Reaction Kinetics
Reaction kinetics is the study of how fast chemical reactions go and what controls their speed. For the MCAT you should be able to define rate, write and interpret rate laws, determine reaction order and the rate constant, apply the Arrhenius equation and activation energy, use collision theory and reaction-coordinate diagrams, identify the rate-determining step of a mechanism, and explain how catalysts work.
Chemical Kinetics
Chemical kinetics is the branch of chemistry that deals with the rate of a reaction and the mechanism by which it proceeds. Rate measures how fast reactants are consumed (or products formed) per unit time:
Rate = −Δ[Reactant] / Δt = +Δ[Product] / Δt
Units of rate: mol L−1 s−1. For aA + bB → cC + dD, rate = −(1/a) d[A]/dt = −(1/b) d[B]/dt = (1/c) d[C]/dt = (1/d) d[D]/dt.
Rate law (rate equation)
For a reaction aA + bB → products, the experimental rate law has the form:
Rate = k [A]m [B]n
where m and n are determined experimentally (not from the balanced equation), k is the rate constant, and m + n is the overall order.
Rate Constant
The rate constant k (also called specific rate constant) is the proportionality constant in the rate law. It is numerically equal to the rate when all reactant concentrations are 1 mol L−1.
- k depends on temperature and the catalyst, but is independent of concentration.
- Units of k depend on the overall order:
- Zero order: mol L−1 s−1
- First order: s−1
- Second order: L mol−1 s−1
- A larger k means a faster reaction.
Order of Reaction
The order with respect to a reactant is the power to which its concentration is raised in the experimentally determined rate law. The overall order is the sum of these powers.
Order vs molecularity
- Order — experimental, can be 0, fractional, or negative; refers to the overall reaction.
- Molecularity — theoretical, always a positive integer (1, 2, 3); refers to a single elementary step (number of species colliding).
Integrated rate laws and half-lives
| Order | Rate law | Integrated form | Half-life t½ | Units of k | Concentration vs time graph |
|---|---|---|---|---|---|
| Zero | rate = k | [A] = [A]0 − kt | [A]0 / (2k) | mol L−1 s−1 | Linear decrease |
| First | rate = k[A] | ln[A] = ln[A]0 − kt | 0.693 / k (constant!) | s−1 | Exponential decay |
| Second | rate = k[A]2 | 1/[A] = 1/[A]0 + kt | 1 / (k[A]0) | L mol−1 s−1 | Slower decay than 1st order |
Zero-order half-life depends on [A]0; first-order half-life is independent of [A]0 (key MCQ point); second-order half-life is inversely proportional to [A]0.
Pseudo-first-order reactions
If one reactant is in such large excess that its concentration is essentially constant, the reaction's apparent kinetic order drops by one. Acid-catalysed hydrolysis of an ester in dilute aqueous solution looks first-order in ester even though water is also a reactant, because [H2O] is virtually constant.
Collision Theory
Collision theory explains rate at the molecular level: molecules must collide to react, but only a fraction of collisions are effective. An effective collision requires (1) sufficient energy—at least the activation energy Ea—and (2) correct orientation of the colliding species. Rate ∝ (collision frequency) × (fraction with E ≥ Ea) × (orientation factor); these three factors map onto the Arrhenius terms A and e−Ea/RT.
Anything that raises collision frequency (higher concentration/pressure, larger surface area) or the fraction of sufficiently energetic collisions (higher temperature, lower Ea via a catalyst) increases the rate.
Activation Energy and Reaction-Coordinate Diagrams
The activation energy Ea is the minimum energy that colliding molecules must possess (above their average) for a successful reaction. It is the height of the energy barrier between reactants and products on a reaction-coordinate (potential-energy) diagram. The peak of that barrier is the transition state (activated complex)—a high-energy, non-isolable arrangement.
Reading the diagram: Ea,forward is measured from the reactants to the peak; Ea,reverse from the products to the peak; and ΔHrxn = Ea,forward − Ea,reverse (the energy gap between reactants and products). If products lie below reactants the reaction is exothermic (ΔH < 0); if above, endothermic. A multi-step mechanism shows one hump per step, with an intermediate sitting in the valley between humps.
Arrhenius equation
The temperature dependence of the rate constant is given by Arrhenius:
k = A · e−Ea/RT
- A = pre-exponential / frequency factor (relates to collision frequency and orientation).
- Ea = activation energy in J mol−1.
- R = gas constant (8.314 J K−1 mol−1); T = temperature in kelvin.
- Linear form: ln k = ln A − Ea / RT — a plot of ln k vs 1/T has slope −Ea / R.
