⚗️ Using an Arrhenius Plot to Determine Kinetic Parameters

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Q. The decomposition of ozone is important to many atmospheric reactions.

O3 (g) → O2 (g) + O (g)

A study of the kinetics of the reaction resulted in the following data:

(a) Determine the value of the frequency factor and activation energy for the reaction.
Gas constant: (8.314 J/(mol⋅K)   where 1 J=1 (kg ⋅ m^2)/s^2 )

(b) Use the results of the Arrhenius analysis to predict the rate constant at 298 K.

Solution:

To determine the frequency factor and activation energy, prepare a graph of the natural log of the rate constant (ln k) versus the inverse of the temperature (1 ∕ T).

The plot is linear, as expected for Arrhenius behavior. The best fitting line has a slope of −1.12 × 104 K and a y-intercept of 26.8. Calculate the activation energy from the slope by setting the slope equal to −Ea ∕R and solving for Ea:

Calculate the frequency factor (A) by setting the intercept equal to ln A.

26.8 = ln A
A = e26.8
= 4.36 × 1011

Since the rate constants are measured in units of M−1 • s−1, the frequency factor has the same units. Consequently, we can conclude that the reaction has an activation energy of 93.1 kJ ∕ mol and a frequency factor of 4.36 × 1011 M−1 • s−1.

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