Reaction Kinetics
Kinetics describes how fast reactions go. Learn rate laws and reaction order, rate constants and the Arrhenius equation, activation energy, half-life, elementary vs non-elementary reactions, reversible reactions, and how to extract kinetics from experimental data.
Thermodynamics tells us whether a reaction can happen; kinetics tells us how fast. Reactor size, temperature, catalyst choice and safety all depend on the rate law.
A classic rule of thumb: many reaction rates roughly double for every 10 °C rise in temperature — the Arrhenius law makes this quantitative.
An analogy
Activation energy is like a hill between two valleys: molecules need enough energy (temperature) to climb over before rolling down to products. A catalyst digs a tunnel through the hill.
Rate and order
Rate is how fast a reactant disappears or a product appears per volume. Order describes how rate depends on concentration: zero order (constant), first order (proportional), second order (∝ C²). Orders are found by experiment, not from the balanced equation (except for elementary reactions).
Temperature: Arrhenius
Rate constants rise exponentially with temperature. With E_a = 80 kJ/mol, a 10 K rise near 300 K nearly triples the rate. This sensitivity makes temperature control crucial — and runaway reactions dangerous.
Getting kinetics from data
Batch experiments give concentration vs time. Integral method: plot ln C vs t (first order) or 1/C vs t (second order) — the straight line wins. Differential and initial-rate methods fit rate vs concentration. Arrhenius plots (ln k vs 1/T) give E_a.
Complex kinetics
Reversible reactions approach equilibrium (net rate = k_f C_A − k_r C_B). Series and parallel reactions govern selectivity. Chain and radical mechanisms, Michaelis–Menten enzyme kinetics and Langmuir–Hinshelwood surface kinetics give non-power-law forms. Microkinetic models and DFT guide catalyst design.
Formulas
- Power-law rate:
−r_A = k C_A^α C_B^β - Arrhenius:
k = A exp(−E_a / RT) - Two-temperature form:
k₂/k₁ = exp[(E_a/R)(1/T₁ − 1/T₂)] - First-order integrated:
ln(C_A0/C_A) = k t, t½ = ln 2 / k - Second-order integrated:
1/C_A − 1/C_A0 = k t
Worked example: Arrhenius temperature effect
Given: E_a = 80 kJ/mol; k = 0.01 /min at 300 K
Find: k at 310 K.
- k₂/k₁ = exp[(80 000/8.314)(1/300 − 1/310)] = exp(1.035) = 2.81
- k₂ = 0.0281 /min
Answer: ≈ 2.8× faster
Worked example: Half-life
Given: First order, k = 0.01 /min
Find: Half-life.
- t½ = 0.693/0.01 = 69.3 min
Answer: ≈ 69 min
Common mistakes
- Wrong: Taking order from stoichiometric coefficients. — Right: Orders must be measured unless the reaction is elementary.
- Wrong: Using °C in Arrhenius. — Right: Always kelvin.
Applications
- Reactor sizing: Rate laws feed every reactor design equation.
- Shelf life & stability: Arrhenius accelerated ageing predicts drug and food shelf life.
- Safety: Temperature sensitivity of rates determines runaway potential.
Key takeaways
- −r_A = k C^n; order from experiment.
- k = A e^(−E_a/RT); kelvin only.
- First order: ln(C₀/C) = kt; t½ = ln2/k.
- Plot data to identify order and E_a.
Going further
- Transition-state theory: Relates A and E_a to activation entropy and enthalpy.
- Pseudo-steady-state hypothesis: Simplifies radical mechanisms by setting intermediate rates to zero.
- Parameter estimation: Nonlinear regression of kinetic models with confidence intervals.