Polyprotic acids are acids that can lose more than one proton. The dissociation constant of the first proton may be denoted as Ka1 and the constants for dissociation of successive protons as Ka2, etc. Common polyprotic acids include sulfuric acid, H2SO4 and phosphoric acid, H3PO4.
To determine equilibrium concentrations of different ions produced by polyprotic acids, the equations can get very complicated to account for all of the different components. For instance, one can calculate the fractional concentration (alpha) of different ions using complex equation that account for hydrogen concentration (pH) and equilibrium constants, as seen in Figure 1.
However, one can simplify the problem, depending on the polyprotic acid. The following examples indicate the mathematics and simplifications for a few polyprotic acids under specific conditions.
H2SO4 → H+ + HSO4-
It also can lose a second proton as a weak acid with a measurable dissociation constant.
Therefore, one can assume that there is no measurable H2SO4 in the solution. Instead, it has completely dissociated to H+ and HSO4-, which in turn has dissociated to more protons and SO42-.
Phosphoric acid, H3PO4, has three dissociations, as can be viewed in Figure 2:
Thus, in an aqueous solution of phosphoric acid, there will theoretically be seven ionic and molecular species present: H3PO4, H2PO-, HPO2-, PO3-, H2O, H+, and OH-. Life might appear impossibly complicated, were we not able to make some approximations.
At a pH equal to the pKa for a particular dissociation, the two forms of the dissociating species are present in equal concentrations, due to the following mathematical observation. For the second dissociation of phosphoric acid, for which pKa2 = 7.21:
- pKa2 = -log(Ka2) = -log([H+]*[HPO42-]/[H2PO4-])
- pH = -log[H+]
Therefore, pH - pKa2 = log([HPO42-]/[H2PO4-])
When pH = pKa2, we have the ratio [HPO42-]/[H2PO4-] = 1.00. Hence, in a neutral solution, H2PO4- and HPO42- are present in about the same concentrations. Very little undissociated H3PO4 and fully dissociated PO43- will be found as can be determined through simliar equation with their given Ka's.
The only phosphate species that we have to consider near pH = 7 are H2PO4- and HPO42-. Similarly, in strong acid solutions near pH = 3, only H3PO4 and H2PO4- are important. As long as the pKa's of successive dissociations are separated by three or four units (as they almost always are), matters are simplified.
There is still another simplification. When a weak polyprotic acid, such as carbonic acid, H2CO3, dissociates, most of the protons present come from the first dissociation:
Since the second dissociation constant is smaller by four orders of magnitude (pKa2 = 10.25 is larger by four units), the contribution of hydrogen ions from the second dissociation will be only one ten-thousandth as large. Correspondingly, the second dissociation has a negligible effect on the concentration of the product of the first dissociation, HCO3-.