Numerical analysis on gas absorption accompanied by an instantaneous reaction or a second-order reaction into a liquid layer of finite thickness in laminar flow is presented. A similar influence of the reactant diffusivity ratio, the Fourier number, and the Hatta number on the enhancement factor is reported compared to the ideal situation in which the liquid layer is in plug flow motion. Approximate enhancement factor expressions are developed for both reaction cases by analogy to the plug flow situation, where the predictions according to the original penetration theory tend to give erroneous results in the enhancement factor at Fourier numbers above 0.1. The developed expressions in the case of a second-order reaction can be extrapolated for estimating the enhancement factor in the more general case of a (1, n)-th-order reaction.