Question

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Complete each of the following nuclear reactions and calculate the energy change (in units J/mol of...

Complete each of the following nuclear reactions and calculate the energy change (in units J/mol of reactant) associated with each one. (Al-27 = 26.981538 amu, He-4=4.002603 amu, P-30=29.981801, W-179=178.94707, Ta- 179=178.94593)

(for below x / y , x = mass number while y = atomic number)

a. 27 / 13 Al + 4 / 2 He → 30 / 15 P + ______

b. 179 / 74 W + ______ →179 / 73 Ta

Solutions

Expert Solution

(a)     27 / 13 Al + 4 / 2 He     30 / 15 P + 1 / 0 n

Mass of product = 29.981801 + 1.00867 = 30.990471 amu

Mass of reactants = 26.981538 + 4.002603 = 30.984141 amu

Change in mass for the reaction (mass of products - mass of reactants) =

m = 30.990471 - 30.984141

= 0.00633 amu

Energy = m* c2

= (0.00633 amu) (1.6606 x 10-27 kg/amu)(2.9979 x 108 m/s)2

= 0.0944 x 10-11 J

= 9.44 x 10-13 J

Energy per mole of reactant = 9.44 x 10-13 J / (6.023 x 1023 atoms/mol)

= 1.56 x 1010 J/mol

(b). 179 / 74 W + 0 / 1 e    179 / 73 Ta

Mass of product =178.94593 amu

Mass of reactants = 178.94707 + 0.00055 = 178.94762 amu

Change in mass for the reaction (mass of products - mass of reactants) =

m = 178.94593 - 178.94762

= - 0.00169 amu

Energy = m* c2

= ( - 0.00169 amu) (1.6606 x 10-27 kg/amu)(2.9979 x 108 m/s)2

= 0.0252 x 10-11 J

= 2.52 x 10-13 J

Energy per mole of reactant = 2.52 x 10-13 J / (6.023 x 1023 atoms/mol)

= 4.18 x 109 J/mol

queen_honey_blossom answered 1 hour ago
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