Exercises

4.1. Ozone, O3, is a weak absorber of electromagnetic radiation in the UV spectral region; its maximum absorption in the near ultraviolet region is at 255 nm.

(a) Calculate the energy of a 255-nm photon in angstrom units (A).

(b) Calculate the energy of a 255-nm photon in joules per photon, in kilojoules per einstein, and in electron-volts.

(c) Calculate the frequency of a 255-nm photon in reciprocal seconds and in reciprocal centimeters.

(d) Calculate the momentum of a 255-nm photon in: kilogram-meters per second and in gram-centimeters per second.

(e) How does the momentum of a 255-nm photon compare with the momentum of an ozone molecule at 25°C moving at a velocity of 400 m/s-that is, what is Pphoton/Pozone?

4.2. Give the spectral region in which each of the following photons might absorb:

(a) a 5000-A-wavelength photon

(b) an 8-eV-energy photon

(c) a 200-mile-wavelength photon

(d) a 1013-s_1-frequency photon

(e) a 5-cm-wavelength photon

4.3. Nitrogen dioxide (NO2) is a major participant in photochemical smog (Chapter 5). It absorbs visible and ultraviolet light, with maximum absorption at 400 nm, where its absorption cross section a is 6 x 10~19 cm2/molecule.

(a) Calculate its molar extinction coefficient sM at 400 nm and its extinction coefficient at 400 nm and 20°C in units of atm_1cm_1.

(b) Assume that the concentration of N02 in a polluted atmosphere above a city is constant at 2 x 1012 molecules/cm3 to an altitude of 1000 ft and that the temperature is also constant at 20°C. Calculate the percent of sunlight absorbed by the N02 at 400 nm.

4.4. EDTA (ethylenediaminetetraacetic acid, MW 292.2) is an important industrial complexing agent (Section 9.5.6). It is poorly degraded in municipal sewage treatment plants and therefore is found in many surface waters. However, it forms a complex with the ferric ion (Fe3+), Fe(III)-EDTA, which can be photochemically degraded [F. G. Kari, S. Hilger, and S. Canonica, Environ. Sci. Technol., 29, 1008-1017 (1995)]. At 366 nm, the molar extinction coefficient of Fe(III)-EDTA is 785 dm3mol 'cm-1 and the quantum yield of degradation is 0.034. In a sample of river water, the concentration of EDTA was found to be 280 ^g/dm3.

(a) Calculate the fraction of light absorbed in 1-cm thickness (light path) of the river water sample at 366 nm if sufficient ferric ion is added to complex all the EDTA.

(b) The intensity of 366-nm sunlight is approximately 1014 photons cm-3s-1. Calculate the time required to degrade all the Fe(III)-EDTA in one cubic centimeter of the sample in a cell 1 cm thick, assuming that the rate of the reaction does not change as the absorbing material is used up (a very poor assumption!).

4.5. We will see in Chapter 5 that the abstraction reaction of a hydrogen atom from an alkane molecule by an hydroxyl radical is an important initiating step in many atmospheric decomposition processes. This is a kinetically simple bimolecular reaction:

At 298 K (25°C), the rate constant k298 = 6.9 x 10-15cm3molecule-1s-1 for RH = CH4. Assume that you could have a closed flask containing initially methane and the hydroxyl radical at their estimated daytime concentrations in a typical polluted urban atmosphere: [CH4] = 4.2 x 1013molecules/cm3 and [.OH] = 2.5 x 106radicals/cm3.

(a) Calculate the initial rate of the reaction r,

(b) Calculate the time required for half the -OH radicals in the flask to be used up. (Hint: The initial concentration of methane is much greater than that of the hydroxyl radical, so the methane concentration can be assumed to be constant, giving an apparent first-order reaction.)

(c) Assume now that all sources of methane in the troposphere were suddenly stopped, but that the hydroxyl radical concentration remained constant. Calculate how long it would take for half the methane molecules to be used up, assuming that the foregoing reaction is the only one leading to the disappearance of methane.

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