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D. Energy Changes and Rates of Reaction · Energy Changes and Rates of Reaction

Collision Theory and the Factors That Affect Reaction Rate

D3.5 D2.1 A1.10About 70 minutes
Learning goals
  • I can state the three conditions of collision theory for an effective collision.
  • I can explain, using collision theory, how the nature of the reactants, concentration, surface area, temperature and catalysts affect reaction rate.
  • I can use a Maxwell–Boltzmann distribution to explain why temperature has such a large effect on rate.
  • I can apply rate ideas to everyday situations such as food storage and dust explosions.

Words to know

collision theory
The model that particles must collide, with enough energy and the correct orientation, in order to react.
activation energy (Ea)
The minimum collision energy needed for a reaction to occur.
effective collision
A collision with enough energy and the correct orientation to form products.
orientation
The direction in which particles face each other when they collide.
Maxwell–Boltzmann distribution
A graph showing how the kinetic energies of particles (or collisions) are spread out at a given temperature.

Why does milk last longer in the fridge?

Milk on the counter turns sour in a day or two in summer; in the fridge it lasts over a week. Sawdust floating in the air of a mill can explode, while a solid wooden beam burns slowly. A tablet in hot water fizzes away much faster than in cold water. Each of these is a difference in reaction rate, and one simple model explains all of them: collision theory.

Collision theory

For particles to react:

  1. They must collide. Particles that never meet cannot react.
  2. The collision must have at least a minimum amount of energy, the activation energy (Ea). This energy is needed to start breaking bonds in the reactants. Slow-moving particles just bounce off each other.
  3. The particles must have the correct orientation: the atoms that will form new bonds must come into contact.

A collision that meets all three conditions is an effective collision. In a typical gas at room temperature, each molecule collides billions of times per second, but only a tiny fraction of collisions are effective. The rate of a reaction depends on the number of effective collisions per second.

Effective: C of CO hits an O of NO₂ with enough energyOCONOOCOCO₂ formsNONO formsIneffective: wrong orientation (the O end of CO hits NO₂)COONOCOONOthey bounce apart unchangedIneffective: right orientation but too little energy → they also bounce apart.
For CO + NO₂ → CO₂ + NO, the carbon atom of CO must strike an oxygen atom of NO₂, with enough energy. Wrong orientation, or too little energy, means the molecules just bounce apart.

Five factors that affect rate

1. Nature of the reactants. Reactions that break few or weak bonds are fast; reactions that must break many strong bonds are slow. Reactions between oppositely charged ions in solution (such as forming a precipitate) are often almost instant, because no covalent bonds need to break. More reactive metals (higher in the activity series you met in SCH3U) react faster.

2. Concentration (and pressure for gases). More particles per litre means more collisions per second, and so more effective collisions per second. Compressing a gas increases its concentration in the same way.

3. Surface area. A reaction involving a solid happens only at its surface. Cutting the solid into smaller pieces exposes more particles, so more collisions can happen. That is why powdered sugar dissolves faster than a sugar cube, and why fine dust from flour, grain or sawdust can burn explosively.

4. Temperature. Raising the temperature makes particles move faster, so they collide more often and, much more importantly, more energetically. A larger fraction of collisions have energy at least equal to Ea. For many reactions near room temperature, a 10 °C rise roughly doubles the rate (a rough rule of thumb, not a law).

5. Catalysts. A catalyst provides a different reaction pathway with a lower activation energy, so a larger fraction of collisions are effective. You will study catalysts in detail in the lesson Catalysts and Enzymes.

kinetic energy of collision →fraction of collisionsactivation energy, Ealower temperature, T₁higher temperature, T₂shaded: collisions withenough energy to react
Distribution of collision energies at two temperatures (a sketch, not to scale). At the higher temperature the curve flattens and shifts right, and the area beyond Ea (the fraction of collisions energetic enough to react) grows from the blue area alone (lower temperature) to the blue plus yellow area (higher temperature).

Why temperature has such a big effect

The graph above, called a Maxwell–Boltzmann distribution, shows how collision energies are spread out in a sample. Most collisions have moderate energy; a few have very high energy. Only the collisions in the tail beyond Ea can react.

When the temperature rises, the average energy increases only a little (the absolute temperature goes from 298 K to 308 K, a rise of about 3%), but the tail beyond Ea grows a lot. That is why a modest temperature change can double a reaction rate. The higher the activation energy, the more sensitive the rate is to temperature.

FactorWhat changesEffect on effective collisionsEveryday example
Nature of reactantsbonds to break; chargesreactions needing fewer/weaker bonds broken have more effective collisionspotassium reacts with water faster than magnesium
Concentration / pressureparticles per litremore collisions per seconda fire burns faster in pure oxygen
Surface areaparticles exposed at the surfacemore collisions per secondkindling catches fire faster than a log
Temperaturespeed and energy of particlesmore frequent and many more energetic collisionsfood spoils more slowly in a refrigerator
Catalystpathway with lower Eaa larger fraction of collisions have enough energyenzymes in your saliva start digesting starch
Collision theory explains every rate factor.
Worked example

Example 1: Explaining a rate change

Explain, using collision theory, why zinc powder reacts faster with 1.0 mol/L hydrochloric acid than a single piece of zinc of the same mass.

  1. The reaction can only happen where acid particles collide with zinc atoms at the surface of the solid.
  2. Powder has a much larger surface area than one piece of the same mass, so many more zinc atoms are exposed.
  3. More exposed atoms means more collisions per second between H⁺ ions and zinc atoms, and so more effective collisions per second.

The powder reacts faster because its larger surface area gives more collisions per second, and therefore more effective collisions per second.

