After assuming that the transport of molecules between phases at thermal equilibrium results primarily from single molecular events, the expression for the rate of molecular transport between phases is developed by using a first order perturbation analysis of the Schrooinger equation and the Boltzmann definition of entropy. This leads to an Einstein-type relation with the constant of proportionality being the average rate of exchange between microscopic states of different molecular distributions. A hypothesis is introduced which leads to the conclusion that this exchange rate is unchanged as the system moves through the molecular distributions leading to equilibrium, and to it being equal to the molecular rate of exchange between phases in the final equilibrium state. This allows a complete expression for the rate of molecular transport between phases to be developed. The validity of the hypothesis can be examined by comparing the predictions that follow from the derived rate expressions with the available experimental data. This comparison is reported in subsequent parts of this work.

The statistical rate theory approach is used to derive the expression for the rate of gas absorption by a liquid. This process involves two sequential rates−the rate of transport from the gas to the surface and the rate of transport from the surface to the bulk liquid. According to the statistical rate theory, the rate limiting step is the rate of transport from the surface. After deriving the rate expression for the rate limiting step, it is incorporated in an integral equation approach for predicting the rate of evolution of a bubble evolving isothermally in a liquid–gas solution. This approach accounts for the movement of the bubble boundary in the diffusion problem. Statistical rate theory leads to a complete expression for the rate of gas absorption; thus by comparing the predicted rate of bubble evolution with a set of measurements, one can investigate the validity of the statistical rate theory. This comparison is carried out and the predictions are found to be in close agreement with the experiments throughout the experimental period.

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