Taking into account this more complicated set of reactions, which are interacting with each other, is still not enough to explain the phenomenon of coupling. To see this, let’s consider the rate equation for the system comprised of all four reactions. To write it down neatly, let’s introduce **reaction velocities** that say the rate at which each forward reaction is taking place, minus the rate of the reverse reaction:
All these follow from the law of mass action, which I explained last time. Remember, this says that any reaction occurs at a rate equal to its rate constant times the product of the concentrations of the species involved. So, for example, this reaction

goes forward at a rate equal to , while the reverse reaction occurs at a rate equal to So, its reaction velocity is

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