Pretend you are a nuclear scientist and try to answer this bonus question. Uranium -235 (235U) is used as a fuel in nuclear power plants. However, natural uranium contains mostly U -238 (238U) and very little uranium -235. Therefore, it is necessary that the natural uranium be enriched in uranium -235 before it can be used. To do this, the natural uranium is first converted to uranium (IV) oxide, UO2, and then to the gaseous compound, uranium (VI) fluoride, UF6, as shown by the equations below.

(1) U(s) + O2(g) -> UO2(s)

(2) UO2(s) + 4 HF(g) -> UF4(s) + 2H2O(g)

(3) UF4(s) + F2(g) -> UF6(g)

The molecules of UF6 that contain the uranium -235 atoms are somewhat lighter in weight than those with the uranium -238 atoms. The difference in mass of the two uranium isotopes enables the molecules of UF6 to be separated by a gaseous diffusion process.

How much energy (in kilojoules) would be involved in producing 100 tons of UF6(g) from UO2(s) (1 ton = 9.08  105 g)? Use the standard heats (enthalpies) of formation below:

COMPOUND HEAT OF FORMATION (ΔHof)
UO2(s) - 1085 kJ/mol
UF4(s) - 1914 kJ/mol
UF6(g) - 2147 kJ/mol
H2O(g) -241.8 kJ/mol
HF(g) -271.1 kJ/mol

To calculate the energy involved in producing 100 tons of UF6(g) from UO2(s), we need to determine the number of moles of each compound involved in the reaction and then use the enthalpies of formation to calculate the energy.

First, let's calculate the number of moles of UO2(s) needed. We know that 1 ton is equal to 9.08 × 10^5 grams, so 100 tons would be equal to 100 × 9.08 × 10^5 g.

Molar mass of UO2(s) = 238.0289 g/mol (uranium isotope 238U)
The number of moles of UO2(s) is given by:
moles of UO2(s) = mass of UO2(s) / molar mass of UO2(s)
moles of UO2(s) = (100 × 9.08 × 10^5 g) / 238.0289 g/mol

Next, let's calculate the number of moles of UF6(g) produced from UO2(s) using the stoichiometry of the reaction.
From equation (2), we can see that 1 mole of UO2(s) reacts to produce 1 mole of UF6(g).
moles of UF6(g) = moles of UO2(s)

Now, we can calculate the energy involved in producing the UF6(g) using the enthalpies of formation.
Energy = (moles of UF6(g) × ΔHof(UF6)) + (moles of H2O(g) × ΔHof(H2O)) + (moles of HF(g) × ΔHof(HF)) - (moles of UO2(s) × ΔHof(UO2)) - (moles of UF4(s) × ΔHof(UF4))

Given values for ΔHof:
ΔHof(UO2) = -1085 kJ/mol
ΔHof(UF4) = -1914 kJ/mol
ΔHof(UF6) = -2147 kJ/mol
ΔHof(H2O) = -241.8 kJ/mol
ΔHof(HF) = -271.1 kJ/mol

Substituting the values:

Energy = (moles of UF6(g) × (-2147 kJ/mol)) + 0 + (0 × (-271.1 kJ/mol)) - (moles of UO2(s) × (-1085 kJ/mol)) - (moles of UF4(s) × (-1914 kJ/mol))

Finally, substitute the calculated values for moles of UF6(g) and moles of UO2(s) into the equation, where moles of UF4(s) can be assumed to be zero since it reacts completely.

Energy = (moles of UO2(s) × (-48.78 kJ/mol))

Note: The actual numerical values for moles of UO2(s) and moles of UF6(g) would need to be calculated based on the given masses and molar masses, as mentioned earlier.

Now, you can calculate the energy involved in producing 100 tons of UF6(g) from UO2(s) using the steps outlined above.

To calculate the energy involved in producing 100 tons of UF6(g) from UO2(s), we need to determine the energy changes for each step in the process and then multiply by the appropriate stoichiometric coefficients.

Step 1: Conversion of UO2(s) to UF4(s)
From the given equation (2): UO2(s) + 4 HF(g) -> UF4(s) + 2H2O(g), we can see that the stoichiometric coefficient of UO2(s) is 1.

To calculate the energy change, we need to know the molar mass of UO2(s). The molar mass of uranium dioxide (UO2) is calculated by adding the atomic masses of uranium (U) and oxygen (O), taking into account the subscripts:
1x Uranium (U) = 238.03 g/mol
2x Oxygen (O) = 2x 16.00 g/mol
Total molar mass of UO2 = 238.03 g/mol + 2x 16.00 g/mol = 270.03 g/mol

Since we're given the heat of formation (ΔHof) of UO2(s) in kJ/mol, which is -1085 kJ/mol, we can calculate the energy change using the following equation:
Energy change (in kJ) = (-ΔHof) x (mass of UO2(s)) / (molar mass of UO2)

Mass of UO2(s) = 100 tons = 100,000 kg = 100,000,000 g
Energy change = (-(-1085 kJ/mol)) x (100,000,000 g) / (270.03 g/mol)

Calculate the energy change for step 1 using the given values.

Step 2: Conversion of UF4(s) to UF6(g)
From the given equation (3): UF4(s) + F2(g) -> UF6(g), we can see that the stoichiometric coefficient of UF4(s) is 1.

Since we're given the heat of formation (ΔHof) of UF6(g) in kJ/mol, which is -2147 kJ/mol, we can calculate the energy change using the following equation:
Energy change (in kJ) = (-ΔHof) x (mass of UF6(g)) / (molar mass of UF6)

Mass of UF6(g) = 100 tons = 100,000 kg = 100,000,000 g
Energy change = (-(-2147 kJ/mol)) x (100,000,000 g) / (molar mass of UF6)

Calculate the energy change for step 2 using the given values.

Finally, sum up the energy changes for steps 1 and 2 to find the total energy involved in producing 100 tons of UF6(g) from UO2(s).