Should bulk cloudwater or fogwater samples obey Henry's law?

Abstract

In this work we prove that mixing of droplets with different pH that are individually in Henry's law equilibrium with the surrounding atmosphere always results in a bulk mixture that is supersaturated with weak acids like S(IV) and HCOOH and bases like NH₃ with respect to the original atmosphere. The degree of supersaturation of the bulk liquid water sample for a particular species depends on its dissociation constant, on the initial pH of the bulk droplet mixture, and on the distribution of the pH and of the liquid water over the droplet spectrum. High supersaturations result only when the pH of the bulk droplet mixture exceeds the pKa of the species, in which pH range large pH differences among droplets of different sizes lead to large deviations from Henry's law for the bulk mixture. The deviation is shown to depend on the ratio of the arithmetic mean to the harmonic mean of the hydrogen ion concentrations of the droplets with the liquid water content used as weighting factor in the calculation of the means. The theory developed can explain observed discrepancies from Henry's law in atmospheric samples and also other observed phenomena like the reported increase of pH values of bulk aqueous samples during storage.