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For a chemical reaction to occur, reactant particles must collide. But not just any collision will do -- the particles must collide with sufficient energy and in the correct orientation. This is the foundation of collision theory, and it explains why reactions happen at the rates they do.
Collision theory states that a reaction occurs when two conditions are met simultaneously:
The particles must collide with energy equal to or greater than the activation energy (Ea). The activation energy is the minimum energy required to break the bonds in the reactants and initiate the reaction. Collisions with less energy than Ea simply result in the particles bouncing apart unchanged.
The particles must collide with the correct orientation. Even if particles have sufficient energy, the reactive parts of the molecules must be aligned appropriately. For example, in the reaction between an OH⁻ ion and a halogenoalkane, the hydroxide must approach the carbon atom bonded to the halogen -- not some other part of the molecule.
Only collisions that satisfy both conditions are called successful collisions (or effective collisions). The rate of reaction depends on the frequency of these successful collisions per unit time.
The rate of reaction can be expressed as:
Rate = collision frequency × fraction with E ≥ Ea × steric factor
| Factor | What it represents | Affected by |
|---|---|---|
| Collision frequency | Number of collisions per unit time per unit volume | Concentration, pressure, temperature |
| Fraction with E ≥ Ea | Proportion of collisions exceeding the energy barrier | Temperature, catalyst (via lowered Ea) |
| Steric factor | Fraction of collisions with correct orientation | Molecular geometry, complexity |
The steric factor is typically much less than 1 for complex molecules (many possible orientations, few correct) and closer to 1 for simple atoms or small molecules.
The activation energy can be visualised on an enthalpy profile diagram. For an exothermic reaction, the products are at a lower energy level than the reactants, but there is an energy "hump" that the reactants must overcome first. This hump represents Ea.
For an endothermic reaction, the products are at a higher energy level, and the activation energy is measured from the reactant energy level to the top of the energy barrier.
The higher the activation energy, the fewer particles have enough energy to react at a given temperature, and the slower the reaction.
| Reaction | Ea / kJ mol⁻¹ | Relative rate at 298 K |
|---|---|---|
| H₂ + I₂ → 2HI | 170 | Very slow |
| 2NOCl → 2NO + Cl₂ | 100 | Slow |
| C₂H₅Br + OH⁻ → C₂H₅OH + Br⁻ | 90 | Moderate |
| 2NO₂ → 2NO + O₂ | 111 | Slow |
| Enzyme-catalysed reactions | 20--50 | Very fast |
Notice that reactions with Ea below about 40 kJ mol⁻¹ tend to be fast at room temperature, while those above 100 kJ mol⁻¹ are extremely slow without heating or a catalyst.
At any given temperature, the particles in a gas or solution have a range of kinetic energies. Some are moving slowly, some are moving very fast, and most have intermediate energies. The Maxwell-Boltzmann distribution shows the spread of these energies.
Key features of the distribution curve:
This last point is critical: only particles in the shaded region beyond Ea can undergo successful collisions.
The following Mermaid diagram describes the key features:
graph LR
A["Number of<br/>particles"] -->|y-axis| B["Energy"]
B -->|x-axis| C["Curve rises<br/>to peak"]
C --> D["Most probable<br/>energy (Emp)"]
D --> E["Curve tails off<br/>asymptotically"]
E --> F["Ea marked<br/>on x-axis"]
F --> G["Shaded area<br/>right of Ea =<br/>particles that<br/>can react"]
When temperature increases:
Even a modest temperature rise (say 10 °C) can dramatically increase the proportion of particles with energy ≥ Ea. This is the primary reason why increasing temperature increases the rate of reaction -- there are far more particles capable of overcoming the activation energy barrier.
At 300 K, the Boltzmann factor for Ea = 50 kJ mol⁻¹ is:
e^(−Ea/RT) = e^(−50000 / (8.314 × 300)) = e^(−20.05) = 1.97 × 10⁻⁹
At 310 K:
e^(−Ea/RT) = e^(−50000 / (8.314 × 310)) = e^(−19.40) = 3.72 × 10⁻⁹
Ratio = 3.72 × 10⁻⁹ / 1.97 × 10⁻⁹ = 1.89 ≈ approximately doubling
This confirms the "rate doubles for every 10 °C" rule of thumb for reactions with moderate activation energies.
Common misconception: Students often say "increasing temperature simply makes particles move faster." While this is true, the key effect is the change in the shape of the distribution -- the proportion of high-energy particles increases disproportionately. The exponential nature of the Boltzmann factor means small temperature changes produce large changes in the fraction exceeding Ea.
Increasing the concentration of reactants in solution (or increasing the pressure of gaseous reactants) means there are more particles per unit volume. This increases the frequency of collisions, which increases the frequency of successful collisions, and therefore increases the rate.
Note: increasing concentration does not change the proportion of particles with energy ≥ Ea. It only changes how often they collide.
As discussed above, increasing temperature increases the proportion of particles with energy ≥ Ea. It also slightly increases collision frequency (particles move faster), but the dominant effect is the increased proportion above Ea.
For reactions involving solids, breaking the solid into smaller pieces increases the surface area exposed to the other reactant. More surface area means more collisions can occur per unit time. This is why powdered reactants react faster than lumps.
A catalyst provides an alternative reaction pathway with a lower activation energy. On a Maxwell-Boltzmann diagram, this shifts the Ea marker to the left. With a lower Ea, a much larger proportion of particles now have sufficient energy to react -- so the rate increases without changing the temperature.
Importantly, a catalyst:
| Factor | Effect on collision frequency | Effect on fraction ≥ Ea | Effect on rate |
|---|---|---|---|
| Increase concentration | Increases | No change | Increases |
| Increase temperature | Slight increase | Large increase | Large increase |
| Increase surface area | Increases (at surface) | No change | Increases |
| Add catalyst | No change | Effectively increases (lower Ea) | Increases |
| Add inert gas (constant V) | No change | No change | No change |
"A catalyst gives particles more energy." Wrong -- a catalyst lowers the energy barrier; it does not change the energy distribution of particles.
"Increasing temperature increases the activation energy." Wrong -- Ea is a property of the reaction, not of the conditions. Temperature changes the fraction of particles exceeding the fixed Ea.
"At higher temperature, the peak of the Maxwell-Boltzmann curve shifts left." Wrong -- the peak shifts RIGHT (to higher energy). The curve becomes broader and flatter.
"Increasing concentration increases the proportion of particles with energy ≥ Ea." Wrong -- concentration changes collision frequency, not the energy distribution.
"The area under the Maxwell-Boltzmann curve increases at higher temperature." Wrong -- the total area (representing total particles) remains constant. The curve flattens but conserves area.
While collision theory provides a qualitative understanding of reaction rates, the quantitative relationship between concentration and rate is described by the rate equation, which you will study in detail in Lesson 3. For now, understand that collision theory is the conceptual foundation upon which the mathematical treatment of kinetics is built.
The rate of a reaction depends on the frequency of successful collisions -- those with energy ≥ Ea and correct orientation. Temperature affects the energy distribution of particles (exponentially, via the Boltzmann factor); concentration affects collision frequency; surface area affects the number of collisions at the solid surface; and catalysts lower the energy barrier. The Maxwell-Boltzmann distribution is the key tool for understanding why temperature and catalysts have such a dramatic effect on rate.