Chapter 18

A friend of yours has seen each of the following items in newspaper articles and would like an explanation: (a) acid rain, (b) greenhouse gas, \((\mathrm{c})\) photochemical smog, \((\mathbf{d})\) ozone depletion. Give a brief explanation of each term and identify one or two of the chemicals associated with each.

Suppose that on another planet the atmosphere consists of \(17 \% \mathrm{Kr}, 38 \% \mathrm{CH}_{4},\) and \(45 \% \mathrm{O}_{2} .\) What is the average molar mass at the surface? What is the average molar mass at an altitude at which all the \(\mathrm{O}_{2}\) is photodissociated?

If an average \(\mathrm{O}_{3}\) molecule "lives" only \(100-200\) seconds in the stratosphere before undergoing dissociation, how \(\operatorname{can} \mathrm{O}_{3}\) offer any protection from ultraviolet radiation?

What properties of CFCs make them ideal for various commercial applications but also make them a long-term problem in the stratosphere?

The hydroxyl radical, \(\mathrm{OH}\), is formed at low altitudes via the reaction of excited oxygen atoms with water: $$ \mathrm{O}^{*}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 2 \mathrm{OH}(g) $$ (a) Write the Lewis structure for the hydroxyl radical. (Hint: It has one unpaired electron.) Once produced, the hydroxyl radical is very reactive. Explain why each of the following series of reactions affects the pollution in the troposphere: (b) \(\mathrm{OH}+\mathrm{NO}_{2} \longrightarrow \mathrm{HNO}_{3}\) (c) \(\mathrm{OH}+\mathrm{CO}+\mathrm{O}_{2} \longrightarrow \mathrm{CO}_{2}+\mathrm{OOH}\) \(\mathrm{OOH}+\mathrm{NO} \longrightarrow \mathrm{OH}+\mathrm{NO}_{2}\) (d) \(\mathrm{OH}+\mathrm{CH}_{4} \longrightarrow \mathrm{H}_{2} \mathrm{O}+\mathrm{CH}_{3}\) \(\mathrm{CH}_{3}+\mathrm{O}_{2} \longrightarrow \mathrm{OOCH}_{3}\) \(\mathrm{OOCH}_{3}+\mathrm{NO} \longrightarrow \mathrm{OCH}_{3}+\mathrm{NO}_{2}\) (e) The concentration of hydroxyl radicals in the troposphere is approximately \(2 \times 10^{6}\) radicals per \(\mathrm{cm}^{3}\). This estimate is based on a method called long path absorption spectroscopy (LPAS), similar in principle to the Beer's law measurement discussed in the Closer Look essay on p. 564 , except that the path length in the LPAS measurement is \(20 \mathrm{~km}\). Why must the path length be so large?

Explain, using Le Châtelier's principle, why the equilibrium constant for the formation of \(\mathrm{NO}\) from \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2}\) increases with increasing temperature, whereas the equilibrium constant for the formation of \(\mathrm{NO}_{2}\) from \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) decreases with increasing temperature.

Natural gas consists primarily of methane, \(\mathrm{CH}_{4}(g) .\) (a) Write a balanced chemical equation for the complete combustion of methane to produce \(\mathrm{CO}_{2}(g)\) as the only carbon-containing product. (b) Write a balanced chemical equation for the incomplete combustion of methane to produce \(\mathrm{CO}(g)\) as the only carbon-containing product. (c) At \(25^{\circ} \mathrm{C}\) and 1.0 atm pressure, what is the minimum quantity of dry air needed to combust \(1.0 \mathrm{~L}\) of \(\mathrm{CH}_{4}(g)\) completely to \(\mathrm{CO}_{2}(g) ?\)

One of the possible consequences of climate change is an increase in the temperature of ocean water. The oceans serve as a "sink" for \(\mathrm{CO}_{2}\) by dissolving large amounts of it. (a) How would the solubility of \(\mathrm{CO}_{2}\) in the oceans be affected by an increase in the temperature of the water? (b) Discuss the implications of your answer to part (a) for the problem of climate change.

The rate of solar energy striking Earth averages 168 watts per square meter. The rate of energy radiated from Earth's surface averages 390 watts per square meter. Comparing these numbers, one might expect that the planet would cool quickly, yet it does not. Why not?

The solar power striking Earth every day averages 168 watts per square meter. The peak electrical power usage in New York City is 12,000 megawatts. Considering that present technology for solar energy conversion is only about \(10 \%\) efficient, from how many square meters of land must sunlight be collected in order to provide this peak power? (For comparison, the total area of the city is \(830 \mathrm{~km}^{2}\).)

Write balanced chemical equations for each of the following reactions: (a) The nitric oxide molecule undergoes photodissociation in the upper atmosphere. (b) The nitric oxide molecule undergoes photoionization in the upper atmosphere. (c) Nitric oxide undergoes oxidation by ozone in the stratosphere. (d) Nitrogen dioxide dissolves in water to form nitric acid and nitric oxide.

