Salty aqueous solutions (brines) occur on Earth and may be prevalent elsewhere. Serpentinization represents a family of geochemical reactions where the hydration of olivine-rich rocks can release aqueous hydrogen, H2(aq), as a byproduct, and hydrogen is a known basal electron donor for terrestrial biology. While the effects of lithological differences on serpentinization products have been thoroughly investigated, effects focusing on compositional differences of the reacting fluid have received less attention. In this contribution, we investigate how the chemistry of seawater-derived brines affects the generation of biologically available hydrogen resulting from the serpentinization of harzburgite. We numerically investigate the serpentinization of ultramafic rocks at equilibrium with an array of brines at different water activities (a proxy for salt concentration in aqueous fluids and a determinant for habitability) derived from seawater evaporation. Because the existing supersaturation of aqueous calcium carbonate, a contributor to dissolved inorganic carbon (DIC) in natural seawater, cannot be captured in equilibrium calculations, we bookend our calculations by enabling and suppressing carbonate minerals when simulating serpentinization. We find that the extent of DIC supersaturation can provide an important control of hydrogen availability. Increased DIC becomes a major sink for hydrogen by producing formate and associated complexes when the reacting fluids are acidic enough to allow for CO2. Indeed, H2(aq) reduces CO2(aq) to formate, leading to a hydrogen deficit. These conclusions provide additional insights into the habitability of brine systems, given their potential for serpentinization across diverse planetary bodies such as on Mars and ocean worlds.