We develop a theoretical framework for investigating the effect of spatial averaging on the rates of chemical reactions. In particular, we study how spatial averaging will affect the calculated rate of ozone depletion due to the ClO dimer (Cl2O2) cycle. It is important to note that changes in the partitioning of active chlorine (ClOx) between ClO and Cl2O2 acts to reduce any nonlinearity in O3 loss due to this cycle. Furthermore, our analysis demonstrates that under conditions of moderate to large chlorine activation within the vortex the effects of averaging small-scale ClOx inhomogeneities on calculated chemical ozone loss are necessarily small. Spatial averaging, and therefore model spatial resolution, becomes a relatively more important issue under low-ClOx conditions. These results are consistent with the model results of Searle et al. who calculated a very weak dependence on model resolution of O3 loss in the polar vortex in the Arctic winter 1994--1995. ¿ 1998 American Geophysical Union