The rate constant of the reaction O + O₃ → 2O₂ is 7.0 × 10⁵ M^-1 s^-1 at -40°C and 4.8 × 10⁶ M^-1 s^-1 at 25°C. Calculate the activation energy of this reaction.

Question

Quizplus · Accepted Answer

The Arrhenius equation relates the rate constant (k) to the temperature (T) and activation energy (Ea):

k = A * exp(-Ea/RT)

where A is the pre-exponential factor, R is the gas constant (8.314 J/mol*K), and T is the temperature in Kelvin (K).

To solve for the activation energy, we need to take the logarithm of the Arrhenius equation and manipulate it to isolate Ea:

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

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

We are given two sets of rate constants at two temperatures. Using the second equation above, we can solve for Ea:

ln[(4.8 × 10^-16)/(7.0 × 10^-15)] = (-Ea/8.314) * [(1/298) - (1/233)]

Ea = (ln[(4.8 × 10^-16)/(7.0 × 10^-15)]) / [(1/298) - (1/233)] * 8.314

Ea = 17 kJ/mol

Therefore, the best choice is B, with an activation energy of 17 kJ/mol.

The Rate Constant of the Reaction O + O3 →

The Rate Constant of the Reaction O + O₃ →