Collision theory — what makes reactions faster — Chemistry

Before this

Gibbs free energy
What is enthalpy
The particle model

This leads to

Factors affecting rate
The Maxwell–Boltzmann distribution
The Arrhenius equation · coming soon

A reaction that wants to happen, and does not

Mix hydrogen and oxygen gas in a balloon. The reaction between them is

2H₂(g) + O₂(g) \to 2H₂O(l) ΔG ⦵ \approx -474 kJ/mol

The Gibbs lecture taught you to read that sign. ΔG^⦵ is very negative, so the reaction is strongly feasible. It can happen by itself. So what happens to the balloon? Make a prediction before you read on.

Predict — hydrogen and oxygen at room temperature

A balloon holds hydrogen and oxygen at room temperature, with no flame, spark or catalyst nearby. What happens? Choose one, then read the explanation.

The four answers students most often give, and the right one.

It explodes at once. Not right. A feasible reaction is not necessarily a fast one.
It turns slowly into water over a day or so. Not right. At room temperature no change can be measured.
Nothing measurable happens, for as long as you wait. Right. The mixture stays unreacted indefinitely, until a flame or spark starts it (LibreTexts).
Nothing happens, because the reaction is not feasible. Not right. ΔG⦵ is strongly negative, so it is feasible. The reason is about speed, not feasibility.

So a reaction can be strongly feasible and still not happen. The Gibbs lecture met the same puzzle twice. Diamond turning into graphite is feasible, yet diamonds last. Making ammonia from nitrogen and hydrogen is feasible at room temperature, yet far too slow to be useful. That lecture ended with a promise: Energetics answers whether a reaction can happen; "Kinetics, the next unit, says how fast." This is the first lecture of that unit.

Here is the difficulty, stated honestly. Feasibility looks only at the start and the end of a reaction. Speed depends on what happens in between, when particles actually meet. So we need a picture of particles meeting. That picture is called collision theory.

Three things that must happen

The particle model says that the particles of a gas or a liquid are always moving and bumping into each other. A reaction between two particles can happen only when they meet. Collision theory says that a reaction needs all three of these:

1. The particles must collide. Particles that never meet cannot react.
2. The collision must have enough energy. The minimum energy that colliding particles need for a reaction is called the activation energy, $E_{a}$ . A gentler collision just makes the particles bounce apart unchanged.
3. The particles must meet the right way round. This is called the orientation of the collision. Even an energetic collision fails if the parts that need to react do not touch.

A collision that meets conditions 2 and 3 is called a successful collision, or an effective collision. Only successful collisions make products.

Now look at how often particles collide. In air at room temperature, a molecule travels only about 68 nm between collisions, and it collides with other molecules several billion times every second. If every collision made products, every reaction between gases would be over in a tiny fraction of a second. The balloon would explode at once. So the important fact is not that particles collide. It is that almost all their collisions fail.

Activation energy: the hill before the valley

Why should a reaction need energy to start, when it gives out energy overall? Think about what has to happen. To make water, the bonds in H₂ and O₂ must start to break before the new O–H bonds can form. Breaking bonds takes energy. For a moment, the atoms are in an awkward, high-energy arrangement: old bonds partly broken, new bonds partly made. This arrangement is called the transition state. It lasts for a tiny moment and cannot be collected.

The enthalpy lecture drew this as a hump on its energy level diagrams. Here it is again, now as the centre of attention.

An energy profile for an invented exothermic reaction. To reach the products, the reacting particles must first climb to the transition state. The height of the climb from the reactants is the activation energy,

E_{a}

. The overall drop from reactants to products is

Δ H

. The two are separate quantities.

A picture to hold in your mind

A boulder rests in a small dip on a hillside, above a deep valley. The valley is lower, so the boulder "wants" to roll down: that is feasibility. But first it must be pushed up over the lip of the dip: that is the activation energy. A push that is too gentle just lets it roll back. The depth of the valley tells you nothing about the height of the lip.

That last sentence matters. A very exothermic reaction can have a high activation energy, like hydrogen and oxygen. A slightly exothermic reaction can have a low one. Feasibility and speed are separate questions, because they depend on different heights in the diagram.

