Reactions Happen in Collisions
The collision model explains rates at the particle level. Reactant particles move constantly, and a reaction can only happen when the particles whose bonds must rearrange actually meet: a collision.
The rate is set by how many collisions per second succeed, not by the total collisions. Three things decide that count: collision frequency, the fraction of collisions with enough energy, and the fraction correctly oriented. A collision meeting both conditions is an effective collision; all others are ineffective and the particles bounce apart unchanged.
Two Conditions for an Effective Collision
The energy condition. Colliding particles must bring at least the activation energy into the collision. Below it they cannot cross the barrier and separate as reactants again.
The orientation condition. The particles must meet in the correct geometric alignment, so the atoms that must form new bonds are the atoms that touch. This is the steric factor, or orientation factor. In Cl + NOCl → NO + Cl₂, the incoming Cl atom must strike the Cl atom of NOCl, the atom it will bond with; a hit at the nitrogen end fails, however energetic it is.
Both must hold in the same collision: an energetic collision at the wrong angle fails, and a well aligned one with too little energy fails.
Activation Energy: The Threshold
Activation energy, Eₐ, is the minimum energy colliding particles need to react. It is fixed by the reaction and its pathway.
The barrier exists because existing bonds must begin to break before new bonds can form, and breaking bonds costs energy up front, before any energy is released later. So even strongly exothermic reactions need activation energy: methane releases much energy overall, CH₄ + 2O₂ → CO₂ + 2H₂O, yet the mixture needs a spark.
A large Eₐ means a tiny reactive fraction and a slow reaction; a small Eₐ means the opposite. Temperature and concentration never change Eₐ, only how many particles exceed it.
The Maxwell-Boltzmann Distribution of Energies
Particles in a sample do not share one energy. A few have very little, most cluster near the average, and a few sit in a long tail of high energies. Plotting number of particles against energy gives the Maxwell-Boltzmann distribution. The area under the whole curve represents all the particles in the sample, and for a sealed sample it cannot change, whatever happens to the shape.
Eₐ is drawn as a vertical line at the threshold. The area to its right is the fraction of particles with enough energy to react, if they also collide correctly oriented.
Average kinetic energy per mole is (3/2)RT: about 3.74 kJ/mol at 300 K and 7.48 kJ/mol at 600 K. A typical Eₐ of 60 kJ/mol lies far above both, so reaction depends on the small tail of energetic particles, not the average particle.
Temperature: Shifting the Distribution
Heating raises the average kinetic energy in proportion to the kelvin temperature. The curve spreads out: the peak shifts right, lower and broader, while the total area stays the same and the Eₐ line does not move.
The area to the right of the line, the fraction able to react, therefore grows steeply. This is the main reason rates rise so sharply with temperature: speeds grow only with the square root of temperature, a factor of about 1.41 between 300 K and 600 K, but the reactive fraction can multiply several times over. Heated particles also collide slightly more often, but that effect is small beside it.
Concentration, Pressure and Surface Area
Raising concentration puts more particles in the same volume, so collisions per second rise. At fixed temperature the energy and orientation fractions stay the same, so a larger collision count gives proportionally more effective collisions per second. Compressing a gas raises pressure by crowding particles into less volume, the same change as raising concentration.
Only a solid’s surface particles can collide with anything. Grinding exposes far more of them, so powdered magnesium reacts with hydrochloric acid, Mg + 2HCl → MgCl₂ + H₂, far faster than one lump of the same mass.
Catalysts in Collision Terms
A catalyst provides an alternative pathway with a lower activation energy. On the same distribution, its Eₐ line sits further left, so a much larger fraction of particles can react.
The catalyst does not heat the mixture or give particles more energy. It lowers the barrier itself, the one thing temperature and concentration cannot do.
Worked Examples
Example 1: reading a distribution in bins. A sample of 1,000 particles is counted in energy bins of 20 kJ/mol. At 300 K the counts from the lowest bin up are 520, 310, 120, 38 and 12. With Eₐ = 60 kJ/mol, the particles above the threshold fill the top two bins: 38 + 12 = 50, or 5.0%. At 400 K the counts are 280, 300, 220, 120 and 80, again totalling 1,000, and the top two bins hold 120 + 80 = 200, or 20.0%. Heating multiplied the reactive fraction by 4, while the total area stayed at 1,000 particles.
Example 2: counting effective collisions. A mixture produces 2.0 × 10⁶ collisions per second. At 300 K, 5.0% have enough energy and 1 in 20 has the correct orientation, a fraction of 0.050, so effective collisions per second = 2.0 × 10⁶ × 0.050 × 0.050 = 5,000. At 400 K the energy fraction is 20.0%; holding the other factors fixed gives 2.0 × 10⁶ × 0.20 × 0.050 = 20,000 per second, four times as many.
Example 3: doubling concentrations. A mixture of A and B has 4.0 × 10⁵ collisions per second, of which 0.10%, a fraction of 0.0010, are effective: 400 per second. Doubling [A] alone doubles collisions to 8.0 × 10⁵ and effective collisions to 800 per second. Doubling both multiplies collisions by 2 × 2 = 4, giving 1,600 effective collisions per second. Eₐ and the effective fraction never move, because temperature is unchanged.
Example 4: a catalyst moves the line, not the curve. Using the Example 1 distribution at 300 K, a catalysed pathway with Eₐ = 40 kJ/mol places the top three bins above the threshold: 120 + 38 + 12 = 170 particles, or 17.0%, instead of 5.0%. With 5.0 × 10⁵ collisions per second and 1 in 10 correctly oriented, the uncatalysed count is 5.0 × 10⁵ × 0.050 × 0.10 = 2,500 per second and the catalysed count is 5.0 × 10⁵ × 0.17 × 0.10 = 8,500 per second, a factor of 3.4 at the same temperature.
Traps That Cost Marks in Topic 5.5
Heating lowers the activation energy. It never does: Eₐ is fixed by the pathway, and heating only moves more particles past the unchanged threshold.
More collisions automatically means more reaction. Only effective collisions count. A huge collision rate still gives a slow reaction if almost no collision clears Eₐ or arrives correctly oriented.
The area under the curve grows on heating. The area counts the particles and is conserved. The hotter curve is lower and broader precisely because the same area spreads wider.
Doubling concentration makes particles more energetic. At fixed temperature the distribution and the fraction above Eₐ are unchanged; concentration changes only how often particles meet.
A catalyst heats the mixture or energises particles. It does neither: it offers a lower Eₐ, so a larger fraction of ordinary collisions succeeds.
Orientation always takes care of itself. Single atoms have no wrong end, but large, complex molecules must align specific atoms, so the steric factor cuts their effective fraction sharply.
Key Relationships
- Effective collision: energy at or above Eₐ and the correct orientation in the same collision, so products form
- Activation energy Eₐ: the minimum energy colliding particles need to react; fixed by the pathway
- Rate is set by collisions per second, times the fraction with energy at or above Eₐ, times the fraction correctly oriented
- Maxwell-Boltzmann energy plot: total area is the total number of particles and never changes; Eₐ is a vertical line, and the area to its right is the fraction with enough energy
- Heating: curve shifts right, lower and broader; Eₐ stays put and the fraction above it grows steeply
- Concentration, gas pressure and surface area change collisions per second only: the energy fraction and Eₐ stay the same
- Catalyst: an alternative pathway with lower Eₐ, so more particles react at the same temperature