The particle grid method is applied to a system of 10 reacting chemical species in a two-dimensional rotating flow field with and without diffusion. Two types of chemistry grids are used to describe the chemical reactions: a fixed coarse grid and a moving (the advection case) or stationary (the advection plus diffusion case) fine grid. Two particle number densities are also used: 256 and 576 particles per fixed coarse grid cell. The species mass redistributed back to the particle after each reaction step is assumed to be proportional to the species mass in the particle before the reaction. The simulation results are very accurate, especially in the advection chemistry case. Accuracy improves with the use of a fine grid. A higher particle number density also reduces the concentration fluctuation in the cases involving diffusion. We also show by examples that chemistry can lead to significantly different results from numerical methods for the diffusion equation (let alone the advection equation) which otherwise yield almost identical solutions. The absence of this difficulty in the particle grid method further enhances its attractiveness.