Chapter 18

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 MW. 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 comparisen, the total area of New York 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) Nitricoxide undergoes oxidation by ozone in the stratesphere. (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 \(\mathrm{Mg}^{2+}\) ?

In 1986 an electrical power plant in Taylorsville, Georgia, burned \(8,376,726\) tons of coal, a national recerd 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, acration, 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 (A Closer Look, p. 582 ). 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?

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 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 $$ \mathrm{O}(g)+\mathrm{O}_{3}(g) \longrightarrow 2 \mathrm{O}_{2}(g) $$ At \(298 \mathrm{~K}\) the rate constant for this reaction is \(4.8 \times 10^{3} \mathrm{M}^{-1} \mathrm{~s}^{-1}\). (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) Use \(\Delta H_{\text {f }}{\underline{\phantom{xx}}}^{\circ}\) 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 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 \(k=1.6 \times 10^{8} \mathrm{M}^{-1} \mathrm{~s}{\underline{\phantom{xx}}}^{-1}\) at \(4^{\circ} \mathrm{C}\). If the tropospheric concentrations of \(\mathrm{OH}\) and \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}\) are \(8.1 \times 10^{3}\) and \(6.3 \times 10^{3}\) molecules/ \(/ \mathrm{cm}^{3}\), respectively, what is the rate of reaction at this temperature in \(M / s\) ?

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

(a) Distinguish between photodissociation and photoionization. (b) Use the energy requirements of these two processes to explain why photodissociation of oxygen is more important than photoionization of exygen at altitudes below about \(90 \mathrm{~km}\).

A first-stage recovery of magnesium from seawater is precipitation of \(\mathrm{Mg}(\mathrm{OH})_{2}\) with \(\mathrm{CaO}\) : $$ \mathrm{Mg}^{2+}(a q)+\mathrm{CaO}(s)+\mathrm{H}_{2} \mathrm{O}(t) \longrightarrow \mathrm{Mg}(\mathrm{OH})_{2}(s)+\mathrm{Ca}^{2+}(a q) $$ What mass of \(\mathrm{CaO}\), in grams, is needed to precipitate \(1000 \mathrm{lb}\) of \(\mathrm{Mg}(\mathrm{OH})_{2}\) ?