Connect 2-Year Access Card for Chemistry: The Molecular Nature of Matter and Change
Connect 2-Year Access Card for Chemistry: The Molecular Nature of Matter and Change
7th Edition
ISBN: 9780078129865
Author: Martin Silberberg Dr., Patricia Amateis Professor
Publisher: McGraw-Hill Education
Question
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Chapter 24, Problem 24.93P

(a)

Interpretation Introduction

Interpretation:

Mass difference of the given reaction has to be calculated

Concept Introduction:

Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.

Change in mass of a given reaction can be determined as given,

  Δm = Mass of reactant Mass of products

(a)

Expert Solution
Check Mark

Explanation of Solution

Given information is shown below,

  Given reaction: 96243Cm 94239Pu+ 24HeMass  of  96243Cm= 243.0614 amuMass  of 94239Pu= 239.0522 amuMass  of 24He= 4.0026 amu

  • Calculate the mass of products:

Mass of products is determined as shown below,

  Mass of products = Mass  of 24He + Mass  of 94239Pu= (4.0026 amu)+(239.0522 amu)= 243.0548 amu

  • Calculate the mass difference:

Mass of reactants (96243Cm) is 243.0614 amu

Mass difference of the reaction can be calculated as given,

  Δm = Mass of reactant Mass of products(243.0614 amu)(243.0548 amu)= 0.0066 amu

Mass difference is 0.0066 amu.

  • Convert unit of mass difference to Kg:

Mass difference for the reaction is converted from amu to kg as follows,

  Δm = (0.0066 amu)(1.661×1024 g1 amu)(1 kg103 kg)= 1.1×1029 kg

Mass difference for the reaction is 1.1×1029 kg.

(b)

Interpretation Introduction

Interpretation:

Energy released (in J)during the given reaction has to be determined.

Concept Introduction:

Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.

Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.

  Nucleus + nuclear binding energy  nucleons

It can be calculated using the given formula,

  ΔE = Δmc2where,Δm = Mass Differencec= Speed of light

(b)

Expert Solution
Check Mark

Explanation of Solution

Given information is shown below,

  Given reaction: 96243Cm 94239Pu+ 24HeMass  of  96243Cm= 243.0614 amuMass  of 94239Pu= 239.0522 amuMass  of 24He= 4.0026 amu

  • Calculate the mass difference:

Mass of reactants (96243Cm) is 243.0614 amu

Mass difference of the reaction can be calculated as given,

  Δm = Mass of reactant Mass of products(243.0614 amu)(243.0548 amu)= (0.0066 amu)(1.661×1024 g1 amu)(1 kg103 kg)= 1.1×1029 kg

Mass difference for the reaction is 1.1×1029 kg.

  • Calculate the energy released:

Energy released is calculated as follows for the reaction,

  Energy released, E = mc2= (1.1×1029 kg)(2.998×108 m/s)2= 9.8527×1013 J

Energy released during the given reaction is 9.8527×10-13 J.

(c)

Interpretation Introduction

Interpretation:

Energy released (in kJ/mol)during the given reaction has to be determined and difference between this energy values of heat of energy in a chemical reaction has to be commented.

Concept Introduction:

Nuclear reaction: A nuclear reaction in which a lighter nucleus fuses together into new stable nuclei or a heavier nucleus split into stable daughter nuclei with the release of large amount of energy.

Nuclear binding energy: It is the energy that requires for the breaking one mole of nuclei of an element to its individual nucleons.

  Nucleus + nuclear binding energy  nucleons

It can be calculated using the given formula,

  ΔE = Δmc2where,Δm = Mass Differencec= Speed of light

(c)

Expert Solution
Check Mark

Explanation of Solution

Given information is shown below,

  Given reaction: 96243Cm 94239Pu+ 24HeMass  of  96243Cm= 243.0614 amuMass  of 94239Pu= 239.0522 amuMass  of 24He= 4.0026 amu

  • Calculate the mass difference:

Mass of reactants (96243Cm) is 243.0614 amu

Mass difference of the reaction can be calculated as given,

  Δm = Mass of reactant Mass of products(243.0614 amu)(243.0548 amu)= (0.0066 amu)(1.661×1024 g1 amu)(1 kg103 kg)= 1.1×1029 kg

Mass difference for the reaction is 1.1×1029 kg.

  • Calculate the energy released:

Energy released for the reaction is calculated as follows,

Energy released, E = mc2= (1.1×1029 kg)(2.998×108 m/s)2= 9.8527×1013 J

Energy released during the given reaction is 9.8527×1013 J.

  • Convert the unit of energy released to kJ/mol :

Unit of energy released is converted as follows,

Binding energy, E in kJ/mol = (9.8527×1013 Jreactions)(6.022×1023 reactions1Emol)(1 kJ103 J)= 5.9×108 kJ/mol

Energy released during the given reaction is 5.9×108 kJ/mol.

Energy released during the given reaction is 5.9×108 kJ/mol whereas the energy values of heat of energy in a chemical reaction are in few hundreds kJ/mol.

This value is about one million times more than a typical heat of energy in a chemical reaction.

