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Most reactions you have written as a single arrow on paper actually proceed by a sequence of two or more elementary steps. The rate-determining step (RDS) is the slowest of those steps; like the narrowest section of a motorway, it dictates how fast the whole system can move. Crucially, the experimental rate equation is shaped by the RDS — the orders with respect to each reactant correspond to the molecularity of the molecules involved up to and including the RDS, not to the stoichiometric coefficients of the balanced overall equation. In this lesson we deduce the RDS from a measured rate equation, check that a proposed mechanism is consistent with the kinetics, and apply the idea to two cornerstone A-Level mechanisms: SN1 versus SN2 hydrolysis of halogenoalkanes. By the end, you will read a rate equation as a window onto the molecular choreography.
Spec mapping (AQA 7405): This lesson maps to §3.1.9 — the rate-determining step and its relationship to the rate equation. It builds on lesson 1 (the form Rate = k[A]^m[B]^n and how orders are obtained from initial-rate data) and lesson 2 (the Arrhenius equation — each elementary step has its own activation energy, and the macroscopic Ea is that of the RDS). It anchors a key skill assessed in lesson 7 (rate measurement via Required Practical 7) and is directly applied across §3.3 (organic mechanisms — SN1 versus SN2 hydrolysis in §3.3.3, E1 versus E2 elimination in §3.3.7, electrophilic aromatic substitution in §3.3.10). Refer to the official AQA specification document for the exact wording.
Assessment objectives: AO1 covers definitions — the RDS, an elementary step, a reaction mechanism, an intermediate, a transition state, and the distinction between them. AO2 dominates the marks: deducing the molecularity of the RDS from a given rate equation, checking that a proposed mechanism is consistent with the experimental rate equation, and using the diagnostic differences between SN1 and SN2 kinetics. AO3 reasoning appears in higher-tariff questions that ask you to evaluate competing mechanisms, propose modifications when the kinetics disagree, or explain the kinetic origin of the SN1/SN2 distinction in terms of carbocation stability and steric access.
A reaction mechanism is the sequence of elementary steps by which reactants are converted to products. An elementary step is a single molecular event — typically the collision of one, two, or (rarely) three particles — that proceeds in one pass over an energy barrier without any further intermediate. The molecularity of an elementary step is the number of particles involved: unimolecular (one particle, usually a dissociation), bimolecular (two — by far the most common), or termolecular (three — rare because simultaneous three-body collisions are improbable).
Sum the elementary steps and you must recover the overall balanced equation: every reactant cancels except the ones in the overall equation, and every product likewise. Species that appear and then disappear during the mechanism are intermediates — real chemical entities, with a finite (if often short) lifetime, that occupy local minima on the potential energy surface. Do not confuse intermediates with transition states: transition states are the species at the very top of each energy barrier, saddle points on the potential energy surface, with vanishingly short lifetimes (~10⁻¹³ s — roughly one bond vibration). They cannot be isolated.
Every elementary step has its own activation energy, Ea. Plot the energy of the system as the reaction proceeds — the reaction coordinate — and you trace a series of hills and valleys: hills are transition states, valleys are reactants, intermediates, or products. The rate-determining step is the step with the largest activation energy and therefore the smallest rate constant; the system is held up at that highest barrier in much the same way as traffic backs up at the steepest hill. Lower-barrier steps before or after the RDS run to completion much faster and are effectively transparent to the overall rate.
Key Definition: The rate-determining step is the slowest elementary step in a multi-step mechanism. Its rate sets the overall rate of the reaction, and its molecularity is reflected in the experimental rate equation.
This is the single most important idea in §3.1.9. The orders in the rate equation tell you which molecules are present in the RDS (and any fast equilibria that precede it), not the stoichiometric coefficients of the overall balanced equation.
Rule of thumb for a mechanism in which the RDS is the first step:
If the RDS comes after a fast pre-equilibrium, the concentrations of intermediates in the RDS must be re-expressed in terms of reactants via the equilibrium constant; this is the pre-equilibrium approximation (see Going Further). Either way, the result is that the experimental orders are determined by the RDS — never read straight off the overall equation.
