Reversible Diffusion-Limited Reactions: "Chemical Equilibrium" State and the Law of Mass Action Revisited

Abstract

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 $\mu$, may react with probability ${\omega }_{+}(\mu )$, and any $B$ may dissociate with probability ${\omega }_{-}(\lambda )$ into a geminate pair of $A$s separated by distance $\lambda$. 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 ${\omega }_{+}(\mu )\equiv {\omega }_{-}(\mu )$ for any value of $\mu$.

4 pages