Stop and think

A reaction has $Δ H = - 40$ kJ/mol and $E_{a} = + 75$ kJ/mol, as in the figure. How large is the activation energy of the reverse reaction, from products back to reactants?

Show the answer

Going backwards, the particles start at the products, 40 kJ/mol below the reactants. They must climb all the way to the same transition state: $40 + 75 = 115$ kJ/mol. So the reverse reaction has the larger activation energy. For an exothermic reaction, the reverse barrier is always $E_{a} + ∣Δ H ∣$ . This is one reason why exothermic reactions rarely run backwards on their own.

Meeting the right way round

Energy is not enough on its own. Look at one step in the reaction of methane with chlorine, in which a chlorine atom pulls a hydrogen atom off a methane molecule:

Cl(g) + CH₄(g) \to HCl(g) + CH₃(g)

The new bond is H–Cl. So the chlorine atom must hit the methane molecule at one of its hydrogen atoms, close to the line of the C–H bond. If it hits the carbon side of the molecule, between the hydrogens, the H–Cl bond cannot form, however fast the chlorine atom was moving. Large, awkward molecules have even stricter needs: only a small part of the molecule can react, so most collisions arrive at the wrong place.

The simulation below fires chlorine atoms at a molecule from random directions, with random energies. The green zone shows the directions that are the right way round. The bar shows each collision's energy against the activation energy.

Simulation — which collisions succeed?

Fire one collision at a time and read why it failed or succeeded. Then fire 1000 and compare the counts. Change the activation energy and the width of the right-way-round zone, and see which one cuts the number of successes faster.

Activation energy: 3.0 × the average collision energy

Right-way-round zone: 60° of the full circle

In this simulation, each collision gets a random energy and a random direction. With the activation energy at 3 times the average collision energy and a right-way-round zone of 60°:

Condition	Share of collisions	In 1000 collisions
Enough energy	≈ 5.0%	≈ 50
Right way round	≈ 16.7% (60° of 360°)	≈ 167
Both: successful	≈ 0.83%	≈ 8

Raising the activation energy from 3 to 5 times the average cuts the successful share from about 0.83% to about 0.11%. Halving the zone only halves it.

What should you have seen? Most collisions fail, and most of them fail for lack of energy. Raising the activation energy a little cuts the successes sharply: each extra step on the slider removes most of the ones that were left. Narrowing the zone cuts them more gently, in proportion. In this model the energies follow a simple rule; real particles share their energies in a pattern that a later lecture draws as the Maxwell–Boltzmann curve. But the lesson is the same: the activation energy is the main gatekeeper.

Rate, in one sentence

The rate of reaction is how quickly reactants are used up or products are made. Collision theory says it depends on how many successful collisions happen each second:

Collision theory

A reaction happens only when particles collide with at least the activation energy, $E_{a}$ , and the right orientation.

Rate ∝ (number of collisions per second) × (fraction with energy ≥ $E_{a}$ ) × (fraction with the right orientation)

That is it. That is the whole idea. Anything that changes a reaction's rate must change one of those three factors. The next lectures use this sentence to explain each way of speeding a reaction up: more concentrated solutions and finer powders give more collisions; a higher temperature gives more energetic collisions; a catalyst gives a route with a lower activation energy.

Working with collision theory

Worked Example 1 — Why three conditions?

For each collision between a chlorine atom and a methane molecule, say whether it can react, and why. (a) A fast chlorine atom hits a hydrogen atom end-on. (b) A fast chlorine atom hits the carbon side of the molecule. (c) A slow chlorine atom hits a hydrogen atom end-on.

(a) Enough energy and the right orientation: a successful collision, so HCl and CH₃ form.

(b) Enough energy, but the wrong orientation: the H–Cl bond cannot form, so the particles bounce apart.

(c) The right orientation, but the energy is below $E_{a}$ : the C–H bond does not begin to break, so the particles bounce apart.

Check: only (a) meets both conditions after the collision itself. ✓

Worked Example 2 — How much does the activation energy matter?

Reaction A has $E_{a} = 50$ kJ/mol and reaction B has $E_{a} = 150$ kJ/mol. Both are gases at 25 °C, so their particles have the same spread of energies and collide equally often. Which is faster, and by how much?