Worked example

Example 2: Concentration versus temperature

A student says, "Doubling the concentration and raising the temperature by 10 °C both double the rate, so they work the same way." Explain why they work differently.

  1. Doubling the concentration doubles the number of collisions per second. The fraction of collisions with energy ≥ Ea stays the same.
  2. Raising the temperature increases the collision frequency only slightly. Its main effect is to increase the fraction of collisions with energy ≥ Ea (the shaded tail).
  3. So concentration changes how many collisions occur; temperature mainly changes how many of them are energetic enough.

Both increase the number of effective collisions per second, but by different routes: concentration increases collision frequency, while temperature mainly increases the fraction of collisions with enough energy.

Worked example

Example 3: Using the 10 °C rule of thumb

A reaction takes 120 s at 20 °C. Estimate the time at 40 °C, assuming the rate doubles for every 10 °C rise.

  1. From 20 °C to 40 °C is two 10 °C steps, so the rate increases by 2 × 2 = 4 times.
  2. Time is inversely proportional to rate: 120 s ÷ 4 = 30 s.

About 30 s. (This is only an estimate; the real factor depends on the activation energy.)

Hands-on activity

Glow sticks and temperature

You need: three glow sticks of the same kind and colour, three tall glasses, ice water, room-temperature water, hot tap water (a grown-up pours it), a thermometer, a dark room, and a timer. Safety: never cut or break open a glow stick: the liquids inside irritate skin and eyes. If one leaks, wash your hands and throw it away.

  1. Fill the three glasses with ice water, room-temperature water and hot tap water. Record each temperature.
  2. Activate all three glow sticks at the same moment (bend them until the inner vial cracks, then shake). Put one in each glass.
  3. In a dark room, compare their brightness after 1 minute and again after 30 minutes and 2 hours. (Brightness shows how fast the light-producing reaction is going.)
  4. Leave the cold one in the freezer overnight and compare it the next day with one left at room temperature.

What to look for: the hot one glows brightest at first but fades soonest; the cold one is dim but lasts much longer. Explain with collision theory: at higher temperature, more collisions have enough energy to react, so the chemicals are used up faster. The same idea explains why putting food in the fridge or freezer slows spoilage.

Just for fun

Why don't chemists ever lose an argument about reaction rates?

Because they always have more effective collisions with the facts.

Your turn

1

State the three conditions of collision theory for a reaction to occur.

2

What is an effective collision?

3

Explain why increasing the concentration of acid increases the rate at which it reacts with magnesium.

4

Explain why sawdust can burn explosively but a wooden beam burns slowly.

5

Use the Maxwell–Boltzmann graph idea to explain why a 10 °C rise can double a rate.

6

Why is a precipitation reaction between two ionic solutions usually very fast?

7

A reaction takes 80 s at 25 °C. Estimate the time at 15 °C using the rule of thumb.

More practice: warm-up

1

What is activation energy?

2

Name the five factors that affect reaction rate.

3

Does a refrigerator speed up or slow down food spoilage?

4

Which has more surface area: one 8 cm³ cube or eight 1 cm³ cubes?

5

Does increasing pressure on a gas-phase reaction usually increase or decrease the rate?

More practice: on your own

1

Why does a campfire burn faster when you blow on it?

2

Two reactions have activation energies of 40 kJ/mol and 120 kJ/mol. At the same temperature, which is faster, and which is more sensitive to a temperature increase? Explain.

3

A reaction takes 4.0 min at 30 °C. Using the rule of thumb, estimate the time at 60 °C and at 0 °C.

4

Explain why chewing food thoroughly helps digestion, using a rate factor.

5

Why do some medicines say "Store at room temperature, away from heat"?

Challenge

1

The Arrhenius equation, which you will use in first-year university, says the rate constant is k = Ae^(−Ea/RT). For Ea = 50.0 kJ/mol, find k(35 °C) ÷ k(25 °C). (R = 8.314 J/(mol·K))

2

A 2.0 cm cube of a solid is cut into cubes of 0.50 cm. By what factor does its surface area increase? What does this predict for the initial rate of a reaction at its surface?

3

Grain elevators and flour mills use dust control and spark-proof equipment. Use at least three ideas from collision theory to explain why.

Check your understanding

Quiz

1.

According to collision theory, which collision will lead to a reaction?

2.

Raising the temperature increases reaction rate mainly because

3.

Which change increases rate by increasing surface area?

4.

Which change would NOT increase the rate of Mg(s) + 2HCl(aq) → MgCl₂(aq) + H₂(g)?

5.

Using the rule that the rate doubles for every 10 °C rise, a reaction that takes 60 s at 20 °C would take about how long at 30 °C?

6.

Reactions between oppositely charged ions in solution are usually fast because

For parents and teachers

Big ideas (D3.5, D2.1): particles react only when they collide with enough energy (at least the activation energy) and the right orientation. Concentration, surface area and pressure change how often collisions happen; temperature mainly changes how many collisions are energetic enough; catalysts lower the energy needed; and the nature of the reactants determines how much energy is needed in the first place.

How to help: Do the glow-stick activity together and ask your teen to explain the result in terms of collisions. Point out rate factors in daily life: kindling versus logs, the fridge, chewing food, a bellows on a fire.

Common difficulties:

  • Saying "particles move faster so they react faster" without mentioning energy relative to Ea; the energetic fraction is the key idea.
  • Thinking temperature lowers the activation energy (it does not; a catalyst does).
  • Confusing surface area with concentration.
  • Treating the "doubles every 10 °C" rule as exact.

Activity safety: never cut open a glow stick; a grown-up pours the hot tap water.