  This work presents an upper bound on the neutrino mass using the emission of
$\nu_e$ from the neutronization burst of a core collapsing supernova at 10~kpc
of distance and a progenitor star of 15~M$_\odot$. The calculations were done
considering a 34 kton Liquid Argon Time Projection Chamber similar to the Far
Detector proposal of the Long Baseline Neutrino Experiment (LBNE). We have
performed a Monte Carlo simulation for the number of events integrated in 5~ms
bins. Our results are $m_\nu<2.71$~eV and $0.18~\mbox{eV}<m_\nu<1.70$~eV, at
95\% C.L, assuming normal hierarchy and inverted hierarchy, respectively. We
have analysed different configurations for the detector performance resulting
in neutrino mass bound of $\mathcal{O}(1)$~eV.
