Chapter 18

It was estimated that the eruption of the Mount Pinatubo volcano resulted in the injection of 20 million metric tons of \(\mathrm{SO}_{2}\) into the atmosphere. Most of this \(\mathrm{SO}_{2}\) underwent oxidation to \(\mathrm{SO}_{3},\) which reacts with atmospheric water to form an aerosol. (a) Write chemical equations for the processes leading to formation of the aerosol. (b) The aerosols caused a \(0.5-0.6^{\circ} \mathrm{C}\) drop in surface temperature in the northern hemisphere. What is the mechanism by which this occurs? (c) The sulfate aerosols, as they are called, also cause loss of ozone from the stratosphere. How might this occur?

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?

In 2008 , the global average electricity consumption per head was \(3.0 \mathrm{MWh}\). The solar power striking Earth every day averages 168 watts per square meter. 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 power?

Write balanced chemical equations for each of the following reactions: (a) The carbon dioxide molecule undergoes photodissociation in the upper atmosphere. (b) The carbon dioxide molecule undergoes photoionization in the upper atmosphere. (c) Carbon monoxide undergoes oxidation by ozone in the stratosphere. (d) Carbon dioxide dissolves in water to form hydrogen carbonate.

(a) When sufficient \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is added to a solution containing \(\mathrm{Mg}^{2+}, \mathrm{Mg}(\mathrm{OH})_{2}\) will precipitate. Explain by writing balanced equations of the reactions. (b) Will \(\mathrm{Mg}(\mathrm{OH})_{2}\) precipitate when \(2.0 \mathrm{~g}\) of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) is added to \(1.00 \mathrm{~L}\) of a solution containing 25 ppm of \(\mathrm{Mg}^{2+}\) ?

The CDC (Centers for Disease Control and Prevention) published a reference blood lead level (BLL), which is based on the BLL distribution among children. It is currently \(5 \mu \mathrm{p} / \mathrm{dL} .\) (a) What is the molarity of an aqueous solution with this concentration? (b) Express this concentration in ppb.

The estimated average concentration of \(\mathrm{NO}_{2}\) in air in the United States in 2015 was 0.010 ppm. (a) Calculate the partial pressure of the \(\mathrm{NO}_{2}\) in a sample of this air when the atmospheric pressure is \(101 \mathrm{kPa} .(\mathbf{b})\) How many molecules of \(\mathrm{NO}_{2}\) are present under these conditions at \(25^{\circ} \mathrm{C}\) in a room that measures \(10 \mathrm{~m} \times 8 \mathrm{~m} \times 2.50 \mathrm{~m} ?\)

A 500 megawatt electrical power plant typically burned 1,430,000 metric tons of coal in a year. (a) Assuming that the coal was \(80 \%\) carbon and \(3 \%\) 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 \(50 \%\) 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?

Common lab spectrometers can detect absorbance down to 0.0002 with good reliability. Consider a dissolved harmful organic substance with a molar mass of \(120.5 \mathrm{~g} / \mathrm{mol}\), which can be detected in this spectrometer. It shows an extinction coefficient of \(\varepsilon=1.43 \times 10^{3} \mathrm{M}^{-1} \mathrm{~cm}^{-1}\) at 320 \(\mathrm{nm}\), its absorption maximum (A Closer Look, p. 620). (a) Calculate the minimum concentration of the organic substance detectable by this spectrometer (path length \(1 \mathrm{~cm}\) ). (b) Convert the minimum observable molarity to ppb.

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 \(2 \times 10^{-6} \mathrm{~s}^{-1}\). 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 \(\mathrm{ClO}\) 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: $$ \begin{array}{l} \mathrm{ClO}(g)+\mathrm{O}_{3}(g) \longrightarrow \mathrm{ClO}_{2}(g)+\mathrm{O}_{2}(g) \\ \mathrm{ClO}_{2}(g)+\mathrm{O}(g) \longrightarrow \mathrm{ClO}(g)+\mathrm{O}_{2}(g) \end{array} $$ 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 \(1.00 \mathrm{~L}\) of water beginning with water at \(25^{\circ} \mathrm{C}\). (b) If the energy is provided by electricity costing \(\$ 0.085 / \mathrm{kWh},\) calculate its cost. \((\mathbf{c})\) If distilled water sells in a grocery store for \(\$ 0.49\) per \(L,\) 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 \(\mathrm{C}\) 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 HFC) by OH radicals in the troposphere is first order in each reactant and has a rate constant of \(k=2.1 \times 10^{8} \mathrm{M}^{-1} \mathrm{~s}^{-1}\) at \(10^{\circ} \mathrm{C}\). If the tropospheric concentrations of \(\mathrm{OH}\) and \(\mathrm{CF}_{3} \mathrm{CH}_{2} \mathrm{~F}\) are \(1.0 \times 10^{12}\) and \(7.5 \times 10^{14}\) molecules \(/ \mathrm{m}^{3}\), 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 \(3.4 \times 10^{-4} \mathrm{~mol} / \mathrm{m}^{3}-\mathrm{Pa}(\mathbf{a})\) 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 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 pH at which precipitation of \(\mathrm{Al}(\mathrm{OH})_{3}\) will begin if \(5.0 \mathrm{~kg}\) of \(\mathrm{Al}_{2}\left(\mathrm{SO}_{4}\right)_{3}\) is added to 10,000 L of water. (b) Approximately how many pounds of CaO must be added to the water to achieve this \(\mathrm{pH}\) ?

The valuable polymer polyurethane is made by a condensation reaction of alcohols (ROH) with compounds that contain an isocyanate group (RNCO). Two reactions that can generate a urethane monomer are shown here: (a) Which process, i or ii, is greener? Explain. (b) What are the hybridization and geometry of the carbon atoms in each C-containing compound in each reaction? (c) If you wanted to promote the formation of the isocyanate intermediate in each reaction, what could you do, using Le Châtelier's principle?

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 \(1.0 \times 10^{-5} \mathrm{M}\). 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 pH? Assume you have a large sample of rain to test.