Answer :
Final answer:
The total energy extracted from U-235 fission reactions from 1 kg of natural UO2 is approximately 9.81 * 10^-13 Joules, considering the given parameters.
Explanation:
To calculate the total energy that can be extracted from U-235 fission reactions from 1 kg of natural UO2, we need to use the given parameters. As the natural abundance of U-235 in natural uranium is 0.72%, the amount of U-235 in 1 kg of natural UO2 would be 0.0072 kg or 7.2 g. Considering the molecular mass of U-235 is 235.044 g/mol, this equates to approximately 0.0306 mol.
Now, each mole of U-235 undergoes fission to release 200 MeV of energy. So, the total energy released could be calculated as 0.0306 mol * 200 MeV/mol = 6.12 MeV. However, 1 MeV is approximately equal to 1.60218 * 10^-13 joules, so the total energy in joules would be 6.12 MeV * 1.60218 * 10^-13 J/MeV = 9.81 * 10^-13 J.
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Final answer:
To calculate the total energy from U-235 fission reactions, we find the number of U-235 atoms in 1 kg of natural UO2 and multiply it by the energy per U-235 fission. The total energy released is approximately 8.09 × 10^13 kJ.
Explanation:
To calculate the total energy that can be extracted from U-235 fission reactions, we need to find the number of U-235 atoms in 1 kg of natural UO2. The natural abundance of U-235 is 0.72%. To find the number of U-235 atoms, we multiply the mass of U-235 by Avogadro's number and divide by the molar mass of U-235. The total energy released is then calculated by multiplying the number of U-235 atoms by the energy per U-235 fission.
Given:
- U-235 natural abundance: 0.72%
- U-235 energy/fission: 200 MeV
- U-235 molecular mass: 235.044 g/mol
- Natural Uranium avg molecular mass: 238.03 g/mol
- Oxygen avg molecular mass: 16.0 g/mol
First, we find the number of moles of U-235 in 1.0 kg of natural UO2:
(1,000 g) / (238.03 g/mol) = 4.20 mol
Next, we find the number of U-235 atoms:
(4.20 mol) x (6.02 × 10^23 U/mol) = 2.53 × 10^24 atoms
Finally, we calculate the total energy released:
(2.53 × 10^24 atoms) x (200 MeV/atom) = 5.06 × 10^26 MeV or 8.09 × 10^13 kJ
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