Key Point: A balanced overall equation tells you nothing about the mechanism. Two reactions with identical overall stoichiometry can have completely different rate equations because they proceed by different mechanisms.
A practical consequence: if you are given a rate equation Rate = k[X]^a[Y]^b and asked to check a proposed mechanism, you check that the species in (and up to) the proposed RDS account for the orders. If they don't, the mechanism is wrong — kinetics has falsified it.
The reaction between nitrogen dioxide and carbon monoxide is exothermic and a classic kinetics teaching example.
If you naively read the orders off the overall equation, you would predict Rate = k[NO₂][CO] (first order in each). The experimental data flatly contradict that, so the mechanism cannot be a single bimolecular step. A two-step mechanism consistent with the data:
Sum: 2 NO₂ + NO₃ + CO → NO₃ + NO + NO₂ + CO₂. Cancel one NO₂ and the NO₃ from each side: NO₂ + CO → NO + CO₂. ✓ The mechanism sums to the overall equation.
Now check the kinetics. The RDS is bimolecular in NO₂ (two NO₂ molecules collide), so the predicted rate equation is Rate = k[NO₂]². Carbon monoxide enters only in the fast post-equilibrium step and therefore does not appear in the rate equation. ✓ Both predictions match experiment.
The intermediate NO₃ — nitrogen trioxide, an electronically excited form of the radical species — is real and short-lived. It has been detected spectroscopically in flash-photolysis studies, providing direct physical evidence for the mechanism.
At higher temperatures (> 650 K) the kinetics change: a different mechanism with a single bimolecular elementary step NO₂ + CO → NO + CO₂ takes over, and the rate equation becomes Rate = k[NO₂][CO]. The Arrhenius plot is therefore curved — a textbook example of the change-of-mechanism phenomenon mentioned in lesson 2.
The hydrogen–iodine reaction was, for decades, taught as the archetype of a single-step termolecular reaction — the rate equation Rate = k[H₂][I₂] (second order overall) was thought to correspond directly to the elementary step H₂ + I₂ → 2 HI. We now know this is wrong. The accepted mechanism is:
The species I (atomic iodine) is an intermediate, generated by the rapid pre-equilibrium dissociation of I₂.
To derive the rate equation, write the rate for the RDS:
Rate = k₂[H₂][I]²
But [I] is an intermediate concentration — we cannot measure it directly, and we need to express it in terms of stable reactants. Use the pre-equilibrium constant K₁ for step 1:
K₁ = [I]² / [I₂] ⇒ [I]² = K₁[I₂]
Substitute:
Rate = k₂ × K₁ × [H₂][I₂] = k_obs × [H₂][I₂]
where k_obs = k₂K₁ is the observed rate constant.
The result is Rate = k_obs[H₂][I₂] — first order in each reactant, second order overall — exactly what experiment gives. The kinetics are consistent with both the old termolecular picture and the new two-step picture; the two mechanisms cannot be distinguished by kinetics alone. The case against the termolecular mechanism rests on isotope-labelling and trapping experiments (notably by J. H. Sullivan, 1967) that detect free I atoms during the reaction.
This worked example illustrates two lessons. First, the orders in the rate equation do not uniquely determine the mechanism — different mechanisms can give the same rate law. Second, the pre-equilibrium approximation gives the rate equation a familiar shape even though an intermediate is present.
The kinetic distinction between SN1 and SN2 hydrolysis is one of the most heavily examined applications of rate-determining-step thinking in the entire A-Level course. You will meet it again in detail in the halogenoalkanes lessons (§3.3.3), but the kinetic reasoning belongs in §3.1.9.
Hydrolysis of a halogenoalkane RX by hydroxide ion gives the alcohol ROH:
R–X + OH⁻ → R–OH + X⁻
Two limiting mechanisms are possible.
For a primary halogenoalkane such as bromomethane (CH₃Br):
The hydroxide attacks from the side opposite the leaving group. C–O bond formation and C–Br bond breaking occur simultaneously, passing through a single five-coordinate transition state — the structure with HO and Br each partially bonded to the central carbon. Because the RDS (the only step) involves both reactants:
Rate = k[CH₃Br][OH⁻] — first order in each, second order overall.
