In: Chemistry
Calculate the ratio of the energy released by the complete fission of 1.0 kg of Uranium-235 to the energy released by burning 1.0 kg of methane, CH4. You can use the fact that one mole of CH4 gives 802 kJ of energy, and recall from your chemistry course that there are 6.02*1023 atoms per mole.
To calculate the energy released by the complete fission of 1.0 kg of Uranium-235 we need to look at the fission first
235U + n ? 139Xe + 95Sr + 2n
The mass deficit for the reaction given is 138.9187869 + 94.9193582 + 1.008665 - 235.04394.
Dm = –0.19713 amu
Now to calculate the energy (MeV) released per one fission.
The annihilation of 1 amu of mass, produces 931.495 MeV. Thus, the mass deficit computed here would produce 183.6 MeV.
Now Calculate the energy released per kilogram of 235U
One MeV = 1.602176462x10-19 MJ and one amu = 1.66053873x10-27 kg. So the energy release per unit mass of the 235U atom for the fission reaction shown above is found as follows.
one mole of CH4 gives 802 kJ of energy
1 Kg of CH4 has 1000 g/16g/mol = 62.5 moles
Energy given out by 62.5 moles is 62.5 x 802kJ = 50.12 x 106 J = 50.12 MJ
So th compute the ratio of the energy released by the complete fission of 1.0 kg of Uranium-235 to the energy released by burning 1.0 kg of methane, CH4
= 7.54 x 107 MJ/50.12 MJ = 1.5 x 106