A Simple Model for the Hygroscopy of Sulfuric Acid

Sulfuric acid is a highly hygroscopic substance, increasing its volume by absorbing water from a high relative-humidity environment. In this paper, we present a mathematical model that describes the hygroscopy of a uniform layer of sulfuric acid with a given initial concentration and relative humidity of the surrounding gaseous environment. We assume that water is absorbed across the gas-liquid interface at a rate proportional to the difference in concentration from the equilibrium value. Our numerical results compare well with asymptotic predictions for small Sherwood number, where we derive an explicit solution. The theory agrees well with the experimental data, which supports the validity of the model, and we are able to use the model to determine the rate of absorption, which cannot be found by a direct experimental measurement.