|The "operational" relationship between pKa and pH is mathematically
represented by Henderson-Hasselbach equation:
pH = pKa + log [A-] / [HA]
where [A-] represents the deprotonated form and [HA] represents the protonated form.
One oft-cited solution to this equation is obtained by arbitrarily setting
pH = pKa.
In this case, log([A-] / [HA]) = 0, and [A-] / [HA] = 1.
In words, this means that when the pH is equal to the pKa of the acid, there are equal amounts of protonated and deprotonated acid molecules. This same relationship holds for bases as well, with [B] substituting for
[A-] as the deprotonated form, and [HB+] substituting for [HA] as the protonated form. It should be emphasized that the Henderson-Hasselbach relationship holds for a specified acid or base even if multiple acids or bases are present.
Other solutions to the Henderson-Hasselbach equation over a range of pH values are displayed in the following figure (for acetic acid).
Several points about this graph deserve mention:
"Net charge on acid" refers to the average of all acid molecules in the solution.
- At the pKa , the acid is 50% deprotonated.
- At the 1 pH unit above (below) the pKa , the acid is 90% deprotonated (protonated).
- At 2 pH unit above (below) the pKa , the acid is 99% deprotonated (protonated).
- At 3 pH unit above (below) the pKa , the acid is 99.9% deprotonated (protonated).
- When fully protonated, charge on acetic acid is 0.
- When fully deprotonated, charge on acetate is -1.