A generalized temperature and acentric factor dependent function of the attractive term, called the alpha function, of the Peng-Robinson cubic equation of state (PR CEOS) is developed. The approach in this work allows the alpha function to become a linear function of the acentric factor at a constant reduced temperature, not a fourth or sixth order function as suggested by Soave and other researchers. The advantage of a linear function in the acentric factor is obvious in the extrapolation of the alpha function to heavy hydrocarbons, petroleum fractions, and gas condensates. The new generalized alpha function, when used with the PR CEOS, allows the accurate reproduction of the vapor pressure data from the triple point to the critical point for hydrocarbons. The new CEOS provides much more reliable and accurate vapor pressure predictions for light as well as heavy hydrocarbons than the original PR equation.