# Strong Acids (HCl, HNO3, H2SO4)

What is the pH of the strong acids HCl, HNO_{3} and H_{2}SO_{4} in the concentration range between 10^{-6} and 1.0 moles per liter?

*Preliminary Considerations*

Strong acids ionize completely in an aqueous solution, *HA → H ^{+} + A^{-}.* Thus, based on the pH definition we can write:

(1) | pH = – log {H^{+}} = – log γ – log [H^{+}] = – log γ – log [HA] |

*Approximations*

If we ignore activity corrections at all, that is, if we set *log γ = 0*, then we get two approximate formulas:

(2) | pH ≈ -log [HA] | (for monoprotic acid HA) |

(3) | pH ≈ -log 2 [H_{2}A] |
(for diprotic acid H_{2}A) |

The factor 2 in *3* results from the fact that H_{2}SO_{4} can release two H^{+} ions. But caution: hydrogen sulfate (HSO_{4}^{-}) is — in contrast to H_{2}SO_{4} — not a strong acid. In other words, *3* isn’t a very good approximation.

*Exact Calculation with aqion*

How to calculate the pH of an acid is explained here. The same procedure is used for all three acids at 8 concentration values. The results are displayed here, together with the two approximations in *2* and (3):

concentration [M] | approx. (2) | HCl | HNO_{3} |
approx. (3) | H_{2}SO_{4} |
---|---|---|---|---|---|

1·10^{-6} |
6.00 | 6.00 | 6.00 | 5.70 | 5.70 |

1·10^{-5} |
5.00 | 5.00 | 5.00 | 4.70 | 4.70 |

1·10^{-4} |
4.00 | 4.00 | 4.00 | 3.70 | 3.71 |

1·10^{-3} |
3.00 | 3.01 | 3.01 | 2.70 | 2.75 |

1·10^{-2} |
2.00 | 2.04 | 2.04 | 1.70 | 1.87 |

1·10^{-1} |
1.00 | 1.08 | 1.08 | 0.70 | 1.01 |

0.5 | 0.30 | 0.42 | 0.42 | 0.00 | 0.38 |

1.0 | 0.00 | 0.13 | 0.13 | -0.3 | 0.10 |

[Be careful with the concentration units in *aqion*: In place of 1·10^{-6} M enter 0.001 mmol/L, etc.]

*Two Conclusions*

**First.** For concentrations up to about 1 mM the approximations coincide with the exact values. At higher concentrations, however, the approximations become worse because they ignore activity corrections. The difference between the exact and approximate pH provides just the activity correction:

(4) | pH_{exact} – pH_{approx} = –log γ |

[An example how to calculate the activity correction (based on the extended Debye-Hückel formula) is given here for *0.1 M HCl*.]

**Second.** The deviation from the exact pH is especially acute for the diprotic H_{2}SO_{4}. It was already mentioned above that *3* is a bad approximation.

**Pitfall.** One might expect that the approximation in *2* becomes especially correct for very small concentrations. But the opposite is true, here is a counter example.