Chapter 18

The rate of solar energy striking Earth averages 169 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 169 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 \(\left.830 \mathrm{~km}^{2} .\right)\)

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 \(\mathrm{CO}_{3}{\underline{\phantom{xx}}}^{2-}\) 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 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?

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, \(\mathrm{pH}\), 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 standard enthalpies of formation of \(\mathrm{ClO}\) and \(\mathrm{ClO}_{2}\) are 101 and \(102 \mathrm{~kJ} / \mathrm{mol}\), respectively. Using these data and the thermodynamic data in Appendix \(C\), calculate the overall enthalpy change for each step in the following catalytic cycle: $$ \begin{aligned} &\mathrm{ClO}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}_{2}(g)+\mathrm{O}_{2}(g) \\ &\mathrm{ClO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \end{aligned} $$ What is the enthalpy change for the overall reaction that results from these two steps?

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 \(1.00 \mathrm{gal}\) 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: $$\mathrm{O}(\mathrm{g})+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g)$$ 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 \(C\) to estimate the enthalpy change for this reaction. Would this reaction raise or lower the temperature of the stratosphere?

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

Nitrogen dioxide \(\left(\mathrm{NO}_{2}\right)\) is the only important gaseous species in the lower atmosphere that absorbs visible light. (a) Write the Lewis structure(s) for \(\mathrm{NO}_{2}\). (b) How does this structure account for the fact that \(\mathrm{NO}_{2}\) dimerizes to form \(\mathrm{N}_{2} \mathrm{O}_{4} ?\) Based on what you can find about this dimerization reaction in the text, would you expect to find the \(\mathrm{NO}_{2}\) that forms in an urban environment to be in the form of dimer? Explain. (c) What would you expect as products, if any, for the reaction of \(\mathrm{NO}_{2}\) with CO? (d) Would you expect \(\mathrm{NO}_{2}\) generated in an urban environment to migrate to the stratosphere? Explain.

The following data was collected for the destruction of \(\mathrm{O}_{3}\) by \(\mathrm{H}\left(\mathrm{O}_{3}+\mathrm{H} \rightarrow \mathrm{O}_{2}+\mathrm{OH}\right)\) at very low concentrations: \(\begin{array}{llll} \text { Experiment } & {\left[\mathrm{O}_{3}\right], M} & {[\mathrm{H}], M} & \text { Initial Rate, } M / \mathrm{s} \\ \hline 1 & 5.17 \times 10^{-33} & 3.22 \times 10^{-26} & 1.88 \times 10^{-14} \\\ 2 & 2.59 \times 10^{-33} & 3.25 \times 10^{-26} & 9.44 \times 10^{-15} \\ 3 & 5.19 \times 10^{-33} & 6.46 \times 10^{-26} & 3.77 \times 10^{-14} \end{array}\) (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 \(\left.\mathrm{HFC}\right)\) 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 tropospheric 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 \(\mathrm{cm}^{-3}\), 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 \(25^{\circ} \mathrm{C}\) is \(3.1 \times 10^{-2} \mathrm{M} \mathrm{atm}^{-1}\). (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 \(\mathrm{H}_{2} \mathrm{O}\) : $$\mathrm{CO}_{2}(a q)+\mathrm{H}_{2} \mathrm{O}(I) \rightarrow \mathrm{H}_{2} \mathrm{CO}_{3}(a q)$$ What is the \(\mathrm{pH}\) of this solution?