Coaching Centre
Collision theory, activation energy and catalysts
Collision theory with energy and orientation, activation energy and energy profile diagrams for exothermic and endothermic reactions, the distribution of particle energies, and explanations of how temperature, concentration, surface area and catalysts change the rate.
Flour sitting in a bag is perfectly safe. The same flour blown into the air as a fine dust near a spark can explode with enough force to flatten a mill, and grain dust explosions still kill workers every year. Nothing about the chemistry of starch has changed. What has changed is how many particles can collide with oxygen at once, and that is the heart of collision theory.
Collision theory
For reactant particles to react, they must:
- collide with each other;
- collide with at least a minimum amount of kinetic energy, the activation energy (Ea), so old bonds can start to break;
- collide with the right orientation, so the atoms that need to bond actually meet.
A collision that meets all three conditions is a successful (effective) collision. In a gas at room temperature, each molecule collides billions of times per second, but only a tiny fraction of those collisions succeed. The rate of reaction is the number of successful collisions per second, so anything that raises the collision frequency, or the fraction of collisions that succeed, increases the rate.
Activation energy and energy profile diagrams
An energy profile diagram plots the enthalpy of the reacting system against reaction progress. As two particles collide, their kinetic energy is converted into potential energy as bonds stretch. At the top of the barrier is the transition state (or activated complex), a short-lived arrangement in which old bonds are partly broken and new ones partly formed.
- Ea (forward) = energy of transition state − energy of reactants.
- ΔH = energy of products − energy of reactants: negative for an exothermic reaction, positive for an endothermic one.
- Ea (reverse) = energy of transition state − energy of products = Ea(forward) − ΔH.
On an energy profile, the reactants are at 50 kJ mol⁻¹, the transition state at 210 kJ mol⁻¹ and the products at −40 kJ mol⁻¹. Find Ea(forward), ΔH and Ea(reverse), and state whether the reaction is exothermic.
Ea(forward) = 210 − 50 = 160 kJ mol⁻¹
ΔH = (−40) − 50 = −90 kJ mol⁻¹, so the reaction is exothermic.
Ea(reverse) = 210 − (−40) = 250 kJ mol⁻¹. Check: Ea(forward) − ΔH = 160 − (−90) = 250 kJ mol⁻¹.
The size of Ea, not ΔH, controls the rate. Petrol and oxygen release a huge amount of energy (very negative ΔH) yet sit together in a fuel tank without reacting, because Ea is high. A spark supplies enough energy to get some molecules over the barrier; the energy released then keeps the reaction going.
Not every particle has the same energy
At any temperature the particles have a range of kinetic energies. The graph of number of particles against kinetic energy (the Maxwell–Boltzmann distribution) has a long tail to the right. Only the particles in the shaded tail, beyond Ea, can react when they collide.
The total area under each curve is the same, since the number of particles hasn't changed. Year 12 (Chemistry lesson 5D) uses this graph again to explain how equilibria respond to temperature.
Explaining the factors
| Factor | Collision theory explanation |
|---|---|
| Concentration (or pressure of a gas) | More particles per unit volume, so more collisions per second. The fraction with enough energy is unchanged. |
| Surface area | Only particles at the surface of a solid can collide. Smaller pieces expose more particles, so more collisions per second. |
| Temperature | Particles move faster, so they collide slightly more often; much more importantly, a far larger fraction of collisions have energy ≥ Ea. |
| Catalyst | Provides an alternative pathway with a lower Ea, so a larger fraction of collisions succeed at the same temperature. |
The temperature effect is the one HSC markers probe most. A 10 °C rise near room temperature raises the average speed of particles by less than 2%, yet it can double the rate. The collision frequency can't explain that; the growth in the energetic tail does.
For a reaction with Ea = 50 kJ mol⁻¹, the fraction of collisions with enough energy is about 8.9 × 10⁻⁹ at 298 K and 1.7 × 10⁻⁸ at 308 K. By what factor does the rate increase?
