Calculate the ratio of the energy released by the complete f

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.

Solution

during fission of one atom of U-235 it releases 202.5MeV i.e 202.5*(10^6)*(1.60218*10^ -19)=3.24*10^ -11J

during fission of one mole of U-235 it releases (3.24*10^ -11)*6.023*10^23=19.51452*10^12J

one mole of U-235= 238g

one gram of U-235=(1/238) moles of U-235

one gram of U-235=(1000/238) moles of U-235

energy released by 1kg of U-235 = (19.51452*10^12J per mole) * ((1000/238) moles per kg of U-235)

=81.993*10^12J/kg=81.993*10^9 kJ/kg

one mole of CH₄=16 g/mol=0.016 kg/mol

energy released by one kg of methane=802 kJ/mol / 0.016 kg/mol = 5.0125* 10⁴ kJ/kg

ratio of energy released by 1kg of U-235 to that of 1kg of methane= (81.993*10^9 kJ/kg)/(5.0125* 10⁴kJ/kg)

=1.635770*10⁶