High School

A gallon of gasoline has an energy output of about [tex]1.3 \times 10^5[/tex] kJ. The energy released in the fission of one mole of uranium-235 is about [tex]2.0 \times 10^{10}[/tex] kJ. How many gallons of gasoline could be replaced by 2.0 kg of uranium-235, assuming the materials and the technology were available?

Answer :

To find out how many gallons of gasoline could be replaced by 2.0 kg of uranium-235, we need to compare the energy outputs of the two substances.

First, let's convert the energy released in the fission of one mole of uranium-235 from kJ to J:
2.0×10^10 kJ = 2.0×10^10 × 1000 J = 2.0×10^13 J

Now, let's calculate the number of moles of uranium-235 in 2.0 kg.

The molar mass of uranium-235 is approximately 235 g/mol:
Number of moles = mass / molar mass

= 2000 g / 235 g/mol

Number of moles of Uranium-235 in 2 kg = 8.51 mol

Since we know the energy released in the fission of one mole of uranium-235 (2.0×10^13 J), we can calculate the total energy released by 2.0 kg of uranium-235:


Total energy = energy per mole × number of moles = 2.0×10^13 J/mol × 8.51 mol

Total energy released by 2 kg of uranium-235 = 1.70×10^14 J

Now, let's convert the total energy released to gallons of gasoline.

1 gallon of gasoline has an energy output of about 1.3×10^5 kJ, which is equal to 1.3×10^8 J.


Number of gallons = Total energy / energy per gallon = 1.70×10^14 J / 1.3×10^8 J/gallon

Calculating this gives us:
Number of gallons = 1.31×10^6 gallons

Therefore, 2.0 kg of uranium-235 could replace approximately 1.31×10^6 gallons of gasoline, assuming the materials and technology were available.

It's important to note that this calculation is based solely on energy output and doesn't take into account other factors like efficiency, availability, and environmental impact. Additionally, the conversion factors and values used are approximations and may vary in practice.

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