  Pre-stellar cores within molecular clouds provide the very initial conditions
in which stars are formed. We use the IRAM 30m telescope and the PdBI to study
the chemical and physical properties of the starless core FeSt 1-457 (Core
109), in the Pipe nebula. We fit the hyperfine structure of the N2H+(1-0) IRAM
30m data. This allow us to measure with high precision the velocity field, line
widths and opacity and derive the excitation temperature and column density in
the core. We use a modified Bonnor-Ebert sphere model adding a temperature
gradient towards the center to fit the 1.2 mm continuum emission and visual
extinction maps. Using this model, we estimate the abundances of the N2H+ and
the rest of molecular lines detected in the 30 GHz wide line survey performed
at 3 mm with IRAM 30m using ARTIST software. The core presents a rich chemistry
with emission from early (C3H2, HCN, CS) and late-time molecules (e.g., N2H+),
with a clear chemical spatial differentiation for nitrogen, oxygen and
sulphurated molecules. For most of the molecules detected (HCN, HCO+, CH3OH,
CS, SO, 13CO and C18O), abundances are best fitted with three values,
presenting a clear decrease of abundance of at least 1 or 2 orders of magnitude
towards the center of the core. The Bonnor-Ebert analysis indicates the core is
gravitationally unstable and the magnetic field is not strong enough to avoid
the collapse. Depletion of molecules onto the dust grains occurs at the
interior of the core, where dust grain growth and dust depolarization also
occurs. This suggests that these properties may be related. On the other hand,
some molecules exhibit asymmetries in their integrated emission maps, which
appear to be correlated with a previously reported submillimetre polarization
asymmetry. These asymmetries could be due to a stronger interstellar radiation
field in the western side of the core.
