Absorption of sparingly soluble gases is conventionally characterized by infinite dilution of absorbate. The present study relates to vapour absorption, where the concentration levels of absorbate and absorbent are comparable (finite dilution of absorbate). Such a process, for instance, is the hygroscopic condensation of cold low pressure vapour on a concentrated hot brine falling film. Isothermal and non-isothermal absorptions are considered. The latter represents coupled heat and mass transfer. It is shown that in the case of finite dilution, the lateral convective term ought to be accounted for. The resulting transfer rates are shown to depend on both the absorbate concentration level and the driving force and are significantly augmented compared to the prediction of Higbie's theory.