Generating hydrogen gas using the least amount of energy possible is very desirable. One suggested scheme is the catalyzed decomposition of formic acid, ${HCO}_2 {H}$.

$${HCO}_2 {H}({g}) \rightleftarrows {CO}_2({~g})+{H}_2({~g})$$

A particularly interesting aspect of this reaction is that it can be run in reverse and so serve as a way of storing hydrogen. Determine the equilibrium constant (at 298 K) for the decomposition reaction using thermodynamic data. Is the decomposition reaction product-favored at equilibrium at 298 K? (For ${HCO}_2 {H}({g}), \Delta_f {H}^{\circ}=-378.6 {~kJ} / {mol}$ and $\left.S^{\circ}=248.70 {~J} / {K} \cdot {mol}.\right)$

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?

Microwave ovens are highly efficient, compared to other cooking appliances. A 1100-watt microwave oven, running at full power for 90 seconds, will raise the temperature of 1 cup of water (225 mL) from 20 $^o$C to 67 $^o$C. As a rough measure of the efficiency of the microwave oven, compare its energy consumption with the energy required to raise the water temperature.

Some fuel-efficient hybrid cars are rated at 55.0 miles per gallon of gasoline. Calculate the energy used to drive 1.00 mile if gasoline produces 48.0 kJ/g and the density of gasoline is 0.737 g/cm$^3$. (1.00 gal = 3.785 L)

Your home loses energy in the winter through doors, windows, and any poorly insulated walls. A sliding glass door (6 ft $\times$ 6.5 ft with 0.5 inch of insulating glass) allows 1.0 $\times$ 10$^6$ J/h to pass through the glass if the inside temperature is 22 $^o$C (72 $^o$F) and the outside temperature is 0 $^o$C (32 $^o$F). What quantity of energy, expressed in kilojoules, is lost per day? Assume that your house is heated by electricity. How many kilowatt-hours of energy are lost per day through the door?

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?