Second-Order Reaction Calculator

Calculate Second-Order Reaction Kinetics

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Rate Constant Calculator

Calculate the rate constant (k) for a second-order reaction

Rate Constant: - M⁻¹s⁻¹

Concentration Calculator

Calculate concentration at any time for a second-order reaction

Concentration: - M

Half-Life Calculator

Calculate the half-life of a second-order reaction

Half-Life: - s

Understanding Second-Order Reactions

What is a Second-Order Reaction?

A second-order reaction is a reaction where the rate depends on either:

  • The concentration of one reactant squared
  • The product of the concentrations of two different reactants

Rate Laws

Two common types of second-order rate laws:

Rate = k[A]² (single reactant)

Rate = k[A][B] (two reactants)

Integrated Rate Law

For a single reactant second-order reaction:

1/[A] = 1/[A]₀ + kt

[A] = [A]₀/(1 + kt[A]₀)

Half-Life

Unlike first-order reactions, the half-life depends on initial concentration:

t₁/₂ = 1/(k[A]₀)

Examples of Second-Order Reactions

  • Dimerization reactions
  • Addition reactions
  • Many organic synthesis reactions
  • Some polymerization reactions

Graphical Analysis

For a second-order reaction:

  • Plot of 1/[A] vs. time gives a straight line
  • Slope = k (rate constant)
  • y-intercept = 1/[A]₀

Essential Second-Order Reaction Formulas

Rate Law

Rate = k[A]²

Integrated Rate Law

1/[A] = 1/[A]₀ + kt

Half-Life

t₁/₂ = 1/(k[A]₀)