Unsteady conjugate mass transfer between a spherical bubble, droplet, or particle and a surrounding fluid flow with chemical reaction in the continuous phase has been analyzed. An algorithm based on spectral methods has been developed and implemented for the simulation of the interphase mass transfer. The influence of Pe (convection) and Da (rate of external reaction), but in particular of D (diffusivity ratio) and H (distribution coefficient), which characterize the coupling features of the conjugate mass transfer, is studied in a wider range of parameters than earlier investigations. The asymptotic regime of mass transfer is investigated for long times, and an upper limit for the corresponding dimensionless mass transfer coefficient is established. A method for decoupling the conjugate problem is proposed that results in a modified version of the addition rule, which is a higher level of approximation than the original one. As measured against the results of our numerical simulations, the modified addition rule yields results in the asymptotic regime that are superior to those obtained using the customary addition rule.