Effect of Concentration, Pressure, Temperature and Surface Area

Spec Mapping — OCR H432 Module 3.2.2 — Factors affecting rate, covering the qualitative and semi-quantitative explanation of how the rate of a reaction responds to changes in concentration (solutions), pressure (gases), temperature (via both collision frequency and the Boltzmann distribution), and surface area (heterogeneous solid reactants). Each factor is explained using collision theory and, where appropriate, the Maxwell–Boltzmann distribution from Lesson 7 (refer to the official OCR H432 specification document for exact wording).

Lesson 6 established collision theory; Lesson 7 explained the Boltzmann distribution. This lesson applies both to explain quantitatively how four practical variables — concentration, pressure, temperature, and surface area — affect the rate of a chemical reaction. The unifying principle is the collision-theory formula introduced in Lesson 6: $\text{rate} \propto Z_{coll} \cdot f_{E \geq E_a} \cdot p$ , where $Z_{coll}$ is the collision frequency, $f$ is the Boltzmann fraction, and $p$ is the steric factor. Concentration, pressure, and surface area alter $Z_{coll}$ alone (without changing $f$ or $p$ ). Temperature is the dramatic outlier — it raises $Z_{coll}$ modestly (~ $\sqrt{T}$ , so ~ $1.7\%$ per 10 K), but raises $f$ exponentially through the Boltzmann factor (~doubling per 10 K near room temperature). This asymmetry is why temperature is the most powerful "knob" in industrial chemistry, and why the Haber process is run hot rather than cold even though the equilibrium favours low $T$ . By the end of the lesson you should be able to explain every rate-effect in OCR-friendly language ("collision frequency", "proportion of molecules with $E \geq E_a$ ", "more sites available for collision"), interpret classic experimental results (thiosulfate–HCl cross, marble-chips–HCl gas evolution), and combine multiple factors multiplicatively in worked examples.

Key Equation: the collision-theory rate expression: $\text{rate} \propto Z_{coll} \cdot f_{E \geq E_a} \cdot p$ Concentration, pressure, surface area increase $Z_{coll}$ only. Temperature increases $Z_{coll}$ slightly and $f$ exponentially. Catalysts (Lesson 9) reduce $E_a$ and thereby increase $f$ .

Concentration and rate

Increasing the concentration of a reactant in solution increases the rate of a reaction. The explanation is direct collision theory: doubling the concentration doubles the number of particles per unit volume, so the frequency of collisions between reactant pairs doubles. Provided the proportion of effective collisions remains unchanged (same temperature, same $E_a$ ), the rate should approximately double.

In equation form, for many simple reactions the rate is first-order in each reactant: $\text{rate} = k [A][B]$ . We will not formally derive rate equations at A-Level Module 3.2 (that is Year 13, Module 5.1.1), but the qualitative proportionality is well within scope.

Classic experiment — sodium thiosulfate and hydrochloric acid

$\text{Na}_2\text{S}_2\text{O}_3\text{(aq)} + 2\text{HCl(aq)} \rightarrow 2\text{NaCl(aq)} + \text{SO}_2\text{(g)} + \text{S(s)} + \text{H}_2\text{O(l)}$

A milky suspension of colloidal sulfur develops as the reaction proceeds, obscuring a black cross drawn on paper beneath the flask. The time taken for the cross to disappear is inversely proportional to the rate (faster reactions → less time). The data below come from a typical school experiment:

[Na $_2$ S $_2$ O $_3$ ] / mol dm $^{-3}$	Time to obscure cross / s	$1/t$ / s $^{-1}$
0.040	200	0.0050
0.080	100	0.0100
0.120	67	0.0149
0.160	50	0.0200
0.200	40	0.0250

A plot of $1/t$ against $[\text{Na}_2\text{S}_2\text{O}_3]$ is approximately linear and passes through the origin: rate is directly proportional to concentration of the thiosulfate (first-order behaviour).

Best-fit straight line through origin → rate ∝ [Na₂S₂O₃]

Pressure and gas-phase reactions

For gas-phase reactions, pressure plays a role exactly analogous to concentration. From the ideal-gas law $pV = nRT$ , the concentration of a gas at fixed $T$ is $[A] = n/V = p_A / RT$ . Doubling the partial pressure of a gas-phase reactant doubles its concentration, hence doubles its collision frequency. So:

Increasing pressure → higher concentration → more collisions per second → higher rate.
For a gas-phase reaction with multiple gaseous reactants, doubling the total pressure (compressing the system) doubles every reactant concentration and multiplies the rate by $2^n$ where $n$ is the total order of the reaction.

Example: The Haber process, $\text{N}_2\text{(g)} + 3\text{H}_2\text{(g)} \rightleftharpoons 2\text{NH}_3\text{(g)}$ , is carried out at $\sim 200$ atm partly to speed the reaction up (rate effect — this lesson) and partly to shift the equilibrium position toward NH $_3$ (Le Chatelier — Lesson 10).

Important caveat: for reactions between gases and solids (e.g. catalytic cracking, the Contact-process SO $_2$ /V $_2$ O $_5$ reaction), only the gas concentration matters for rate. Increasing pressure on a pure solid has no effect on its "concentration" — the lattice spacing is essentially incompressible. Similarly, for reactions in dilute aqueous solution, raising atmospheric pressure has no perceptible effect.

