elimination rate constant
The elimination rate constant is the fraction of the drug remaining in the body that gets removed each unit of time. If it equals 0.1 per hour, then in each hour the body eliminates 10 percent of whatever drug is left at that moment — not a fixed amount, but a fixed slice of the remainder. It is the speed dial of elimination.
Because a constant fraction is removed per unit time, the amount of drug falls along a smooth exponential decay, the hallmark of first-order kinetics. The elimination rate constant is the steepness of that decay on a logarithmic plot, and it is directly tied to the half-life: half-life equals about 0.693 divided by the rate constant, so a bigger constant means faster removal and a shorter half-life.
Conceptually, the rate constant connects the two more tangible parameters: it equals clearance divided by volume of distribution. So it rises when the eliminating organs work harder (more clearance) and falls when the drug hides in a large tissue volume. It is the parameter that appears directly in the exponential equations describing how concentration changes over time.
A drug with an elimination rate constant of 0.347 per hour has a half-life of about two hours (0.693 divided by 0.347), since the constant and the half-life are just two ways of expressing the same exponential decay.
The rate constant and half-life are two faces of one decay.
The rate constant has units of inverse time (per hour, per day) — a fraction per unit time, not an amount. It equals clearance divided by volume of distribution, and equals 0.693 divided by the half-life.