We present a semiempirical approach to the density functional theory of bubble nucleation in binary mixtures. Intermolecular forces between solvent and solute molecules are modeled using Lennard-Jones potentials whose interaction parameters are determined by equilibrium properties of the pure liquids and the liquid mixtures. We study the temperature variation of the critical supersaturation for carbon dioxide, oxygen, nitrogen, and hydrogen dissolved in water at 1 atm pressure. Our results are consistent with experimental trends that show an "inverse" dependence of the nucleation rates on temperature for the case of hydrogen. In the different mixtures, critical nuclei for gas formation exhibit fluid densities at their centers that are a substantial fraction of the density of the corresponding pure liquids.