A reactiodffusion system of polymers undergoing interchange reactions is studied. The equation that describes the dynamics of the system is similar to the Boltzmann equation for a gas of hard spheres. We consider a one-dimensionsl system in which the average length and the concentrations at the boundaries are fixed. The resulting steady states are obtained analytically and with numerical integration of equations obtained by using a local equilibrium approximation. Monte Carlo simulations of experimentally realizable conditions were performed and compared. The results reveal a nonlinear distribution of molecular concentration and mass. The entropy of the polymer distributions is calculated as function of position and shown to be less than the entropy for the distributions without interchange reactions. The diffusion of a square pulse is also considered.