Explaining rate factors with collisions

Key idea: Reaction rate depends on successful collisions per second. Higher temperature makes collisions more frequent and gives a greater fraction of particles enough energy to react.

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Particles react only when they collide with enough energy. Concentration, pressure, particle size and temperature each change the rate of a reaction by changing how often those successful collisions happen.

Compare volume and concentration

Check your understanding 1 More acid, or more concentrated acid?

A bottle contains 1.0 mol/dm³ hydrochloric acid. You pour 50 cm³ into one beaker and 100 cm³ into another. Which beaker has the higher concentration?

Concentration comparison

Show answer
Both are 1.0 mol/dm³. The larger portion has twice the acid amount and twice the volume, so its concentration is unchanged.

Count successful collisions

Reacting particles must collide to react. Not every collision works: a collision leads to reaction only if the particles have enough energy when they meet. The rate depends on the number of successful collisions per unit time.

A change can increase the rate in two ways:

  • the reacting particles collide more often;
  • a greater fraction of the collisions have enough energy to react.

Concentration, pressure and particle size work through the first. Temperature works through both.

The four factors

  1. Higher concentration: there are more reactant particles per unit volume, so collisions occur more frequently and rate increases.
  2. Higher pressure for reacting gases: the gas particles are closer together, so collisions occur more frequently and rate increases.
  3. Smaller solid particles: the same mass has a larger total surface area, so collisions at the solid surface occur more frequently and rate increases.
  4. Higher temperature: particles have more kinetic energy and move faster. They collide more frequently and, more importantly, a greater fraction of collisions have enough energy to react. Both effects increase the rate.

Concentration: more particles per unit volume

Concentration is the amount of solute in a fixed volume of solution. A larger volume of the same acid has the same concentration: it contains more acid particles, but not more per unit volume.

Two runs use the same length of magnesium ribbon (0.048 g) with 50 cm³ of dilute hydrochloric acid at 20 °C. The acid is in excess in both. Only the acid concentration changes. Hydrogen volumes are compared at the same temperature and pressure.

Time / s0102030405060
Hydrogen, run A (1.0 mol/dm³ acid) / cm³0203442464848
Hydrogen, run B (0.5 mol/dm³ acid) / cm³0101927344044

Check your understanding 2 Read the data before explaining the difference

Use the table above. Calculate each average rate over 0–10 s in cm³/s. Has run B finished at 60 s? Predict its final volume from the equal magnesium amounts and excess acid.

Unit: cm³/s
Unit: cm³/s
Has B finished at 60 s?
Unit: cm³

Show answer
A: 20/10 = 2.0 cm³/s; B: 10/10 = 1.0 cm³/s. B is still reacting at 60 s but should eventually reach 48 cm³, the same as A. Now follow the model to explain why the initial averages differ.

Worked example 1

Compare two concentrations from raw data

Problem

Use both rows of the table. Which run is faster, what does each run make in total, and why does concentration change the rate?

Show solution step by step
  1. Check the comparison is fair

    Method

    List what changed and what stayed the same.

    Reason

    A difference in rate can be linked to one factor only if everything else was controlled.

    Working

    Answer

    Same magnesium, acid volume and temperature; only the concentration differs.

  2. Compare the same interval

    Method

    Calculate the average rate for 0–10 s in each run.

    Reason

    Use the same initial interval to compare the two runs near their starts.

    Working

    Answer

    A: 20 ÷ 10 = 2.0cm³s⁻¹. B: 10 ÷ 10 = 1.0cm³s⁻¹.

  3. Read the final amounts

    Method

    Look at where each row stops changing.

    Reason

    The final amount depends on how much magnesium there is, not on how fast it reacts.

    Working

    Answer

    A stays at 48 cm³ from 50 s. B is still rising at 60 s; it has the same magnesium, so it will also reach 48 cm³.

  4. Explain with collisions

    Working

    Answer

    Run A is faster. The more concentrated acid has more acid particles per unit volume, so they collide with the magnesium surface more often. There are more successful collisions per unit time, so the rate is higher. Both runs make the same amount of hydrogen.

Check your understanding 3 Twice the acid volume

Two equal magnesium ribbons are fully immersed, with the same exposed surface, in 50 cm³ and 100 cm³ portions of 1.0 mol/dm³ acid at the same temperature. Acid is in excess in both runs. A student predicts that the larger portion gives twice the initial rate and twice the final hydrogen amount. Correct both predictions and explain each correction.

Compare your answer against concentration, successful collisions per unit time and the amount of magnesium that reacts.

Show answer
Both have the same initial rate: the acid concentration is the same, so the same number of acid particles per unit volume can collide with the equal exposed magnesium surfaces. Doubling the acid volume does not double successful collisions per unit time at those surfaces. Both fully use equal magnesium amounts and therefore give the same final hydrogen amount, measured at the same temperature and pressure. The extra acid remains unused.

