Physical chemistry
Activation energy and Arrhenius
Activation energy is a kinetic energy barrier; the Arrhenius equation describes the strong increase in rate as temperature rises.
The rate constant varies with temperature as . A plot of ln k against 1/T is approximately linear with slope .
Model and quantities
Read the relation together with assumptions about state, experimental conditions, and sign conventions. Keep units consistent and check dimensions before interpreting a result.
Definition: Activation energy
E_a is the effective energy barrier for reaching reactive configurations; A is the pre-exponential factor, R the gas constant, and T absolute temperature. The model treats these quantities as nearly constant over the range considered.
Quantities in the relation are defined for the reaction or system at hand. In particular, distinguish standard-state quantities from actual conditions and do not infer a mechanism from a general expression alone.
Example: Worked example
A reaction has E_a=50 kJ/mol. Estimate k(310 K)/k(290 K), assuming A is unchanged and R=8.314 J/(mol·K).
Solution
The ratio is ≈ exp(1.35) ≈ 3.9. A 20 K rise nearly quadruples the rate in this model.
| Concept | Description | Unit / note |
|---|---|---|
| Key relation | Use under stated conditions | Check units and sign convention |
| Measured quantity | Relates a state or process | Compare data with model |
| Scope | Model specific conditions | Check assumptions first |
A catalyst often lowers the effective barrier through an alternative mechanism without changing thermodynamic equilibrium. In a simple model, A groups collision frequency and orientation.
In the worked example, which result follows from the given data?
Which statement is consistent with this lesson?
References
- Peter Atkins, Julio de Paula (2014). Physical Chemistry