We conducted high pressure and temperature experiments to determine the pressure, temperature, H2O content, and oxygen fugacity dependence of CO2 solubility on natural hydrous rhyolitic melts. These studies are applicable to subduction zone settings of the Earth throughout its history. Carbon concentrations and speciation were measured using FTIR, and in the process, we determined absorption coefficients for the CO2 species (CO2mol. and CO32-) for natural rhyolitic glass. We also developed empirical and thermodynamically-based models that describe the CO2 content of our compositions as a function of pressure, temperature, H2O content, and oxygen fugacity. We applied these models to predict the amount of CO2 that could be released via partial melt from subducted slab and carried up to the source region of arc volcanoes. We also conducted experiments to determine the compositional dependence of CO2 solubility on compositions spanning the range from natural basalt toward peridotite. These mafic to ultramafic compositions were used to constrain the carbon content of early Earth’s magma ocean. Combining our experiments with previous work, we developed an empirical model that describes the dissolved CO2 content as a function of pressure, temperature, H2O content, oxygen fugacity, and silicate composition. This model was applied to determine the amount of carbon contained in terrestrial magma oceans, and place constraints on the mantle carbon budget of the Earth.