Chemical Kinetics
Chemical kinetics tests rate expressions, order versus molecularity, integrated rate laws, half-life, the Arrhenius equation and collision theory.
Rate, order and molecularity
Rate = −Δ[reactant]/Δt = +Δ[product]/Δt. The rate law is determined experimentally; order is the sum of the exponents and can be zero, fractional or negative. Molecularity belongs to an elementary step only and is a whole number ≥ 1. Units of k: mol L⁻¹ s⁻¹ (zero order), s⁻¹ (first order), L mol⁻¹ s⁻¹ (second order).
Integrated rate laws
- Zero order: [A] = [A]₀ − kt, t½ = [A]₀/2k.
- First order: k = (2.303/t)·log([A]₀/[A]), t½ = 0.693/k, independent of initial concentration - the reason radioactive decay and many decompositions obey first order.
Arrhenius
k = A·e^(−Ea/RT) and log(k₂/k₁) = (Ea/2.303R)(1/T₁ − 1/T₂). A catalyst lowers Ea; it does not change ΔH, ΔG° or the equilibrium constant, only the speed of approach.
Worked example
A first-order reaction is 75% complete in 60 min. Find k and t½. Remaining fraction = 0.25, so [A]₀/[A] = 4. k = (2.303/60)·log 4 = (2.303 × 0.6021)/60 = 0.0231 min⁻¹. t½ = 0.693/0.0231 = 30.0 min, exactly half the time for 75% completion - as expected, since 75% is two half-lives.
Traps that cost marks
- Mixing ln with the constant 2.303; the two must be used together.
- Quoting k without units, or with units that belong to a different order.
- Equating order with stoichiometric coefficients - valid only for elementary steps.
- Saying a catalyst increases A only, or that it shifts the equilibrium position.