(abridged) [...] Methods: In a continued study of the molecular corepopulation of the Pipe Nebula, we present a molecular-line survey of 52 cores.Previous research has shown a variety of different chemical evolutionary stagesamong the cores. Using the Mopra radio telescope, we observed the groundrotational transitions of HCO+, H13CO+, HCN, H13CN, HNC, and N2H+. These dataare complemented with near-infrared extinction maps to constrain the columndensities, effective dust temperatures derived from Herschel data, andNH3-based gas kinetic temperatures. Results: The target cores are locatedacross the nebula, span visual extinctions between 5 and 67 mag, and effectivedust temperatures (averaged along the lines of sight) between 13 and 19 K. Theextinction-normalized integrated line intensities, a proxy for the abundance inconstant excitation conditions of optically thin lines, vary within an order ofmagnitude for a given molecule. The effective dust temperatures and gas kinetictemperatures are correlated, but the effective dust temperatures areconsistently higher than the gas kinetic temperatures. Combining the molecularline and temperature data, we find that N2H+ is only detected toward thecoldest and densest cores while other lines show no correlation with these coreproperties. Conclusions: Within this large sample, N2H+ is the only species toexclusively trace the coldest and densest cores, in agreement with chemicalconsiderations. In contrast, the common high-density tracers HCN and HNC arepresent in a majority of cores, demonstrating the utility of these molecules tocharacterize cores over a large range of extinctions. The correlation betweenthe effective dust temperatures and the gas kinetic temperatures suggests thatthe former are dominated by dust that is both dense and thermodynamicallycoupled to the dense gas traced by NH3. [...]
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