Reversible reaction opposing first-order reactions

If the interchange reaction is reversible, a more complicated treatment is required to deal with the approach towards the resulting equilibrium. A common experimental condition is to employ high [Y] and [X] to approximate the reaction as a pair of opposing pseudo-first order reactions. 

The only reactions considered so far have been those that proceed to all intents and purposes (>95%) to completion. The treatment of revers/We reactions is analogous to that given above, although now it is even more important to establish the stoichiometry and the thermodynamic characteristics of the reaction. A number of reversible reactions are reduced to pseudo first-order opposing reactions when reactants or products or both are used in excess... 

First-Order Reversible Reactions. Though no reaction ever goes to completion, we can consider many reactions to be essentially irreversible because of the large value of the equilibrium constant. These are the situations we have examined up to this point. Let us now consider reactions for which complete conversion cannot be assumed. The simplest case is the opposed unimolecular-type reaction... 

Opposing (Reversible) Reactions The rate laws presented so far are applicable to irreversible reactions only. If the observed reaction does not go to completion, then the treatment changes. For a simple case of opposing first-order reactions,... 

Consider the simplest case of an opposing reaction in which the forward as well as the reverse reactions are both first-order ... 

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