The reactive uptake of gases by a particle is explored by numerically solving the associated partial differential equations. These equations explicitly couple the diffusion and reaction of multiple species in the particle. This approach makes it possible to calculate the concentration of each reactant within the particle as a function of both time and position and to examine the impact of concentration gradients on the rate of uptake. The effect of liquid diffusion on the rate of uptake is explored for a reference reaction (O-3 + oleic acid particles) as a function of the particle size and the liquid-state concentration of the species taken up from the gas phase. Diffusion within the particle is found to significantly limit uptake for large particles and the large gas-phase concentrations often used in laboratory experiments, although it is typically less important under atmospheric conditions. This numerical approach to solving the diffusion-reaction equations is also used to modify the common electric circuit resistance model for heterogeneous uptake to make it more applicable when diffusion within the particle is limiting.