There is no intermediate. The species [HO···CH₃···Br]‡ is a transition state (a saddle point on the potential energy surface), not an isolable carbocation.
For a tertiary halogenoalkane such as 2-bromo-2-methylpropane ((CH₃)₃CBr):
The first step is heterolytic dissociation of the C–Br bond, generating a tertiary carbocation intermediate. The cation is stabilised by hyperconjugation and the inductive effect of the three methyl groups; this stabilisation lowers the activation energy for ionisation enough to make the unimolecular path competitive. The carbocation is then rapidly captured by hydroxide (or any nearby nucleophile) in a low-barrier post-equilibrium step.
Because only the halogenoalkane appears in the RDS:
Rate = k[(CH₃)₃CBr] — first order in the halogenoalkane, zero order in hydroxide.
Doubling [OH⁻] at constant [RX] gives a direct experimental discrimination:
This is one of the cleanest examples in undergraduate chemistry of kinetics revealing molecular structure: the rate equation tells us whether the C–X bond breaks before, after, or simultaneously with the attack of the nucleophile. Primary halogenoalkanes are SN2 (no carbocation stability), tertiary are SN1 (excellent carbocation stability), secondary sit in between and can show mixed kinetics.
A catalyst provides an alternative mechanism with a lower activation energy for the RDS. The kinetic signature differs between the two main classes.
Homogeneous catalysts are in the same phase as the reactants. The catalyst is consumed in one step and regenerated in a later step; while it does not appear in the overall equation, it generally does appear in the RDS and therefore in the rate equation. A familiar example is the H⁺-catalysed iodination of propanone: Rate = k[CH₃COCH₃][H⁺]. The acid concentration appears explicitly in the rate equation even though H⁺ is regenerated by the end of the cycle.
Heterogeneous catalysts are in a different phase from the reactants — most commonly a solid catalyst with gaseous or liquid reactants. Here the catalyst concentration does not appear in the conventional rate equation in the same way, because the active species is a fixed surface site whose population is set by the catalyst's surface area and the surface coverage of reactants. The rate often becomes zero order in a gaseous reactant when the surface is fully covered (the Langmuir-Hinshelwood saturation regime).
In both cases the catalyst alters the mechanism, not the overall thermodynamics. The position of equilibrium is unchanged.
A multi-step mechanism is best visualised as an energy profile — a plot of system energy against the reaction coordinate. For a two-step mechanism with a fast first step and a slow second step:
Energy
|
| ___TS2___ <- highest barrier (RDS)
| / \
| TS1/ \
| /\___________ \___
| R/ Intermediate \Products
|/
+---------------------> reaction coordinate
Reading the diagram:
A useful exam skill is to sketch the profile, label every species (R, TS1, intermediate, TS2, P), mark Ea_slow versus Ea_fast, and identify which barrier is the RDS. SN1 profiles have two clear peaks (ionisation, capture); SN2 profiles have a single peak through a five-coordinate transition state.
Exam Tip: When asked to sketch a multi-step energy profile, always mark Ea explicitly as the height from the reactant level to the highest transition state peak. A common error is to mark it as the height of the second barrier above the intermediate — that is Ea₂ for the second elementary step, not the macroscopic Ea.
When measuring a rate equation in the lab (as in Required Practical 7, anchored in lesson 7 of this course), the chain of inference is: measure initial rates at varying initial concentrations → deduce orders → propose a rate equation → propose a mechanism whose RDS matches those orders → check the mechanism sums to the overall equation. Two very common mark-loss patterns:
A third subtler pitfall: proposing a termolecular RDS. Three-body collisions are vanishingly rare; if you find yourself writing an elementary step with three reactant molecules, look for a fast pre-equilibrium that generates one of them, then write the RDS as bimolecular.
The rate-determining step is one of the most widely-used concepts in A-Level Chemistry. It connects directly to every other rate or mechanism topic:
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