  At higher altitudes, for high temperature gases, for instance near space
shuttles moving at hypersonic speed, not only mechanical collisions are
affecting the gas flow, but also chemical reactions have an impact on such
hypersonic flows. In this work we insert chemical reactions, in form of
dissociations and recombinations (associations), in an existing model for a
mixture of mono- and polyatomic (non-reacting) species. More general chemical
reactions, e.g., bimolecular ones, can be obtained by instant combinations of
associations and dissociations. The polyatomicity is modelled by a continuous
internal energy variable and the evolution of the gas is described by a
Boltzmann equation.
  In, e.g., the Chapman-Enskog process - and related half-space problems - the
linearized Boltzmann collision operator plays a central role. Here we extend
some important properties of the linearized Boltzmann collision operator to the
introduced model with chemical reactions. A compactness result, stating that
the linearized operator can be decomposed into a sum of a positive
multiplication operator - the collision frequency - and a compact integral
operator, is proven under reasonable assumptions on the collision kernel. The
strategy is to show that the terms of the integral operator are (at least)
uniform limits of Hilbert-Schmidt integral operators and therefore also compact
operators. Self-adjointness of the linearized operator is a direct
consequences. Moreover, bounds on - including coercivity of - the collision
frequency are obtained for hard sphere like, as well as hard potentials with
cutoff like models. As consequence, Fredholmness, as well as, the domain, of
the linearized collision operator are obtained
