Why some reactions race and others crawl: collisions, energy and catalysts

How to use this simulation

1. Press Play and watch the box for ten seconds. Two kinds of reactant particles, A and B, bounce around; every flash is a collision that was energetic enough, and it leaves behind a green C particle.
2. Look at the right-hand graphs. The top one is the spread of collision energies with a dashed red line at the activation energy; the green area beyond the line is the share of collisions that can react. The bottom one is the product made against time.
3. Drag the temperature slider up. The green share grows, the flashes come faster and the product curve steepens. Notice that the number of collisions per second changes only a little, while the successful ones jump.
4. Tick the catalyst box. The dashed line slides left to a lower activation energy, the green area widens at once, and the old position stays on the graph as a grey line so you can see what moved.
5. Change the concentration slider. The run restarts with more or fewer particles, and your previous product curve stays on the graph as a dashed grey line to compare against. Press Reset to clear it.

Why milk goes off on the counter but lasts in the fridge

Leave a glass of milk on the kitchen counter in summer and by evening it smells sour. Put the same milk in the fridge and it stays fresh for days. The chemistry did not change: the same bacteria, the same sugars, the same reactions. Only the speed changed. That speed is what this page is about.

Once you start looking, rates are everywhere. An effervescent tablet vanishes in a glass of hot water in half a minute but drags on in cold water. An iron nail takes years to rust, yet iron wool glows and burns when you light it. A pressure cooker cooks lentils in a quarter of the time of an open pot. Same ingredients, wildly different speeds.

The questions worth asking are simple. Why does heating speed things up? Why does crushing a solid help? What does a catalyst actually do, and why is it not used up? Collision theory answers all three with one picture: tiny particles bumping into each other, and only the hardest bumps counting. The simulation above lets you turn each knob and see that picture respond.

From zero: what is the rate of a reaction

A chemical reaction is not instant. Reactants turn into products over some stretch of time, and the amounts change as it goes. Some reactions finish in a blink, like silver nitrate solution meeting salt solution and turning cloudy white at once. Others take years, like the slow rusting of a gate. The rate of reaction tells you how fast, as a number.

Because the amounts change, we describe the rate by how quickly a concentration changes. Concentration is the amount of a substance in a litre of mixture, in mol L⁻¹. If the concentration of a reactant falls, that is a consumption; if the concentration of a product rises, that is a formation. The rate is the size of the change divided by the time it took.

Collision theory in plain words

Collision theory says a reaction can only happen when reactant particles hit each other. Two molecules that never meet cannot react. That alone explains why a gas at higher pressure or a solution at higher concentration reacts faster: there are simply more meetings per second.

But most meetings do nothing. At room temperature, billions upon billions of collisions happen every second in a flask, and still the reaction might take minutes. The theory therefore adds two more conditions for a collision to count as effective.

• The particles must collide. No contact, no reaction.
• The collision must carry at least the activation energy. A gentle bump just makes the particles bounce apart, unchanged.
• The particles must meet in the right orientation. A molecule has a reactive end, and hitting it side-on may do nothing even with plenty of energy.

The words you need

Learn these terms first. Most definition questions in exams come straight from this table.

Activation energy: the hill every reaction must climb

Picture a ball that needs to roll over a hill to reach the valley on the other side. Even if the valley is lower, the ball must first be pushed up the hill. For molecules, the hill is the activation energy. Bonds in the reactants have to stretch and start breaking before new bonds can form, and that needs energy, which comes from the kinetic energy of the collision.

In the simulation the hill is the dashed red line on the top graph. A collision whose energy is below the line makes the particles bounce, and a collision above it makes C and a flash. Without a catalyst the line sits at 3.5 RT; with one it moves to 2.0 RT.

Notice what the hill does not tell you. A reaction can be strongly downhill overall (releasing lots of heat) and still be slow, because of a tall hill. Coal burning in air is hugely favourable, yet a lump of coal sits in the air for centuries until a flame lifts a few particles over the hill. Whether a reaction is favourable and whether it is fast are two separate questions.

The energy graph: why a small shift matters so much

Not all particles have the same energy. In any sample, most are near the average, some are slow and a few are very fast. The top graph in the simulation draws how the energies of collisions are spread out, and the thin tail on the right is the small group of collisions that carry a lot.

