A rate expression with first- and second-order terms in the concentration of extractable compounds in solid coal particles is derived from a fundamental free-radical mechanism. The expression was suggested empirically by prior experiments for coal liquefaction in the presence of a hydrogen-donor solvent. Radical reactions are considered to occur in both coal and in solvent. The long-chain approximation justifies the neglect of initiation, hydrogen abstraction, and termination rates as quantitatively insignificant relative to propagation reaction rates.