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Notes · ChemistryUK · A-Levels

Kinetics

Kinetics is the study of how fast reactions go and why. This chapter builds collision theory - that particles must meet with at least the activation energy and the correct orientation - and uses the Maxwell-Boltzmann distribution of molecular energies to explain, in a single unified picture, why concentration, temperature and catalysts all change the rate of a reaction.

4 sections·~13 min reading time·3 competencies·Level Foundation 1 · Standard 2 · Advanced 1

T·0555 / 18
Exam profile
AO1 · State collision theory and describe the shape and features of the Maxwell-Boltzmann distributionAO2 · Explain the effect of concentration, pressure, temperature and catalysts on rate using the distributionAO3 · Interpret rate data and Maxwell-Boltzmann diagrams and evaluate the action of a catalyst
Operators:statedescribeexplainpredictinterpretsketch

basic level

AS-Level requires collision theory, the Maxwell-Boltzmann distribution, and qualitative explanations of the effect of concentration, temperature and catalysts on rate.

higher level

The full A-Level develops this into quantitative rate equations, orders of reaction and the Arrhenius equation in the thermodynamics topic; the collision-theory reasoning here is the foundation.

Depth

Reading depth: In depth

Text

Text size: Standard

Contents · 4 sections▾
  1. Kinetics
    • 01Collision theory and activation energy○
    • 02The Maxwell-Boltzmann distribution◐
    • 03Temperature, concentration and rate◐
    • 04Catalysts and the distribution●
§ 01

Collision theory and activation energy#

●○○FoundationLPAQA 7405 3.1.5.1LPDfE GCE Chemistry - kinetics

Key points

Collision theory explains reaction rate at the level of individual particles: for a reaction to happen, particles must collide, and the collision must be successful. A successful collision has two requirements - the particles must collide with a combined kinetic energy of at least the activation energy EaE_aEa​, the minimum energy needed to start breaking bonds, and they must collide in the correct orientation, so that the reacting parts of the molecules meet. Most collisions do not satisfy both conditions and simply bounce apart unchanged.
The rate of a reaction depends on the frequency of successful collisions per second. Anything that increases either the number of collisions or the fraction of them that are successful will speed the reaction up. Because only a small proportion of collisions have enough energy, the activation energy acts as an energy barrier that controls how fast even a very exothermic reaction proceeds - it is why fuels are stable in air until ignited.
The activation energy is the same quantity marked on the reaction profile from the energetics chapter: the height of the hump above the reactants. A reaction with a low activation energy has many collisions able to surmount the barrier and so is fast; a reaction with a high activation energy has very few and is slow. Catalysts and temperature both work by changing how many particles can clear this barrier.
It is important to separate the two factors that make a collision successful. Increasing concentration, pressure or surface area increases the collision frequency (more collisions per second) but does not change the fraction that has enough energy. Increasing temperature, or adding a catalyst, changes the energy factor - the proportion of collisions with energy ≥Ea\ge E_a≥Ea​. Keeping these two mechanisms distinct is the key to explaining every rate change correctly.
Worked example

Why increasing pressure speeds up a gas reaction

Explain in terms of collision theory why increasing the pressure of a gaseous reaction increases its rate.

  1. 01Effect of pressure on the gas

    Increasing the pressure (at constant temperature) pushes the same number of molecules into a smaller volume, so the molecules are closer together.

  2. 02Effect on collisions

    The concentration of molecules per unit volume rises, so collisions occur more frequently.

  3. 03Effect on rate

    More frequent collisions means more successful collisions per second, so the rate increases (the energy of each collision is unchanged).

Result: Higher pressure raises the concentration of gas molecules, increasing collision frequency and hence the rate.

Exam focus

  • State the two conditions for a successful collision (energy >= Ea and correct orientation).
  • Distinguish clearly between changes that increase collision frequency and changes that increase the fraction of collisions with sufficient energy.

