Additional Problems
1. The common tropospheric pollutant gases S02 and NOz have molecular structures which, like that of CO?, have the central atom connected to two oxygen atoms, but, unlike C02, they are nonlinear. The wavelengths for their vibrations are given in the table below, (a) Which of the vibrations are capable of absorbing infrared energy? (b) Based on the wavelengths for the IRabsorbing vibrations and the spectrum in Figure 67, decide which, if any, vibrations could contribute much to global warming, (c) What lifetime characteristic of these gases would limit their role in global warming?
Gas 
stretch 
stretch 
Bending 
so2 
8.7 fim 
7.3 fim 
19.3 ¿an 
no2 
7.6 /im 
6.2 fim 
13.3 fim 
2. (a) How can the fact that nitrous oxide has three vibrations that absorb infrared light be used to prove that its linear structure is NNO rather than NON? (b) Would methane molecules absorb IR during the vibration in which all four C — H bonds stretched or contracted in phase?
3. Anthropogenic carbon dioxide emissions into the atmosphere amounted to 178 Gt from January 1990 to December 1997. Calculate the fraction of this emitted carbon dioxide that remained in the air, given that in that same eightyear period, the carbon dioxide concentration in air rose by 11.1 ppm. Note that the molar masses of C, O, and air, respectively, are 12.0, 16.0, and 29.0 g, that the mass of the atmosphere is 5.1 X 1021 g, and that 1 Gt is 1015 g.
4. The total amount of methane in the atmosphere in 1992 was about 5000 Tg and was then increasing by about 0.6% annually due to the fact that the annual input rate exceeded the annual destruction rate of 530 Tg/yr. Calculate the percentage by which anthropogenic releases of methane, which account for twothirds of the total, had to be reduced if the atmospheric concentration of this gas was to be stabilized in 1992.
5. As mentioned in the text, the fraction F of light that is absorbed by any gas in air is logarithmically related to the concentration C of the gas and the distance d through which the light travels; this relationship is called the BeerLambert law:
Here K is a proportionality constant. Show by simple trial calculations that for concentrations near zero (e.g., where KCd = 0.001), F is related almost linearly to C, whereas for larger KCd values (e.g., near 2), doubling the concentration does not nearly double the light absorption.
6. The vapor pressure P of a liquid rises exponentially when it is heated according to the equation ln(P2/P1) = AH/R(l/T1l/T2)
Here P2 and Pj are the vapor pressures of the liquid at the Kelvin temperatures T2 and T, after and before the temperature increase, R is the gas constant 8.3 J/K mol, and AH is the liquid's enthalpy of vaporization, which for water is 44 kj/mol. Calculate the percentage increase in the vapor pressure of water that occurs if the temperature is raised from 15°C to 18°C. Give several reasons why the amount of outgoing thermal infrared in water's absorption bands may not be increased by exactly the percentage you calculate if the average surface air temperature is increased to 18°C.
7. Suppose that some climatic crisis inspired the Earth's population to switch to energy systems that did not emit carbon dioxide and that the transition occurred within a decade. What would be the immediate effect of this change on the Earth's average air temperature, given that both carbon dioxide and sulfur dioxide emissions from fossil fuels would have rapidly declined?
8. Explain why CHF,C1 (HCFC22) has more IR absorption bands with a greater range of IR wavelengths absorbed, and absorbs IR much more efficiently on a per molecule basis, than CH4, the hydrocarbon from which it is derived.
9. Calculate the volume of C02 produced at 1 atm and 20.0°C from the complete combustion of 1.00 L of gasoline. Although gasoline is a mixture of hydrocarbons (as described in Chapter 7), for the purposes of this calculation consider gasoline to have the chemical formula C8Hlg and the same density as noctane: 0.702 g/mL. Calculate the volume of C02 produced by driving 100 miles on the highway in a midsize sedan compared to an SUV, given their highway fuel efficiencies of 33 and 19 mpg, respectively. Note that 1 gal = 3.785 L.
10. Given that the 2002 concentration of CH4 in the atmosphere was 1.77 ppm, calculate the total mass of CH4 in the atmosphere in 2002. Note that the total mass of the atmosphere is 5.1 X 1018 kg and the average molar mass of the atmosphere is 29.0 g/mol.
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If you suffer with asthma, you will no doubt be familiar with the uncomfortable sensations as your bronchial tubes begin to narrow and your muscles around them start to tighten. A sticky mucus known as phlegm begins to produce and increase within your bronchial tubes and you begin to wheeze, cough and struggle to breathe.
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