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8.1 Rate of reaction

$\mathrm{rate=\frac{change\ in\ reactant\ or\ product\ concentration}{time}}$

Term	Meaning
rate of reaction	change in the amount or concentration of a reactant consumed or product formed per unit time
frequency of collisions	number of collisions between reacting particles per unit time
effective collision	collision with sufficient energy and a suitable orientation, so reaction occurs
non-effective collision	collision with insufficient energy and/or unsuitable orientation, so particles separate without reacting

Reaction rate depends on the frequency of effective collisions, not simply the total collision frequency. Conditions can increase the number of collisions per second, the fraction that meet the energy/orientation requirements, or both.

A collision is not automatically effective, and an effective collision is not defined by high frequency alone. Rate describes change per time; it does not state the final yield or equilibrium position.

Change at constant temperature	Particle-level effect	Rate consequence
increase solution concentration	more reacting particles occupy the same solution volume, so collisions occur more frequently	more effective collisions per second; rate increases
decrease solution concentration	fewer reacting particles occupy the same volume	fewer effective collisions per second; rate decreases
increase gas pressure by decreasing volume	the same gas particles occupy less space and collide more frequently	more effective collisions per second; rate increases
decrease gas pressure by increasing volume	particles are farther apart and collide less frequently	fewer effective collisions per second; rate decreases

At constant temperature, the energy distribution and activation-energy threshold are not changed by concentration or pressure alone. The qualitative rate change is explained by collision frequency and therefore effective-collision frequency.

Pressure is the relevant concentration-like variable for gaseous reactants, not for an incompressible liquid or solid. Do not explain these changes by saying particles move faster: at fixed temperature their average kinetic energy is unchanged.

Data representation	Rate calculation
two concentration–time readings	secant gradient: Δconcentration / Δtime gives average rate over the interval
one point on a concentration–time curve	draw a tangent and calculate its gradient for instantaneous rate
mass, moles or gas volume against time	calculate change/time in the measured quantity, or convert to concentration if the requested rate requires it

Product concentration has a positive gradient; reactant concentration has a negative gradient. Unless a signed derivative is requested, report the positive magnitude of a reactant-consumption rate and state which species was followed.

A product concentration increases from 0.100 to 0.340 mol dm⁻³ between 20.0 s and 80.0 s. The average rate is (0.340 − 0.100)/(80.0 − 20.0) = 4.00 × 10⁻³ mol dm⁻³ s⁻¹.

For a tangent, choose two well-separated points on the straight tangent—not two points on the curve—and calculate vertical change divided by horizontal change. A shallower concentration–time curve means a smaller rate magnitude.

Do not divide by the final clock reading when the interval begins later, mix minutes with seconds, or label mass-loss rate with concentration-rate units. The numerical unit must follow the measured vertical quantity and time unit.

8.2 Temperature, rate and activation energy

Activation energy, Eₐ, is the minimum energy required for a collision to be effective. Colliding particles with energy below Eₐ cannot follow that reaction pathway to products.

Meeting the energy threshold is necessary but does not remove the orientation requirement: particles must also collide in a suitable orientation for the required bonds to rearrange.

Eₐ is an energy barrier, not the reaction enthalpy ΔH and not the average kinetic energy of the particles. An exothermic reaction can still be slow if few collisions overcome a large Eₐ.

Sketch feature	Required representation	Meaning
horizontal axis	particle energy, E	energy increases to the right
vertical axis	number or fraction of particles with energy E	population at each energy
distribution curve	begins at the origin, rises to one peak, then falls with a long tail approaching the axis	particles have a spread of energies, not one energy
total area under curve	fixed for a fixed number of particles	total particle population
vertical Eₐ line	placed to the right of the peak	minimum effective-collision energy
area to right of Eₐ	shade beneath the tail	fraction with energy at least Eₐ

Only the shaded fraction has sufficient energy for an effective collision; a suitable collision orientation is still required. The area, not the height of the curve where it crosses Eₐ, represents the relevant fraction.

Do not make the curve touch the energy axis at a finite high energy, start above the origin, or label the peak as Eₐ. Eₐ is a threshold line and the high-energy tail approaches the axis asymptotically.

On raising temperature for the same particle population	Boltzmann-distribution consequence
particles have greater average speed and kinetic energy	the curve becomes lower and broader and its peak moves to higher energy
total number of particles is unchanged	both curves enclose the same total area and cross
Eₐ for the unchanged pathway is unchanged	the area to the right of the same Eₐ line increases

Faster particles collide slightly more frequently. More importantly, a much larger fraction of collisions now has energy at least Eₐ. Together these effects increase the frequency of effective collisions, so the reaction rate rises.

Lowering temperature reverses the comparison: collision frequency falls and the area beyond Eₐ becomes smaller, so there are fewer effective collisions per second and the rate decreases.

Temperature changes the distribution, not Eₐ. Do not shift the Eₐ line when comparing temperatures for the same mechanism, and do not claim that every collision in the high-energy area reacts because orientation can still be unsuitable.

8.3 Homogeneous and heterogeneous catalysts

A catalyst increases the rate of a reaction without being chemically changed overall. Catalysis occurs because the catalyst provides a different reaction mechanism with a lower activation energy, Eₐ.

Catalyst type	Phase relationship	Typical mechanism location
homogeneous	catalyst and reactants are in the same phase	intermediate species form within the shared phase
heterogeneous	catalyst is in a different phase from the reactants	reaction occurs at active sites on the catalyst surface

At the same temperature, the Boltzmann distribution is unchanged. Draw the catalysed Eₐ line to the left of the uncatalysed Eₐ line: the area to the right of the lower threshold is larger, so a greater fraction of collisions has sufficient energy and effective collisions occur more frequently.

Reaction-pathway feature	Uncatalysed	Catalysed
reactant enthalpy level	same	same
product enthalpy level	same	same
peak / forward Eₐ	higher	lower for the alternative mechanism
ΔH from reactants to products	same	same

On one enthalpy-versus-reaction-progress diagram, use common reactant and product levels and draw two labelled pathways. Measure each forward Eₐ from the reactant level to its own peak; the catalysed peak must be lower, while the product–reactant difference remains unchanged.

A catalyst does not raise particle energies, shift the Boltzmann distribution, change ΔH, or alter the equilibrium constant or equilibrium composition. It is regenerated overall even though it may form intermediates during the mechanism.

8. Reaction kinetics

Exam analysis

Most tested topics

8.1 Rate of reaction

Rate depends on how often collisions are effective

Concentration and gas pressure change effective-collision frequency

Use experimental gradients to calculate average or instantaneous rate

8.2 Temperature, rate and activation energy

Activation energy is the minimum energy for an effective collision

The area beyond Eₐ identifies collisions with sufficient energy

Higher temperature increases effective collisions in two linked ways

8.3 Homogeneous and heterogeneous catalysts

A catalyst changes the mechanism and lowers the activation-energy threshold