First-order kinetics

First-order kinetics refers to a chemical reaction rate that is directly proportional to the concentration of one of the reactants. This type of reaction is common in chemistry and pharmacology, where it is used to describe processes such as the enzyme-catalyzed reactions in the body and the degradation of pharmaceutical drugs.

Definition

In a first-order reaction, the rate of reaction is directly proportional to the concentration of one reactant. Mathematically, this can be expressed as:

\(\frac{d[A]}{dt} = -k[A]\)

where:

• \(\frac{d[A]}{dt}\) is the rate of change in concentration of the reactant A over time,
• \(k\) is the first-order rate constant, and
• \([A]\) is the concentration of the reactant A.

The negative sign indicates that the concentration of the reactant decreases over time.

Characteristics

First-order kinetics has several key characteristics:

• The half-life of the reaction, which is the time required for the concentration of the reactant to decrease by half, is constant and does not depend on the initial concentration of the reactant.
• The rate of reaction decreases over time as the concentration of the reactant decreases.
• The plot of the natural logarithm of the concentration of the reactant versus time yields a straight line, indicating a linear relationship.

Applications

First-order kinetics is widely applied in various fields:

• In pharmacokinetics, it describes the rate of drug elimination from the body, which is crucial for determining dosing schedules.
• In environmental science, it is used to model the degradation of pollutants in the environment.
• In biochemistry, it explains the kinetics of enzyme-catalyzed reactions that follow the Michaelis-Menten mechanism.

Examples

A classic example of a first-order reaction is the radioactive decay of isotopes, where the rate of decay is proportional to the amount of the isotope present. Another example is the hydrolysis of esters in the presence of a base, which proceeds at a rate proportional to the concentration of the ester.

See also

• Chemical kinetics
• Second-order kinetics
• Reaction rate
• Pharmacokinetics
• Enzyme kinetics