Question

For the fission reaction ²³²U + n -----> ¹³⁷Te + ⁹⁷Zr + 2n

(a) Calculate the amount of energy produced per mol; (b) The heat of combustion of TNT, C₇H₅N₃O₆, is 3406 kJ/mol. FInd the mass of TNT needed to produce the same energy as 1.000 mol of the fission reaction above. (c) Calculate the energy released in (a) per gram of ²³⁵ U.

Answer 1

(a) The mass converted into energy is difference between sum of the mass of reactants and sum of mass of products. Here, its

Mass of Reactant: 235.04 + 1 = 236.04 g/mol

Mass of Product: 136.9 + 96.9 + 2 = 235.8 g/mol

Difference = 236.04 - 235.8 = 0.24 g/mol

As per Einstein Equation, E = mc²

where, m is the difference in mass of the reactants consumed and products formed, in kg

c is the velocity of light in m/s = 3 X 10⁸ m/s

E is the energy released in Joule/mol

putting the values in the equation we get

E = 0.24 X 10^-3 X (3 X 10⁸)² X 6.023 x 10²³ = 13 X 10³⁶ J/mol or 13 X 10³³ KJ/mol (Answer)

factor used for conversion of g to kg 10^-3

factor used for no of molecules in a mol 6.023 x 10²³