Intermediate Topic 429 of 1102 Kinetics & Equilibrium
Half-life of Reactions
First-order half-life equals 0.693 over k and is independent of initial concentration.
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In-depth explanation of Half-life of Reactions
The half-life is the time required for a reactant concentration to fall to half of its initial value, and it is a convenient way to describe reaction speed. For a first order reaction the half-life is 0.693/k and is independent of starting concentration, so it stays constant throughout the reaction. For a second order reaction the half-life depends on the initial concentration and lengthens as the reaction proceeds, while for a zero order reaction it shortens as concentration falls. Measuring the half-life at two different starting concentrations is therefore a quick test for the reaction order.
Going deeper: Half-life of Reactions
Key ideas: Formulas: zero order t1/2 = [A]0/2k, first order 0.693/k, second order 1/(k[A]0). General form for order n is proportional to [A]0^(1-n). Plot log t1/2 against log [A]0 and the slope is 1-n, giving the order. Half-life is also useful for estimating completion: seven half-lives leaves under one percent.
Common mistakes and connections: Students apply the first order formula to every reaction, or think half-life means half the reaction time overall. Another mistake is claiming that two half-lives equal the full reaction: after two half-lives one quarter remains. Remember the units: k for first order has inverse time, so half-life has time. The idea ties into radioactive decay and drug dosing schedules.
Visualization of Half-life of Reactions
Each half-life removes half of what remains: 50, 25, 12.5 percent and so on, so after four half-lives only 6.25 percent is left (first order). The interactive lesson shows this as a live animation or chart.
Worked example and use case
After four half-lives, (1/2)^4 = 1/16 of the original reactant remains, which is 6.25 percent.
Frequently asked questions about Half-life of Reactions
What is Half-life of Reactions?
First-order half-life equals 0.693 over k and is independent of initial concentration.
Is Half-life of Reactions a beginner, intermediate or advanced topic?
Half-life of Reactions is a intermediate topic in Kinetics & Equilibrium. It builds on the vocabulary of beginner topics in this area.
What should I learn before Half-life of Reactions?
Study these earlier topics in Kinetics & Equilibrium first: Zero Order Reaction, First Order Reaction, Second Order Reaction.
What comes after Half-life of Reactions?
The next topics in Kinetics & Equilibrium are Pseudo First Order Reaction and Method of Initial Rates.
Can I practise Half-life of Reactions with quizzes?
Yes. The interactive lesson includes a self-check question on Half-life of Reactions, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Half-life of Reactions fits in Kinetics & Equilibrium
Half-life of Reactions is topic 10 of 91 in Kinetics & Equilibrium.