## Phosphoric Acid H3PO4

Phosphoric acid H_{3}PO_{4} as a *ployprotic* acid is defined by the following three dissociation reactions and pK_{a} values ^{1}:

(1) | H_{3}PO_{4} = H^{+} + H_{2}PO_{4}^{-} | pK_{a} = 2.14 |

(2) | H_{2}PO_{4}^{-} = H^{+} + HPO_{4}^{-2} | pK_{a} = 7.207 |

(3) | HPO_{4}^{-2} = H^{+} + PO_{4}^{-3} | pK_{a} = 12.346 |

the corresponding anions are

H_{2}PO_{4}^{-} | dihydrogen phosphate |

HPO_{4}^{-2} | hydrogen phosphate |

PO_{4}^{-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 pK_{a} = 2.14, giving an equimolar mixture of H_{3}PO_{4} and H_{2}PO_{4}^{-}.

Below 10^{-3} M, the solution is mainly composed of H_{2}PO_{4}^{-}, while HPO_{4}^{-2} becoming non negligible for very dilute solutions. The orthophosphate ion, PO_{4}^{-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.