1. Collision Theory and Activation Energy
For a chemical reaction to occur between reacting particles, they must satisfy two essential conditions:
- Particles must collide with kinetic energy equal to or greater than the activation energy (\(E \ge E_a\)).
- Particles must collide with the correct steric orientation.
The minimum kinetic energy required for colliding reactant particles to result in a successful reaction.
2. The Maxwell-Boltzmann Distribution
In any gas or liquid sample, molecular speeds vary across a broad spectrum due to random collisions. The energy distribution is described by the Maxwell-Boltzmann curve:
Mathematical Characteristics
- Starts at the origin \((0,0)\): No molecules have zero kinetic energy.
- Peak of the curve: Corresponds to the most probable energy (\(E_{mp}\)).
- Mean energy: Located slightly to the right of the peak because of the extended high-energy tail.
- Asymptotic tail: The curve never touches the x-axis at high energy because there is no theoretical upper limit to molecular velocity.
- Area under the curve: Represents the total number of particles in the sample.
3. The Effect of Temperature on Reaction Rate
When the temperature of a reaction mixture increases from \(T_1\) to \(T_2\):
- Molecules gain kinetic energy and move faster.
- The distribution curve flattens and broadens; the peak shifts to the right and downwards.
- The total area under the curve remains identical (total particle count is constant).
- The fraction of molecules possessing energy equal to or greater than the activation energy (\(E \ge E_a\)) increases significantly (shaded area expands dramatically).
- Consequently, the frequency of successful collisions increases markedly, producing a sharp rise in reaction rate.
4. Catalysts and Reaction Pathways
A substance that increases the rate of a chemical reaction without undergoing permanent chemical change or being consumed.
Mechanism of Action
A catalyst provides an alternative reaction pathway with a lower activation energy (\(E_{cat} < E_a\)).
On the Maxwell-Boltzmann distribution, the threshold line shifts to the left from \(E_a\) to \(E_{cat}\). A much larger proportion of colliding particles now possess sufficient energy to react successfully upon collision.
5. Practice Questions
Mark Scheme:
- At higher temperature, average kinetic energy increases, shifting the Maxwell-Boltzmann distribution peak right and down. (1 mark)
- A much larger fraction of particles possess kinetic energy equal to or greater than the activation energy (\(E \ge E_a\)). (1 mark)
- Therefore, the frequency of successful collisions increases significantly, far outweighing the small increase in total collision rate. (1 mark)