The lower critical mass boundaries (CM) for various atmospheric gas species on terrestrial planets are estimated. The CM is different for different gas molecules. Except for He, the observed atmospheric compositions of the terrestrial planets are consistent with these estimates. The lower CM boundary for gaseous H2O is calculated as 8.06 × 1026 g, which is significantly greater than the Martian mass (6.419 × 1026 g). Thus, Mars is not capable of retaining H2O in its atmosphere. If the speculated ocean on Mars and the claimed H2O ice in the Martian soil are true, both the ocean and ice had to be derived earlier from H2O degassed from the Martian interior after the surface temperature cooled much below 100°C. These watery bodies cannot be sustained for long durations because evaporation and sublimation would turn them into gaseous H2O, which would be lost to outer-space. It is concluded that H2O in/on Mars is inherent and that the primordial planetesimals that formed Mars must have contained appreciable amounts of hydrous minerals, if the oceans and/or H2O ice on Mars are true.