The probabilities that a water vapor molecule striking a liquid water surface will (1) thermally equilibrate with the liquid surface and (2) penetrate that surface and be incorporated into the bulk liquid are parameters of fundamental importance to both chemical physics and atmospheric science. Here we report values for these parameters as a function of temperature in the range of 258-280 K, measured with a droplet train flow reactor under conditions that circumvent difficulties encountered in earlier studies. The mass accommodation coefficient (alpha) of H2O(g) on water was determined by measuring the uptake of O-17 labeled gas-phase water under near equilibrium conditions. The mass accommodation coefficient has a negative temperature dependence, with the magnitude ranging from 0.17 +/- 0.03 at 280 K to 0.32 +/- 0.04 at 258 K. The temperature dependence and the magnitude of a are consistent with the critical complex theory of mass accommodation, previously applied to the uptake of other gas-phase species by aqueous surfaces. Experiments with D2O(g) on liquid water show that D-H isotope exchange on the liquid surface proceeds with unit probability, independent of temperature. This result implies that the thermal accommodation coefficient of H2O(g) on liquid water is I in the temperature range studied.