One approach to modelling asphaltene solubility is regular solution theory. The key parameters for this approach are the molar volume and solubility parameters of each constituent. However, these parameters are largely unknown for crude oils. Some authors have used cubic equations of state (CEOS) to estimate the solubility parameters and molar volumes of solvents and C-7(+) fractions, but CEOS have yet to be applied in this way to asphaltenes due to their high molar mass and unknown critical properties. In this work, a modified Soave-Redlich-Kwong EOS with the Peneloux correction is used to estimate the molar volumes and solubility parameter of the four solubility classes (saturates, aromatics, resins, and asphaltenes) of bitumens. The EOS is modified for the asphaltenes, which are assumed to be polymeric-like compounds consisting of aggregates of monodisperse asphaltene monomers. Correlations are developed for the critical properties and acentric factor of each solubility class. The EOS-predicted properties are tested against density measurements of SARA fractions from several bitumens. The predicted parameters are used to determine the onset of asphaltene precipitation from bitumen upon the addition of heptane and the predictions are compared with measured onsets.