A simple and realistic model of a bistable chemical system in which running fronts can be observed is studied. The stochastic dynamics of this model is described by the master equation for a spatially extended system. The results are compared with microscopic simulations of the system, performed using the molecular dynamics technique for reactive hard spheres. The velocity of the front and its shape obtained in both simulations agree well with the phenonenological description. For small volumes of the systems fluctuations grow locally and create pulses of concentrations.