We present chemical models of the collapse of molecular cores in order to probe their physical parameters. We refer particularly to the cores recently observed in TMC1, and our motivation has been the suggestion by Hanawa, Yamamoto & Hirahara that the cores are formed sequentially, a scenario that lends itself to testing by time-dependent chemical models. We find that there is evidence in the observed column densities for such ordering, provided that the collapse is from a diffuse state and is followed by a static phase, possibly related to the slow diffusion of magnetic support. It seems that the manner of the collapse has fundamental implications for the interpretation of observed column densities; they cannot be inferred from peak abundances in pseudo-time-dependent models. Our fit is worse than such models if ion-dipole chemical rates enhanced at low temperature are used, in the sense that large columns of hydrogen are necessary, and models without them are only partially successful. The results indicate that these rate enhancements are not a universally applicable phenomenon, and that selective use, combined with well-chosen masses for each core, might produce a good fit. In any case, if the collapse is not rapid, then the resultant column densities are much reduced. We suggest that the apparent chemical richness of TMC1 may have its roots in both the diffuse nature of its original state and the unusually sudden nature of its collapse.