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

Question

Quizplus · Accepted Answer

The activation energy can be calculated using the Arrhenius equation:k = Ae^(-Ea/RT)where k is the rate constant, A is the pre-exponential factor, Ea is the activation energy, R is the gas constant, and T is the temperature in Kelvin.We can take the natural logarithm of both sides of the equation to get:ln(k) = ln(A) - (Ea/RT)If we plot ln(k) versus 1/T, we will get a straight line with a slope of -Ea/R.We can use the given data to plot the following graph:[Image of a graph of ln(k) versus 1/T]The slope of the graph is -Ea/R = -4.60 x 10^3 K/mol.Therefore, the activation energy is:Ea = -slope x R = -(-4.60 x 10^3 K/mol) x 8.314 J/mol K = 38.2 kJ/molThe closest answer choice is B) 17 kJ/mol.

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

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