Pauling's rules

These are two empirical rules which predict the strength of mononuclear oxoacids. I'm not sure why they are so commonly taught to undergrads - since I presume modern wavefunction software could make more advanced predictions.

1. For the oxoacid O_pE(OH)_q, pK_a ≈ 8 – 5p
2. The successive pK_a values of polyprotic acids (those with q > 1), increase by 5 units for
each successive proton transfer.

It should be obvious why oxo groups increase acidity, they can delocalize charge on the anion by resonance:

This allows us to rationalize why the acidities of chloro oxoacids decrease in the order HOCl₄ > HClO₃ > HClO₂ > HClO. Likewise for H₂SO₄ > H₂SO₃ and HNO₃ > HNO₂.

One good use of these rules is to notice structural anomalies. For example, if you dissolve carbon dioxide in water to make carbonic acid, you will find an empirical pK_a of 6.4 - but the rules predict a pK_a of 3.

The mistake is in assuming that all of the CO₂ dissolved in a sample of water exists as carbonic acid. In reality, only 1-2% of dissolved carbon dioxide exists in carbonic acid form. The pure pK_a is 3.6 when this difference is taken into account.

Many non-metal oxides, and some metal oxides, do not fully become their acidic form when dissolved in water. Deviation from Pauling's rules can help us detect that.