Reaction Rates and Collision Theory

Spec Mapping — OCR H432 Module 3.2.2 — Reaction rates, covering the definition of rate of reaction as $\Delta[\text{concentration}]/\Delta t$ with units mol dm $^{-3}$ s $^{-1}$ , methods for monitoring rate experimentally (gas volume, mass loss, colorimetry, pH, conductivity, titration of quenched samples), the qualitative model of collision theory requiring sufficient kinetic energy and correct orientation for a reaction to occur, the definition of activation energy $E_a$ as the minimum energy required for a successful collision, and the construction of enthalpy-profile diagrams showing reactant level, transition state, $E_a$ (forward and reverse), and overall $\Delta H$ (refer to the official OCR H432 specification document for exact wording).

Module 3.2.2 turns from thermodynamics (Lessons 1–5) to kinetics — the study of how fast reactions proceed. Thermodynamics tells us whether a reaction is energetically feasible (does $\Delta G < 0$ ?); kinetics tells us how fast it actually happens. A reaction can be highly exothermic and yet stable for centuries (graphite → diamond at room temperature, or H $_2$ + O $_2$ → H $_2$ O at room temperature without a spark). The kinetic explanation is that almost no colliding molecules have enough energy at room temperature to break the existing bonds — they are thermodynamically unstable but kinetically stable. This lesson develops the foundational kinetics of OCR Module 3.2.2: how we measure rates experimentally, how collision theory explains rate at the molecular level, and how the activation energy $E_a$ controls what fraction of collisions are "successful". Lessons 7 (Boltzmann distribution), 8 (factors affecting rate), and 9 (catalysts) build directly on the concepts established here, and Lesson 10 fuses kinetics with equilibrium to complete the OCR specification 3.2 block. The historical heritage runs from Wilhelmy's first experimental rate law (1850, sucrose hydrolysis) through Arrhenius's 1889 activation-energy theory to the modern transition-state theory of Eyring (1935) — all of which remain the conceptual backbone of every chemical-kinetics problem on the OCR paper.

Key Equation: the rate of a reaction is the change in concentration of a reactant (or product) per unit time: $\text{rate} = -\frac{\Delta[\text{reactant}]}{\Delta t} = +\frac{\Delta[\text{product}]}{\Delta t} \quad \text{(mol dm}^{-3}\text{ s}^{-1}\text{)}$ Collision theory: an effective collision requires both (i) total kinetic energy $\geq E_a$ and (ii) correct orientation. Rate $\propto$ frequency of effective collisions.

Rate of reaction — definition and units

The rate of reaction is the rate of change of concentration of a reactant (which decreases) or a product (which increases) with time:

$\text{rate} = \frac{|\Delta[\text{species}]|}{\Delta t}$

For a reaction $aA + bB \rightarrow cC + dD$ , the rates of disappearance of $A$ and appearance of $C$ are related by the stoichiometric coefficients:

$-\frac{1}{a}\frac{d[A]}{dt} = -\frac{1}{b}\frac{d[B]}{dt} = +\frac{1}{c}\frac{d[C]}{dt} = +\frac{1}{d}\frac{d[D]}{dt}$

Units: mol dm $^{-3}$ s $^{-1}$ (for solutions) or mol dm $^{-3}$ min $^{-1}$ for slow reactions. Rate can also be expressed in terms of mass loss (g s $^{-1}$ ), volume of gas produced (cm $^{3}$ s $^{-1}$ ), or any other measurable quantity that changes during the reaction.

Because concentrations of reactants fall and products rise during a reaction, a concentration-time graph is a curve. The rate at any instant is the gradient (slope) of the tangent at that point. The initial rate ( $t = 0$ ) is usually the steepest part of the curve — concentrations are highest, collision frequency is highest, and the rate is correspondingly highest. As the reaction proceeds the rate decreases until reactants are exhausted or equilibrium is reached.

Reactant disappearing

time / s [product]

Product appearing initial rate = steepest slope

Measuring rate experimentally

Any property that changes systematically during a reaction can be tracked against time to deduce the rate. Common experimental methods:

Method	Suitable for	Comments
Volume of gas collected	Reactions producing gas (CaCO $_3$ + HCl, Mg + HCl, H $_2$ O $_2$ → O $_2$ )	Gas syringe (1 cm $^3$ resolution) or inverted measuring cylinder over water
Mass loss	Reactions producing gas that escapes (open vessel + cotton-wool plug)	Top-pan balance ( $\pm 0.01$ g); plot mass against time
pH	Reactions involving H $^+$ or OH $^-$	pH meter with data logger; sample frequency $\sim 1$ Hz
Colour change (colorimetry)	Reactions with coloured species (MnO $_4^-$ , I $_2$ /starch, dichromate)	Colorimeter or spectrophotometer; tracks absorbance vs time
Conductivity	Reactions with changing ion concentration (e.g. ester hydrolysis)	Conductivity probe; useful when no other property changes obviously
Titration of quenched aliquots	Slow reactions where small samples can be withdrawn, mixed with cold inert solvent, and titrated	"Stopping the clock" — the dilution and cold quenches the reaction
Polarimetry	Reactions of chiral species (e.g. sucrose inversion — Wilhelmy's classic experiment)	Optical rotation tracked against time
Pressure	Gas-phase reactions in sealed vessel with $\Delta n_{gas} \neq 0$	Pressure transducer; converts to rate via $pV = nRT$

The initial rate (slope at $t = 0$ ) is the cleanest experimental observable because at $t = 0$ concentrations are known exactly and back-reaction is negligible. Initial-rate experiments at varying initial concentrations are the standard route to determining the rate equation (Year 13, OCR Module 5.1.1).

