0.406 x

The time required for the concentration to fall to C0/2 is called the half-life, and the foregoing example shows that the half-life for a first-order or pseudo-first-order process is a constant throughout the process; it also demonstrates that a first-order process theoretically never reaches completion, since even the lowest concentration would only fall to half its value in one half-life.

For most practical purposes, a first-order process may be deemed "complete" if it is 95% or more complete. Table 1 shows that five half-lives must elapse to reach this point. Thus the elimination of a drug from the body may be considered to be complete after five half-lives have elapsed (i.e., 97% completion). This principle becomes important, for example, in crossover bioavailability studies in which the subjects must be rested for sufficient time between each drug administration to ensure that "washout" is complete.

The half-life of a first-order process is very important. Since it is often desirable to convert a half-life to a rate constant, and vice versa, a simple relationship between the two is very useful. The relationship may be derived as follows:

Table 1 Approach to Completeness with Increasing Half-Lives

Number of half-lives elapsed

Initial concentration remaining (%)

"Completeness" of process (%)

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