The area under the curve beyond the activation energy is the fraction of collisions that can react. In the box it is exactly e^(−Ea/RT), and the grey bars behind the curve are the collisions the box actually counted, so you can check the theory against the experiment. At the start settings (300 K, no catalyst) the fraction is 3.0%.

A small change in the position of the line, or the height of the tail, makes a large change in that area, because the tail falls off steeply. This is the secret behind everything else on this page: the rate is controlled by the tail, not by the middle of the crowd.

Factor 1: temperature

Raise the temperature slider and two things happen. The particles move faster, so they collide more often. And a much bigger effect: a larger share of the collisions now carry enough energy to clear the hill. The second effect is the main one.

Factor 2: concentration (and pressure for gases)

More particles in the same space means more meetings per second. If you double the number of A particles, each B particle has twice as many chances to hit an A. If you also double B, there are twice as many B particles to do the hitting. The number of A–B encounters grows with the product of the two numbers.

In the simulation the box has 25 of each at the start, so there are 625 possible A–B pairs. Move the slider to 40 and there are 1,600 pairs, 2.56 times as many, and the collisions per second rise by about the same factor. The fraction above Ea does not change, because temperature and Ea did not change.

For gases, raising the pressure squeezes the same particles into less space, which is the same as raising the concentration. For a pure solid or liquid, concentration does not change (its density is fixed), which is why only the surface matters in the next section.

Factor 3: surface area of a solid

Reactions between a solid and a liquid or gas happen only where they touch, on the surface. A sugar cube dissolves slowly in cold tea, but the same weight of fine sugar disappears in seconds. Crushing does not change what the sugar is. It exposes more of it to the tea.

In terms of collisions, a bigger surface means more places where the other particles can hit the solid. The fraction of successful collisions stays the same and the number of collisions per second goes up, just as it does with a higher concentration. The box here is a mixed gas or solution with no solid in it, so surface area has no slider. The effect works exactly like adding more particles to the box.

Fine powders can be dangerous for the same reason. Flour dust in a mill, coal dust in a mine and the wood dust in a furniture workshop all have a huge surface area, and a spark can set the whole cloud off in an explosion even though a heap of the same stuff would only smoulder.

Factor 4: a catalyst

A catalyst speeds up a reaction without being used up. It does that by offering a different route with a lower activation energy. In the simulation, tick the catalyst box and the dashed line jumps from 3.5 RT to 2.0 RT. The green share of collisions above the line grows from 3.0% to 13.5% at 300 K, about 4.5 times as many successful collisions, with no change in temperature or concentration.

In real life the effect can be enormous, because the Boltzmann factor is so sensitive. Lowering Ea by 25 kJ mol⁻¹ at 300 K speeds a reaction up by a factor of about 2.25 × 10⁴; you will calculate this in the worked problems below. Catalysts you meet in school include manganese dioxide for hydrogen peroxide, iron in the Haber process, vanadium pentoxide for sulfuric acid and the enzymes in your own body.

• A catalyst lowers Ea for both the forward and the reverse reaction, so it speeds both up equally.
• It does not change ΔH. The reactants and products sit at the same energy; only the hill between them is lower.
• It does not change the equilibrium position or the equilibrium constant. It only helps the system get there sooner.
• It is not consumed overall. It may take part in an intermediate step but is regenerated at the end.
• It works only for particular reactions. A catalyst for one reaction may do nothing for another.

Other things that change the rate

Light can start or speed up some reactions. Photographic film and the reaction of hydrogen with chlorine in sunlight both use light energy to break bonds, so photons act as the energy source instead of collisions.

The nature of the reactants matters a great deal. Sodium reacts violently with water; iron barely does. Ionic reactions in solution, such as silver ions meeting chloride ions, are very fast because no bonds need to break, while reactions that must break strong covalent bonds are slow.

The state of the reactants and stirring matter too. Particles in a gas or a stirred liquid meet more often than particles stuck in a solid. A reaction in a well-stirred beaker finishes sooner than in one left still, because the stirring keeps bringing fresh reactant to the surface.

Try it in the simulation

Pick up a notebook and make a prediction before you press anything. Then run the experiment and compare.

