gen-define-activation-energy-and-give-one-short-worked-example-3d0b

Define activation energy and give one short worked example.

# Activation Energy **Definition:** Activation energy (Ea) is the minimum amount of energy that reactant molecules must possess for a chemical reaction to occur. It represents the energy barrier that must be overcome to break existing bonds and form new ones during a reaction. --- ## Worked Example **Problem:** A reaction has a rate constant of 2.5 × 10⁻³ s⁻¹ at 25°C and 8.9 × 10⁻³ s⁻¹ at 45°C. Calculate the activation energy. **Solution:** Use the Arrhenius equation in its two-point form: $$\ln\left(\frac{k_2}{k_1}\right) = \frac{E_a}{R}\left(\frac{1}{T_1} - \frac{1}{T_2}\right)$$ Given: - k₁ = 2.5 × 10⁻³ s⁻¹ at T₁ = 298 K (25°C) - k₂ = 8.9 × 10⁻³ s⁻¹ at T₂ = 318 K (45°C) - R = 8.314 J/(mol·K) $$\ln\left(\frac{8.9 \times 10^{-3}}{2.5 \times 10^{-3}}\right) = \frac{E_a}{8.314}\left(\frac{1}{298} - \frac{1}{318}\right)$$ $$\ln(3.56) = \frac{E_a}{8.314}(2.11 \times 10^{-4})$$ $$1.27 = \frac{E_a}{8.314}(2.11 \times 10^{-4})$$ $$E_a = \frac{1.27 \times 8.314}{2.11 \times 10^{-4}} = 50,100 \text{ J/mol} = \mathbf{50.1 \text{ kJ/mol}}$$