Intermediate Topic 427 of 1102 Kinetics & Equilibrium
First Order Reaction
Rate is proportional to one concentration; ln of concentration falls linearly with time.
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In-depth explanation of First Order Reaction
In a first order reaction the rate is proportional to the concentration of a single reactant, rate = k[A]. Integration of the rate law gives ln[A] = ln[A]0 - kt, so a plot of ln[A] against time is a straight line with slope minus k. The half-life t1/2 = 0.693/k is constant and independent of the starting concentration, which makes it a useful diagnostic. Many important processes follow first order kinetics, including radioactive decay, many unimolecular decompositions and isomerizations, and the hydrolysis of some esters in excess water. Because the rate depends on only one concentration, first order models are widely used to describe drug elimination.
Going deeper: First Order Reaction
Key ideas: Use ln([A]0/[A]) = kt, or [A] = [A]0 exp(-kt), and t1/2 = ln2/k = 0.693/k. Fraction remaining after n half-lives is (1/2)^n. You can substitute pressures or any quantity proportional to concentration, so ratios work without absolute concentrations. Time for 90 percent completion is 2.303/k, about 3.32 half-lives.
Common mistakes and connections: Students often plot [A] instead of ln[A] and expect a line, or forget that the slope is negative k. Another slip is mixing log base 10 and natural log: with log10 the slope is -k/2.303. Remember half-life is constant only for first order. Radioactive decay and many drug eliminations share this exponential form.
Visualization of First Order Reaction
Concentration decays exponentially and the half-life 0.693/k is constant, which is the signature of first order kinetics such as radioactive decay. The interactive lesson shows this as a live animation or chart.
Worked example and use case
Radioactive carbon-14 decays with a half-life of about 5730 years, whatever the amount of sample present.
Frequently asked questions about First Order Reaction
What is First Order Reaction?
Rate is proportional to one concentration; ln of concentration falls linearly with time.
Is First Order Reaction a beginner, intermediate or advanced topic?
First Order Reaction is a intermediate topic in Kinetics & Equilibrium. It builds on the vocabulary of beginner topics in this area.
What should I learn before First Order Reaction?
Study these earlier topics in Kinetics & Equilibrium first: Rate Constant, Order of Reaction, Zero Order Reaction.
What comes after First Order Reaction?
The next topics in Kinetics & Equilibrium are Second Order Reaction and Half-life of Reactions.
Can I practise First Order Reaction with quizzes?
Yes. The interactive lesson includes a self-check question on First Order Reaction, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where First Order Reaction fits in Kinetics & Equilibrium
First Order Reaction is topic 8 of 91 in Kinetics & Equilibrium.