When small amounts of a good hydrogen-bond acceptor such as pyridine or THF are added to a nonpolar swelling solvent such as chlorobenzene or toluene, there is a very rapid increase in coal swelling with increasing acceptor concentration which presently almost levels off. When swelling is plotted against pyridine concentration, the result is what appears to be a titration curve. This curve permits an estimation of the number of hydrogen-bond cross-links in the coal. We believe that this behavior is due to the selective association between the hydrogen-bond acceptor (e.g., pyridine) and hydroxyl groups which are cross-links between macromolecular chains in the coal. The selectivity of the acceptor for cross-linking hydroxyls over other hydroxyls (more favorable free energy for association of pyridine with the cross-linking hydroxyl) is due to the much more favorable entropy change which occurs when one of these cross-links is disrupted by formation of a new hydrogen bond to pyridine. This disruption frees a portion of the coal to adopt many more possible conformations lending to the favorable entropy change. This model leads directly to the prediction that this titration curve will be independent of the hydrogen-bond acceptor, a prediction which is verified by the identical curves observed using pyridine or THF in chlorobenzene with Illinois No. 6 coal. Changing the nonpolar solvent does not result in a change in the number of hydrogen bonds in agreement with this model. About 1/3 of the hydroxyl groups in Illinois No. 6 coal form network-active hydrogen bonds (cross-links) and there are about 1.7 hydrogen bonds per 100 carbon atoms. In the higher rank Pittsburth No. 8 coal there are approximately 0.3 cross-linking hydrogen bonds per 100 carbon atoms.