## Problems

1. For the oxidation of NO by 02,

the third-order rate constant at 298 K is kt = 2.0 X 10~3X cm6 molecule-2 s_l. (a) What is the effective second-order rate constant at f atm in air? (b) Calculate the half-life for conversion of NO to N02 at 298 K and NO concentrations of O.f, fO, and 10,000 ppm, respectively, at the earth's surface.

2. You see a brown plume starting about 5 m above the exit of a power plant stack and want to estimate the concentration of NO that must be in the plume initially. Assume your eye can detect an effective ab-sorbance (base fO) due to N02 of 0.05 and that all of the N02 is formed by the thermal oxidation of NO by 02 (see Problem 1). Assume the stack is 3 m in diameter and that this determines the effective path length through the plume. Also assume that the vertical plume speed is 1 m s~' and the temperature is 298 K. Take the absorption cross section of N02 to be its peak value in the visible as given in Chapter 4. Estimate the approximate concentration of NO leaving the stack that gives this intensity of absorbance due to NOz. Use the kinetic data given in Problem 1.

3. Derive the Leighton relationship, Eq. (A), in terms of the ratio [N02]/[N0] and its modification for the oxidation of NO by H02 and R02.

4. (a) Calculate the rate constant for the OH + N02 reaction at 1 atm and 300 K, using the DeMore et al. (1997) recommended values of k() and /cx given in the text.

(b) By how much does the rate constant change when the conditions are 250 K and 2 Torr total pressure, as might be found at 40 km in the stratosphere, for example?

5. (a) Using the data in Fig. 4.13 and Table 4.12, calculate the lifetime of HN03 with respect to photolysis at a solar zenith angle of 0° at the earth's surface and at an altitude of 40 km on July 1. Comment on the significance of the difference in photolysis rates and lifetimes.

(b) A typical peak OH concentration in the troposphere could be about 5 X 106 radicals cm~3 at noon and about 1 X 105 cm-3 at sunrise or sunset. Using the kinetics for the OH + HN03 reaction in Eq. (D), calculate the lifetime of HN03 with respect to this reaction at noon and at sunrise or sunset, respectively, at 298 K. How does this compare to the rate of photolysis at a solar zenith angle of 0°?

6. Using the kinetics for the OH + NO reaction discussed in this chapter, estimate the steady-state concentration of HONO that would exist at noon at the earth's surface if the OH radical concentration is 5 X 106 radicals cm~3, the NO concentration is 1 ppb, and the photolysis rate constant for HONO is 1.4 X 10~3 s_1.

7. Use the kinetics parameters for the OH + N02 reaction reported by Brown et al. (1999a) to compare the overall rate constants for this reaction at temperatures and pressures of (a) 300 K and f atm and (b) 220 K and 20 Torr to those calculated using the DeMore et al. (1997) recommendation (see Problem 4).

8. Compare the values for the rate constant of the OH + HN03 reaction at 220 K and 100 Torr total pressure using Eq. (D) based on the DeMore et al. (1997) recommendations to that of Eq. (E) based on subsequent studies (Brown et al., 1999b).

9. As discussed in Chapter 6.J.3, the ratio NO^/NO measured in the upper troposphere is larger than predicted by many models. One potential factor is uncertainties in the reaction kinetics involving these species. Consider only the following two reactions:

Assume HN03 is in a steady state. Calculate the ratio [N02]/[HN03] at a temperature of 300 K and f atm pressure using the DeMore et al. (1997) recommendations and those of Brown et al. (1999a, 1999b). For (a) T = 300 K and P = 1 atm and (b) T = 220 K and P = 150 Torr, characteristic of the lower stratosphere/ upper troposphere, would the revised kinetics be expected to bring the measurements and models into better agreement?

10. The rate of photolysis of N02 at Raleigh, North Carolina (35.8°N, 78.6°W) between 8 and 9 a.m. on a clear day, October 22, 1975, has been measured to be /(N02) = 3.5 X 10~3 s" 1 (Demerjian et al., 1980). Use the OZIPR model (see Appendix III) to look at the rate of change of the N02 concentration under these conditions. For the purposes of this calculation, set the initial NOz concentration to 100 ppb and make all of the initial NOx in the form of N02. Modify the inputs so that no dilution is occurring and there is no deposition of N02. Be sure to change the output concentrations printed so that NO, N02, and 03 are shown explicitly.

a. Based on the value for /(N02) given above and applying simple kinetics, approximately what concentration of NOz do you expect after this 1 h of photolysis?

b. Compare your calculation in part (a) to the predicted change in N02. How do they compare?

c. You should find that the model predicts relatively little N02 loss compared to your calculated loss in part (a). Why? What could you do to test this hypothesis? Try it! Note: This will require that you edit the meccm.rad file.

d. The Leighton relationship described in your text gives the relationship expected between 03, NO, and NOz in a relatively simple system where a steady state is reached during photolysis. How well do your model calculations agree with the predictions of the Leighton relationship? Why might there be deviations?

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