Abstract
By introducing the concept of nanoreaction-based fluctuating mixing entropy, the challenge posed by the smallness of a closed molecular system is addressed through equilibrium statistical-mechanical averaging over fluctuating reaction extent. Based on the canonical partition function, the interplay between the mixing entropy and fluctuations in the reaction extent in nanoscale environments is unraveled while maintaining consistency with macroscopic behavior. The nanosystem size dependence of the mixing entropy, the reaction extent, and a concept termed the "reaction extent entropy" are modeled for the combination reactions A+B↔2C and the specific case of H2+I2↔2HI. A distinct inverse correlation is found between the first two properties, revealing consistency with the nanoconfinement entropic effect on chemical equilibrium (NCECE). To obtain the time dependence of the instantaneous mixing entropy following equilibration, the Stochastic Simulation (Gillespie) Algorithm is employed. In particular, the smallest nanosystems exhibit a step-like behavior that deviates significantly from the smooth mean values and is associated with the discrete probability distribution of the reaction extent. As illustrated further for molecular adsorption and spin polarization, the current approach can be extended beyond nanoreactions to other confined systems with a limited number of species.