Problems

1. The rate constants for the reactions of propene with OH, 03, and N03 at 1 atm pressure and 298 K are 2.6 X 10""^ 1.0 X 10"17, and 9.5 X 10"15 cm3 molecule s-1, respectively. Typical peak concentrations at the surface in a moderately polluted atmosphere are 5 X 106 OH cm"3, 100 ppb 03, and 50 ppt N03. Assume 298 K and 1 atm pressure, (a) What are the half-lives of propene with respect to removal from the atmosphere by each of these species? (b) What is the half-life of propene with respect to all three acting simultaneously (which does not actually happen since they peak at different times of the day; see Chapter 6). (c) Repeat parts (a) and (b) but calculate the lifetimes instead of the half-lives.

2. Much of the total oxides of nitrogen in the Arctic at surface level in the winter is tied up in the form of PAN. (a) Use the kinetic parameters in the text to calculate the lifetime of PAN with respect to thermal decomposition under typical temperatures of — 35°C. (b) What would the temperature have to be to give it a lifetime of half a day?

3. Table 5.8 gives some of the kinetic parameters for some termolecular reactions of atmospheric interest. Choose one of these reactions and do the following:

(a) Calculate the overall effective bimolecular rate constant at a typical surface pressure of 750 Torr and temperature of 300 K.

(b) Calculate the effective overall rate constant at the following total pressures: 0, 150, 300, 450, 600, and 750 Torr. Assume the temperature is 300 K. Plot the rate constant as a function of pressure and explain the shape of the curve on a molecular level.

(c) Some cities such as Mexico City are at higher elevations (~ 2200 m) where the air pressure is lower. Calculate the rate constant at a pressure of 630 Torr, assuming a temperature of 300 K. Comment on the direction of change in the rate constant on a molecular level.

(d) Temperatures as low as — 50°F can be found at some polar locations at the earth's surface, while temperatures as high as 120°F are found in desert regions. Calculate the following, assuming a pressure of 750 Torr:

i. The values of k() and at these two temperatures. Do the directions of the change in these two limiting rate constants as a function of temperature make sense on a molecular level? Explain why or why not.

ii. Calculate the overall rate constant at these two temperature extremes and comment on the reason for the direction of the change, on a molecular level, in going from low to high temperatures.

TABLE 5.8 Some Kinetic Parameters for Some Termolecular Reactions"

kfi kfi Reaction (cm6 molecule ~2 s ~') n (cm5 molecule ~1 s ~1) m

TABLE 5.8 Some Kinetic Parameters for Some Termolecular Reactions"

kfi kfi Reaction (cm6 molecule ~2 s ~') n (cm5 molecule ~1 s ~1) m

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