Seven isolated, nearby low-mass starless molecular cloud cores have been observed as part of the Herschel key program Earliest Phases of Star formation (EPoS). By applying a ray-tracing technique to the obtained continuum emission and complementary (sub)mm emission maps, we derive the physical structure (density, dust temperature) of these cloud cores. We present observations of the 12CO, 13CO, and C18O (2-1) and N2H+ (1-0) transitions towards the same cores. Based on the density and temperature profiles, we apply time-dependent chemical and line-radiative transfer modeling and compare the modeled to the observed molecular emission profiles. CO is frozen onto the grains in the center of all cores in our sample. The level of CO depletion increases with hydrogen density and ranges from 46% up to more than 95% in the core centers in the core centers in the three cores with the highest hydrogen density. The average hydrogen density at which 50% of CO is frozen onto the grains is 1.1+-0.4 10^5 cm^-3. At about this density, the cores typically have the highest relative abundance of N2H+. The cores with higher central densities show depletion of N2H+ at levels of 13% to 55%. The chemical ages for the individual species are on average 2+-1 10^5 yr for 13CO, 6+-3 10^4 yr for C18O, and 9+-2 10^4 yr for N2H+. Chemical modeling indirectly suggests that the gas and dust temperatures decouple in the envelopes and that the dust grains are not yet significantly coagulated. We observationally confirm chemical models of CO-freezeout and nitrogen chemistry. We find clear correlations between the hydrogen density and CO depletion and the emergence of N2H+. The chemical ages indicate a core lifetime of less than 1 Myr.
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