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Chapter 8: Problem 65

Natural gas companies in the United States use the "therm" as a unit of energy. One therm is \(1 \times 10^{5} \mathrm{BTU}\). (a) How many joules are in one therm? \(\left(1 \mathrm{~J}=9.48 \times 10^{-4} \mathrm{BTU}\right)\) (b) When propane gas, \(\mathrm{C}_{3} \mathrm{H}_{8}\), is burned in oxygen, \(\mathrm{CO}_{2}\) and steam are produced. How many therms of energy are given off by \(1.00 \mathrm{~mol}\) of propane gas?

Short Answer

Expert verified
Answer: When 1.00 mol of propane gas is burned in oxygen, 1.94 x 10^(-2) therms of energy are given off.

Step by step solution

01

Convert 1 therm to Joules

To find how many joules are in one therm, we will use the given conversion factor: $$1 \mathrm{~J} = 9.48 \times 10^{-4} \mathrm{BTU}$$ We know that 1 therm is \(1 \times 10^{5} \mathrm{BTU}\). To convert it to Joules, we will multiply the number of therms by the conversion factor: $$\mathrm{Joules} = \mathrm{therms} \times \frac{1 \mathrm{~J}}{9.48 \times 10^{-4} \mathrm{BTU}}$$
02

Calculate the Joules in 1 therm

Now, we can replace the number of therms with 1 and calculate the Joules: $$\mathrm{Joules} = 1 \times 10^{5} \mathrm{BTU} \times \frac{1 \mathrm{~J}}{9.48 \times 10^{-4} \mathrm{BTU}}$$ After calculating, we find: $$\mathrm{Joules} = 1.055 \times 10^{8} \mathrm{~J}$$
03

Write the balanced equation for propane combustion

The balanced chemical equation for propane combustion in oxygen is: $$\mathrm{C}_{3}\mathrm{H}_{8} + 5\mathrm{O}_{2} \rightarrow 3\mathrm{CO}_{2} + 4\mathrm{H}_{2}\mathrm{O}$$
04

Calculate the energy released per mole of propane

For this step, we will use the enthalpy of combustion, which represents the energy released when 1 mole of propane reacts completely in oxygen to form products. The enthalpy of combustion for propane is approximately \(-2044 \mathrm{~kJ/mol}\) (this value may vary depending on reference sources).
05

Convert energy released per mole of propane to therms

We know that 1 mole of propane releases \(-2044 \mathrm{~kJ}\) of energy. First, we need to convert kJ to J: $$-2044 \mathrm{~kJ} \times \frac{10^{3} \mathrm{~J}}{1 \mathrm{~kJ}} = -2.044 \times 10^{6} \mathrm{~J}$$ Now, we can use the conversion factor from Step 1 to convert Joules to therms: $$\mathrm{therms} = \frac{-2.044 \times 10^{6} \mathrm{~J}}{1.055 \times 10^{8} \mathrm{~J/therm}}$$
06

Calculate the number of therms released by 1 mole of propane

Finally, we can calculate the number of therms released by 1 mole of propane: $$\mathrm{therms} = \frac{-2.044 \times 10^{6} \mathrm{~J}}{1.055 \times 10^{8} \mathrm{~J/therm}} = -1.94 \times 10^{-2} \mathrm{~therms}$$ (rounded to two decimal places) So, (a) There are \(1.055 \times 10^{8} \mathrm{~J}\) in one therm. (b) When 1.00 mol of propane gas is burned in oxygen, \(1.94 \times 10^{-2}\) therms of energy are given off.

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Most popular questions from this chapter

For the vaporization of one mole of water at \(100^{\circ} \mathrm{C}\) determine (a) \(\Delta H\) (Table 8.3) (b) \(\Delta P V\) (in kilojoules) (c) \(\Delta E\)

Some solar-heated homes use large beds of rocks to store heat. (a) How much heat is absorbed by \(100.0 \mathrm{~kg}\) of rocks if their temperature increases by \(12^{\circ} \mathrm{C} ?\) (Assume that \(c=0.82 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\).) (b) Assume that the rock pile has total surface area \(2 \mathrm{~m}^{2}\). At maximum intensity near the earth's surface, solar power is about 170 watts \(/ \mathrm{m}^{2}\). (1 watt = \(1 \mathrm{~J} / \mathrm{s}\).) How many minutes will it take for solar power to produce the \(12^{\circ} \mathrm{C}\) increase in part (a)?

Nitroglycerine, \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l)\), is a powerful explosive used in rock blasting when roads are created. When ignited, it produces water, nitrogen, carbon dioxide, and oxygen. Detonation of one mole of nitroglycerine liberates \(5725 \mathrm{~kJ}\) of heat. (a) Write a balanced thermochemical equation for the reaction for the detonation of four moles of nitroglycerine. (b) What is \(\Delta H_{\mathrm{f}}^{\circ}\) for \(\mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(l) ?\)

Titanium is a metal used in jet engines. Its specific heat is \(0.523 \mathrm{~J} / \mathrm{g} \cdot{ }^{\circ} \mathrm{C}\). If \(5.88 \mathrm{~g}\) of titanium absorbs \(4.78 \mathrm{~J}\), what is the change in temperature?

Find (a) \(\Delta E\) when a gas absorbs \(18 \mathrm{~J}\) of heat and has \(13 \mathrm{~J}\) of work done on it. (b) \(q\) when 72 J of work is done on a system and its energy is increased by \(61 \mathrm{~J}\).
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