Chapter 18

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 highest ever recorded electrical power usage in New York City was \(13,200 \mathrm{MW} .\) A record established in July of \(2013 .\) Considering that present technology for solar energy conversion is 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 New York City is 830 km.)

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 Mg \(\mathrm{Mg}(\mathrm{OH})_{2}\) precipitates when \(\mathrm{CO}_{3}^{2-}\) ion is added to a solution containing \(\mathrm{Mg}^{2+} .\) (b) Will 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 \(\mathrm{ppm}\) of \(\mathrm{Mg}^{2+} ?\)

(a) The EPA threshold for acceptable levels of lead ions in water is \(<15\) ppb. What is the molarity of an aqueous solution with a concentration of 15 ppb? (b) Concentrations of lead in the bloodstream are often quoted in units of \(\mu g / d L\) . Averaged over the entire country, the mean concentration of lead in the blood was measured to be 1.6 \(\mu g / d L\) in \(2008 .\) Express this concentration in ppb.

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 100 \(\mathrm{m}\) above the ground) if ozone was at this concentration?

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 SO \(_{2}\) could be removed by reaction with powdered 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 ions, 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 \(3.45 \times 10^{3} M^{-1} \mathrm{cm}^{-1}\) at \(280 \mathrm{nm},\) its absorption maximum (A Closer Look, p. 576\() .\) Below 50 \(\mathrm{ppb}\) , 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 a water sample at 280 \(\mathrm{nm}\) a good way to detect concentrations of the impurity above the 50 -ppb threshold?

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 \(2 \times 10^{-6} \mathrm{s}^{-1} .\) At that rate, how many days would it take for the hydrocarbons to decrease to 10\(\%\) of their initial value?

The standard enthalpies of formation of 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: $$\begin{array}{l}{\mathrm{ClO}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}_{2}(g)+\mathrm{O}_{2}(g)} \\ {\mathrm{ClO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g)}\end{array}$$ 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 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 \(4.8 \times 10^{5}\) \(M^{-1} \mathrm{s}^{-1} .\) (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) 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 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: $$\begin{array}{lll}{\text { Trial }} & {\left[0_{3}\right](M)} & {[\mathrm{H}](M)} & {\text { Initial Rate }(M / s)} \\ \hline 1 & {5.17 \times 10^{-33}} & {3.22 \times 10^{-26}} & {1.88 \times 10^{-14}} \\ {2} & {2.59 \times 10^{-33}} & {3.25 \times 10^{-26}} & {9.44 \times 10^{-15}} \\\ {3} & {5.19 \times 10^{-33}} & {6.46 \times 10^{-26}} & {3.77 \times 10^{-14}}\end{array}$$ \begin{equation}\begin{array}{l}{\text { (a) Write the rate law for the reaction. }} \\ {\text { (b) Calculate the rate constant. }}\end{array}\end{equation}

The degradation of \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{F}(\) an \(\mathrm{HFC})\) by \(\mathrm{OH}\) radicals in the troposphere is first order in each reactant and has a rate constant of \(k=1.6 \times 10^{8} M^{-1} \mathrm{s}^{-1}\) 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/cm\(^{3},\) respectively, what is the rate of reaction at this temperature in \(M / \mathrm{s} ?\)

The Henry's law constant for \(\mathrm{CO}_{2}\) in water at \(25^{\circ} \mathrm{C}\) is \(3.1 \times 10^{-2} \mathrm{Matm}^{-1}\) . (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 pH of this solution?

The 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 \(1.0 \times 10^{-5} \mathrm{M}\) . The appropriate \(K_{a}\) values are given in Table \(16.3 .\) (b) What experiments could you do to test the hypothesis the rain also contains sulfur-containing species that contribute to its pH? Assume you have a large sample of rain to test.