Unlike chemical reactions, for which mass is conserved, nuclear reactions result

Question

Unlike chemical reactions, for which mass is conserved, nuclear reactions result in slight changes in mass. When mass is lost, it becomes energy according to the equation E=mc2

where E is the energy in joules, m is the mass defect in kilograms, and c is the speed of light (c=3.00×108 m/s). The mass defect is the difference between the total mass of the products and the total mass of reactants.

The following values can be used to calculate the mass defect. Particle Mass (g/mol)

01e 0.00054858

11H 1.00782

42He 4.00260

Part A The sun produces energy via fusion. One of the fusion reactions that occurs in the sun is 411H42He+201e How much energy in joules is released by the fusion of 2.84 g of hydrogen-1?

Explanation / Answer

Solution:- The given balanced equation is....

4 1H1 --------> 2He4 + 2 1e0

for this equation,

delta m = 4(1.00782) - 4.00260 + 2(0.00054858)

delta m = 4.03128 - 4.00369716

delta m = 0.02758 g

Convert mass from g to kg.

0.02758 g x 1kg/1000 g = 2.758 x 10-5 kg

now plug in the values in the energy equation, delta E = delta m.c2

delta E = 2.758 x 10-5 kg x (3.0 x 108 m.s-1)2 = 2.48 x 1012 J

2.48 x 1012 J of energy is released by the fusion of 4 moles of H-1. To calculate the energy for the fusion of 2.84 g let's convert the grams into moles.

2.84 g x (1mol/1.00782 g) = 2.82 mol

Now we will calculate the energy...

2.82 mol x 2.48 x 1012 J/4 mol = 1.75 x 1012 J.

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