More on Residence Times and Half-lifes
The terms residence time and half-life are sometimes confused. To make matters worse, in some
contexts (particularly chemical kinetics) the residence time is referred to as the lifetime.
Residence times can be determined for a reservoir itself (such as the water in a lake) or for a
substance within it (such as a contaminant). The residence time for any reservoir can be
determined by taking the ratio of the total amount (mass or volume) of the reservoir to the flux
(expressed in units consistent with those in the numerator). Either the total rate of influx or
outflux can be used, since for any system at steady state, the two are equal in magnitude.
outflux)(or influx of rate
reservoir thein substance of amount
timeResidence =
The residence time (or lifetime) of a substance within a reservoir may be governed not only by
the residence time of the reservoir itself (essentially a dilution or flushing effect), but also by a
variety of physical, chemical and biological processes. Sedimentation, degradation and microbial
action often accelerate the removal of contaminant species. The residence time (lifetime) of a
substance is determined with the knowledge of the amount (or concentration) of that substance
and the combined rate of loss of the substance from the reservoir. Alternately, the residence time
can be calculated as the reciprocal of the sum of all first order rate constants.
∑
== constants rate removal
1
rates removal all of total
substance ofamount
substance of timeResidence
Although the residence time (or lifetime) is often easier to directly estimate than the half-life, the
latter can be easier to interpret. It turns out that for first order processes, the half-life is roughly
70% of the lifetime as shown by the equations below.
Half-life: kk
0.6932 ln
t 2/1 ==
Residence time:
k
1
τ=, where k’ represents the sum of all first order (or pseudo-first order) rate constants
Therefore;
Half-life = 0.693 x (Residence time)
