Subscribe $4.99/month

Un-lock Verified Step-by-Step Experts Answers.

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

Our Website is free to use.
To help us grow, you can support our team with a Small Tip.

All the data tables that you may search for.

Need Help? We got you covered.

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Products

Find the Source, Textbook, Solution Manual that you are looking for in 1 click.

For Arabic Users, find a teacher/tutor in your City or country in the Middle East.

Need Help? We got you covered.

Chapter 13

Q. 13.7

Using an Arrhenius Plot to Determine Kinetic Parameters

The decomposition of ozone is important to many atmospheric reactions.

O_{3}(g) → O_{2}(g) + O(g)

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

Temperature (K) Rate Constant (M^{-1} . s^{-1}) Temperature (K) Rate Constant (M^{-1} . s^{-1})
600 3.37×10³ 1300 7.83×10^{7}
700 4.85×10^{4} 1400 1.45×10^{8}
800 3.58×10^{5} 1500 2.46×10^{8}
900 1.70×10^{6} 1600 3.93×10^{8}
1000 5.90×10^{6} 1700 5.93×10^{8}
1100 1.63×10^{7} 1800 8.55×10^{8}
1200 3.81×10^{7} 1900 1.19×10^{9}

Determine the value of the frequency factor and activation energy for the reaction.

Step-by-Step

Verified 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 × 10^{4} K and a y-intercept of 26.8. Calculate the activation energy from the slope by setting the slope equal to -E_{a}/R and solving for E_{a}:
-1.12 × 10^{4}K = \frac{-E_{a}}{R}
E_{a} = 1.12 \times 10^{4} K (8.314 \frac{J}{mol . K})
= 9.31 ×10^{4} J/mol
= 93.1 kJ/mol
Calculate the frequency factor (A) by setting the intercept equal to ln A.
26.8 = ln A
A = e^{26.8}
= 4.36 × 10^{11}
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 × 10^{11} M^{-1} . s^{-1}.

Screenshot 2022-10-08 162636