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------------------------------------------------ Determine the molar enthalpy of fission for Uranium-235 if the fission of 1.00 kg of pure Uranium-235 generates [tex]8.1 \times 10^{10} \, \text{KJ}[/tex] of energy.

The molar enthalpy of fission for Uranium-235 is approximately -1.9 x 10^10 KJ/mol, calculated by dividing the total energy released by the number of moles of Uranium-235 in 1 kg.

Explanation:

To determine the molar enthalpy of fission for Uranium-235, we need to understand that the energy released during the fission process is a result of mass being converted into energy, according to Einstein's equation, E=mc2. The provided information states that the fission of 1.00 kg of Uranium-235 generates 8.1 x 1010 KJ of energy. We will use Avogadro's number and the molar mass to find the number of moles of Uranium-235 in 1.00 kg and then calculate the molar enthalpy of fission.

The molar mass of Uranium-235 is 235.04 g/mol, which means that in 1.00 kg (or 1000 grams) of Uranium-235, there are (1000 g) / (235.04 g/mol) = approximately 4.25 moles of Uranium-235. Using Avogadro's number, 6.02 x 1023 atoms/mol, we find that there are (4.25 mol) x (6.02 x 1023 atoms/mol) = 2.56 x 1024 atoms of Uranium-235 in 1 kg.

Since the entire sample of 1 kg Uranium-235 produced 8.1 x 1010 KJ of energy, we calculate the energy per mole by dividing the total energy by the number of moles. The energy per mole is (8.1 x 1010 KJ) / (4.25 mol) = 1.9 x 1010 KJ/mol. Therefore, the molar enthalpy of fission for Uranium-235 is approximately -1.9 x 1010 KJ/mol, where the negative sign indicates that energy is released in the process.