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Chapter 24 Solutions

Connect 2-Year Access Card for Chemistry: The Molecular Nature of Matter and Change

Ch. 24.2 - Prob. 24.6AFPCh. 24.2 - Prob. 24.6BFPCh. 24.6 - Prob. 24.7AFPCh. 24.6 - Prob. 24.7BFPCh. 24.7 - Prob. B24.1PCh. 24.7 - Prob. B24.2PCh. 24.7 - Prob. B24.3PCh. 24.7 - Prob. B24.4PCh. 24 - Prob. 24.1PCh. 24 - Prob. 24.2PCh. 24 - Prob. 24.3PCh. 24 - Prob. 24.4PCh. 24 - Prob. 24.5PCh. 24 - Prob. 24.6PCh. 24 - Prob. 24.7PCh. 24 - Prob. 24.8PCh. 24 - Prob. 24.9PCh. 24 - Prob. 24.10PCh. 24 - Prob. 24.11PCh. 24 - Prob. 24.12PCh. 24 - Prob. 24.13PCh. 24 - Prob. 24.14PCh. 24 - Prob. 24.15PCh. 24 - Prob. 24.16PCh. 24 - Prob. 24.17PCh. 24 - Prob. 24.18PCh. 24 - Prob. 24.19PCh. 24 - Prob. 24.20PCh. 24 - Prob. 24.21PCh. 24 - Prob. 24.22PCh. 24 - Prob. 24.23PCh. 24 - Prob. 24.24PCh. 24 - Prob. 24.25PCh. 24 - Prob. 24.26PCh. 24 - Prob. 24.27PCh. 24 - Prob. 24.28PCh. 24 - Prob. 24.29PCh. 24 - Prob. 24.30PCh. 24 - Prob. 24.31PCh. 24 - Prob. 24.32PCh. 24 - Prob. 24.33PCh. 24 - Prob. 24.34PCh. 24 - Prob. 24.35PCh. 24 - Prob. 24.36PCh. 24 - Prob. 24.37PCh. 24 - Prob. 24.38PCh. 24 - Prob. 24.39PCh. 24 - Prob. 24.40PCh. 24 - Prob. 24.41PCh. 24 - Prob. 24.42PCh. 24 - Prob. 24.43PCh. 24 - Prob. 24.44PCh. 24 - Prob. 24.45PCh. 24 - Prob. 24.46PCh. 24 - Prob. 24.47PCh. 24 - Prob. 24.48PCh. 24 - Prob. 24.49PCh. 24 - Prob. 24.50PCh. 24 - Prob. 24.51PCh. 24 - Prob. 24.52PCh. 24 - Prob. 24.53PCh. 24 - Prob. 24.54PCh. 24 - Prob. 24.55PCh. 24 - Prob. 24.56PCh. 24 - Prob. 24.57PCh. 24 - Prob. 24.58PCh. 24 - Prob. 24.59PCh. 24 - Prob. 24.60PCh. 24 - Prob. 24.61PCh. 24 - Prob. 24.62PCh. 24 - Prob. 24.63PCh. 24 - Prob. 24.64PCh. 24 - Prob. 24.65PCh. 24 - Prob. 24.66PCh. 24 - Prob. 24.67PCh. 24 - Prob. 24.68PCh. 24 - Prob. 24.69PCh. 24 - Prob. 24.70PCh. 24 - Prob. 24.71PCh. 24 - Prob. 24.72PCh. 24 - Prob. 24.73PCh. 24 - Prob. 24.74PCh. 24 - Prob. 24.75PCh. 24 - Prob. 24.76PCh. 24 - Prob. 24.77PCh. 24 - Prob. 24.78PCh. 24 - Prob. 24.79PCh. 24 - Prob. 24.80PCh. 24 - Prob. 24.81PCh. 24 - Prob. 24.82PCh. 24 - Prob. 24.83PCh. 24 - Prob. 24.84PCh. 24 - Prob. 24.85PCh. 24 - Prob. 24.86PCh. 24 - Prob. 24.87PCh. 24 - Prob. 24.88PCh. 24 - Prob. 24.89PCh. 24 - Prob. 24.90PCh. 24 - Prob. 24.91PCh. 24 - Prob. 24.92PCh. 24 - Prob. 24.93PCh. 24 - Prob. 24.94PCh. 24 - Prob. 24.95PCh. 24 - Prob. 24.96PCh. 24 - Prob. 24.97PCh. 24 - Prob. 24.98PCh. 24 - Prob. 24.99PCh. 24 - Prob. 24.100PCh. 24 - Prob. 24.101PCh. 24 - Prob. 24.102PCh. 24 - Prob. 24.103PCh. 24 - Prob. 24.104PCh. 24 - Prob. 24.105PCh. 24 - Prob. 24.106PCh. 24 - Prob. 24.107PCh. 24 - Prob. 24.108PCh. 24 - Prob. 24.109PCh. 24 - Prob. 24.110PCh. 24 - Prob. 24.111PCh. 24 - Prob. 24.112PCh. 24 - Prob. 24.113PCh. 24 - Prob. 24.114PCh. 24 - Prob. 24.115PCh. 24 - Prob. 24.116PCh. 24 - Prob. 24.117PCh. 24 - Prob. 24.118PCh. 24 - Prob. 24.119PCh. 24 - Prob. 24.120PCh. 24 - Prob. 24.121PCh. 24 - Prob. 24.122PCh. 24 - Prob. 24.123PCh. 24 - Prob. 24.124PCh. 24 - Prob. 24.125PCh. 24 - Prob. 24.126PCh. 24 - Prob. 24.127PCh. 24 - Prob. 24.128PCh. 24 - Prob. 24.129PCh. 24 - Prob. 24.130PCh. 24 - Prob. 24.131PCh. 24 - Prob. 24.132PCh. 24 - Prob. 24.133PCh. 24 - Prob. 24.134PCh. 24 - Prob. 24.135PCh. 24 - Prob. 24.136PCh. 24 - Prob. 24.137PCh. 24 - Prob. 24.138PCh. 24 - Prob. 24.139PCh. 24 - Prob. 24.140PCh. 24 - Prob. 24.141PCh. 24 - Prob. 24.142PCh. 24 - Prob. 24.143PCh. 24 - Prob. 24.144P
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