Thermolysis of coal yields a complex mixture of many extract products whose molecular-weight distribution (MWD) varies with time for continuous-flow, semibatch experiments. A laboratory flow reactor with a differential fixed bed of coal particles contacted by supercritical tert-butanol was used to provide dynamic MWD data by means of HPLC gel permeation chromatography of the extract. The experimental results, multipeaked, time-dependent MWDs of extract molecules, are interpreted by a novel mathematical model based on continuous-mixture kinetics for thermal cleavage of chemical bonds in the coal network. The parameters for the MWDs of extractable groups in the coal and the rate constants are determined from the experimental data. The effect of temperature on the kinetics of the extraction is explained in terms of one- and two-fragment reactions of the extractable groups in the coal. At lower temperatures (613 and 633 K) single-fragment reactions dominate, but at higher temperatures (653 and 673 K) more bonds in the coal are broken and the two-fragment reactions become significant. Also, the detailed MWDs are related to conventional lumped data for the thermolytic extraction process. The results yield information about the structure of coal, as well as the kinetics and mechanism of supercritical thermolytic reactions.