Natural gas (mainly CH_4) is used in many power plants to generate electrical po

Question

Natural gas (mainly CH_4) is used in many power plants to generate electrical power utilizing combustion reactions. Uranium-235 is used to generate power utilizing nuclear fission. Fusion reactions involving hydrogen-1 are under investigation as a future source of electrical power. 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 Delta E = Delta m middot c^2 where Delta E is the energy in joules, Delta m is the mass defect in kilograms, and c is the speed of light (c = 3.00 times 10^8 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. The sun produces energy via fusion. One of the fusion reactions that occurs in the sun is 4^1_1 H rightarrow^4_2 He + 2^0_1 e How much energy in joules is released by the fusion of 1.21 g of hydrogen-1? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

No. of moles of hydrogen-1 = 1.21g / 1.00782 g mol-1 = 1.2006 mol

4 mol hydrogen-1 fuses to give 1 mole Helium and 2 mol electrons

So no. of moles of helium formed = 1.2006 / 4 = 0.30015 mol

No. of moles of electrons = (1.2006 x 2) / 4 = 0.6003 mol

Mass of helium formed = 0.30015 mol x 4.00260 g mol-1 = 1.20138 g

Mass of electrons = 0.6003 mol x 0.00054858 g mol-1 = 0.000329 g

Mass of products = 1.20138 + 0.000329 = 1.2017 g

Mass defect (?m) = Reactant mass - Product mass = 1.21 - 1.2017 = 0.0083 g

?E = 0.0083 x 10-3 kg x (3.00 x 108 ms-1)2

= 7.47 x 1011 kg m2 s-2

= 7.47 x 1011 Joules

Related Questions

Navigate

• Browse (All)
• Browse N
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.