Pyrolysis occurs in the initial stage of coal combustion where the volatile tar is generated. An important property of this volatile tar is its molecular-weight distribution. Coal tar contains varying sizes of monomers which are connected by linkages of varying strengths, thereby necessitating a stochastic approach. The present work has adopted the stochastic population balance of the system to derive the master equation for predicting the statistics of this molecular weight distribution of tar as functions of time. The tar produced during pyrolysis is assumed to undergo decomposition to low molecular weight compounds. Moreover, the system containing all tar molecules is lumped into a limited number of states, each representing a particular molecular weight range. The equations for the means, variances, and covariances of the random variables, each representing the number of tar molecules in an individual state in the system, have been derived from the master equation. The model has been compared with the experimental data obtained with both a heated-grid reactor and an entrained-flow reactor to recover the major parameters of the model, i.e. the transition and exit intensity functions. The transition intensity functions exhibit the temperature dependence of the Arrhenius type.