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Answer :
Final answer:
4.0 lb of uranium-235 can replace approximately 1.41x10^8 cubic feet of natural gas.
Explanation:
To calculate how many cubic feet of natural gas can be replaced by 4.0 lb of uranium-235, we need to convert the mass of uranium-235 to moles. The molar mass of uranium-235 is approximately 235 g/mol. Therefore, 4.0 lb of uranium-235 is equal to:
(4.0 lb) * (453.592 g/lb) / (235 g/mol) = 7.75 mol
Now, we can calculate the energy released by 7.75 moles of uranium-235:
(7.75 mol) * (2.0x10^10 kJ/mol) = 1.55x10^11 kJ
Next, we can calculate how many cubic feet of natural gas are equivalent to 1.55x10^11 kJ. We know that 1 cubic foot of natural gas has an energy output of about 1.1x10^3 kJ. Therefore:
(1.55x10^11 kJ) / (1.1x10^3 kJ/cubic foot) = 1.41x10^8 cubic feet
Therefore, 4.0 lb of uranium-235 can replace approximately 1.41x10^8 cubic feet of natural gas, assuming the materials and the technology were available.
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