All chemical reactions are reversible in principle, and for many the reverse reaction is readily observable in practice as well, and must be allowed for in the rate equation:
This differential equation is of exactly the same form as equation , and can be solved in the same way:
Taking exponentials of both sides, we have
which can be rearranged to give
This is the value of p after infinite time, because the exponential term approaches zero as t becomes large. The expected behavior is illustrated in Figure 1.
Figure 1. First-order decay for a reversible reaction