• Leave everything at its starting values and read the successful-collision rate and the fraction above Ea after ten seconds. Write both numbers down, then press Reset.
• Raise the temperature to 600 K and compare the collisions per second with the successful collisions per second. Which one changed by more? This shows that heat acts mainly through the tail of the energy curve.
• Lower the temperature to 200 K. Expect a very flat product curve; try the 2× speed button to see anything happen at all.
• Tick the catalyst box in the middle of a run. Watch the product curve bend upward at that moment while the temperature stays put.
• Set the concentration to 40, then back to 10. Use the grey dashed curve of the previous run to see how much sooner the big box finishes.
• Compare the theory fraction with the counted fraction for several seconds. They should agree roughly. If they differ a little, count how many collisions have happened, because a small sample is noisy.

Solved problems

Every number below is computed from the inputs stated at the top of each problem. Follow the steps and then try changing the inputs yourself.

Common mistakes

These are the slips that cost marks every year.

• "A catalyst changes ΔH." No. It lowers the hill, not the energy of the start or the finish.
• "A catalyst shifts the equilibrium." No. It speeds the forward and reverse reactions equally, so the equilibrium position stays where it was.
• "A catalyst is used up." No. It is regenerated; you can recover it unchanged at the end.
• "Higher temperature works only because particles collide more often." It helps a little that way, but the main effect is the larger share of collisions that exceed Ea.
• "Every collision is a reaction." Most are not. Most bounce apart because they lack the energy or the orientation.
• "Rate order equals the coefficient." Orders are found from experiments. Only a single-step reaction has orders equal to its coefficients.
• "Rate stays the same over a whole reaction." It falls as reactants are used up, which is why the product curve flattens.

Where you see this in real life

Food storage is collision theory in the kitchen. A fridge at about 4 °C slows the reactions of bacteria and decay, and a freezer almost stops them. Pressure cookers do the opposite: higher pressure raises the boiling point of water, and the hotter water cooks food in a fraction of the time.

Industry cares about rate as much as yield. The Haber process makes ammonia from nitrogen and hydrogen with an iron catalyst, because without the catalyst the reaction would be far too slow at any practical temperature. Catalytic converters in car exhausts use platinum, palladium and rhodium to turn carbon monoxide and nitrogen oxides into harmless gases within seconds.

Your own body runs on catalysts. Enzymes such as amylase in saliva break starch into sugars in the minute you chew a piece of rice, a reaction that would take days in a test tube without them. Each enzyme works only on its own reaction and works best in a narrow temperature range, which is why a high fever is dangerous.

Safety depends on rate too. Flour mills ventilate dust, miners control coal dust, and pharmacies store some medicines cold, all because surface area and temperature can make a harmless material react far faster than expected.

Exam corner

Exam boards ask rate questions in three ways: a definition or explanation, a graph to interpret, and a short calculation. The points below cover the usual marking schemes for school-leaving exams in many countries.

• Define the rate of reaction, with units, and say what sign convention you used for reactants and products.
• Explain the effect of temperature: more collisions and a bigger fraction of collisions with energy at least Ea. Give the second reason the larger weight.
• Explain how a catalyst works in one sentence: it provides an alternative path with a lower activation energy, so a greater fraction of collisions are effective.
• Draw and label a Boltzmann distribution with Ea marked and the area beyond it shaded. Draw it again for a higher temperature (the peak lower and the tail longer) with the same Ea line.
• Calculate an average rate from a table of concentrations and times. Always keep the units.
• Use the Arrhenius equation, with R = 8.314 J mol⁻¹ K⁻¹ and Ea converted to joules.

Revision summary

Read this five-minute version the night before an exam, and come back to the simulation when any line feels shaky.

• Rate = change in concentration per unit time, in mol L⁻¹ s⁻¹.
• Collision theory: reaction needs collisions with energy at least Ea and the right orientation.
• Fraction with energy at least Ea is proportional to e^(−Ea/RT).
• Temperature: a little more collisions, a much larger fraction above Ea. A common rule of thumb is a doubling per 10 °C.
• Concentration, pressure and surface area raise the number of collisions per second.
• A catalyst lowers Ea, speeds forward and reverse reactions equally, and is not consumed. It does not change ΔH or the equilibrium position.
• The rate falls during a reaction as reactants are used up.

Frequently asked questions