The first-order elimination rate constant is the rate constant for the elimination of the drug from the body. The elimination rate constant and the half life are dependent on the total body clearance and the volume of distribution of the drug.

This rate constant represents drug elimination through all routes of drug elimination such as metabolism, renal excretion, and other routes.

The first-order elimination rate constant has units of time^-1.

The first-order elimination rate constant of the metabolite is the rate constant responsible for the elimination of the metabolite from the body. This rate constant is dependent on the clearance and the volume of distribution of the metabolite. (CL_T(m)) / Vd_(m) = k_(m))

The elimination rate constant of the metabolite is the same when the metabolite is formed in vivo after the parent drug administration and after administration of the preformed metabolite.

This constant represents the metabolite elimination through all routes of metabolite elimination including secondary metabolism and renal excretion.

The first-order elimination rate constant of the metabolite has units of time ^-1.

A first-order process is a process that has a rate proportional to the amount of the reactant involved in this process.

For example, if the drug elimination rate is proportional to the amount of the drug in the body, this means that this drug is eliminated by a first-order process. The proportionality constant is the first-order elimination rate constant. i.e.

Elimination rate = elimination rate constant x drug amount

The rate of drug elimination decreases with time because the amount of the drug remaining decreases with time.