Temperature and rate — the dominant factor

Temperature is the most dramatic rate-affecting variable because it operates through two simultaneous channels:

Collision frequency $Z_{coll}$ rises modestly with $T$ . Mean molecular speed $\bar{v} \propto \sqrt{T}$ , and $Z_{coll} \propto \bar{v} \cdot n_{density}$ . For an ideal gas at fixed volume, $\sqrt{308/298} - 1 \approx 1.7\%$ over a 10 K rise — a barely measurable change.
The Boltzmann fraction $f_{E \geq E_a}$ rises exponentially with $T$ . As established in Lesson 7, $f \propto e^{-E_a/RT}$ ; near room temperature, this fraction roughly doubles for a 10 K rise. The exponential dominates.

The combined effect: the rate roughly doubles for every 10 K rise in temperature near room temperature, and the dominant contribution (~98%) comes from the Boltzmann factor, not from the collision-frequency rise.

Exam-style explanation of a temperature rise:

"When temperature increases, the particles have greater average kinetic energy. According to the Maxwell–Boltzmann distribution, a greater proportion of molecules now have kinetic energy greater than or equal to the activation energy $E_a$ , so more collisions are effective. Additionally, the frequency of collisions increases because molecules move faster, but this is a much smaller effect. The combined result is that the rate of reaction increases — typically by roughly a factor of two for every 10 K rise near room temperature."

The two-part structure ("Boltzmann argument first, collision-frequency argument second") is the mark-scheme template for a full-mark answer.

Surface area (heterogeneous reactions)

When a solid reacts with a liquid or a gas, only the particles at the surface of the solid can collide with the other reactant. Atoms in the interior of a marble chip are inaccessible until the surface layers have reacted away. Breaking the solid into smaller pieces — or grinding it to powder — increases the total surface area dramatically:

For a single 1 cm cube of marble, surface area = $6 \times 1^2 = 6$ cm $^2$ . Cutting it into 1000 cubes of 1 mm each gives total surface area $1000 \times 6 \times 0.1^2 = 60$ cm $^2$ — ten times larger. Powdering to particles of 10 μm size increases the surface area another 100-fold to ~6000 cm $^2$ . The rate of the heterogeneous reaction increases in roughly direct proportion.

Classic experiment — marble chips and HCl

$\text{CaCO}_3\text{(s)} + 2\text{HCl(aq)} \rightarrow \text{CaCl}_2\text{(aq)} + \text{CO}_2\text{(g)} + \text{H}_2\text{O(l)}$

Large marble chips react slowly; small chips react faster; powder reacts fastest. In each case the same mass of CaCO $_3$ produces the same final volume of CO $_2$ — only the rate changes.

Form of CaCO $_3$	Initial rate (relative)	Final CO $_2$ volume
Large chips	1.0	48 cm $^3$
Small chips	2.1	48 cm $^3$
Powder	4.5	48 cm $^3$

A graph of CO $_2$ volume against time starts steeper (higher initial rate) for powder and levels off earlier, but at the same final volume as for chips. Surface area affects the rate, not the yield.

The graph illustrates the conceptual point: kinetics (curve steepness) and thermodynamics/stoichiometry (final volume) are independent. Doubling surface area doubles the initial rate, but produces the same total volume of CO $_2$ because the same number of moles of CaCO $_3$ is being consumed.

Safety — dust explosions

Finely divided solids — flour, custard powder, sulfur dust, aluminium powder, coal dust — have enormous surface-area-to-mass ratios (sometimes $> 10$ m $^2$ per gram). When suspended in air, they can react with oxygen so rapidly that the energy release is essentially instantaneous, producing a dust explosion. Historically, dust explosions have caused major industrial disasters in flour mills (Washburn A mill, Minneapolis, 1878 — 18 dead), coal mines (Senghenydd, Wales, 1913 — 439 dead), and sugar refineries (Imperial Sugar, Georgia, 2008 — 14 dead). The same chemical reaction that is harmless when the substance is in bulk (a sack of flour, a pile of coal) becomes catastrophic when surface area is maximised. This is a vivid practical illustration of how surface area governs reaction rate, with consequences that are anything but academic.

Worked example — combining factors

Q: A reaction is carried out between zinc metal and dilute HCl. Estimate the initial rate change if you simultaneously: (a) double the HCl concentration, (b) raise the temperature by 20 K, (c) replace granules with fine powder (giving ~5× the surface area).

(a) Concentration doubled: collision frequency doubles, rate approximately doubles (factor of 2).

(b) Temperature $+20$ K: the "doubles per 10 K" rule of thumb applied twice gives rate $\times 2^2 = 4$ . This is the dominant single contribution because the Boltzmann fraction $f \propto e^{-E_a/RT}$ grows exponentially with $T$ .

(c) Powdered zinc: ~5× surface area means ~5× more collision sites at the interface, so the rate rises by approximately a factor of 5.

Combined effect: the factors are multiplicative, not additive. Total rate increase ≈ $2 \times 4 \times 5 = \mathbf{40}\times$ . A reaction that took 40 minutes to complete under the original conditions now takes 1 minute.

This worked example illustrates a key point: variable factors compound. Industrial chemists must therefore think carefully about which lever to push: in many cases, the largest single rate effect for the lowest capital cost is temperature, but this also lifts the position of equilibrium for an exothermic reaction the wrong way (Lesson 10). The Haber process famously operates at "only" $\sim 450$ °C, not higher, despite its huge thermodynamic backward shift, because the rate-vs-yield compromise lies there.

Effect of Concentration, Pressure, Temperature and Surface Area

Effect of Concentration, Pressure, Temperature and Surface Area

Concentration and rate

Classic experiment — sodium thiosulfate and hydrochloric acid

Pressure and gas-phase reactions

Temperature and rate — the dominant factor

Surface area (heterogeneous reactions)

Classic experiment — marble chips and HCl

Safety — dust explosions

Worked example — combining factors

Summary table — all four factors at a glance

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