Diffusion rates of molecular Bromine (Br-2) through a CMV cation exchange membrane have been measured using a dialysis filled either with water or 0.5 M HCl + 0.5 M HBr solution as solvents. Continuous registration of concentration change is performed by precision densitometry using the vibrating tube technique, Along with experimental data of sorption isotherms of Br-2 in the membrane material the dialysis data are evaluated in the framework of the solution diffusion model providing diffusion coefficients of Br-2 in the CMV membrane. The dialysis process is slower for 0.5 M HCl + 0.5 M HBr than for pure water. Theoretical analysis shows that membrane sorption capacity for Br-2 is smaller in case of the acid solvent. This is the reason for the different diffusive behaviour while the diffusion coefficients in the membrane are unaffected by the kind of solvent. The results are of importance for estimating the extent of cross contamination for the Cr/Br flow battery.