Chemical kinetics
Kinetics questions ask you to extract a rate law from experimental data, relate concentration to time, apply the Arrhenius equation, and propose a mechanism consistent with the observed order. Justifying an order from evidence is where most marks lie.
Rate laws and order
Rate = k[A]^m[B]^n, with overall order m + n. Orders are experimental, not taken from stoichiometry, and can be zero or fractional. Determine each order by comparing runs where only one concentration changes: if doubling [A] quadruples the rate, the reaction is second order in A. Units of k follow from the overall order, for example s⁻¹ for first order and mol⁻¹·L·s⁻¹ for second order.
Integrated rate laws
- Zero order: [A] = [A]₀ − kt, t½ = [A]₀/2k, [A] versus t is linear.
- First order: ln[A] = ln[A]₀ − kt, t½ = ln2/k independent of concentration, ln[A] versus t is linear.
- Second order: 1/[A] = 1/[A]₀ + kt, t½ = 1/(k[A]₀), 1/[A] versus t is linear.
Arrhenius equation
k = A·e^(−Ea/RT), so ln k = ln A − Ea/RT. Between two temperatures, ln(k₂/k₁) = (Ea/R)(1/T₁ − 1/T₂). A larger Ea means a steeper temperature dependence. Catalysts lower Ea and raise k without altering ΔH or K.
Mechanisms and catalysis
Elementary steps must sum to the overall equation, and the slow step controls the rate law: a unimolecular slow step gives first order, a bimolecular step in A and B gives second order in both. Intermediates appear in the mechanism but not the overall equation. Homogeneous catalysts share the phase of the reactants, heterogeneous ones act on a surface, and enzymes saturate according to Michaelis–Menten kinetics.
Worked example
A reaction doubles its rate between 300 K and 310 K. Then ln 2 = (Ea/8.314)(1/300 − 1/310). The bracket equals 1.075 × 10⁻⁴ K⁻¹, so Ea = 8.314 × 0.693 / 1.075 × 10⁻⁴ = 5.36 × 10⁴ J/mol, about 53.6 kJ/mol.
Traps
- Reading reaction orders from the balanced equation.
- Forgetting to convert to kelvin in Arrhenius calculations.
- Including a pure solid in the rate law for a heterogeneous reaction.
- Confusing a catalyst with a species that shifts the equilibrium position.