(a) Explain why \(\mathrm{Mg}(\mathrm{OH})_{2}\) precipitates when \(\mathrm{CO}_{3}^{2-}\) ion is added to a solution containing \(\mathrm{Mg}^{2+}\). . (b) Will \(\mathrm{Mg}(\mathrm{OH})_{2}\) precipitate when \(4.0 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is added to \(1.00 \mathrm{~L}\) of a solution containing 125 ppm of \(\mathrm{Mg}^{2+}\) ?

It has been pointed out that there may be increased amounts of \(\mathrm{NO}\) in the troposphere as compared with the past because of massive use of nitrogen-containing compounds in fertilizers. Assuming that NO can eventually diffuse into the stratosphere, how might it affect the conditions of life on Earth? Using the index to this text, look up the chemistry of nitrogen oxides. What chemical pathways might \(\mathrm{NO}\) in the troposphere follow?

As of the writing of this text, EPA standards limit atmospheric ozone levels in urban environments to 84 ppb. How many moles of ozone would there be in the air above Los Angeles County (area about 4000 square miles; consider a height of 10 \(\mathrm{m}\) above the ground) if ozone was at this concentration?

The estimated average concentration of \(\mathrm{NO}_{2}\) in air in the United States in 2006 was 0.016 ppm. (a) Calculate the partial pressure of the \(\mathrm{NO}_{2}\) in a sample of this air when the atmospheric pressure is 755 torr \((99.1 \mathrm{kPa})\). (b) How many molecules of \(\mathrm{NO}_{2}\) are present under these conditions at \(20{ }^{\circ} \mathrm{C}\) in a room that measures \(15 \times 14 \times 8 \mathrm{ft}\) ?

In 1986 an electrical power plant in Taylorsville, Georgia, burned 8,376,726 tons of coal, a national record at that time. (a) Assuming that the coal was \(83 \%\) carbon and \(2.5 \%\) sulfur and that combustion was complete, calculate the number of tons of carbon dioxide and sulfur dioxide produced by the plant during the year. (b) If \(55 \%\) of the \(\mathrm{SO}_{2}\) could be removed by reaction with powdered \(\mathrm{CaO}\) to form \(\mathrm{CaSO}_{3},\) how many tons of \(\mathrm{CaSO}_{3}\) would be produced?

The water supply for a midwestern city contains the following impurities: coarse sand, finely divided particulates, nitrate ion, trihalomethanes, dissolved phosphorus in the form of phosphates, potentially harmful bacterial strains, dissolved organic substances. Which of the following processes or agents, if any, is effective in removing each of these impurities: coarse sand filtration, activated carbon filtration, aeration, ozonization, precipitation with aluminum hydroxide?

An impurity in water has an extinction coefficient of \(3.45 \times 10^{3} \mathrm{M}^{-1} \mathrm{~cm}^{-1}\) at \(280 \mathrm{nm}\), its absorption maximum Closer Look, p. 564). Below 50 ppb, the impurity is not a problem for human health. Given that most spectrometers cannot detect absorbances less than 0.0001 with good reliability, is measuring the absorbance of water at \(280 \mathrm{nm}\) a good way to detect concentrations of the impurity above the 50 -ppb threshold?

The concentration of \(\mathrm{H}_{2} \mathrm{O}\) in the stratosphere is about \(5 \mathrm{ppm}\). It undergoes photodissociation according to: $$ \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{H}(g)+\mathrm{OH}(g) $$ (a) Write out the Lewis-dot structures for both products and reactant. (b) Using Table \(8.4,\) calculate the wavelength required to cause this dissociation. (c) The hydroxyl radicals, OH, can react with ozone, giving the following reactions: $$ \begin{array}{l} \mathrm{OH}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{HO}_{2}(g)+\mathrm{O}_{2}(g) \\ \mathrm{HO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{OH}(g)+\mathrm{O}_{2}(g) \end{array} $$ What overall reaction results from these two elementary reactions? What is the catalyst in the overall reaction? Explain.

Bioremediation is the process by which bacteria repair their environment in response, for example, to an oil spill. The efficiency of bacteria for "eating" hydrocarbons depends on the amount of oxygen in the system, pH, temperature, and many other factors. In a certain oil spill, hydrocarbons from the oil disappeared with a first-order rate constant of \(2 \times 10^{-6} \mathrm{~s}^{-1}\). How many days did it take for the hydrocarbons to decrease to \(10 \%\) of their initial value?

