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}.
