What is the activation energy Ea of a reaction whose reaction-rate constant k increases by a factor of 100 upon increasing the temperature from 300K to 400K?

Question

| General Chemistry 2

Accepted Answer

Arrhenius equation: k = Ae^-Ea/RT

Exp 1: reaction-rate constant = k₁ and T₁ = 300K
k₁ = Ae^-Ea/RT1

Exp 2: reaction-rate constant = k₂ = 100 k₁ and T₂ = 400K
k₂ = Ae^-Ea/RT2

k₂ / k₁ = Ae^-Ea/RT2 / Ae^-Ea/RT1

k₂ / k₁ = e^{-E_a/RT₂ + E_a/RT₁}

ln (k₂ / k₁) = $\frac{E_{a}}{R}$ $(\frac{1}{T_{1}} - \frac{1}{T_{2}})$

⇒ E_a =

\frac{\ln 100 \times 8.314}{(\frac{1}{300} - \frac{1}{400})}

= 4.59 x 10⁴ J = 45.9 kJ

Arrhenius equation - 1 | Chemical Kinetics: Mechanisms

General Chemistry 2 - Arrhenius equation - 1