximately pKa ± 1. When choosing a buffer for use at a specific pH, it should have a pKa value as close as possible to that pH. With strongly acidic solutions, pH less than about 2 (coloured red on the plot), the first term in the equation dominates, and buffer capacity rises exponentially with decreasing pH: This results from the fact that the second and third terms become negligible at very low pH. This term is independent of the presence or absence of a buffering agent. With strongly alkaline solutions, pH more than about 12 (coloured blue on the plot), the third term in the equation dominates, and buffer capacity rises exponentially with increasing pH: This results from the fact that the first and second terms become negligible at very high pH. This term is also independent of the presence or absence of a buffering agent. Applications of buffers The pH of a solution containing a buffering agent can only vary within a narrow range, regardless of what else may be present in the solution. In biological systems this is