Problem 65 - Chemistry: Principles and Reactions

Question

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?

Step-by-Step Solution

Answer

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

Step 1: 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: $$\mathrm{Joules} = \mathrm{therms} \times \frac{1 \mathrm{~J}}{9.48 \times 10^{-4} \mathrm{BTU}}$$

Step 2: 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: $$\mathrm{Joules} = 1.055 \times 10^{8} \mathrm{~J}$$

Step 3: Write the balanced equation for propane combustion

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

Step 4: 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).

Step 5: 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: $$\mathrm{therms} = \frac{-2.044 \times 10^{6} \mathrm{~J}}{1.055 \times 10^{8} \mathrm{~J/therm}}$$

Step 6: 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.

Key Concepts

Energy Conversion

In thermodynamics, energy conversion is the process of transforming energy from one form to another, such as converting chemical energy into thermal energy. This plays a crucial role in how energy is utilized in everyday applications, such as heating or powering engines.

• Understanding Energy Units: Energy is measured in various units. Two common ones are British Thermal Units (BTU) and Joules (J). In the United States, a unit called a "therm" is often used, which equals 100,000 BTU. It's essential to know how to convert these units to understand energy consumption effectively.
• Conversion Factors: To convert energy from one unit to another, a conversion factor must be used. For example, knowing that 1 J equals approximately 9.48 x 10^-4 BTU allows you to convert BTU into Joules. For instance, using this factor, 1 therm (100,000 BTU) converts to 1.055 x 10⁸ Joules.

Grasping the concept of energy conversion is vital in fields like engineering and environmental science, where understanding the flow and transformation of energy can lead to more efficient systems and sustainable practices.

Chemical Reactions

Chemical reactions involve the transformation of reactants into products, often accompanied by the release or absorption of energy. These reactions are fundamental in fields like chemistry and physics, extensively used in industry and research.

• Balanced Equations: A chemical equation must be balanced, meaning the number of each type of atom on the reactant side equals the number on the product side. For instance, the combustion of propane is represented as \( \mathrm{C}_3\mathrm{H}_8 + 5\mathrm{O}_2 \rightarrow 3\mathrm{CO}_2 + 4\mathrm{H}_2\mathrm{O} \). This equation shows balanced carbon, hydrogen, and oxygen atoms.
• Energy in Reactions: Reactions can either be exothermic or endothermic, depending on whether they release or absorb energy. The combustion of propane is exothermic, releasing energy as heat and light.

Understanding chemical reactions involves knowing how substances interact and change, providing insights into natural processes and industrial manufacturing.

Combustion

Combustion is a specific type of chemical reaction where a substance reacts with oxygen, releasing heat and typically producing a flame. This process is crucial for energy production in engines, power plants, and even household heating systems.

• Propane Combustion: When propane \(\mathrm{C}_3\mathrm{H}_8\) burns in oxygen, it undergoes a combustion reaction that releases a significant amount of energy. This reaction is represented by the equation \( \mathrm{C}_3\mathrm{H}_8 + 5\mathrm{O}_2 \rightarrow 3\mathrm{CO}_2 + 4\mathrm{H}_2\mathrm{O} \). This transformation allows propane to serve as a powerful energy source for cooking and heating.
• Energy Release: The energy released during combustion is often expressed in kilojoules per mole (kJ/mol). For propane, the enthalpy of combustion is approximately -2044 kJ/mol. This value indicates how much energy is released when one mole of propane is burned.

Understanding combustion is essential for developing efficient and cleaner burning technologies, as it plays a central role in reducing emissions and improving air quality.