Question

Il Review | Constants Periodic Table 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 Natural gas (mainly CH4) 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. AE=Amục where AE is the energy in joules, Am is the mass defect in kilograms, and c is the speed of light (c = 3.00 x 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) 0.00054858 1.00782 He 4.00260 Part A The sun produces energy via fusion. One of the fusion reactions that occurs in the sun is 4 H+He +2e How much energy in joules is released by the fusion of 1.67 g of hydrogen-1? Express your answer to three significant figures and include the appropriate units.

Answer 1

Part- A

For the given reaction 41H1 -----------> 2He4 + 21e0  

The energy released from the reaction is calculated as (ΔE) = Δm * C2

where Δm = mass deffect of the reaction

= difference in total mass of product - total mass of reactants

= (mass of 2He4 + 2 * mass of 1e0) - 4 * (mass of 1H1)

= (4.00260 g + 2 mole * 0.00054858 g/mole) - 4 mole * (1.00782 g/mole)

= 4.00260 g + 0.00109716‬ g - 4.03128‬ g

= -0.02758284‬ g

Here the possitive value of the mass differecne will be taken

Thus Δm = 0.02758284‬ g

= 2.758284‬ * 10-2 g

= 2.758284‬ * 10-5 Kg (1 g = 10-3 Kg)

And C = speed of light

= 3 * 108 m/sec

So putting the values-

(ΔE) = Δm * C2

= 2.758284‬ * 10-5 Kg * (3 * 108 m/sec)2

= 2.758284‬ * 10-5 Kg * (9 * 1016 m2 /sec2)

= 24.824556‬‬ * 1011 Kg *m2 /sec2  

= 24.824556‬‬ * 1011 J ( 1 J = 1 Kg *m2 /sec2)

= 24.824556‬‬ * 1011 J

= 2.48‬‬ * 1010 J

That means from the fusion of 4 moles of Hydrogen, we get 2.48‬‬ * 1010 J of Energy

Now given mass of Hydrogen taken = 1.67 g

That means moles of Hydrogen taken = mass / molar mass

= 1.67 g / 1.00782 g/mole

= 1.657 moles

Then the amount of heat released from the fusion of 1.657 moles of Hyrogen is

= 2.48‬‬ * 1010 J/ 4 moles * 1.657 moles

= 1.03 ‬‬ * 1010 J