Five model systems, the van der Waals fluid, the Soave-Redlich-Kwong fluid, the Peng-Robinson fluid, the hard-sphere fluid, and the square-well fluid, are used to examine the performance of the truncated virial expansion in describing the fugacity of a solute at infinite dilution in a solvent. It is demonstrated that the virial fugacity results deteriorate at significantly lower densities as the solute becomes larger. This has consequences for attempts to describe the solubility of solids in supercritical fluids, where the virial expansion, truncated after the third virial coefficient, has been considered as a modeling option. The results of this work suggest that, for the densities and solute-to-solvent size ratios commonly encountered in supercritical extraction, the truncated virial expansion should not be expected to describe correctly the solute fugacity, and therefore any success it has in fitting solubility data should be viewed with caution.