Catalysts and Ea
A catalyst provides an alternative pathway with a lower activation energy. It speeds up forward and reverse reactions equally, so equilibrium position is unaffected; only the speed at which equilibrium is reached changes. A catalyst is recovered chemically unchanged at the end of the reaction. Catalysts lower Ea but never change ΔH, ΔG, or K.
Reaction Mechanism and Rate-Determining Step
Most reactions proceed through a series of elementary steps (a mechanism), not in a single collision. The slowest step is the rate-determining step (RDS); it acts as a bottleneck and dictates the overall rate law.
- For an elementary step (and only an elementary step) the rate law can be written directly from its molecularity—the exponents equal the stoichiometric coefficients of that step.
- The overall rate law is the rate law of the RDS, expressed in terms of reactants (a fast pre-equilibrium before the RDS may need to be substituted in).
- A valid mechanism must (1) have elementary steps that add up to the overall balanced equation and (2) predict the experimentally observed rate law.
- A reaction intermediate is produced in one step and consumed in a later one; it does not appear in the overall equation (unlike a catalyst, which is consumed early and regenerated).
Factors Affecting Rate of Reaction
- Concentration of reactants: increasing [reactants] increases collision frequency, raising rate (up to the order). For gases, increasing pressure does the same thing.
- Temperature: a 10 °C rise typically doubles the rate. Higher T → higher fraction of molecules with energy ≥ Ea (the Maxwell–Boltzmann tail).
- Catalyst: lowers Ea, providing an alternative pathway. Heterogeneous (Pt, Ni, V2O5) or homogeneous (acids in ester hydrolysis).
- Surface area (heterogeneous reactions): finer particles → greater contact area → faster reaction. Powdered Mg burns faster than ribbon.
- Nature of reactants: ionic reactions in solution are nearly instantaneous; covalent bond rearrangements (organic) are slower.
- Light (photochemical reactions): H2 + Cl2 reacts violently in sunlight but very slowly in the dark.
Worked MCQs
Six MCQs that capture the high-yield testing patterns for this chapter. Read the explanation even when you get the answer right — it's where the deeper concept lives.
Q1. Which of the following is true about a catalyst?
A catalyst lowers Ea by offering an alternative path. It speeds up both forward and reverse reactions equally, so the equilibrium position is unchanged, and it is recovered chemically unchanged at the end.
Q2. The half-life of a first-order reaction is:
For first-order kinetics, t½ = 0.693 / k — it depends only on k (and therefore on temperature/catalyst), not on the starting concentration. This is why radioactive decay has a fixed half-life.
Q3. For a reaction with rate law rate = k[A]2[B], the overall order is:
Overall order is the sum of the powers in the experimentally determined rate law. Here 2 + 1 = 3, so the reaction is third order overall (second order in A and first order in B).
Q4. Increasing the temperature of a reaction by 10 °C usually:
A 10 °C rise typically doubles the rate because a much larger fraction of molecules now have energy above Ea (Maxwell–Boltzmann distribution shifts right). Ea itself is unchanged — only k changes (Arrhenius).
Q5. The units of the rate constant for a first-order reaction are:
For first order, rate = k[A]. Rate has units mol L−1 s−1 and [A] has mol L−1, so k has units of s−1. (Zero order: mol L−1 s−1; second order: L mol−1 s−1.)
Q6. For A + B → products, doubling [A] doubles the rate; doubling [B] quadruples the rate. The rate law is:
Order is found from initial-rate data. Doubling [A] ×2 the rate → first order in A (21 = 2). Doubling [B] ×4 the rate → second order in B (22 = 4). So rate = k[A][B]2, third order overall. Orders come from the data, never from the coefficients.
Quick Recap
- Rate = −d[reactant]/dt = +d[product]/dt; units mol L−1 s−1.
- Rate law: rate = k[A]m[B]n; m + n = overall order (experimental).
- Order vs molecularity: order is experimental and can be 0/fractional; molecularity is theoretical, integral, for elementary steps only.
- First-order half-life: t½ = 0.693 / k (independent of [A]0).
- Arrhenius: k = A e−Ea/RT; ln k vs 1/T has slope −Ea/R; +10 °C ~ doubles rate.
- Collision theory: effective collisions need enough energy (≥ Ea) and correct orientation.
- Reaction-coordinate diagram: peak = transition state; ΔH = Ea,fwd − Ea,rev.
- Mechanism: slowest step = rate-determining step; it sets the overall rate law.
- Catalyst ↓ Ea via alternative pathway; ΔH, ΔG, K and equilibrium unchanged.
- Factors: concentration, temperature, catalyst, surface area, nature of reactants, light.