This paper presents an approach for predicting the solubility of hydrogen in hydrocarbons using a cubic equation of state. Because the alpha function from the Soave-Redlich-Kwong and Peng-Robinson equations of state is inadequate at temperatures far above the critical temperature, the binary interaction parameters required for hydrogen-hydrocarbon systems using these equations are typically large and strongly dependent on the temperature. An approach is proposed for developing a temperature-dependent alpha function for hydrogen which minimizes the need for interaction parameters. The minimization of the values of the binary interaction parameters between hydrogen and heavy hydrocarbons is desirable because this produces better predictions when the binary interaction parameters are not known and are set to zero. A universal procedure is also presented for interconverting the binary interaction parameters between the new hydrogen alpha function developed in this work and the traditional Soave alpha function or any other type of alpha function.