In methane hydrate the methane molecule is trapped in a cage of water molecules. Describe the structure: (a) how many water molecules make up the cage, (b) how many hydrogen bonds are involved, and (c) how many faces does the cage have?

A parking lot in Los Angeles receives an average of 2.6 $\times$ 10$^7$ J/m$^2$ of solar energy per day in the summer.

(a) If the parking lot is 325 m long and 50.0 m wide, what is the total quantity of energy striking the area per day?

(b) What mass of coal would have to be burned to supply the quantity of energy calculated in (a)?

(Assume the enthalpy of combustion of coal is 33 kJ/g.)

List the following substances in order of energy released by combustion per gram: C$_8$H$_{18}$, H$_2$, C(s), CH$_4$. (See Study Question 22 for the enthalpy of combustion of isooctane, C$_8$H$_{18}$.) Which is the best fuel based on a comparison of kJ/g of fuel?

Confirm the statement in the text that oxidation of 1.0 L of methanol to form CO$_2$(g) and H$_2$O(l) in a fuel cell will provide at least 5.0 kW-h of energy. (The density of liquid methanol is 0.787 g/mL. See Study Question 24 for definition of kW-h.)

Major home appliances purchased in the United States are labeled with bright yellow "Energy Guide" ${ }^{\mathrm{N}}$ tags showing anticipated energy consumption. The tag on a recently purchased washing machine indicated the anticipated energy use would be $940 \mathrm{~kW}$-h per yeas. Calculate the anticipated annual energy use in kilojoules. (See Question 20 for a definition of kilowatt-hour.) At 8 cents/kW-h, how much would it cost per month to operate this machine?

Calculate the energy used, in kilojoules, to power a 100-watt lightbulb continuously over a 24-hour period. How much coal would have to be burned to provide this quantity of energy, assuming that the enthalpy of combustion of coal is 33 kJ/g and the power plant has an efficiency of 35%? [Electrical energy for home use is measured in kilowatt hours (kW-h). One watt is defined as 1 J/s, and 1 kW-h is the quantity of energy transferred when 1000 watt is dispensed over a 1.0-hour period.]

Energy consumption in the United States amounts to the equivalent of the energy obtained by burning 7.0 gal of oil or 70. lb of coal per day per person. Using data in Table 20.4, carry out calculations to show that the energy evolved from these quantities of oil and coal is approximately equivalent. The density of fuel oil is approximately 0.8 g/mL. (1.00 gal = 3.785 L and 1.00 lb = 454 g)

Assume the average $\mathrm{CO}_2$ concentration in the atmosphere is $397 \mathrm{ppm}$ (as of February 2013). The actual concentration of $\mathrm{CO}_2$ at different sites will vary. Speculate on whether the concentration of $\mathrm{CO}_2$ would be expected to be higher, lower, or the same as this average value in a typical large city.

The enthalpy of combustion of isooctane (C$_8$H$_{18}$), one of the many hydrocarbons in gasoline, is 5.45 $\times$ 10$^3$ kJ/mol. Calculate the enthalpy change per gram of isooctane and per liter of isooctane (d = 0.688 g/mL).

In the discussion on the composition of air, mention is made of the fact that water vapor may have a concentration as high as 40,000 ppm. Calculate the partial pressure exerted by water vapor at this concentration. Assume that this represents a situation with 100% humidity. What temperature would be needed to achieve this value?

Per capita energy consumption in the United States has been equated to the energy obtained by burning 70. lb of coal per day. Use enthalpy of formation data to calculate the energy transferred as heat, in kilojoules, when 70. lb of coal is burned. (Assume the enthalpy of combustion of coal is 33 kJ/g.)

Hydrogen can be produced using the reaction of steam (H$_2$O) with various hydrocarbons. Compare the mass of H$_2$ expected from the reaction of steam with 100.g each of methane, petroleum, and coal. (Assume complete reaction in each case. Use CH$_2$ and C as the representative formulas for petroleum and coal, respectively.)

Silver ions have long been known to have biocidal properties. The increasing use of silver for this purpose has led to greater silver concentrations in waste water, and there has been several concern regarding it. However, recent studies revealed that the silver was largely put back into the environment as ${Ag}_2 {~S}$. The solubility of this sulfide is $1.4 \times 10^{-4} {~g} / {L}$.

(a) Calculate the $K_{\text {sp }}^{\prime}$ for ${Ag}_2 {~S}$.

(b) How does the solubility of ${Ag}_2 {~S}$ change as the pH decreases?

A 2010 article in Science magazine described "Sewage Treatment with Anammox." The authors noted that "Fixed nitrogen such as ammonium and nitrate [ions] should be removed [from sewage] to avoid toxic algal blooms in the environment." One approach to removing ammonium ions is to use ammonium-oxidizing (anammox) bacteria. Two (unbalanced) reactions that are involved are:

$$\begin{aligned} & {NH}_4{ }^{+}({aq})+{NO}_2{ }^{-}({aq}) \rightarrow {N}_2({~g})+{H}_2 {O}(\ell) \\ & {NH}_4{ }^{+}({aq})+{O}_2({~g}) \rightarrow {NO}_2{ }^{-}({aq})+{H}_2 {O}(\ell) \end{aligned}$$

Balance these two equations in acid solution.