ln([A]₀ / [A]) = k × t
Integrated Rate Law
t₁/₂ = 0.693 / k
Half-Life Formula
[A]₀ = Initial concentration
[A] = Concentration at time t
k = Rate constant (time⁻¹)
t = Time elapsed
t₁/₂ = Half-life
What is a First-Order Reaction?
A first-order reaction is one where the rate of reaction is directly proportional to the concentration of a single reactant. The rate law is: Rate = k[A].
Characteristic Half-Life
For first-order reactions, the half-life is constant and independent of the initial concentration. This makes it easy to predict how long it takes for any given fraction to react.
Common Examples
Radioactive decay, many enzyme reactions, drug metabolism in the body, and the decomposition of hydrogen peroxide are examples of first-order kinetics.
Important Note
First-order kinetics assume the reaction rate depends on the concentration of a single reactant. Real systems may deviate under non-ideal conditions such as temperature changes, competing reactions, or concentration extremes.
First-order reaction kinetics describes chemical reactions where the reaction rate is directly proportional to the concentration of only one reactant. This means that if you double the concentration of the reactant, the reaction rate will also double. The mathematical treatment of first-order reactions is fundamental to understanding chemical kinetics and has widespread applications in chemistry, biology, pharmacology, and nuclear physics.
The integrated rate law for first-order reactions, ln([A]₀/[A]) = kt, allows us to calculate concentration changes over time, determine how long a reaction will take to reach a certain point, or find the rate constant from experimental data. This equation shows that a plot of ln[A] versus time will yield a straight line with a slope equal to -k for a true first-order reaction.
First-order kinetics plays a crucial role in many scientific and practical applications. In pharmacology, drug elimination from the body often follows first-order kinetics, which is essential for determining proper dosing schedules. The half-life of a drug tells healthcare providers how often a medication needs to be administered to maintain therapeutic levels in the bloodstream.
In nuclear chemistry, radioactive decay is a perfect example of first-order kinetics. The half-life concept originated from studying radioactive isotopes, where it represents the time required for half of the radioactive nuclei in a sample to decay. This principle is used in carbon-14 dating, nuclear medicine, and understanding nuclear reactor behavior. Environmental scientists also use first-order kinetics to model the degradation of pollutants in ecosystems.