A Pre-University formula gives the fraction of collisions with at least $E_{a}$ . At 25 °C it gives about 1 in 600 million for 50 kJ/mol, and about 1 in 2 × 10²⁶ for 150 kJ/mol.

So reaction A has far more successful collisions: about $3 \times 1 0^{17}$ times as many. Tripling the activation energy did not make the reaction three times slower. It made it slower by a factor with eighteen digits.

Put it in time (a rough estimate with simple assumptions). Suppose each molecule collides about 5 billion times a second, and 1 collision in 10 has the right orientation. Then a molecule of A reacts after about 1 second on average. With $E_{a} = 100$ kJ/mol it would take about 20 years. With 150 kJ/mol it would take about 12 billion years, close to the age of the universe.

Check the direction: a higher barrier means fewer energetic enough collisions, so B must be slower. ✓

Worked Example 3 — Reading an energy profile (invented)

On an energy profile, the reactants are at 0 kJ/mol, the transition state at +75 kJ/mol and the products at −40 kJ/mol. Find $E_{a}$ , $Δ H$ , and the activation energy of the reverse reaction.

$E_{a}$ is measured from the reactants up to the transition state: $75 - 0 = 75$ kJ/mol.

$Δ H$ is products minus reactants: $- 40 - 0 = - 40$ kJ/mol, exothermic.

The reverse reaction starts at the products: $75 - (- 40) = 115$ kJ/mol.

Check: reverse $E_{a}$ = forward $E_{a}$ + $∣Δ H ∣$ = $75 + 40 = 115$ . ✓

Worked Example 4 — Why a spark is enough

Return to the balloon from the hook. Why does a single small spark set off the whole mixture?

The spark heats a tiny region strongly. There, many collisions now have at least $E_{a}$ , so some hydrogen and oxygen react.

That reaction is very exothermic. The energy it releases heats the gas around it, so collisions there become energetic enough too. They react, release more energy, and heat the next layer.

So the spark only has to start the reaction once. After that, the reaction supplies its own activation energy, faster and faster: an explosion.

Check: the same reasoning explains why a match must be struck, but then keeps burning by itself. ✓

Three classic mistakes

Trap 1 — "Every collision causes a reaction"

Particles collide billions of times a second, but only a tiny fraction of collisions are successful. A collision must have at least $E_{a}$ and the right orientation. Rate depends on successful collisions, not on all collisions.

Trap 2 — Mixing up

E_{a}

and

Δ H

$E_{a}$ is the climb from the reactants to the transition state. $Δ H$ is the difference between reactants and products. An exothermic reaction still has a positive activation energy, and a large $Δ H$ says nothing about how high the barrier is.

Trap 3 — "Feasible means fast"

A negative $Δ G$ says a reaction can happen by itself. It does not say how quickly. Hydrogen and oxygen, diamond and air, and nitrogen and hydrogen are all feasible mixtures that hardly react at room temperature, because their activation energies are high.

Try it yourself

Work each one on paper first. Open a hint only when you are stuck.

Two gases A and B can react. For each collision, decide whether it can make products, and give the reason. (a) A and B meet head-on with energy above $E_{a}$ , at the reacting parts. (b) A and B meet with energy above $E_{a}$ , but at the wrong parts. (c) Two molecules of A collide with plenty of energy. (d) A and B meet at the reacting parts, with energy just below $E_{a}$ .

Hint 1
Check the three conditions in order: a collision of the right particles, enough energy, the right orientation.

Hint 2
In (c), think about which particles must meet for this reaction.

Full answer
(a) Yes: a successful collision. (b) No: wrong orientation. (c) No: the reaction needs A to meet B. Two A molecules colliding cannot make the product. (d) No: the energy is below $E_{a}$ , and "just below" still fails, because $E_{a}$ is a minimum.
An energy profile (invented) shows the reactants at +20 kJ/mol, the transition state at +150 kJ/mol and the products at +60 kJ/mol. (a) Find $E_{a}$ and $Δ H$ . Is the reaction exothermic or endothermic? (b) Find the activation energy of the reverse reaction. (c) Sketch the profile and label both quantities.