The main reason that distillation is a costly method for purifying water is the high energy required to heat and vaporize water. (a) Using the density, specific heat, and heat of vaporization of water from Appendix \(\mathrm{B}\), calculate the amount of energy required to vaporize 1.00 gal of water beginning with water at \(20^{\circ} \mathrm{C}\). (b) If the energy is provided by electricity costing \(\$ 0.085 / \mathrm{kWh},\) calculate its cost. (c) If distilled water sells in a grocery store for \(\$ 1.26\) per gal, what percentage of the sales price is represented by the cost of the energy?

A reaction that contributes to the depletion of ozone in the stratosphere is the direct reaction of oxygen atoms with ozone: \(\mathrm{O}(g)+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)\) At \(298 \mathrm{~K}\) the rate constant for this reaction is \(4.8 \times 10^{5} \mathrm{M}^{-1} \mathrm{~s}^{-1}\). (a) Based on the units of the rate constant, write the likely rate law for this reaction. (b) Would you expect this reaction to occur via a single elementary process? Explain why or why not. (c) From the magnitude of the rate constant, would you expect the activation energy of this reaction to be large or small? Explain. (d) Use \(\Delta H_{f}^{\circ}\) values from Appendix \(\mathrm{C}\) to estimate the enthalpy change for this reaction. Would this reaction raise or lower the temperature of the stratosphere?

The following data were collected for the destruction of \(\mathrm{O}_{3}\) by \(\mathrm{H}\left(\mathrm{O}_{3}+\mathrm{H} \longrightarrow \mathrm{O}_{2}+\mathrm{OH}\right)\) at very low concentrations: $$ \begin{array}{llll} \hline \text { Trial } & {\left[\mathrm{O}_{3}\right](\boldsymbol{M})} & {[\mathrm{H}](\boldsymbol{M})} & \text { Initial Rate }(\boldsymbol{M} / \mathrm{s}) \\ \hline 1 & 5.17 \times 10^{-33} & 3.22 \times 10^{-26} & 1.88 \times 10^{-14} \\\ 2 & 2.59 \times 10^{-33} & 3.25 \times 10^{-26} & 9.44 \times 10^{-15} \\ 3 & 5.19 \times 10^{-33} & 6.46 \times 10^{-26} & 3.77 \times 10^{-14} \\ \hline \end{array} $$ (a) Write the rate law for the reaction. (b) Calculate the rate constant.

The degradation of \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}\) (an HFC) by OH radicals in the troposphere is first order in each reactant and has a rate constant of \(k=1.6 \times 10^{8} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) at \(4{ }^{\circ} \mathrm{C}\). If the tropo- spheric concentrations of \(\mathrm{OH}\) and \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}\) are \(8.1 \times 10^{5}\) and \(6.3 \times 10^{8}\) molecules/cm \(^{3}\), respectively, what is the rate of reaction at this temperature in \(M / s ?\)

The Henry's law constant for \(\mathrm{CO}_{2}\) in water at \(25^{\circ} \mathrm{C}\) $$ \text { is } 3.1 \times 10^{-2} M \mathrm{~atm}^{-1} $$ (a) What is the solubility of \(\mathrm{CO}_{2}\) in water at this temperature if the solution is in contact with air at normal atmospheric pressure? (b) Assume that all of this \(\mathrm{CO}_{2}\) is in the form of \(\mathrm{H}_{2} \mathrm{CO}_{3}\) produced by the reaction between \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2} \mathrm{O}:\) $$ \mathrm{CO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{CO}_{3}(a q) $$ What is the \(\mathrm{pH}\) of this solution?

If the \(\mathrm{pH}\) of a 1.0 -in. rainfall over \(1500 \mathrm{mi}^{2}\) is 3.5 , how many kilograms of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) are present, assuming that it is the only acid contributing to the \(\mathrm{pH}\) ?

The precipitation of \(\mathrm{Al}(\mathrm{OH})_{3}\left(K_{s p}=1.3 \times 10^{-33}\right)\) is sometimes used to purify water. (a) Estimate the \(\mathrm{pH}\) at which precipitation of \(\mathrm{Al}(\mathrm{OH})_{3}\) will begin if \(5.0 \mathrm{lb}\) of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is added to 2000 gal of water. (b) Approximately how many pounds of \(\mathrm{CaO}\) must be added to the water to achieve this \(\mathrm{pH}\) ?

The \(\mathrm{pH}\) of a particular raindrop is 5.6. (a) Assuming the major species in the raindrop are \(\mathrm{H}_{2} \mathrm{CO}_{3}(a q), \mathrm{HCO}_{3}^{-}(a q),\) and \(\mathrm{CO}_{3}^{2-}(a q),\) calculate the concentrations of these species in the raindrop, assuming the total carbonate concentration is \(1.0 \times 10^{-5} M .\) The appropriate \(K_{a}\) values are given in Table 16.3. (b) What experiments could you do to test the hypothesis that the rain also contains sulfur-containing species that contribute to its \(\mathrm{pH}\) ? Assume you have a large sample of rain to test.