We study the competition between the Turing instability to steady patterns and the Hopf instability to oscillations in diffusively coupled open reactors. Our approach is based on exact, analytical criteria for the occurrence of these instabilities in arrays of coupled reactors. We consider a general two-variable kinetic model that represents an activator- inhibitor scheme with a complexing agent or substrate for the activator. We apply our results to the Lengyel-Epstein model of the chlorine dioxide-iodine-malonic acid reaction. Using symbolic computation software, we derive exact conditions for the Turing and Hopf bifurcations in small, linear arrays of coupled reactors with an inhomogeneous concentration profile of the substrate. Our main result is the determination of the critical substrate concentration profile, above which the Turing instability occurs before the Hopf instability. This provides the condition for stationary Turing patterns to be experimentally observable in arrays of coupled reactors.