Typical mistakes

  • Giving only the energy condition and forgetting the orientation requirement.
  • Saying a higher concentration gives the particles more energy - it increases collision frequency, not the energy of each collision.

Active revision

Explain, in terms of collisions, why powdered marble chips react faster with acid than a single large lump of the same mass.

Active recall

Recall the key points — then reveal.

Sources: GCE AS and A level subject content for the sciences (Department for Education) · AQA A-level Chemistry 7405 specification (AQA)

§ 02

The Maxwell-Boltzmann distribution#

●●○StandardLPAQA 7405 3.1.5.1LPDfE GCE Chemistry - Maxwell-Boltzmann distribution

Maxwell-Boltzmann distribution with activation energy

Function graph, molecular energies = (x/1.6)*exp(-x/40), 1 marked pointsGraph of molecular energies, roots at x = 0, maximum at (40, 9.197), y-intercept at y = 0, on the interval x from 0 to 25050100150200250246810most probableenergyEamolecularenergiesfraction of moleculeskinetic energy
Fig. 1Only the molecules in the shaded tail beyond Ea have enough energy to react on collision.

Key points

In any sample of gas the molecules do not all have the same energy; they have a wide spread of kinetic energies because of their constant random collisions. The Maxwell-Boltzmann distribution is a graph of the number (or fraction) of molecules against their kinetic energy. Its shape is distinctive: it starts at the origin (no molecule has zero energy), rises steeply to a peak at the most probable energy, then falls away with a long tail towards high energies that never quite reaches the axis.
Two features carry all the meaning. The most probable energy is the position of the peak - the energy that more molecules have than any other. The mean (average) energy lies a little to the right of the peak, because the long high-energy tail pulls the average up. The total area under the curve represents the total number of molecules, and is fixed for a given sample - a crucial fact when comparing curves.
The activation energy is marked as a vertical line well to the right of the peak. Only the molecules in the shaded area beyond EaE_aEa​ - those in the high-energy tail - have enough energy to react on collision. At ordinary temperatures this is a small fraction of the total, which is why most reactions are slow unless helped. The whole of kinetics comes down to explaining how the size of this shaded area changes.
Reading the distribution is a core skill. Because the area beyond EaE_aEa​ is small, any change that increases it (raising the temperature, or lowering EaE_aEa​ with a catalyst) has a large proportional effect on rate - which is why a modest temperature rise can double a reaction's rate. When you sketch the distribution, remember it must start at the origin, never touch the axis at high energy, and (when comparing samples of the same size) enclose the same total area.
Worked example

Reading the distribution

Using the Maxwell-Boltzmann distribution, explain why only a small fraction of collisions lead to reaction at room temperature.

  1. 01Locate the activation energy

    Ea is marked well to the right of the peak of the distribution.

  2. 02Identify the reacting molecules

    Only molecules with energy at or beyond Ea (the shaded tail) can react on collision.

  3. 03Judge the fraction

    At room temperature this tail area is a small fraction of the total area under the curve, so most collisions lack the energy to react.

Result: Only the small high-energy tail of molecules (area beyond Ea) has enough energy, so most collisions are unsuccessful and the reaction is slow.

Exam focus

  • Sketch the Maxwell-Boltzmann distribution correctly (through the origin, peak, long tail not touching the axis) and mark the most probable energy and Ea.
  • Identify the shaded area beyond Ea as the molecules able to react, and explain why it is small at ordinary temperatures.

Typical mistakes

  • Drawing the curve starting above the origin, or letting the tail touch the energy axis.
  • Placing the mean energy at the peak - it lies slightly to the right because of the high-energy tail.

