Consider a fuel moderator mixture consisting of 1 mole U-233 to 5 moles of Th-23

Question

Consider a fuel moderator mixture consisting of 1 mole U-233 to 5 moles of Th-232 to 500 moles light water. At the operating temperature of 400 oC and pressure of 15 MPa, the density of water is 0.0639 g/cc. Note that the atomic weights of U-233 and Th-232 are 233.039627 and 232.03805, respectively. Assuming that the density of the water for this fuel mixture is the same as for pure water and assuming that ep = 0.8:

What are the atom densities for U233, Th232, and water?

solve as fast as possible . thank you

Explanation / Answer

Given data:

no. of moles of U-233 = 1 , no. of moles of Th-232 = 5 , no. of moles of water = 500.

density of water == density of mixture = p = 0.0639 g/cc

Atomic density is given as N = p*NA / M, where M is molecular weight in gram/moles and NA is the Avogadro's no.

for mixture Nmix = p*NA / Mmix

Mmix = 1xMU-233 +5xMTh-232 +500xMH2O = 1x233.039627 + 5x232.03805 + 500x18 = 10393.23

thus, Nmix = (0.0639 g/cc) x (6.02x1023 nuclei/mol) / (10393.23 g/mol) = 3.701 x 1018 molecules/cc

individually, atomic density for:

NU-233 = 1x3.701x1018 =3.701x1018 atoms of U-233 /cc

NTh-232 = 5x3.701x1018 = 18.505x1018 atoms of Th-232 /cc

NH2O = 500x3.701x1018 = 1850.5x1018 molecules of water /cc

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