  The past few decades have seen robust research on questions regarding the
existence, form, and properties of stationary distributions of stochastically
modeled reaction networks. When a stochastic model admits a stationary
distribution an important practical question is: what is the rate of
convergence of the distribution of the process to the stationary distribution?
With the exception of \cite{XuHansenWiuf2022} pertaining to models whose state
space is restricted to the non-negative integers, there has been a notable lack
of results related to this rate of convergence in the reaction network
literature. This paper begins the process of filling that hole in our
understanding. In this paper, we characterize this rate of convergence, via the
mixing times of the processes, for two classes of stochastically modeled
reaction networks. Specifically, by applying a Foster-Lyapunov criteria we
establish exponential ergodicity for two classes of reaction networks
introduced in \cite{anderson2018some}. Moreover, we show that for one of the
classes the convergence is uniform over the initial state.
