The penetration-theory solution for the effect of a second-order irreversible liquid-phase chemical reaction on the rate of gas absorption has been computed numerically on an IBM-704 computer. A linearized, time-centered, implicit finite-difference method was used to solve the nonlinear partial-differential equations. The method was very effective, permitting the solution of the equations for a wide range of the parameters of interest. The penetration-theory results are compared with the film-theory solution, and it is shown that the solutions to the two theories agree within 16% if they are compared for conditions which produce the same asymptotic solution for an infinitely rapid chemical reaction. A simplified equation and some correction charts are presented which permit a rapid, accurate estimation of the penetration-theory solution over a wide range of variables.