Hint 1
$E_{a}$ is measured from the reactants, not from zero.

Hint 2
The reverse reaction starts at the products and climbs to the same transition state.

Full answer
(a) $E_{a} = 150 - 20 = 130$ kJ/mol. $Δ H = 60 - 20 = + 40$ kJ/mol, so it is endothermic. (b) $150 - 60 = 90$ kJ/mol. Check: for an endothermic reaction, reverse $E_{a}$ = forward $E_{a}$ − $Δ H$ = $130 - 40 = 90$ . ✓ (c) The products sit higher than the reactants, and the hump rises 130 above the reactants.
In a gas (an invented example), each molecule collides 5 × 10⁹ times every second. One collision in 10⁹ has enough energy, and of those, one in 20 has the right orientation. (a) How many successful collisions does each molecule make per second? (b) On average, how long does one molecule wait before it reacts? (c) A change in conditions makes one collision in 10⁸ energetic enough. How long is the wait now?

Hint 1
Multiply the collision rate by both fractions.

Hint 2
If a molecule makes $r$ successful collisions per second, the average wait is $1 \div r$ seconds.

Full answer
(a) $5 \times 1 0^{9} \times \frac{1}{1 0 ^{9}} \times \frac{1}{20} = 0.25$ per second. (b) $1 \div 0.25 = 4$ seconds. (c) Ten times as many energetic collisions gives 2.5 successful collisions per second, so the wait is $1 \div 2.5 = 0.4$ seconds: the reaction is ten times faster. Check: the rate is proportional to the fraction with enough energy. ✓
Paper burns in air with $Δ H$ strongly negative, yet a book can sit on a shelf for a hundred years without catching fire. (a) Use collision theory and the idea of feasibility to explain both facts. (b) Explain why a match held to the corner of a page sets the whole page burning. (c) A student says: "Old books slowly turn yellow and brittle, so paper must be reacting with air after all." Is this a contradiction of your answer to (a)? Explain.

Hint 1
Feasible says "can". The activation energy decides "how fast".

Hint 2
For (b), compare with Worked Example 4. For (c), a high barrier makes a reaction slow, not impossible, and different reactions have different barriers.

Full answer
(a) Burning is feasible, but its activation energy is high. At room temperature almost no collisions between paper and oxygen have enough energy, so the rate is too small to notice. (b) The flame heats one corner so that many collisions there exceed $E_{a}$ . Burning is very exothermic, so the heat released raises the next part of the page above the barrier, and the reaction spreads by itself. (c) No contradiction. Slow yellowing comes from other, slower reactions in the paper, with lower barriers than burning. Collision theory predicts that reactions are slow, not that they never happen. A fraction that is tiny but not zero still adds up over a hundred years.

The bigger idea

Collision theory was put forward by two chemists working separately: Max Trautz in Germany in 1916 and William Lewis in Britain in 1918. Because of the First World War, neither knew of the other's work. The Pre-University lecture on the Arrhenius equation turns their picture into a formula that predicts how rates change with temperature.

The idea has a surprising consequence for you. Your body, your food, your clothes and the paper of your books are all feasible fuels in an atmosphere full of oxygen. Thermodynamics says they "should" burn. They survive because the activation energy is high, so almost no collisions succeed at room temperature. A chemical world without activation energies would have burnt up long ago. Living things go one step further: they use enzymes to lower the barrier for exactly the reactions they need, and only those. Chemists ask two questions about every reaction, "Can it happen?" and "How fast?", because the world depends on both answers.

Key concepts in this lesson

Collision theory says that particles react only when they collide with at least the activation energy and with the right orientation.
The activation energy, $E_{a}$ , is the minimum energy that colliding particles need to react, shown as the climb from the reactants to the transition state on an energy profile.
The activation energy and the enthalpy change are separate quantities, so an exothermic reaction still needs energy to get started.
Only a tiny fraction of collisions are successful, and a small rise in the activation energy cuts that fraction enormously.
The rate of reaction depends on the number of successful collisions per second, so any change in rate must come from more collisions, more energetic ones or better-oriented ones.
A feasible reaction can be extremely slow, because feasibility depends on the start and end of a reaction while the rate depends on the barrier in between.