Asymptotic power series solutions for the mass-transfer enhancement factor for absorption of a gas component into a liquid where it undergoes irreversible instantaneous chemical reaction(s) with one and two liquid-phase reactants are developed in this work. The Padé technique is used to extend the region of applicability (accelerate the convergence) of the four-term asymptotic power series solutions. The resulting modified asymptotic expressions for the enhancement factor show excellent accuracy over a wide range and can be used to predict enhancement factors as low as 2 with an error of about 5% compared to the exact numerical solution. Predictions of these new asymptotic solutions are compared with experimental absorption data for H2S absorption into aqueous methyldiethanolamine and H2S absorption into aqueous mixtures of methyldiethanolamine and diethanolamine obtained in a laminar-jet absorber. The absolute mean deviations of the predictions from the experimental absorption data for the single and mixed amine solutions were 4.6% and 2.4%, respectively.