We discuss at some length the relationship between solutions to the time-dependent, multiple-well master equation and a macroscopic description of the chemistry in terms of phenomenological rate coefficients. In so doing, we derive two different methods of obtaining the rate coefficients from the eigenvalues and eigenvectors of G, the transition matrix of the master equation. We apply the first of the two methods to the C2H3 + C2H2 and C3H3 + C3H3 reactions, problems we have treated previously using the "experimental" (or exponential-decay) approach, and obtain considerably more and somewhat different results than we obtained in our earlier work.