  (abridged) [...] Methods: In a continued study of the molecular core
population of the Pipe Nebula, we present a molecular-line survey of 52 cores.
Previous research has shown a variety of different chemical evolutionary stages
among the cores. Using the Mopra radio telescope, we observed the ground
rotational transitions of HCO+, H13CO+, HCN, H13CN, HNC, and N2H+. These data
are complemented with near-infrared extinction maps to constrain the column
densities, effective dust temperatures derived from Herschel data, and
NH3-based gas kinetic temperatures. Results: The target cores are located
across the nebula, span visual extinctions between 5 and 67 mag, and effective
dust temperatures (averaged along the lines of sight) between 13 and 19 K. The
extinction-normalized integrated line intensities, a proxy for the abundance in
constant excitation conditions of optically thin lines, vary within an order of
magnitude for a given molecule. The effective dust temperatures and gas kinetic
temperatures are correlated, but the effective dust temperatures are
consistently higher than the gas kinetic temperatures. Combining the molecular
line and temperature data, we find that N2H+ is only detected toward the
coldest and densest cores while other lines show no correlation with these core
properties. Conclusions: Within this large sample, N2H+ is the only species to
exclusively trace the coldest and densest cores, in agreement with chemical
considerations. In contrast, the common high-density tracers HCN and HNC are
present in a majority of cores, demonstrating the utility of these molecules to
characterize cores over a large range of extinctions. The correlation between
the effective dust temperatures and the gas kinetic temperatures suggests that
the former are dominated by dust that is both dense and thermodynamically
coupled to the dense gas traced by NH3. [...]

Solar and Stellar Astrophysics;Astrophysics of Galaxies