The rate of gas absorption at a liquid interface

Abstract

To determine the diffusion coefficient of a gas in a liquid the usual procedure is to expose the liquidinterface for a period of time, measure the amount of gas absorption, and from this infer the diffusion coefficient. The usual assumption to make at the liquid–gasinterface is that equilibrium is established immediately upon exposure of the liquid to the gas. This assumption has led to the illogical consequence of the inferred diffusion coefficient depending upon the period of time for which the liquidinterface is exposed to the gas. We use the Einstein expression for the probability of a transition in a system to derive an expression for the rate of gas absorption. When this derived rate is used to infer the diffusion coefficient, the same value is found from experimental techniques with extreme values of the exposure time. The accuracy of the predicted gas absorption rate supports the view that the Einstein relation is not limited to predicting fluctuations about an equilibrium state.