Active revision

On a sketch of the Maxwell-Boltzmann distribution, mark the activation energy and shade the region representing the molecules that can react, then explain why raising the activation energy would slow the reaction.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Chemistry 7405 specification (AQA)

§ 03

Temperature, concentration and rate#

●●○StandardLPAQA 7405 3.1.5.1LPDfE GCE Chemistry - factors affecting rate

The distribution at two temperatures

Function graph, lower T = (x/1.6)*exp(-x/40); higher T = (x/4.9)*exp(-x/70)Graph of lower T, roots at x = 0, maximum at (40, 9.197), y-intercept at y = 0, on the interval x from 0 to 280, Graph of higher T, roots at x = 0, maximum at (70, 5.255), y-intercept at y = 0, on the interval x from 0 to 28050100150200250246810Ealower Thigher Tfraction of moleculeskinetic energy
Fig. 2At higher temperature the peak is lower and shifted right, and more molecules lie beyond Ea, so the rate rises steeply.

Key points

Raising the temperature increases rate for two reasons, but one dominates. The molecules move faster, so collisions are slightly more frequent; far more importantly, the whole Maxwell-Boltzmann distribution shifts to higher energies and flattens, so a much larger fraction of molecules now has energy ≥Ea\ge E_a≥Ea​. The area of the high-energy tail beyond EaE_aEa​ increases sharply, so the proportion of successful collisions rises steeply. This energy effect, not the small increase in collision frequency, is the main reason a roughly 10 ∘C10\ ^{\circ}\text{C}10 ∘C rise can double the rate.
When two Maxwell-Boltzmann curves are drawn for the same sample at different temperatures, the higher-temperature curve has a lower, broader peak shifted to the right, but encloses the same total area (the number of molecules is unchanged). The two curves cross once; to the right of EaE_aEa​ the higher-temperature curve lies above the lower, showing the greater fraction able to react. Drawing this comparison correctly - same area, lower and broader at higher temperature - is a frequent exam requirement.
Increasing the concentration of a solution, or the pressure of a gas, increases the number of particles in a given volume, so collisions happen more often. This raises the collision frequency and hence the rate, but it does not change the shape of the energy distribution or the fraction of collisions with enough energy - the individual collisions are no more energetic. The same is true of increasing the surface area of a solid, which exposes more particles for collision.
Keeping the mechanisms straight is what earns full marks: temperature changes the energy distribution (more molecules exceed EaE_aEa​), whereas concentration, pressure and surface area change the collision frequency (more collisions, same energy spread). A complete answer names the factor, states which mechanism it affects, and links that to more successful collisions per second and hence a faster rate.
Worked example

Why a small temperature rise doubles the rate

Explain, using the Maxwell-Boltzmann distribution, why raising the temperature from 25 C to 35 C can roughly double the rate of a reaction.

  1. 01Effect on the distribution

    The higher temperature shifts the distribution to higher energies and flattens it, so more molecules have energy >= Ea.

  2. 02Effect on the tail

    Because Ea is far out in the tail, even a small rightward shift greatly increases the fraction of molecules beyond Ea.

  3. 03Effect on rate

    A large increase in the fraction of successful collisions produces a large increase in rate, far outweighing the small rise in collision frequency.

Result: The steep increase in the fraction of molecules with energy >= Ea, not the small rise in collision frequency, roughly doubles the rate.

Exam focus

  • Explain a temperature increase in terms of the shift of the Maxwell-Boltzmann distribution and the increased area beyond Ea.
  • Draw two distribution curves for different temperatures with the same area, the higher one lower, broader and shifted right.

Typical mistakes

  • Attributing the temperature effect mainly to more frequent collisions rather than to more molecules exceeding Ea.
  • Drawing the higher-temperature curve enclosing more area, or with the same peak height.

Active revision

Explain, using the Maxwell-Boltzmann distribution, why increasing the temperature has a much larger effect on rate than increasing the concentration by the same proportion.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Chemistry 7405 specification (AQA)

§ 04

Catalysts and the distribution#

●●●AdvancedLPAQA 7405 3.1.5.1LPDfE GCE Chemistry - catalysts

Catalysed and uncatalysed reaction profiles

Effect of a catalystreaction energy profile, 2 states, activation energy Eₐ = 50, reaction enthalpy ΔH = -30no catalystwith catalystEareactantsuncatalysedproductsenthalpy / kJ mol−1reaction pathway
Fig. 3A catalyst provides a route with a lower activation energy; the reactants, products and delta H are unchanged.

