FLASHCHAIN is being developed to predict yields and product characteristics from any coal for any operating conditions. This extension demonstrates the theory’s utility for the usual situation where the ultimate analysis is the only sample-specific information available. The original formulation is intact, although the submodel for coal constitution has been extended to assign the elemental compositions of bridges, nuclei, char links, and peripheral groups. This analysis reveals that the elemental compositions of whole coals are very poor indicators of the compositions of labile bridges, the key reaction centers. Most striking of all, the H/C ratios of bridges actually increase with increasing carbon content, whereas the whole-coal ratios diminish. All three atomic ratios for bridges, (H/C)B, (O/C)B, and (O/H)B, exhibit a far stronger rank dependence than their analogs for the whole coal, with very much more sample-to-sample variability. In light of these findings, it is inconceivable that the rates of bridge conversions are rank-independent. Parameters in the rate law for bridge conversion in FLASHCHAIN are now explicitly related to the elemental compositions of bridges. The (O/C)B ratio is the best regression variable for the rate constant for bridge conversion because oxygen is the most effective promoter of pyrolytic decompositions. The (O/H)B ratio is best for the selectivity between scission and condensation into char links because oxygen promotes cross-linking but hydrogen addition to broken bridge fragments stabilizes them. These extensions are evaluated in comparisons against a database of 21 coals that span all ranks from lignite to anthracite. In four out of five cases, predicted total and tar yields are within experimental uncertainties. Accurate predictions for an additional eight high-volatile (hv) bituminous coals stringently demonstrate the theory’s ability to chart the substantial variation in yields often seen for a group of coals with similar nominal properties. In light of this performance and the compelling chemical implications of the atomic ratios for bridges, FLASHCHAIN’s bridge properties should also be useful for interpreting yields from other coal conversion schemes, regardless of any connections to devolatilization modeling.