The concentration of a drug in the body is often expressed...

The concentration of a drug in the body is often expressed in units of milligrams per kilogram of body weight. The initial dose of a drug in an animal was $25.0 \mathrm{mg} / \mathrm{kg}$ body weight. After 2.00 hours, this concentration had dropped to $15.0 \mathrm{mg} / \mathrm{kg}$ body weight. If the drug is eliminated metabolically by a first-order process, what is the rate constant for the process in units of $\min ^{-1}$ ?

Key Concepts

Rate Constant

The rate constant is a fundamental parameter in chemical and biochemical kinetics that quantifies the speed at which a process occurs. In a first-order process, it has units of inverse time (e.g., min?¹), and it represents the proportion of the substance eliminated or transformed per unit time.

Unit Conversion

Accurate kinetic calculations often require converting time or concentration units to maintain consistency across equations. For example, when the elapsed time is provided in hours but the rate constant must be in per minute units, the necessary conversion ensures that the mathematical relationships remain valid and the results are meaningful.

First-Order Kinetics

This concept refers to reaction or elimination processes where the rate is directly proportional to the concentration of the substance present. In pharmacokinetics, many drugs are cleared from the body following first-order kinetics, meaning that a constant fraction of the drug is eliminated per unit time regardless of concentration.

Integrated Rate Law

This mathematical expression relates the concentration of a substance at any time point to its initial concentration, the rate constant, and elapsed time. For first-order processes, it is commonly written as ln(C/C0) = -kt, which allows for the determination of the rate constant or time required for a given change in concentration.

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