The first-order renal excretion rate constant is the rate constant for the drug elimination by the kidney. The renal excretion rate constant is dependent on the renal clearance and the volume of distribution.

This rate constant represents drug elimination by the kidney in the urine. The renal excretion rate constant cannot be bigger than the overall elimination rate constant (k). When the drug is excreted entirely through the kidney, the renal clearance will be equal to the CL_T and the renal excretion rate constant will be equal to the overall elimination rate constant.

The first-order renal excretion rate constant 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 dg 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.

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.

A semilog graph paper is a graph paper in which the x-axis is a normal linear scale, but the y-axis is a logarithmic scale. Semilog graph paper allows plotting the data at logarithmic intervals without the need for logarithmic transformation.

The y-axis is divided into cycles, each represents 10-fold increase in values (a single log₁₀ unit).

A rectangular graph paper is a graph paper where the x-axis and the y-axis are divided into equal divisions. Each of these divisions represents a fixed value throughout the x or the y axes (linear scale).

The x-axis and the y-axis may cover different ranges of the graphed variables. The minimum value on the axes may or may not be zero.

The semilog graph paper allows plotting the data at logarithmic intervals without doing the actual logarithmic transformation of the numbers.

In order to determine the slope of a line drawn on a semilog graph paper it is necessary to do logarithmic transformation for the y values. The slope of the line in this case will be determined from the following relationship:

The half life is the time required for the amount of the drug or the plasma concentration of the drug to decrease by 50%. The half life has units of time.

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

The half life of a drug is constant within a patient (dose and concentration independent) when the drug elimination process follows first-order kinetics. However different patients may have different half lives for the same drug.

The half life is a very important parameter, because it indicates how fast the drug is eliminated from the body. Drugs with shorter half lives are eliminated faster than those with longer half lives.