A detailed study of the interaction of HOBr and HCl in cold Sulfuric acid solutions has been performed using a coated-wall flow tube coupled to an electron-impact mass spectrometer. The liquid-phase bimolecular rate constants, measured over a temperature range from 213 to 238 K and in solutions from 59.7 to 70.1 wt % composition, show a strong positive dependence on both acid composition and temperature. The solubility of HOBr has also been measured in these solutions by analyzing its time-dependent uptake. Henry's Law constants (H) determined from the measured values of HD1/2 and the liquid-phase diffusion coefficient (D) are independent of acid composition over the above range of solution compositions. The values of H demonstrate a clear Clausius-Clapeyron temperature dependence, with a heat of solution of -9 +/- 1 kcal/mol. When the atmospheric importance of these data is assessed, two conclusions are reached. In the stratosphere, under aerosol conditions observed soon after the Mt. Pinatubo volcanic eruption, the rates of HCl activation via the HOBr/HCl heterogeneous reaction are comparable with the rate of activation via gas-phase reaction with OH at relatively warm temperatures (205-220 K), where other HCl-activating heterogeneous reactions occur slowly. In the high Arctic boundary layer, it is possible that significant HCl activation could occur when elevated levels of photochemically active bromine are present.