Estimate the difference in energy produced when we burn 1kg of carbon vs producing nuclear energy from 1kg of U-235.
C + O2(g) -> CO2(g)
The fission of one atom of U-235 generates 202.5 MeV = 3.244 × 10−11 J, which translates to 19.54 TJ/mole,
To estimate the difference in energy produced when burning 1 kilogram (kg) of carbon vs producing nuclear energy from 1kg of U-235, we need to calculate the energy released in each process.
First, let's calculate the energy released when burning 1kg of carbon:
The balanced chemical equation for burning carbon in the presence of oxygen is:
C + O2(g) -> CO2(g)
To calculate the energy released, we need to know the enthalpy of combustion (∆H) for carbon. The ∆H for carbon combustion is approximately -394 kilojoules per mole (kJ/mol).
The molar mass of carbon (C) is 12.01 grams per mole (g/mol). Therefore, the number of moles in 1kg of carbon is:
(1 kg)*(1000 g/kg) / (12.01 g/mol) ≈ 83.28 mol
To calculate the energy released, we multiply the number of moles by the enthalpy of combustion:
Energy released = (∆H) * (moles of carbon)
Energy released = (-394 kJ/mol) * (83.28 mol) ≈ -32,791.52 kJ
Now, let's calculate the energy produced from 1kg of U-235:
The amount of energy released from nuclear fission reactions depends on a variety of factors, including the efficiency of the reactor and the fission process itself.
The average energy released per fission for U-235 is about 200 MeV (million electron volts), which is equivalent to approximately 3.206 × 10^-11 Joules (J) using the conversion factor 1 MeV = 1.602 × 10^-13 J.
The molar mass of U-235 is approximately 235 grams per mole (g/mol). Therefore, the number of moles in 1kg of U-235 is:
(1 kg)*(1000 g/kg) / (235 g/mol) ≈ 4.26 mol
To calculate the energy released, we multiply the number of moles by the energy released per fission:
Energy released = (Energy released per fission) * (moles of U-235)
Energy released = (3.206 × 10^-11 J/fission) * (4.26 mol) ≈ 1.37 × 10^-10 J
Now, to compare the energy released from burning 1kg of carbon vs producing nuclear energy from 1kg of U-235, we convert the energy released from carbon combustion to Joules and then calculate the difference:
Energy difference = (Energy produced from U-235) - (Energy released from carbon combustion)
Energy difference = (1.37 × 10^-10 J) - (-32,791.52 kJ) ≈ -32,791.52 kJ
It is important to note that the negative sign indicates that nuclear energy from U-235 produces significantly more energy compared to burning carbon. However, the absolute value of the difference is approximately 32,791.52 kJ.