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Chapter 6: Problem 93

Assume that \(4.19 \times 10^{6} \mathrm{~kJ}\) of energy is needed to heat a home. If this energy is derived from the combustion of methane \(\left(\mathrm{CH}_{4}\right)\), what volume of methane, measured at STP, must be burned? \(\left(\Delta H_{\text {combustion }}^{\circ}\right.\) for \(\mathrm{CH}_{4}=-891 \mathrm{~kJ} / \mathrm{mol}\) )

Short Answer

Expert verified
To heat a home with \(4.19 \times 10^6 \mathrm{kJ}\) of energy using methane, approximately 105,378.43 liters of methane, measured at STP, must be burned.

Step by step solution

01

Determine the number of moles of methane needed to provide the required energy

Since the energy required is \(4.19 \times 10^6 \mathrm{kJ}\), we can calculate the number of moles of methane needed based on its enthalpy of combustion: Number of moles = \(\frac{ \text{Energy needed}}{ \text{Enthalpy of combustion}}\) Number of moles = \(\frac{4.19 \times 10^6 \mathrm{kJ}}{-891 \mathrm{kJ/mol}}\)
02

Calculate the number of moles of methane

Now that we have the formula, we can calculate the number of moles of methane required to generate the needed energy: Number of moles = \(\frac{4.19 \times 10^6 \mathrm{kJ}}{-891 \mathrm{kJ/mol}}\) Number of moles = \(4,706.18 \mathrm{mol}\)
03

Find the volume of methane at STP

At STP (Standard Temperature and Pressure), 1 mole of any gas occupies a volume of 22.4 L. Therefore, we can calculate the volume of methane needed by multiplying the number of moles by the volume occupied by 1 mole at STP: Volume of methane = \(4,706.18 \mathrm{mol} \times 22.4 \mathrm{L/mol}\)
04

Calculate the volume of methane needed

Now we can calculate the volume of methane needed to heat the home: Volume of methane = \(4,706.18 \mathrm{mol} \times 22.4 \mathrm{L/mol}\) Volume of methane = \(105,378.43 \mathrm{L}\) The volume of methane needed to heat the home, measured at STP, is approximately 105,378.43 liters.

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Most popular questions from this chapter

Consider the dissolution of \(\mathrm{CaCl}_{2}\) : \(\mathrm{CaCl}_{2}(s) \longrightarrow \mathrm{Ca}^{2+}(a q)+2 \mathrm{Cl}^{-}(a q) \quad \Delta H=-81.5 \mathrm{~kJ}\) An \(11.0-\mathrm{g}\) sample of \(\mathrm{CaCl}_{2}\) is dissolved in \(125 \mathrm{~g}\) water, with both substances at \(25.0^{\circ} \mathrm{C}\). Calculate the final temperature of the solution assuming no heat loss to the surroundings and assuming the solution has a specific heat capacity of \(4.18 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\)

Given the following data $$ \begin{aligned} \mathrm{P}_{4}(s)+6 \mathrm{Cl}_{2}(g) & \longrightarrow 4 \mathrm{PCl}_{3}(g) & & \Delta H=-1225.6 \mathrm{~kJ} \\ \mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) & \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s) & & \Delta H=-2967.3 \mathrm{~kJ} \\ \mathrm{PCl}_{3}(g)+\mathrm{Cl}_{2}(g) \longrightarrow \mathrm{PCl}_{5}(g) & & \Delta H=-84.2 \mathrm{~kJ} \\ \mathrm{PCl}_{3}(g)+\frac{1}{2} \mathrm{O}_{2}(g) \longrightarrow \mathrm{Cl}_{3} \mathrm{PO}(g) & & \Delta H=-285.7 \mathrm{~kJ} \end{aligned} $$ calculate \(\Delta H\) for the reaction $$ \mathrm{P}_{4} \mathrm{O}_{10}(s)+6 \mathrm{PCl}_{5}(g) \longrightarrow 10 \mathrm{Cl}_{3} \mathrm{PO}(g) $$

A cubic piece of uranium metal (specific heat capacity \(=\) \(0.117 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) ) at \(200.0^{\circ} \mathrm{C}\) is dropped into \(1.00 \mathrm{~L}\) deuterium oxide ("heavy water," specific heat capacity \(=4.211 \mathrm{~J} /{ }^{\circ} \mathrm{C} \cdot \mathrm{g}\) ) at \(25.5^{\circ} \mathrm{C}\). The final temperature of the uranium and deuterium oxide mixture is \(28.5^{\circ} \mathrm{C}\). Given the densities of uranium \((19.05\) \(\mathrm{g} / \mathrm{cm}^{3}\) ) and deuterium oxide \((1.11 \mathrm{~g} / \mathrm{mL})\), what is the edge length of the cube of uranium?

Hydrogen gives off \(120 . \mathrm{J} / \mathrm{g}\) of energy when burned in oxygen, and methane gives off \(50 . \mathrm{J} / \mathrm{g}\) under the same circumstances. If a mixture of \(5.0 \mathrm{~g}\) hydrogen and \(10 . \mathrm{g}\) methane is burned, and the heat released is transferred to \(50.0 \mathrm{~g}\) water at \(25.0^{\circ} \mathrm{C}\), what final temperature will be reached by the water?

The enthalpy change for the reaction $$ \mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l) $$ is \(-891 \mathrm{~kJ}\) for the reaction as written. a. What quantity of heat is released for each mole of water formed? b. What quantity of heat is released for each mole of oxygen reacted?
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