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Chapter 7: Problem 17

The combustion of methane gas, the principal constituent of natural gas, is represented by the equation $$\begin{aligned} \mathrm{CH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+& 2 \mathrm{H}_{2} \mathrm{O}(1) \\ \Delta H^{\circ} &=-890.3 \mathrm{kJ} \end{aligned}$$ (a) What mass of methane, in kilograms, must be burned to liberate \(2.80 \times 10^{7} \mathrm{kJ}\) of heat? (b) What quantity of heat, in kilojoules, is liberated in the complete combustion of \(1.65 \times 10^{4} \mathrm{L}\) of \(\mathrm{CH}_{4}(\mathrm{g})\) measured at \(18.6^{\circ} \mathrm{C}\) and \(768 \mathrm{mmHg} ?\) (c) If the quantity of heat calculated in part (b) could be transferred with \(100 \%\) efficiency to water, what volume of water, in liters, could be heated from 8.8 to \(60.0^{\circ} \mathrm{C}\) as a result?

Short Answer

Expert verified
In part (a), the approximate mass of the methane is 50268 kg. For part (b), the heat liberated is roughly \(1.372 \times 10^{9}\) kJ. Finally, for part (c), the volume of the water that can be heated is about \(3.279 \times 10^{7}\) L.

Step by step solution

01

Calculate the mass of methane for Part (a)

The heat of combustion of methane (\(CH_{4}\)) is -890.3 kJ. This means that 890.3 kJ of heat is produced when 1 mole of \(CH_{4}\) (which is approximately 16 g) is burned. Use the relationship to find mass of \(CH_{4}\) that produces \(2.80 \times 10^{7}\) kJ of heat. Set up a ratio: \[ \frac{890.3 \mathrm{ kJ}}{16 \mathrm{g}} = \frac{2.80 \times 10^{7}\mathrm{ kJ}}{ x} \]Solve for x (mass of methane).
02

Calculate quantity of heat for Part (b)

The volume of methane \(1.65 \times 10^{4} \mathrm{L}\) is given under conditions of \(18.6^{\circ} \mathrm{C}\) and \(768 \mathrm{mmHg}\). Convert this to number of moles (\(n\)) using the ideal gas law, \(PV=nRT\), where R is the ideal gas constant in appropriate units. Next, use the heat of combustion to calculate the total heat produced.
03

Calculate the volume of water for Part (c)

Assume that all the heat generated heats the water with 100% efficiency. Use the formula for heat transfer, \(q=mc\Delta T\), where \(m\) is the mass of water, \(c\) is the specific heat capacity of water (\(4.184 \mathrm{ kJ/kg \cdot K}\)), and \(\Delta T\) is the change in temperature (final - initial). Rearrange the formula to solve for mass (m) and then convert mass to volume using the density of water (1 g/mL or 1 kg/L).

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Most popular questions from this chapter

The method of Exercise 97 is used in some bomb calorimetry experiments. A 1.148 g sample of benzoic acid is burned in excess \(\mathrm{O}_{2}(\mathrm{g})\) in a bomb immersed in 1181 g of water. The temperature of the water rises from 24.96 to \(30.25^{\circ} \mathrm{C}\). The heat of combustion of benzoic acid is \(-26.42 \mathrm{kJ} / \mathrm{g} .\) In a second experiment, a \(0.895 \mathrm{g}\) powdered coal sample is burned in the same calorimeter assembly. The temperature of \(1162 \mathrm{g}\) of water rises from 24.98 to \(29.81^{\circ} \mathrm{C}\). How many metric tons (1 metric ton \(=1000 \mathrm{kg}\) ) of this coal would have to be burned to release \(2.15 \times 10^{9} \mathrm{kJ}\) of heat?

The heat of solution of \(\mathrm{NaOH}(\mathrm{s})\) in water is \(-41.6 \mathrm{kJ} / \mathrm{mol} \mathrm{NaOH} .\) When \(\mathrm{NaOH}(\mathrm{s})\) is dissolved in water the solution temperature (a) increases; (b) decreases; (c) remains constant; (d) either increases or decreases, depending on how much NaOH is dissolved.

\(\mathrm{CCl}_{4},\) an important commercial solvent, is prepared by the reaction of \(\mathrm{Cl}_{2}(\mathrm{g})\) with a carbon compound. Determine \(\Delta H^{\circ}\) for the reaction $$ \mathrm{CS}_{2}(1)+3 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CCl}_{4}(1)+\mathrm{S}_{2} \mathrm{Cl}_{2}(1) $$ Use appropriate data from the following listing. $$\begin{aligned} \mathrm{CS}_{2}(\mathrm{l})+3 \mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g})+2 \mathrm{SO}_{2}(\mathrm{g}) & \\ \Delta H^{\circ}=&-1077 \mathrm{kJ} \end{aligned}$$ $$2 \mathrm{S}(\mathrm{s})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{S}_{2} \mathrm{Cl}_{2}(1) \quad \Delta H^{\circ}=-58.2 \mathrm{kJ}$$ $$\mathrm{C}(\mathrm{s})+2 \mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{CCl}_{4}(1) \quad \Delta H^{\circ}=-135.4 \mathrm{kJ}$$ $$\mathrm{S}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-296.8 \mathrm{kJ}$$ $$\mathrm{SO}_{2}(\mathrm{g})+\mathrm{Cl}_{2}(\mathrm{g}) \longrightarrow \mathrm{SO}_{2} \mathrm{Cl}_{2}(1) \quad \Delta H^{\circ}=+97.3 \mathrm{kJ}$$ $$\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{g}) \quad \Delta H^{\circ}=-393.5 \mathrm{kJ}$$ $$\begin{aligned} \mathrm{CCl}_{4}(1)+\mathrm{O}_{2}(\mathrm{g}) \longrightarrow \mathrm{COCl}_{2}(\mathrm{g})+\mathrm{Cl}_{2} \mathrm{O}(\mathrm{g}) & \\ \Delta H^{\circ}=&-5.2 \mathrm{kJ} \end{aligned}$$

A 1.397 g sample of thymol, \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O}(\mathrm{s})\) (a preservative and a mold and mildew preventative), is burned in a bomb calorimeter assembly. The temperature increase is \(11.23^{\circ} \mathrm{C},\) and the heat capacity of the bomb calorimeter is \(4.68 \mathrm{kJ} /^{\circ} \mathrm{C}\). What is the heat of combustion of thymol, expressed in kilojoules per mole of \(\mathrm{C}_{10} \mathrm{H}_{14} \mathrm{O} ?\)

In each of the following processes, is any work done when the reaction is carried out at constant pressure in a vessel open to the atmosphere? If so, is work done by the reacting system or on it? (a) Neutralization of \(\mathrm{Ba}(\mathrm{OH})_{2}(\mathrm{aq})\) by \(\mathrm{HCl}(\mathrm{aq}) ;\) (b) conversion of gaseous nitrogen dioxide to gaseous dinitrogen tetroxide; (c) decomposition of calcium carbonate to calcium oxide and carbon dioxide gas.
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