We report here the first experimental determination of the mass accommodation coefficient (alpha) of (H2O)-O-17(g) on aqueous sulfuric acid solutions. The uptake of O-17-labeled gas-phase water was measured as a function of temperature (250-295 K) and acid concentration (50-82 wt % H2SO4) using a droplet train flow reactor. The mass accommodation coefficient exhibits a negative temperature dependence and increases with increasing H2SO4 concentration. For 50 wt % sulfuric acid solution, the mass accommodation coefficient ranges from 0.50 +/- 0.05 at 250 K to 0.41 +/- 0.07 at 278 K, and for 70 wt % solution, it ranges from 0.69 +/- 0.07 at 252 K to 0.54 +/- 0.05 at 295 K. The dependence of the mass accommodation coefficient on the sulfuric acid composition correlates with surface coverage of water. The uptake coefficient of D2O was measured to be unity on 70 wt % H2SO4, independent of temperature between 263 and 293 K. The D20 uptake coefficient is larger than the mass accommodation coefficient for (H2O)-O-17 because D-H isotope exchange opens another channel for the disappearance of D2O from the gas phase. The D2O uptake coefficient of unity implies that the thermal accommodation coefficient of water on sulfuric acid surfaces is also unity.