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The chemistry of developing and collapsing low-mass protostellar cores is followed using a chemical code with a time-varying density. Two evolutionary scenarios are represented, gravitational collapse in the presence of magnetic fields and the slow core growth by accretion near equilibrium. The chemical code includes gas-phase reactions and depletion onto grains with both CO and H2O ice mantles. We find that various species will selectively deplete from the gas phase at times that correspond to the middle to late stages of dynamical evolution when the densities are highest. These depletions do not depend in detail on the dynamical solution and should exist for any centrally condensed density profile. Sulfur-bearing molecules are particularly sensitive to the density increase: CS, SO, and C2S show significant depletions both on a strongly bound water mantle and on the weakly bound CO-covered grain surface. In contrast, CO and HCO+ show large depletions only for an H2O grain mantle and remain in the gas phase for models with CO grain mantles. Two species, NH3 and N2H+, do not deplete from the gas phase for the densities considered in our models. We also find that for very high densities, nH2>106 cm-3, depletion becomes important for all molecules. The effects of coupling chemistry and dynamics on the resulting physical evolution are discussed. We compare our results with current high-resolution observations of preprotostellar cores and to more evolved objects and suggest that ratios of the abundances of few species can be used in concert with our models as sensitive discriminators between different stages of core and star formation.