Ozone Depletion Cycles

Objective

The objective of the exercise is to calculate the thermodynamic feasibility of several possible ozone depletion cycles.

Procedure

Stratospheric ozone that protects the earth against harmful ultraviolet radiation is being depleted by the anthropogenic introduction of various gases into the atmosphere. The most destructive ozone depletion processes are catalytic cycles in which trace amounts of gases are able to destroy large quantities of ozone. In this question, you will study the thermodynamic feasibility of two such cycles.

A. The following catalytic cycle has been proposed as the mechanism for ozone depletion by nitric oxide (NO) and nitrogen dioxide (NO2).

O3 + NO ® NO2 + O2 (step 1)
NO2 + O ® NO + O2 (step 2)
O3 + O ® O2 + O2 (overall)

Use PM3 to calculate DfH for each compound involved in the above process. Do not attempt to Clean-Up the molecules, as there are many valence exceptions for these unstable species. After completing each calculation, view the final, optimized geometry to make sure it is reasonable. Enter your results in the first blank column of the following table.

Species Multiplicity Geometry DfHPM3
(kJ/mol)		 DfHlit
(kJ/mol)		 Difference
(kJ/mol)
O3 1 bent 213.6 142.7 70.9
NO 2 - 61.4 90.4 -29
ONO 2 bent -7.9 33.1 -41
O 3 - 249.1 249.4 -.3
O2 3 - -17,6 0 -17.6
CO 1 - -82.7 -110.5 27.8
CO2 1 linear -355.9 -393.7 37.8

In order for the above mechanism to remove ozone effectively, both steps must be spontaneous (DG = DH - TDS < 0). Calculate DrxnH for each reaction by combining the PM3 DfH values. When determining DG, you may assume DS to be approximately zero for each reaction since the number of gas molecules does not change. Enter your results in the following table.

NO Catalysis Reaction DG (=DH)
(kJ/mol)
step 1 -300.5
step 2 -197.4
overall -497.9

Predict whether or not you expect the proposed cycle to be a mechanism for ozone depletion.

It is possible that the proposed mechanism could be a pathway for ozone depletion. Since all steps in the reaction are thermodynamically favorable, each step, and thus the net reaction, will proceed spontaneously. However, the more relevant question is at what rate the reactions occurs, and the atmospheric lifetimes of the species involved. Only this information can tell us if this series of reactions is a significant source of ozone depletion.

B. Write down a catalytic ozone depletion mechanism which involved CO and CO2 instead of NO and NO2. Use PM3 values for DfH to predict whether or not you expect CO and CO2 to remove ozone from the stratosphere by means of your proposed mechanism.

O3 + CO ® CO2 + O2 (step 1)
CO2 + O ® CO + O2 (step 2)
O3 + O ® O2 + O2 (overall)

CO Catalysis Reaction DG (=DH)
(kJ/mol)
step 1 -504.4
step 2 6.5
overall -497.9

This series of reactions cannot be seriously considered a candidate for ozone depletion because it is not thermodynamically favorable. The second step in the reaction will not proceed spontaneously at the temperature in question, and thus the catalytic cycle as a whole will not proceed.

C. This exercise can also be used to assess the accuracy of PM3 calculations. Use the NIST Chemistry WebBook to lookup literature DfH values for the species involved in the above mechanisms. Place these values and the difference between the PM3 and literature values into the last two columns of the table above. Calculate the rms (root mean square) difference between PM3 DfH and the literature DfH values.

rms = [S(DfHPM3 - DfHlit)2/n]1/2 = 37.9 kJ/mol

Observe that to calculate a root mean square of the difference (DfHPM3 - DfHlit), one squares the differences, takes the mean, and then takes the square root. Thus, this formula is very similar to a standard deviation, s = [S(x - )2/n]1/2.

On the basis of this calculation, estimate how accurate PM3 is for determining DfH values.

PM3 is not very good for determining enthalpies of formation. A rms difference of 37.9 kJ/mol is VERY significant in most cases, and thus the values calculated by PM3 should not be used to make comparisons between theoretical and experimental/literature values. However, the values calculated by PM3 are useful qualitatively, and are valid to compare to other PM3 enthalpies of formation.

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