What this chapter is about
Chemical kinetics is the branch of chemistry that studies the rates of chemical reactions and the factors that influence them. While thermodynamics tells us whether a reaction is feasible and how much product can form, kinetics tells us how fast the reaction proceeds. Many thermodynamically favourable reactions are practically useless because they occur too slowly, and understanding kinetics helps us control reaction speeds in industrial processes, biological systems and everyday life.
In this chapter, you will learn to define and measure reaction rates, understand how concentration, temperature, catalysts and other factors affect these rates, and connect experimental observations to mathematical rate laws. You will also explore the concept of reaction mechanisms — the step-by-step pathways through which reactants become products — and how the slowest step determines the overall rate.
After studying this chapter, you should be able to write rate expressions for reactions, determine the order of a reaction from experimental data, calculate rate constants and half-lives, apply the Arrhenius equation to relate temperature and rate, and explain how catalysts speed up reactions without being consumed.
Key ideas
- Rate of reaction is defined as the change in concentration of a reactant or product per unit time. For a reaction A → B, rate = –d[A]/dt = +d[B]/dt, where the negative sign accounts for decreasing reactant concentration.
- Rate law is an experimentally determined expression that relates the rate to the concentrations of reactants raised to certain powers: rate = k[A]^m[B]^n. The exponents m and n are the orders with respect to A and B, and their sum is the overall order.
- Rate constant (k) is a proportionality constant specific to a reaction at a given temperature; its units depend on the overall order of the reaction.
- Order of reaction cannot be predicted from the stoichiometric equation; it must be found by experiment. Reactions can be zero order, first order, second order, or even fractional order.
- Integrated rate equations connect concentration with time. For first-order reactions: ln[A]₀/[A] = kt, or [A] = [A]₀ × e^(–kt).
- Half-life (t₁/₂) is the time for half the reactant to be consumed. For first-order reactions, t₁/₂ = 0.693/k, which is independent of initial concentration.
- Arrhenius equation describes how the rate constant changes with temperature: k = A × e^(–Ea/RT), where Ea is the activation energy and A is the pre-exponential factor.
- Catalysts increase the reaction rate by providing an alternative pathway with lower activation energy; they are regenerated and do not appear in the overall stoichiometry.
Formulas and facts to remember
- Average rate = Δ[product]/Δt or –Δ[reactant]/Δt (units: mol L⁻¹ s⁻¹).
- Instantaneous rate = d[product]/dt, found as the slope of the concentration–time curve at a point.
- First-order integrated rate law: ln[A] = ln[A]₀ – kt, or equivalently k = (2.303/t) × log([A]₀/[A]).
- Half-life for first order: t₁/₂ = 0.693/k (constant, independent of [A]₀).
- Zero-order integrated rate law: [A] = [A]₀ – kt; half-life t₁/₂ = [A]₀/(2k).
- Arrhenius equation (logarithmic form): log k = log A – Ea/(2.303 RT).
- Two-temperature form: log(k₂/k₁) = (Ea/2.303 R) × (1/T₁ – 1/T₂).
- Units of k: For zero order, mol L⁻¹ s⁻¹; for first order, s⁻¹; for second order, L mol⁻¹ s⁻¹.
Worked examples
Example 1: Calculating average rate
A reaction 2N₂O₅(g) → 4NO₂(g) + O₂(g) is monitored. The concentration of N₂O₅ falls from 0.080 mol L⁻¹ to 0.060 mol L⁻¹ in 200 s. Find the average rate of reaction with respect to N₂O₅.
Solution
Change in concentration Δ[N₂O₅] = 0.060 – 0.080 = –0.020 mol L⁻¹.
Average rate = –Δ[N₂O₅]/Δt = –(–0.020)/200 = 1.0 × 10⁻⁴ mol L⁻¹ s⁻¹.
Because 2 moles of N₂O₅ decompose for every mole of O₂ formed, the rate of formation of O₂ = (1/2) × 1.0 × 10⁻⁴ = 5.0 × 10⁻⁵ mol L⁻¹ s⁻¹.
Example 2: First-order rate constant and half-life
A certain radioactive decay follows first-order kinetics. If 75% of the substance remains after 40 minutes, calculate the rate constant and half-life.
Solution
For first-order: k = (2.303/t) × log([A]₀/[A]).
Here [A]/[A]₀ = 0.75, so [A]₀/[A] = 1/0.75 = 1.333.
k = (2.303/40) × log(1.333) = (2.303/40) × 0.125 = 7.2 × 10⁻³ min⁻¹.
Half-life t₁/₂ = 0.693/k = 0.693/(7.2 × 10⁻³) ≈ 96 min.
Example 3: Applying the Arrhenius equation
The rate constant for a reaction is 2.0 × 10⁻³ s⁻¹ at 300 K and 8.0 × 10⁻³ s⁻¹ at 320 K. Calculate the activation energy. (R = 8.314 J mol⁻¹ K⁻¹)
Solution
Using log(k₂/k₁) = (Ea/2.303 R) × (1/T₁ – 1/T₂):
log(8.0 × 10⁻³ / 2.0 × 10⁻³) = log 4 = 0.602.
(1/T₁ – 1/T₂) = 1/300 – 1/320 = (320 – 300)/(300 × 320) = 20/96000 = 2.08 × 10⁻⁴ K⁻¹.
Ea = 0.602 × 2.303 × 8.314 / (2.08 × 10⁻⁴) = 11.53 / (2.08 × 10⁻⁴) ≈ 55 400 J mol⁻¹ = 55.4 kJ mol⁻¹.
Common mistakes
- Confusing order with stoichiometric coefficient → Order is found only from experiment; never assume it equals the coefficient in the balanced equation.
- Using natural log (ln) formula but substituting log₁₀ values → Remember ln x = 2.303 × log₁₀ x; keep logarithm bases consistent.
- Forgetting to include the negative sign when writing rate in terms of a reactant → Rate is always positive; the negative sign compensates for decreasing reactant concentration.
- Assuming half-life is constant for all reaction orders → Half-life is concentration-independent only for first-order reactions; for zero and second order, it depends on initial concentration.
- Mixing up activation energy (Ea) with enthalpy change (ΔH) → Ea is the energy barrier to reach the transition state; ΔH is the overall energy difference between reactants and products.
Quick revision
- Rate = change in concentration per unit time; units are mol L⁻¹ s⁻¹.
- For first-order reactions, plot ln[A] vs t gives a straight line with slope = –k, and t₁/₂ = 0.693/k.
- Order must be determined experimentally; it can be zero, fractional or integer.
- Arrhenius equation: k = A × e^(–Ea/RT); higher temperature or lower Ea means faster reaction.
- Catalysts lower Ea without changing the equilibrium position or being consumed.