Free-volume theories have been used the last century in various areas of science including polymer thermodynamics and studies related to viscosity and diffusion. Irrespective of the exact free-volume formula employed, there is a need for an equation for the so-called "hard-core" (or inaccessible) volume, which is the volume occupied by the molecules. Numerous such expressions have been proposed, but it is often recognized that the hard-core volume should be close to the packed molecular volume at 0 K. The so-estimated hard-core volume is often related to, and is actually a bit higher than, the van der Waals volume. Other theories, though, relate the hard-core volume with the; less known for heavy molecules, critical volume. Such an expression proposed several years ago by Guggenheim is here analyzed in light of experimental critical density data and molecular simulation studies for n-alkanes. These studies, in addition to the physical significance of the hard-core volume, lead us to the conclusion that the Guggenheim and similar hard-core volume expressions are not accurate for high molecular weight compounds.