World energy supplies are often measured in the unit of quadrillion British thermal units (10^12 btu), generally called a "quad." In 2015, world energy consumption is projected to be 5.81*10^17kJ.
Current annual energy consumption in the United States is 99.3 quads. Assume that all this energy is to be generated by burning CH4(g) in the form of natural gas. If the combustion of the CH4(g) were complete and 100% efficient, how many moles of CH4(g) would need to be combusted in order to provide the U.S. energy demand?
I am clueless as to how to solve this. My teacher did not go over this material so if someone could show me step by step how to solve this, that would be very much appreciated!!
See your post above.
5.51*10^5 quads
To solve this problem, you need to use the knowledge of the molar mass of CH4 (methane) and the energy released per mole of CH4 when it is burned completely. Here's a step-by-step method to solve this problem:
Step 1: Find the molar mass of CH4
The molar mass of methane (CH4) can be found by summing up the atomic masses of its constituent elements. Carbon (C) has an atomic mass of approximately 12.01 g/mol, and hydrogen (H) has an atomic mass of approximately 1.008 g/mol. Since there is only one carbon atom and four hydrogen atoms in methane, the molar mass can be calculated as follows:
Molar mass of CH4 = (12.01 g/mol) + (4 × 1.008 g/mol) = 16.04 g/mol
Step 2: Convert the US energy consumption from quads to joules
Given that the US energy consumption is 99.3 quads, we need to convert this to joules. One quad is equal to 1 × 10^15 British thermal units (BTU). And 1 BTU is approximately equal to 1,055 joules (J). Thus, we can use these conversion factors:
1 quad = 1 × 10^15 BTU
1 BTU ≈ 1,055 J
So, the energy consumption in joules can be calculated as follows:
Energy in joules = (99.3 quads) × (1 × 10^15 BTU/quad) × (1,055 J/BTU)
Step 3: Convert the energy from joules to kilojoules
Given that the energy consumption in the question is projected to be 5.81 × 10^17 kJ, we need to convert the energy from joules to kilojoules by dividing by 1000:
Energy in kilojoules = (Energy in joules) / 1000
Step 4: Calculate the number of moles of CH4 required
To find the number of moles of CH4 needed to produce this energy, we use the information that 1 mole of CH4 releases approximately 802 kJ of energy when burned completely and efficiently. We can use this information along with the energy consumption in kilojoules to calculate the moles of CH4:
Number of moles of CH4 = (Energy in kilojoules) / (Energy released per mole of CH4)
Step 5: Plug in the values and calculate
Now, we can substitute the values into the formula:
Number of moles of CH4 = (5.81 × 10^17 kJ) / (802 kJ/mol)
Calculating this equation will give you the final answer.