Any general model for a molecular communication system must account for both chemical reactions and diffusion. In particular, the chemical reactions capture processes of information molecule production and detection as well as inter-symbol mitigation methods in the channel. A popular model for such reaction-diffusion systems is the reaction-diffusion master equation. In this paper, we study the statistics for the number of molecules at the receiver, yielding a stochastic input-output relationship. Our focus is on a general class of first-order reactions and linear diffusion. This class of models admits a stationary distribution for the long-term behavior. We obtain a simple Gaussian approximation for this stationary distribution by exploiting recent results characterizing the underlying deterministic reaction-diffusion system. We prove exponential rates of convergence in the underlying deterministic system and verify our approximation via stochastic simulation.