  Understanding the degree of chemical complexity that can be reached in
star-forming regions, together with the identification of precursors of the
building blocks of life in the interstellar medium, is one of the goals of
astrochemistry. Unbiased spectral surveys with large bandwidth and high
spectral resolution are thus needed, to resolve line blending in chemically
rich sources and identify complex organic molecules. This kind of observations
has been successfully carried out, mainly towards the Galactic Center, a region
that shows peculiar environmental conditions. We present an unbiased spectral
survey at 3mm of one of the most chemically rich hot molecular cores located
outside the Galactic Center, in the high-mass star-forming region G31.41+0.31.
In this first paper, we present the survey and discuss the detection of the 3
isomers of C$_{2}$H$_{4}$O$_{2}$: methyl formate, glycolaldehyde and acetic
acid. Observations were carried out with ALMA and cover the entire Band 3 from
84 to 116 GHz with an angular resolution of $1.2^{''}$x$1.2^{''}$ and a
spectral resolution of $\sim0.488$ MHz. The transitions of the 3 molecules have
been analyzed with the software XCLASS. All three isomers were detected and
methyl formate and acetic acid abundances in G31 are the highest detected up to
now, if compared to sources in literature. The size of the emission varies
among the three isomers with acetic acid showing the most compact emission
while methyl formate the most extended. The comparison with chemical models
suggests the necessity of grain-surface routes for the formation of methyl
formate in G31, while for glycolaldehyde both scenarios could be feasible.
Proposed grain-surface reaction for acetic acid is not able to reproduce the
observed abundance in this work, while gas-phase scenario should be further
tested due to large uncertainties.
