How can the relaxation time of nitrogen tetroxide reveal the rates of both dissociation and recombination?

The relaxation time of nitrogen tetroxide ($N_2{O}_4$) provides a window into its chemical kinetics by measuring how the system returns to chemical equilibrium after a disturbance.1

Because nitrogen tetroxide exists in a reversible equilibrium with nitrogen dioxide ($N{O}_2$), the system maintains a balance where the rate of dimer dissociation equals the rate of monomer recombination. When external conditions like temperature or pressure are altered, the system shifts to a new equilibrium at a finite rate determined by the reactivities of the species.1

By measuring the relaxation time—often through ultrasonic methods or temperature-jump experiments—scientists observe the exponential decay of the displacement from equilibrium. Because the relaxation time is mathematically related to the reaction mechanism, it allows for the derivation of the specific rate constants for both the forward (dissociation) and reverse (recombination) reactions. Essentially, the relaxation time captures the speed at which the system re-establishes the balance between these two opposing processes.123