At Equilibrium, Rates Obey Detailed Balance

The principle of detailed balance says that the forward and reverse rates must be identical for an elementary reaction at equilibrium  

Equation (19.6) relates rate coefficients kf and kr to the equilibrium constant K  

Equiition (19.9) is two independent equations in three unknown concentrations. It has an infinite number of solutions. 

Equation (19.10) cannot be satisfied in mechanism (b) because the denominator would be zero if the reverse rates were zero. The principle of detailed balancing 

The principle of detailed balancing can be derived from the principle of microscopic reversibility (see Chapter 18), which says that Newton s laws of motion for the collisions between atoms and molecules arc symmetrical in time— they would look the same if time ran backward. The proof of detailed balance from microscopic reversibility is given in [3]. Detailed balance is helpful in understanding the mechanisms of chemical reactions, the molecular steps from reactants to products. 

---