Pressure: crowd reacting gas particles together

Compressing the same amount of reacting gas at constant temperature raises its pressure and puts more reactant particles in each unit volume. This is the gas version of increasing concentration. A liquid hardly compresses under ordinary laboratory pressure changes, so the concentration of dissolved reactants changes very little. Pressure does not appreciably change the rate of a reaction between solutions by this collision-frequency mechanism.

Guided practice 2

Where does pressure matter?

About 5 min

Problem

Nitrogen monoxide reacts with oxygen: 2NO(g) + O₂(g) → 2NO₂(g). The same amounts of the two gases are kept at 100 kPa in one container and at 200 kPa in a smaller container, at the same temperature. Decide, for each reaction below, whether a higher pressure would increase the rate.

Look at the state of each reactant

Nitrogen monoxide with oxygen
Hydrochloric acid with sodium hydroxide solution
Marble chips with hydrochloric acid, which gives off carbon dioxide

Hints

Hint 1

state symbols

Read the state symbol of every reactant.
Hint 2

product

A gas that is made is a product, not a reacting particle.
Show solution step by step
  1. Gaseous reactants

    Method

    Apply the pressure effect to nitrogen monoxide and oxygen.

    Reason

    Doubling the pressure of the same amount of gas halves its volume, so the particles are twice as crowded.

    Working

    Answer

    More gas particles per unit volume → more frequent collisions → higher rate.
  2. Solutions and solids

    Working

    Answer

    An ordinary increase in pressure does not appreciably change the rate of the other two reactions by this mechanism: their reactants are solutions and a solid. Giving off a gas does not make pressure a factor.

Particle size: expose more solid surface

Only particles at the surface of a solid can collide with the other reactant, so exposing more surface makes collisions more frequent. Cutting a solid exposes new faces only if the pieces are separated so the other reactant can reach them.

Check your understanding 4 Predict the exposed area

A solid cube has edge length 2 cm. Cut it into eight separate cubes, each with edge length 1 cm, so acid can reach every face. Use six faces per cube: total area = number of cubes × 6 × edge length². Calculate the area before and after cutting, then compare with the diagram.

Show the steps Optional working
Unit: cm²
Unit: cm²
Show the steps Optional working
Unit: cm²
Unit: cm²

Show answer
Before: 1 × 6 × 2² = 24 cm². After: 8 × 6 × 1² = 48 cm². The total volume remains 8 cm³, so the same mass exposes twice the area. Cutting does not add any marble or give its particles more energy.

Compare the separated cube surfaces

Same mass of solid, more exposed surfaceBefore cutting, one cube has edge length 2 centimetres, volume 8 cubic centimetres and total surface area 24 square centimetres. After cutting and separating the pieces, eight cubes each have edge length 1 centimetre. Their total volume is still 8 cubic centimetres, but their total surface area is 48 square centimetres. Each cube has six faces; only three are visible in this drawing. The new faces must be accessible to acid; touching pieces hide part of their surface.Before: one cubeedge length 2 cm6 × (2 × 2) = 24 cm²volume = 2³ = 8 cm³After: eight separate cubeseach edge length 1 cm8 × 6 × (1 × 1) = 48 cm²total volume = 8 × 1³ = 8 cm³Same mass; twice the surface area
Cutting a 2 cm cube into eight separate 1 cm cubes doubles its total surface area while keeping its volume and mass unchanged.

Try it yourself 3

Explain a surface-area effect

Minimal support

Problem

Two 5.0 g samples of the same marble powder are treated with excess acid of the same concentration and temperature. Sample A is spread out so acid can reach each grain. Sample B is pressed into a tight pellet, so acid initially reaches only its outside. Predict which has the faster initial reaction and explain why equal grain size can still give different rates.

Build the surface-to-rate chain

Hints

Hint 1

same mass

The amount of marble is controlled; focus on how much solid is exposed.
Show solution step by step
  1. Compare exposed marble

    Method

    Compare the surface the acid can actually reach.

    Reason

    Pressing grains together hides surfaces inside the pellet, even though the grain sizes and total masses match.

    Working

    Answer

    A has more initially accessible surface than B.
  2. Connect exposure to rate

    Method

    Increase collisions at the marble surface per unit time.

    Reason

    More exposed sites allow acid particles to meet marble particles more frequently.

    Working

    Answer

    A has more successful collisions per unit time and a faster initial reaction. Grains of the same size do not mean the same surface is open to the acid.

Temperature: more collisions can succeed

Temperature is the only factor here that works in both ways: particles collide more often, and a greater fraction of collisions have enough energy to react. An answer that gives only the first is incomplete.

