The rate constant of the reaction O + O₃ $\rarr$2O₂ is 7.0 *10⁵ M^-1 s^-1 at -40^$\circ$C and 4.8 * 10⁶ M^-1s^-1 at 25^$\circ$C. Calculate the activation energy of this reaction. A) 2.0 kJ/mol B) 17 kJ/mol C) 1100 kJ/mol D) 25. kJ/mol E) 0.13 kJ/mol

Question

Quizplus · Accepted Answer

We can use the Arrhenius equation to solve for the activation energy:

k = A * exp(-Ea/RT)

Taking the natural logarithm of both sides:

ln(k) = ln(A) - (Ea/RT)

We can then use the given rate constants at two different temperatures to solve for the activation energy:

ln(k2/k1) = (-Ea/R) * [(1/T2) - (1/T1)]

ln[(4.8*10^-10)/(7.0*10^-11)] = (-Ea/8.314) * [(1/298) - (1/233)]

ln[6.86] = (-Ea/8.314) * [0.00425]

Solving for Ea:

Ea = (-ln[6.86] * 8.314)/(0.00425)

Ea ≈ 17 kJ/mol

The Rate Constant of the Reaction O + O3 →\rarr→ 2O2 Is 7

The Rate Constant of the Reaction O + O₃ $\rarr$ 2O₂ Is 7