  Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT) provides a general
framework for the description of non-equilibrium phenomena at any level,
particularly the atomistic one. This theory and its dynamical postulate are
used here to develop a general mathematical framework, which at an atomistic
level, in particular, can be used to predict the non-equilibrium evolution in
state of a closed, chemically reactive mixture such as the one examined here,
i.e., a mixture of hydrogen (H2) and flourine (F) contained in an isolated tank
of fixed volume. The general framework provided, however, is written for a
reactive system subject to multiple reaction mechanisms. To predict this
evolution in state, both the energy and particle number eigenvalue problems for
a dilute gas are set up and solved analytically. Wall and non-ideal-gas
behavior effects are neglected, although the extension to dense gases is
straightforward but left for a future paper. The system-level energy and
particle number eigenvalues and eigenstates found are used in the nonlinear
equation of motion of SEAQT to determine the time evolution of the
thermodynamic state of the system, thus, effectively describing the reaction
kinetics of the reaction and the system's relaxation to stable equilibrium. The
predicted time evolution is then compared to the results of a standard detailed
kinetic model used, in the near-equilibrium limit, to extract the single time
constant needed by the SEAQT equation of motion.
