Chapter 7

Use standard enthalpies of formation to calculate \(\Delta H_{\mathrm{rxn}}^{\circ}\) for each reaction. a. \(2 \mathrm{H}_{2} \mathrm{~S}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(I)+2 \mathrm{SO}_{2}(g)\) b. \(\mathrm{SO}_{2}(g)+{ }^{1} /{ }_{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{3}(g)\) c. \(\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)\) d. \(\mathrm{N}_{2} \mathrm{O}_{4}(g)+4 \mathrm{H}_{2}(g) \longrightarrow \mathrm{N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\)

Determine the mass of \(\mathrm{CO}_{2}\) produced by burning enough of each fuel to produce \(1.00 \times 10^{2} \mathrm{~kJ}\) of heat. Which fuel contributes least to global warming per kJ of heat produced? MISSED THIS? Read Sections 7.4,\(7.6 ; \mathrm{KCV} 7.4,7.6, \mathrm{HE} 7.2,7.7\) a. \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(g)\) $$\Delta H_{\mathrm{rxn}}^{\circ}=-802.3 \mathrm{~kJ}$$ b. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2}\mathrm{O}(g)\) $$\Delta H_{\mathrm{rxn}}^{\circ}=-2043 \mathrm{~kJ} $$c. \(\mathrm{C}_{8} \mathrm{H}_{18}(l)+{ }^{25} /{ }_{2} \mathrm{O}_{2}(g) \longrightarrow 8 \mathrm{CO}_{2}(g)+9 \mathrm{H}_{2} \mathrm{O}(g)\) $$\Delta H_{\mathrm{rnn}}^{\circ}=-5074.1 \mathrm{~kJ}$$

The citizens of the world burn the fossil fuel equivalent of \(7 \times 10^{12} \mathrm{~kg}\) of petroleum per year. Assume that all of this petroleum is in the form of octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) and calculate how much \(\mathrm{CO}_{2}\) (in kg) the world produces from fossil fuel combustion per year. (Hint: Begin by writing a balanced equation for the combustion of octane.) If the atmosphere currently contains approximately \(3 \times 10^{15} \mathrm{~kg}\) of \(\mathrm{CO}_{2}\), how long will it take for the world's fossil fuel combustion to double the amount of atmo- spheric carbon dioxide?

In a sunny location, sunlight has a power density of about \(1 \mathrm{~kW} / \mathrm{m}^{2} .\) Photovoltaic solar cells can convert this power into electricity with \(15 \%\) efficiency. If a typical home uses \(385 \mathrm{kWh}\) of electricity per month, how many square meters of solar cells are required to meet its energy requirements? Assume that electricity can be generated from the sunlight for 8 hours per day.

Evaporating sweat cools the body because evaporation is an endothermic process: $$\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{H}_{2} \mathrm{O}(g) \quad \Delta H_{\mathrm{rxn}}^{\circ}=+44.01 \mathrm{~kJ}$$ Estimate the mass of water that must evaporate from the skin to cool the body by \(0.50^{\circ} \mathrm{C}\). Assume a body mass of \(95 \mathrm{~kg}\) and assume that the specific heat capacity of the body is \(4.0 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).

A 25.5-g aluminum block is warmed to \(65.4^{\circ} \mathrm{C}\) and plunged into an insulated beaker containing 55.2 g water initially at \(22.2^{\circ} \mathrm{C} .\) The aluminum and the water are allowed to come to thermal equilibrium. Assuming that no heat is lost, what is the final temperature of the water and aluminum?

Under certain nonstandard conditions, oxidation by \(\mathrm{O}_{2}(g)\) of \(1 \mathrm{~mol}\) of \(\mathrm{SO}_{2}(g)\) to \(\mathrm{SO}_{3}(g)\) absorbs \(89.5 \mathrm{~kJ}\). The enthalpy of formation of \(\mathrm{SO}_{3}(g)\) is -204.2 kJ under these conditions. Find the enthalpy of formation of \(\mathrm{SO}_{2}(g)\).

One tablespoon of peanut butter has a mass of \(16 \mathrm{~g}\). It is combusted in a calorimeter whose heat capacity is \(120.0 \mathrm{~kJ} /{ }^{\circ} \mathrm{C}\). The temperature of the calorimeter rises from \(22.2^{\circ} \mathrm{C}\) to \(25.4^{\circ} \mathrm{C}\). Find the food caloric content of peanut butter.

Starting from the relationship between temperature and kinetic energy for an ideal gas, find the value of the molar heat capacity of an ideal gas when its temperature is changed at constant volume. Find its molar heat capacity when its temperature is changed at constant pressure.