Spot the mistake 4

“More collisions” is not the whole answer

About 4 min

Two answers

Two students explain why a reaction is faster at 50 °C than at 20 °C. P: “The particles move faster, so they collide more often. More collisions per second means a faster rate.” Q: “The particles have more kinetic energy on average and move faster, so they collide more often. More importantly, a greater fraction of the collisions have enough energy to react. There are more successful collisions per unit time, so the rate is higher.” Which answer is complete, and what is missing from the other?

Compare the two answers

Complete answer
Missing from the other answer

Show solution step by step
  1. Test answer P

    Method

    Check what P says about each collision.

    Reason

    P counts collisions but says nothing about whether they have enough energy to react.

    Working

    Answer

    P: faster particles → more collisions. Only part of the account.

  2. Accept answer Q

    Working

    Answer

    Q adds the main effect: a greater fraction of collisions have enough energy, so there are more successful collisions per unit time.

Exam-style question 1

Explain the temperature effect

4 marks

Examination question

A reaction is faster at 40 °C than at 20 °C. Explain this difference using the G3 Science particle model. [4 marks]

Build a linked particle explanation

Show solution step by step
  1. Change particle motion

    1 mark

    Method

    State that reacting particles move faster at the higher temperature.

    Reason

    Heating increases their motion.

    Working

    Answer

    higher temperature → faster-moving particles

  2. Change encounters

    1 mark

    Method

    State that particles meet more often.

    Reason

    Faster motion produces more collisions in a given time.

    Working

    Answer

    faster motion → more collisions

  3. Explain successful collisions

    1 mark

    Method

    State that a greater fraction of collisions have enough energy to react.

    Reason

    Heating increases particle kinetic energy; more encounters alone are not the complete account.

    Working

    Answer

    higher kinetic energy → greater fraction of collisions able to react

  4. Reach the rate

    1 mark

    Method

    Conclude that reactant is used or product is formed more quickly.

    Reason

    More successful collisions per unit time increase the measured rate.

    Working

    Answer

    more successful collisions per unit time → higher rate

Build a clear explanation

A full explanation states the factor that changed, its effect on the reacting particles, and how that gives more successful collisions per unit time. For temperature, give both reasons: the particles collide more often, and a greater fraction of collisions have enough energy to react.

  • Saying a larger volume of acid means a higher concentration. Concentration is particles per unit volume.
  • Saying pressure affects a reaction between solutions. Pressure is a rate factor here only when reacting particles are gases.
  • Saying smaller solid particles have less mass when the experiment uses the same total mass.
  • Explaining temperature with “more frequent collisions” alone.
  • Crediting one factor when the comparison changed two.

Check your understanding 5 Cut a cube

A 3 cm cube of marble is cut into twenty-seven 1 cm cubes, which are separated so acid can reach every face. Calculate the total surface area before and after, then explain what happens to the rate with the same acid.

Show answer

Before: 6 faces × (3 cm × 3 cm) = 54 cm². After: 27 cubes × 6 faces × (1 cm × 1 cm) = 162 cm². The mass is unchanged but the surface area triples. More marble is exposed, so acid particles collide with it more often, giving more successful collisions per unit time and a higher rate.

Check your understanding 6 Judge a pressure claim

Nitrogen monoxide and oxygen react in a sealed container of fixed volume. More of both gases is pumped in at the same temperature, which raises the pressure. A student says, “The volume has not changed, so the rate cannot change.” Is the student right? Explain.

Compare particles per unit volume, collision frequency and successful collisions per unit time. Compression is not the only way to crowd reacting gases.

Show answer

No. More gas in the same volume means more gas particles per unit volume: a higher concentration of each reactant. The particles collide more often, so there are more successful collisions per unit time and the rate increases. The pressure rises for the same reason.

Check your understanding 7 A small warming, a large effect

A reaction mixture is warmed from 20 °C to 30 °C at constant volume, with the same reactant amounts. Its rate roughly doubles, but the number of collisions per second rises by only a few per cent. A student writes, “Heating must have increased the concentration.” Correct the student, and explain why the rate rises so much more than the collision frequency.

Compare the small change in collision frequency with the larger change in the fraction that can react. State why the concentration explanation is wrong under the given conditions.

Show answer

Heating does not change the concentration: the same particles are in the same volume. The particles move faster, which gives only slightly more collisions per second. Most of the increase comes from the greater fraction of collisions that have enough energy to react, so successful collisions per unit time rise far more than collisions overall.

Common mistakes

  • Saying particles collide more, without “per unit time”.
  • Explaining a temperature rise only by more frequent collisions, and leaving out the greater fraction with enough energy.
  • Saying a larger surface area gives particles more energy. It gives more particles exposed to collisions.
  • Saying more concentrated solutions make more product, when the question is about rate.

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