  We investigate the existence of weak solutions to a multi-component system,
consisting of compressible chemically reacting components, coupled with the
compressible Stokes equation for the velocity. Specifically, we consider the
case of irreversible chemical reactions and assume a nonlinear relation between
the pressure and the particular densities. These assumptions cause the
additional difficulties in the mathematical analysis, due to the possible
presence of vacuum.
  It is shown that there exists a global weak solution, satisfying the
$L^\infty$ bounds for all the components. We obtain strong compactness of the
sequence of densities in $L^p$ spaces, under the assumption that all components
are strictly positive. The applied method captures the properties of models of
high generality, which admit an arbitrary number of components. Furthermore,
the framework that we develop can handle models that contain both diffusing and
non-diffusing elements.
