Activation Energy (Ea) Definition

The minimum energy that reacting species must possess for an effective collision to produce the transition state (activated complex) and lead to products.

Energy Profile Diagram

Key Relationships

For any reaction: $\Delta H = E_a(\text{forward}) - E_a(\text{backward})$

For exothermic reactions ($\Delta H$ < 0): $E_a(\text{forward}) < E_a(\text{backward})$

For endothermic reactions ($\Delta H$ > 0): $E_a(\text{forward}) > E_a(\text{backward})$

Effect of a Catalyst

A catalyst creates a new, lower-energy pathway: $E_{a,\text{cat}} < E_a \quad \text{but} \quad \Delta H \text{ unchanged}$

Because catalyst lowers both Ea(fwd) and Ea(bwd) by the same amount: $\Delta H_\text{cat} = E_{a,\text{cat}}(\text{fwd}) - E_{a,\text{cat}}(\text{bwd}) = \Delta H$

Consequences:

• Rate constant k increases (from Arrhenius)
• Equilibrium constant K unchanged ($\Delta G$ unchanged)
• Same equilibrium position, reached faster

Calculating Ea from Activation Energies

If Ea(fwd) = 120 kJ/mol and $\Delta H$ = −40 kJ/mol: $E_a(\text{bwd}) = E_a(\text{fwd}) - \Delta H = 120 - (-40) = 160 \text{ kJ/mol}$