## Phosphoric Acid H3PO4

Phosphoric acid H3PO4 as a ployprotic acid is defined by the following three dissociation reactions and pKa values 1:

 (1) H3PO4 = H+ + H2PO4- pKa = 2.14 (2) H2PO4- = H+ + HPO4-2 pKa = 7.207 (3) HPO4-2 = H+ + PO4-3 pKa = 12.346

the corresponding anions are

 H2PO4- dihydrogen phosphate HPO4-2 hydrogen phosphate PO4-3 phosphate (orthophosphate)

Based on these reaction data, aqion is able to calculate the equilibrium composition and pH of a given phosphoric acid aqueous solution 2. This is done for the concentration range between 1 and 10-10 mol/L in the following table:

PO4_total PO4_total pH H3PO4 H2PO4- HPO4-2 PO4-3
mol/L mM % % % %
1E+00 1000 1.08 89.91 10.09 0.0000158 2.94E-16
1E-01 100 1.63 73.54 26.46 0.000112 4.72E-15
1E-02 10 2.26 41.32 58.68 0.000852 1.06E-13
1E-03 1 3.06 10.51 89.48 0.00709 4.36E-12
1E-04 0.1 4.01 1.33 98.6 0.0649 3.18E-10
1E-05 0.01 5.00 0.139 99.2 0.662 2.85E-08
1E-06 0.001 5.97 0.0141 94.5 5.54 2.36E-06
1E-07 0.0001 6.74 0.00189 74.4 25.6 6.39E-05
1E-08 0.00001 6.97 0.000951 63.3 36.7 0.000155
1E-09 0.000001 7.00 0.000874 61.8 38.2 0.000171
1E-10 0.0000001 7.00 0.000866 61.7 38.3 0.000173

Notation:

 PO4_total = initial concentration of phosphoric acid in mol/L and in mM spezies in % = (spezies in mM) / (PO4_total in mM) × 100 %

The molar concentration of the species H3PO4, H2PO4-, HPO4-2, and PO4-3 are taken from the output table Ions. In the calculations activity corrections are considered.

Discussion

For large acid concentrations, the solution is mainly dominated by the undissociated H3PO4. At 10-2 M, the pH is close to pKa = 2.14, giving an equimolar mixture of H3PO4 and H2PO4-.

Below 10-3 M, the solution is mainly composed of H2PO4-, while HPO4-2 becoming non negligible for very dilute solutions. The orthophosphate ion, PO4-3, is always negligible.

It is quite instructive to compare these calculations with the table in Wikipedia based on a numerical solution of an equation of 5th degree in H+. In contrast to the aqion, however, activity corrections are ignored. This causes some deviations, in particular, at high acid concentrations.

1 The thermodynamic database wateq4f contains only Eq.(2) and Eq.(3). Thus, in order to be complete it was necessary to implement the missing species “H2PO4”, i.e. Eq.(1), into aqion. The missing data where taken from the thermodynamic database minteq.

2 Examples how to calculate pH values are given here.