Chemical Kinetics
Unit 10 tests rate expressions, order and molecularity, integrated rate laws, half-life, the Arrhenius equation and collision theory.
Core rules
- Rate = −d[reactant]/dt = +d[product]/dt, with coefficients as reciprocal factors.
- Rate law is determined experimentally; order is the sum of exponents, while molecularity counts species in an elementary step.
- 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.
- Units of k: mol L⁻¹ s⁻¹ for zero order, s⁻¹ for first order.
- Arrhenius equation: k = Ae^(−Ea/RT); a plot of ln k versus 1/T has slope −Ea/R.
- Catalyst lowers Ea without changing ΔH or equilibrium position.
Worked example
A first-order reaction has a half-life of 20 min. Find the time for 87.5% decomposition. After one half-life 50% remains, after two 25%, after three 12.5%. Since 87.5% has decomposed, 12.5% remains, which requires three half-lives: t = 3 × 20 = 60 min. Alternatively, k = 0.693/20 = 0.0347 min⁻¹ and t = (2.303/0.0347)·log(100/12.5) = 60 min.
Traps
- Order cannot be read from the balanced equation unless the step is elementary.
- A zero-order half-life depends on initial concentration; a first-order half-life does not.
- Rate constants increase with temperature, but rate laws do not change.
- Average rate and instantaneous rate differ; use a tangent for the latter.
- Overall order can be fractional or zero.