We study the changes in physical and chemical conditions during the early stages of collapse of a pre-protostellar core, starting from initial conditions appropriate to a dense molecular cloud and proceeding to the "completely depleted" limit. We allow for molecular desorption from the grain surfaces and follow the evolution of the ionization degree and the ionic composition as functions of time and density. The timescale for collapse is treated as a parameter and taken equal to either the free-fall or the ambipolar diffusion time. The processes of freeze-out on to the dust grains and of coagulation of the grains were treated simultaneously with the chemical evolution of the medium in the course of its collapse. When proceeding at close to its maximum rate, coagulation has important consequences for the degree of ionization and the ionic composition of the medium, but its effect on the freeze-out of the neutral species is modest. An innovation of our study is to calculate the grain charge distribution; this is done in parallel with the chemistry and the dynamics. The grain charge distribution is significant because H⁺ ions recombine predominantly on the surfaces of negatively charged grains. We have also attempted to reproduce with our models the observational result that nitrogen-containing species, such as NH3 and N2H^+, remain in the gas phase at densities for which CO and other C-containing molecules appear to have frozen on to grain surfaces. We conclude that recent measurements of the adsorption energies of N2 and CO invalidate the interpretation of these observations in terms of the relative volatilities of N2 and CO. We consider an alternative explanation, in terms of low sticking coefficients for either molecular or atomic N; but this hypothesis requires experimental confirmation. We find that, irrespective of the nitrogen chemistry, the main gas phase ion is either H⁺ or H3⁺ (and its deuterated isotopes) at densities above 10⁵ cm^-3; whether H⁺ or H3⁺ predominates depends sensitively on the rate of increase in grain size (decrease in grain surface area per unit volume of gas) during core contraction. Our calculations show that H⁺ will predominate if grain coagulation proceeds at close to its maximum rate, and H3⁺ otherwise.