Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited
The validity of two fundamental concepts of classical chemical kinetics - the notion of "Chemical Equilibrium" and the "Law of Mass Action" - are re-examined for reversible \textit{diffusion-limited} reactions (DLR), as exemplified here by association/dissociation $A+A \rightleftharpoons B$ reactions. We consider a general model of long-ranged reactions, such that any pair of $A$ particles, separated by distance $μ$, may react with probability $ω_+(μ)$, and any $B$ may dissociate with probability $ω_-(λ)$ into a geminate pair of $A$s separated by distance $λ$. Within an exact analytical approach, we show that the asymptotic state attained by reversible DLR at $t = \infty$ is generally \textit{not a true thermodynamic equilibrium}, but rather a non-equilibrium steady-state, and that the Law of Mass Action is invalid. The classical picture holds \text{only} in physically unrealistic case when $ω_+(μ) \equiv ω_-(μ)$ for any value of $μ$.