Collision theory — the molecular picture

Reactions occur because particles collide. But not every collision produces a reaction — in fact at room temperature, only about one in $10^{10}$ collisions between gas-phase molecules is "effective". The collision theory of Lewis (1918) and Hinshelwood (1927) postulates two requirements for an effective collision:

Sufficient energy — the colliding particles must have total kinetic energy (in the direction of approach) at least equal to the activation energy $E_a$ .
Correct orientation — the reactive parts of the colliding molecules must meet each other.

A collision satisfying both criteria is an effective (or successful) collision. The rate of reaction is proportional to the frequency of effective collisions:

$\text{rate} \propto Z_{coll} \times f_{E \geq E_a} \times p_{orientation}$

where $Z_{coll}$ is the total collision frequency (depends on concentration and temperature via mean speed), $f_{E \geq E_a}$ is the fraction with sufficient energy (Boltzmann factor — Lesson 7), and $p_{orientation}$ is the steric factor (between 0 and 1) for the geometric requirement.

flowchart TD
  A[Two particles collide] --> B{Total KE ≥ Ea?}
  B -->|No| C[Bounce apart - no reaction]
  B -->|Yes| D{Correct orientation?}
  D -->|No| C
  D -->|Yes| E[Effective collision: bonds reorganise → products]

Activation energy $E_a$

Activation energy is the minimum energy that the colliding particles must possess (collectively, along the direction of approach) for a reaction to occur. Equivalently: the height of the energy barrier on an enthalpy-profile diagram between reactants and transition state.

$E_a$ is a property of the reaction pathway, not of the individual reactants — different mechanisms have different $E_a$ . It does not depend on initial concentrations, and it is modulated (lowered) by a catalyst (Lesson 9) by opening an alternative pathway.

A high $E_a$ ( $\gtrsim 100$ kJ mol $^{-1}$ ) means very few collisions at room temperature have enough energy, so the rate is slow. Examples: N $_2$ + 3H $_2$ → 2NH $_3$ ( $E_a \sim 230$ kJ mol $^{-1}$ uncatalysed — hence the need for the Haber catalyst).
A low $E_a$ ( $\lesssim 30$ kJ mol $^{-1}$ ) means a large fraction of collisions succeed, and the rate is fast or essentially instantaneous. Example: H $^+$ (aq) + OH $^-$ (aq) → H $_2$ O(l) at $E_a \approx 0$ — diffusion-controlled.

Importantly, $E_a$ applies to both forward and reverse reactions; the reverse has $E_a^{rev} = E_a^{fwd} - \Delta H$ (with the correct sign of $\Delta H$ ).

For an exothermic reaction, $E_a^{rev} > E_a^{fwd}$ — the products must climb a bigger barrier to return. For an endothermic reaction the opposite is true. In both cases $E_a$ refers to the barrier height from the relevant starting level to the transition-state peak, never from reactants to products directly.

Factors that affect the rate — preview

Collision theory lets us predict how various factors affect rate, all through one of two channels: (a) the frequency of collisions, or (b) the fraction that are effective:

Factor	Microscopic effect	Effect on rate
Increase concentration	More particles per unit volume → more collisions per second	Increases (often linearly)
Increase pressure (gas)	Same as concentration (compress → higher number density)	Increases
Increase temperature	More particles have $E \geq E_a$ (Boltzmann) and more collisions per second	Increases sharply (often $\sim 2 \times$ per 10 K)
Increase surface area (solid)	More reactant atoms exposed at the phase boundary	Increases
Add catalyst	Alternative pathway with lower $E_a$ → more effective collisions	Increases (Lesson 9)
Add inert gas at constant volume	No change in reactant concentration	No effect
Add inert gas at constant pressure	Dilutes reactants	Decreases

Lessons 7–9 develop these in quantitative depth. The key idea now: temperature has a disproportionately large effect because it changes the energy distribution (Boltzmann factor — Lesson 7), not just the collision frequency. A 10 K rise typically doubles the rate even though collision frequency rises by only ~2%.

Orientation requirement — the steric factor

Even with sufficient energy, two molecules must collide with their reactive parts facing each other. Consider the nucleophilic substitution:

$\text{CH}_3\text{Br} + \text{OH}^- \rightarrow \text{CH}_3\text{OH} + \text{Br}^-$

For an $S_N 2$ mechanism, the hydroxide must attack the carbon atom from the opposite side of the bromine (backside attack). A collision where OH $^-$ strikes a methyl hydrogen, or approaches from the same side as Br, is ineffective regardless of energy. The fraction of geometrically-correct collisions is the steric factor $p$ in the formula $k = pZ_{coll} e^{-E_a/RT}$ .

Symmetric molecules (H $_2$ + Cl $_2$ → 2HCl) have $p$ close to 1 — almost any orientation works.
Reactions at a specific active site (enzyme + substrate, large organic molecule + reagent) have $p$ as small as $10^{-4}$ — only collisions oriented correctly at the active site succeed.

Reaction Rates and Collision Theory

Reaction Rates and Collision Theory

Rate of reaction — definition and units

Measuring rate experimentally

Collision theory — the molecular picture

Activation energy EaE_aEa​

Factors that affect the rate — preview

Orientation requirement — the steric factor

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Activation energy $E_a$