The heat of vaporization of water at \(373 \mathrm{~K}\) is \(40.7 \mathrm{~kJ} / \mathrm{mol}\). Find \(q, w, \Delta E,\) and \(\Delta H\) for the evaporation of \(454 \mathrm{~g}\) of water at this temperature at 1 atm.

Find \(\Delta H\) for the combustion of ethanol \(\left(\mathrm{C}_{2} \mathrm{H}_{6} \mathrm{O}\right)\) to carbon dioxide and liquid water from the following data. The heat capacity of the bomb calorimeter is \(34.65 \mathrm{~kJ} / \mathrm{K},\) and the combustion of \(1.765 \mathrm{~g}\) of ethanol raises the temperature of the calorimeter from \(294.33 \mathrm{~K}\) to \(295.84 \mathrm{~K}\).

Which statement is true of the internal energy of the system and its surroundings following a process in which \(\Delta E_{\mathrm{sys}}=+65 \mathrm{~kJ} ?\) Explain. a. The system and the surroundings both lose 65 kJ of energy. b. The system and the surroundings both gain 65 kJ of energy. c. The system loses \(65 \mathrm{~kJ}\) of energy and the surroundings gain \(65 \mathrm{~kJ}\) of energy. d. The system gains 65 kJ of energy and the surroundings lose

The internal energy of an ideal gas depends only on its temperature. Which statement is true of an isothermal (constant-temperature) expansion of an ideal gas against a constant external pressure? Explain. a. \(\Delta E\) is positive. b. \(w\) is positive. c. \(q\) is positive. d. \(\Delta E\) is negative.

When 1 mol of a gas burns at constant pressure, it produces \(2418 \mathrm{~J}\) of heat and does \(5 \mathrm{~J}\) of work. Determine \(\Delta E, \Delta H, q,\) and \(w\) for the process.

In an exothermic reaction, the reactants lose energy, and the reaction feels hot to the touch. Explain why the reaction feels hot even though the reactants are losing energy. Where does the energy come from?

Which statement is true of a reaction in which \(\Delta V\) is positive? Explain. a. \(\Delta H=\Delta E\) b. \(\Delta H>\Delta E\) c. \(\Delta H<\Delta E\)

Classify each process as endothermic or exothermic. What is the sign of \(\Delta H\) for each process? Explain your answers. a. gasoline burning in an engine b. steam condensing on a mirror c. water boiling in a pot Provide at least two additional examples of exothermic processes and two additional examples of endothermic processes. Have each member of your group provide an example.

The heating value of combustible fuels is evaluated based on the quantities known as the higher heating value (HHV) and the lower heating value (LHV). The HHV has a higher absolute value and assumes that the water produced in the combustion reaction is formed in the liquid state. The LHV has a lower absolute value and assumes that the water produced in the combustion reaction is formed in the gaseous state. The LHV is therefore the sum of the HHV (which is negative) and the heat of vaporization of water for the number of moles of water formed in the reaction (which is positive). The table lists the enthalpy of combustion which is equivalent to the HHV-for several closely related hydrocarbons. $$\begin{array}{lc} \text { Hydrocarbon } & \Delta H_{\text {comb }}(\mathrm{kJ} / \mathrm{mol}) \\\ \mathrm{CH}_{4}(\mathrm{~g}) & -890 \\ \hline \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{~g}) & -1560 \\ \hline \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{~g}) & -2219 \\ \hline \mathrm{C}_{4} \mathrm{H}_{10}(\mathrm{~g}) & -2877 \\ \hline \mathrm{C}_{5} \mathrm{H}_{12}(I) & -3509 \\ \hline \mathrm{C}_{6} \mathrm{H}_{14}(I) & -4163 \\ \hline \mathrm{C}_{7} \mathrm{H}_{16}(I) & -4817 \\ \hline \mathrm{C}_{8} \mathrm{H}_{18}(I) & -5470 \\ \hline\end{array}$$ Use the information in the table to answer the following questions. a. Write two balanced equations for the combustion of \(\mathrm{C}_{3} \mathrm{H}_{8}\) one assuming the formation of liquid water and the other assuming the formation of gaseous water. b. Given that the heat of vaporization of water is \(44.0 \mathrm{~kJ} / \mathrm{mol}\), what is \(\Delta H_{\mathrm{rxn}}\) for each reaction in part a? Which quantity is the HHV? The LHV? c. When propane is used to cook in an outdoor grill, is the amount of heat released the HHV or the LHV? What amount of heat is released upon combustion of \(1.00 \mathrm{~kg}\) of propane in an outdoor grill? d. For each \(\mathrm{CH}_{2}\) unit added to a hydrocarbon, what is the average increase in the absolute value of \(\Delta H_{\mathrm{comb}} ?\)