Intermediate Topic 428 of 1102 Kinetics & Equilibrium
Second Order Reaction
Rate depends on the square of concentration, with 1 over concentration rising linearly in time.
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In-depth explanation of Second Order Reaction
A second order reaction has a rate that depends on the square of one concentration, rate = k[A]^2, or on the product of two different concentrations, rate = k[A][B]. For rate = k[A]^2 the integrated form is 1/[A] = 1/[A]0 + kt, so a plot of 1/[A] against time is a straight line with slope k. The half-life t1/2 = 1/(k[A]0) depends on the starting concentration and lengthens as the reaction proceeds. Second order kinetics is typical of bimolecular elementary steps, in which two particles must collide to react. Gas phase dimerizations and many organic addition and substitution reactions follow this pattern.
Going deeper: Second Order Reaction
Key ideas: For rate = k[A]^2 use 1/[A] = 1/[A]0 + kt, with k in L per mol per s. For rate = k[A][B] with different initial amounts, a more involved form with ln([B][A]0/([A][B]0)) is needed, and under equal initial amounts it reduces to the simple form. Each successive half-life is double the previous one.
Common mistakes and connections: Be careful with the definition of rate when the stoichiometry is 2A -> products: the rate of loss of A is 2k[A]^2 if the reaction rate is written as k[A]^2, so conventions matter. Students also use 1/[A] plots for first order data and vice versa. Second order often comes from bimolecular elementary steps, linking to molecularity and collision theory.
Visualization of Second Order Reaction
For rate = k[A]^2 the decay is hyperbolic: fast at first, then a long slow tail, with 1/[A] growing linearly in time and half-life lengthening. The interactive lesson shows this as a live animation or chart.
Worked example and use case
For 2NO2 -> 2NO + O2 the rate is second order in NO2, so a plot of 1/[NO2] against time gives a straight line.
Frequently asked questions about Second Order Reaction
What is Second Order Reaction?
Rate depends on the square of concentration, with 1 over concentration rising linearly in time.
Is Second Order Reaction a beginner, intermediate or advanced topic?
Second 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 Second Order Reaction?
Study these earlier topics in Kinetics & Equilibrium first: Order of Reaction, Zero Order Reaction, First Order Reaction.
What comes after Second Order Reaction?
The next topics in Kinetics & Equilibrium are Half-life of Reactions and Pseudo First Order Reaction.
Can I practise Second Order Reaction with quizzes?
Yes. The interactive lesson includes a self-check question on Second Order Reaction, and the Kinetics & Equilibrium quiz draws on every topic in this area.
Where Second Order Reaction fits in Kinetics & Equilibrium
Second Order Reaction is topic 9 of 91 in Kinetics & Equilibrium.