Because H2 reacts efficiently with O+, CO2+, CO+, and N2+, the molecular hydrogen abundance assumed in models of the Martian ionosphere greatly affects the high altitude density profiles of these ions. We have found that models of the low solar activity Martian ionosphere exhibit much smaller O+ densities than the measured values if the adopted H2 abundance is of the order of 40 ppm, the value proposed in a 1998 model of the Martian atmosphere. For a model based on the recently measured H2 abundance of 15 ppm <Krasnopolsky and Feldman, 2001a, 2001b>, the O+ densities are closer to, but still somewhat less than the Viking densities. The O+ peak densities of ~600--750 cm-3 measured by the retarding potential analyzers on Vikings 1 and 2 <Hanson et al., 1977> are best reproduced with H2 abundances less than ~4 ppm. We have investigated the effect of various H2 mixing ratios at the lower boundary of our model, and we find that the high altitude densities of O+, CO2+, CO+, and N2+ ions decrease as the H2 abundance increases, and are much less for H2 mixing ratios greater than 4 ppm than previous models have shown. Moreover, the photochemical escape rates of heavy atoms, such as C and N that are due to reactions of these ions, are also reduced. The Martian atmosphere was probably more reducing in past epochs, and therefore consisted of a larger fraction of H2. As the abundance of H2 increases, the composition of the exosphere will also be altered, and the altitude of the exobase will rise. At very large mixing ratios, H and H2 could potentially dominate the absorption of EUV radiation. Thus the escape of species by other photochemical mechanisms such as photodissociation and photodissociative ionization could also be reduced. If so, the nonthermal escape rates of heavy atoms in past epochs may have been much lower than previous estimates in which it is assumed that the oxidation state of the Martian atmosphere has remained constant over time.