Chapter 25, Problem 37PS

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074

Chapter
Section

### Chemistry & Chemical Reactivity

10th Edition
John C. Kotz + 3 others
ISBN: 9781337399074
Textbook Problem

# Calculate the binding energy per mole of nucleons for O 8 16 . Masses needed for this calculation are H 1 1 = 1.00783, n 0 1 = 1.00867, and O 8 16 = 15.99492.

Interpretation Introduction

Interpretation:

The binding energy per mole of nucleons for Oxygen-16 has to be calculated.

Concept Introduction:

Nuclear fusion: A nuclear reaction in which a lighter nucleus fuse together spontaneously into new stable nuclei with the release of large amount of energy.

Binding energy: The amount of energy required to disassemble a system of particles into separate part is called binding energy and also separation energy.

Energy released in nuclear fusion: The mass change of the reaction is calculated; and using Einstein mass-energy relation, ΔE = Δmc2

Explanation

The masses of atoms have considered rather the mass of nuclei, because the number of electrons are same in both reactants and products and get cancelled. Subtracting the masses of the products from the mass of 235U reactant gives the mass change in the reaction. ReactantÂ â†’fusionÂ ProductsÂ +Â EnergyÂ (Massâ€‰Defect)

Given info:

Mass of proton =1.00783g/mole

Mass of neutron =1.00867g/mole

Mass of oxygen-16=15.99492g/mole

• Calculate the mass change:

By subtracting the masses of products from mass of reactant gives the mass defect of the fusion reaction.

8â€‰11HÂ +â€‰â€‰8â€‰01nÂ â†’Â â€‰816OÂ

MassÂ ofÂ 8(11H)=â€‰â€‰â€‰â€‰8.06264Â â€‰â€‰uMassÂ ofÂ 8â€‰01nÂ Â Â Â =Â â€‰â€‰â€‰8.06936Â Â uMassÂ ofÂ Â 816OÂ =â€‰â€‰-â€‰â€‰15.99492Â â€‰u_MassÂ changeÂ Â Â =Â Â â€‰0.13708Â u_

• Conversion of Mass defect in grams:

Asâ€‰known,0.13708Â Â uÂ =â€‰0.13708Â g/molByÂ dividingÂ withÂ Avagradro'sÂ number,=Â (0.13708Â Â uatom)â€‰(1.6605Ã—10-24gu)â€‰=Â â€‰0.2276â€‰Ã—10-24g/atom

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