Problem 3: Look up electricity and natural gas prices on the internet. Use these to compare the cost of energy derived from electricity and natural gas. Assume natural gas is entirely methane (CHa) and that all the energy comes from its combustion. We know that the enthalpy of combustion of methane is 890 kJ. There are several ways to proceed. Here is one suggestion: For electricity, you can find the cost of a kilowatt-hour. Simply express this as Joules and divide the cost by the number of Joules to get price per Joule. If the number is inconveniently small, multiply by 106 to get cost per 1000 kJ. For natural gas you have the cost per 1000 ft3. Convert this to m3, and use the density given above to find the mass of methane contained in this volume. Convert mass to moles and use the known heat of combustion to get the energy content. Divide cost by energy content in Joules. The cost per Joule can be compared to the number you get for electricity. Again, if the cost per Joule is very low, write the amount as cost per 1000kJ.

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Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
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Chapter1: Chemical Foundations
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**Problem 3:**

**Objective:** Compare the cost of energy derived from electricity and natural gas. Assume natural gas is entirely methane (CH₄) with the enthalpy of combustion being 890 kJ.

**Procedure Suggestion:**

1. **Electricity:**
   - Determine the cost of a kilowatt-hour (kWh).
   - Convert this cost to Joules.
   - To find the price per Joule, divide the cost by the number of Joules.
   - If the price per Joule is very small, multiply by 10⁶ to express the cost per 1000 kJ.

2. **Natural Gas:**
   - Use the cost per 1000 cubic feet (ft³).
   - Convert the volume from cubic feet to cubic meters (m³).
   - Using the given density, find the mass of methane in this volume.
   - Convert the mass to moles.
   - Use the heat of combustion to calculate the energy content in Joules.
   - Divide the cost by the energy content to find the cost per Joule.
   - Compare this value to the electricity cost. If the cost per Joule is very low, express it as the cost per 1000 kJ. 

This method allows for the comparison of energy costs from different sources on an equivalent basis.
Transcribed Image Text:**Problem 3:** **Objective:** Compare the cost of energy derived from electricity and natural gas. Assume natural gas is entirely methane (CH₄) with the enthalpy of combustion being 890 kJ. **Procedure Suggestion:** 1. **Electricity:** - Determine the cost of a kilowatt-hour (kWh). - Convert this cost to Joules. - To find the price per Joule, divide the cost by the number of Joules. - If the price per Joule is very small, multiply by 10⁶ to express the cost per 1000 kJ. 2. **Natural Gas:** - Use the cost per 1000 cubic feet (ft³). - Convert the volume from cubic feet to cubic meters (m³). - Using the given density, find the mass of methane in this volume. - Convert the mass to moles. - Use the heat of combustion to calculate the energy content in Joules. - Divide the cost by the energy content to find the cost per Joule. - Compare this value to the electricity cost. If the cost per Joule is very low, express it as the cost per 1000 kJ. This method allows for the comparison of energy costs from different sources on an equivalent basis.
Expert Solution
Step 1

Average cost of electricity per kilowatt-hour = 10.42 cent or $ 0.1042 

Average cost of natural gas = $ 9.52 per 1000 ft3 

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