Ratio = 1.7 × 10⁻⁸ ÷ 8.9 × 10⁻⁹ ≈ 1.9. The rate almost doubles, even though the average kinetic energy rises by only 308 ÷ 298 = 1.03 times (3%).
So: a small rise in average energy pushes a much larger proportion of particles past Ea. This is the explanation markers want.
- With Ea = 50 kJ mol⁻¹ at 298 K, read the fraction of collisions with enough energy (8.9 × 10⁻⁹) and the rate ratio for +10 K (× 1.90).
- Raise Ea to 100 kJ mol⁻¹. What happens to the fraction, and to the rate ratio for a 10 K rise? Reactions with higher Ea are more sensitive to temperature.
- Return to 50 kJ mol⁻¹ and add the catalyst. The new path has Ea = 30 kJ mol⁻¹. By roughly what factor does the fraction of successful collisions rise? Has ΔH changed?
- Drag ΔH to +40 kJ mol⁻¹. The diagram now shows an endothermic reaction. Read the reverse activation energy from the top-right label.
Catalysts
A catalyst increases the rate of a reaction without being consumed. It works by providing an alternative reaction pathway with a lower activation energy. It speeds up the forward and reverse reactions equally and doesn't change ΔH or the amount of product.
- Heterogeneous catalysts are in a different state from the reactants, usually a solid with gases or solutions. Reactant molecules adsorb onto the surface, where bonds are weakened and the molecules are held in a favourable orientation. Examples: MnO₂ decomposing H₂O₂; iron in the Haber process; platinum, palladium and rhodium in a car's catalytic converter.
- Homogeneous catalysts are in the same phase as the reactants, such as H⁺ ions catalysing the formation of esters (Year 12 Module 7).
- Enzymes are protein catalysts in living things. Catalase in liver decomposes hydrogen peroxide millions of times faster than with no catalyst.
Because the catalyst is regenerated, a small amount can be used over and over. That is why so much industrial chemistry depends on them: lower temperatures save energy and money.
Test yourself
An energy profile shows reactants at 30 kJ mol⁻¹, the transition state at 140 kJ mol⁻¹ and products at 80 kJ mol⁻¹. What is the activation energy of the reverse reaction?
140 − 80 = 60 kJ mol⁻¹.
Which statement best explains why increasing the temperature increases the rate of a reaction?
Ea doesn't change with temperature; the energy distribution does.
Which change would NOT increase the rate of reaction between zinc granules and hydrochloric acid?
The concentration, and so the collision frequency, is unchanged by adding more of the same solution.
A catalyst is added to a reaction at equilibrium. Which property of the reaction changes?
The catalysed pathway has a lower Ea; everything else stays the same.
Label the energy profile diagram.
Label the energy distribution graph.
Which effect does each change mainly have?
The minimum energy needed for a collision to be successful is the . The high-energy arrangement at the top of an energy profile is the . Colliding particles must also have the correct . A catalyst provides an alternative and is not .
A catalytic converter contains platinum and rhodium on a honeycomb support with a very large surface area. It converts CO and NO in car exhaust into CO₂ and N₂. Using collision theory and an energy profile diagram, explain how the converter increases the rate of these reactions, and why the large surface area and the high exhaust temperature both help.
Platinum and rhodium are heterogeneous catalysts. CO and NO molecules adsorb onto the metal surface, which weakens their bonds and holds them in positions where they can react. This provides an alternative pathway with a lower activation energy. On an energy profile, the catalysed path has a lower peak than the uncatalysed path, but the reactant and product energies, and so ΔH, are the same.
With a lower Ea, a much greater fraction of collisions between the gas molecules have enough energy to react, so the rate of successful collisions increases. The catalyst is not used up, so a small amount works for years.
The honeycomb support spreads the metal over a very large surface area, so there are many more sites where gas molecules can adsorb and react each second.
The hot exhaust means the molecules have a higher average kinetic energy, so a greater proportion of them have energy at or above even the lowered Ea, and they collide with the surface more often. That is why converters work poorly for the first minute after a cold start.