The pH of Aqueous Ammonium Hydrogen Carbonate

The calculation of the pH of an aqueous solution of ammonium hydrogen carbonate is discussed. Two different approaches are employed for this purpose: 1) a purely mathematical one, based on the use of numerical methods for finding polynomial roots, and 2) a chemically intuitive one based on simple acid-base chemistry considerations. While numerical methods yield the correct answer, they provide no chemical insight into the problem. The chemical approach is shown to give a reasonably good approximation with simple mathematical operations. Several additional cases of salts with analogous composition to ammonium hydrogen carbonate are also discussed, with emphasis on the possible violations of the simplifying assumptions adopted by the chemically intuitive method. In some of the latter cases, the simplified answers can be significantly improved by chemical intuition.