Key points

A catalyst is a substance that increases the rate of a reaction without being used up, by providing an alternative reaction pathway with a lower activation energy. It is regenerated at the end, so only a small amount is needed, and it does not change the products or the enthalpy change ΔH\Delta HΔH of the reaction - only the height of the barrier. Because it lowers EaE_aEa​, a larger fraction of molecules in the Maxwell-Boltzmann distribution now has energy ≥Ea\ge E_a≥Ea​, so more collisions are successful and the rate rises.
On the reaction profile a catalyst lowers the hump: the reactants and products stay at the same enthalpy levels, but the transition state is lower, so both the forward and reverse activation energies fall by the same amount. On the Maxwell-Boltzmann distribution the catalyst is shown by moving the EaE_aEa​ line to the left; the shaded area beyond it grows, representing the extra molecules that can now react. This is exactly the same 'more molecules beyond EaE_aEa​' idea as for temperature, but achieved by lowering the barrier rather than raising the energies.
Catalysts are classified by their phase. A heterogeneous catalyst is in a different phase from the reactants (typically a solid catalysing gas or solution reactions), and works by adsorbing reactants onto active sites on its surface, where bonds are weakened and the reaction proceeds, before the products desorb; iron in the Haber process and platinum in a catalytic converter are examples. A homogeneous catalyst is in the same phase as the reactants (often aqueous), and works by forming an intermediate that then reacts on to give the products and regenerate the catalyst.
The economic and environmental importance of catalysts is examinable. By allowing a reaction to run at a lower temperature and pressure for the same rate, catalysts save energy and cost, and can improve atom economy by favouring the desired product and avoiding waste. When you explain how a catalyst works, always specify that it provides an alternative route of lower activation energy - not that it 'lowers the energy of the reactants' or 'gives the particles more energy', both of which are wrong.
Worked example

How a catalyst increases rate

Explain, referring to the Maxwell-Boltzmann distribution, how adding a catalyst increases the rate of a reaction.

  1. 01Effect of the catalyst

    The catalyst provides an alternative pathway with a lower activation energy, so the Ea line moves to the left on the distribution.

  2. 02Effect on the molecules

    A greater fraction of molecules now has energy >= the lowered Ea (the shaded area increases).

  3. 03Effect on rate

    More collisions are therefore successful per second, so the rate increases, without any change to the products or delta H.

Result: By lowering Ea, the catalyst increases the fraction of molecules able to react, raising the rate while leaving delta H unchanged.

Exam focus

  • Explain how a catalyst increases rate by providing an alternative route of lower activation energy, showing it on a profile and on the distribution.
  • Distinguish heterogeneous (different phase, surface adsorption) from homogeneous (same phase, intermediate) catalysis with examples.

Typical mistakes

  • Saying a catalyst lowers delta H or changes the products - it changes only the activation energy.
  • Claiming a catalyst gives the molecules more energy, rather than lowering the barrier they must clear.

Active revision

Sketch the Maxwell-Boltzmann distribution with two activation-energy lines, one for the uncatalysed and one for the catalysed reaction, and use it to explain how the catalyst increases the rate.

Active recall

Recall the key points — then reveal.

Sources: AQA A-level Chemistry 7405 specification (AQA)

Contents

Section -- / 04

    • 01Collision theory and activation energy○
    • 02The Maxwell-Boltzmann distribution◐
    • 03Temperature, concentration and rate◐
    • 04Catalysts and the distribution●

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Sources

Department for Education

  • GCE AS and A level subject content for the sciences

AQA

  • AQA A-level Chemistry 7405 specification

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