  Using a high resolution simulation of an isolated dwarf galaxy, accounting
for multi-channel stellar feedback and chemical evolution on a star-by-star
basis, we investigate how each of 15 metal species are distributed within our
multi-phase interstellar medium (ISM) and ejected from our galaxy by galactic
winds. For the first time, we demonstrate that the mass fraction probability
distribution functions (PDFs) of individual metal species in the ISM are well
described by a piecewise log-normal and power-law distribution. The PDF
properties vary within each ISM phase. Hot gas is dominated by recent
enrichment, with a significant power-law tail to high metal fractions, while
cold gas is predominately log-normal. In addition, elements dominated by
asymptotic giant branch (AGB) wind enrichment (e.g. N and Ba) mix less
efficiently than elements dominated by supernova enrichment (e.g. $\alpha$
elements and Fe). This result is driven by the differences in source energetics
and source locations, particularly the higher chance compared to massive stars
for AGB stars to eject material into cold gas. Nearly all of the produced
metals are ejected from the galaxy (only 4% are retained), but over 20% of
metals dominated by AGB enrichment are retained. In dwarf galaxies, therefore,
elements synthesized predominately through AGB winds should be both
overabundant and have a larger spread compared to elements synthesized in
either core collapse or Type Ia supernovae. We discuss the observational
implications of these results, their potential use in developing improved
models of galactic chemical evolution, and their generalization to more massive
galaxies.
