  A one-dimensional reaction-diffusion model consisting of two species of
particles and vacancies on a ring is introduced. The number of particles in one
species is conserved while in the other species it can fluctuate because of
creation and annihilation of particles. It has been shown that the model
undergoes a continuous phase transition from a phase where the currents of
different species of particles are equal to another phase in which they are
different. The total density of particles and also their currents in each phase
are calculated exactly.
