We investigate a class of reactive advection-diffusion problems motivated by an ecological mixing process. We use analytical and numerical methods to determine reaction rates between two initially distinct scalar point masses that are separated from one another by a third (nonreactive) scalar. The scalars are stirred by a single two-dimensional vortex in a variety of geometrical configurations. We show that the aggregate second-order reaction rate in the low-concentration limit is enhanced by the instantaneous stirring processes, relative to the rate predicted by an equivalent eddy diffusivity. The peak reaction rate grows as P(1/3), and the time to reach the peak decreases as P(-2/3), where P is the Péclet number. The results of this study have important implications not only for ecological modeling, but for the general understanding of turbulent reactive flows.