Question

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.

Answer 1

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 produce183.6 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