Reaction kinetics: study guide

Key ideas

Kinetics is about how fast reactions go. The rate law ties the rate to concentrations through a rate constant k, and the order of the reaction decides how concentration changes with time.

• The rate law is rate = k[A]ⁿ, where the order n must be found by experiment, not from the coefficients.
• For a first-order reaction ln[A] falls linearly with time and the half-life t½ = 0.693 ÷ k does not depend on the starting concentration.
• Zero order falls linearly in [A], and second order is linear in 1 ÷ [A]; their half-lives depend on the starting concentration.
• The Arrhenius equation k = A·e^(−Eₐ ÷ RT) says that a higher temperature or a lower activation energy gives a faster reaction.

Key equations

• rate = k[A]ⁿ
• ln[A] = ln[A]₀ − kt (first order)
• t½ = ln 2 ÷ k = 0.693 ÷ k
• 1 ÷ [A] = 1 ÷ [A]₀ + kt (second order)
• k = A·e^(−Eₐ ÷ RT)

Worked example

A first-order reaction has k = 0.0231 min⁻¹. The half-life is 0.693 ÷ 0.0231 = 30 min. After 90 min, which is three half-lives, the fraction left is (½)³ = 12.5 %. Check: e^(−0.0231 × 90) = e^(−2.08) = 0.125.

Common mistakes

• Reading the reaction order from the coefficients of the balanced equation.
• Using the first-order half-life formula for a reaction that is not first order.
• Forgetting to use kelvin and to match the units of R and Eₐ in the Arrhenius equation.

Practice

Test yourself with practice questions on this topic: Reaction kinetics