Connect 1 Semester Access Card for General Chemistry: The Essential Concepts
Connect 1 Semester Access Card for General Chemistry: The Essential Concepts
7th Edition
ISBN: 9781259692543
Author: Raymond Chang Dr.; Kenneth Goldsby Professor
Publisher: McGraw-Hill Education
Question
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Chapter 21, Problem 21.70QP

(a)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

  • Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy
  • This quantity represents the conversion of mass to energy occurs during an exothermic reaction.
  • Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is,ΔE =(Δm)c2

    Where, (Δm) is called mass defect.

  • The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

(a)

Expert Solution
Check Mark

Answer to Problem 21.70QP

The energy released in the above two decays is 5.59×10-15 J and 2.84×10-13J.

The total amount of energy released is:

(5.59×10-15 J)+2.84×10-13J=2.90×10-13J

Explanation of Solution

In case of Sr90 decay, the mass defect is

Δm=(massY90+mass e-)-massSr90

=[ (89.907152amu+5.4857×10-4amu)-89.907738amu ]=-3.7430×10-5amu

=(-)3.7430× 10-5 amu)×1g6.022×1023amu  =6.216 10-29 g =-6.216×10-32kg

The energy change is given by :

ΔE(Δm)c2

(-6.216×10-32kg)(3.00×108m/s)2

=5.59×10-15kgm2/s2=5.59×10-15J

Similarly for Y90 decay, we have

Δm=(massZr90+masse-)-massY90

[(89.904703 amu + 5.4857 ×10-4amu-89.907152amu]=-1.9004×10-3amu

(-1.9004 ×103 amu)×1 g6.022×1023 amu=3.156× 1027g

=- 3.156× 1030kg

And the energy change is given by:

ΔE=(-3.156×10-30kg)(3.00×108m/s)2=-2.84×10-13J

The energy released in the above two decays is 5.59×10-15 J and 2.84×10-13J.

The total amount of energy released is:

(5.59×10-15 J)+2.84×10-13J=2.90×10-13J

(b)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

  • Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy
  • This quantity represents the conversion of mass to energy occurs during an exothermic reaction.
  • Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is,ΔE =(Δm)c2

    Where, (Δm) is called mass defect.

  • The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The number of moles 90Sr decaying in a year.

(b)

Expert Solution
Check Mark

Answer to Problem 21.70QP

The number of moles of nuclei which decay in a year is :

(1- 0.9756) mol = 0.0244 mol

This is a reasonable number since it takes 28.1 years for 0.5 moles of 90Sr to decay

Explanation of Solution

This calculation requires that we know the rate constant for the decay.

From half-life, we can calculate k.

k = 0.693t1/2=0.69328.1yr=0.0247 yr-1

To calculate the number of moles 90Sr decaying in a year, we apply the following equation:

ln NtN0=-kt

lnx1=-(0.0247yr-1)(1yr)

Where x is the number of moles nuclei left over .solving, we obtained the value of x

x = 0.9756 mol 90Sr

Thus the number of moles of nuclei which decay in a year is :

(1- 0.9756) mol = 0.0244 mol

This is a reasonable number since it takes 28.1 years for 0.5 moles of 90Sr to decay

(c)

Interpretation Introduction

Interpretation: For the given cases number of moles amount of heat released, energy released for each cases for both decay should be determined.

Concept Introduction:

  • Energy required to break the nucleus into its corresponding proton and neutron is called nuclear binding energy
  • This quantity represents the conversion of mass to energy occurs during an exothermic reaction.
  • Nuclear binding energy can be calculated by Einstein’s mass energy equivalence relationship that is,ΔE =(Δm)c2

    Where, (Δm) is called mass defect.

  • The difference between mass of an atom and the sum of the masses of its proton, electron, and neutron is called Mass defect

To calculate: The heat released from 1 mole of 90Sr waste in a year.

(c)

Expert Solution
Check Mark

Answer to Problem 21.70QP

The heat released from 1 mole of 90Sr waste in a year is given by:

heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ

Explanation of Solution

The half –life of Y90 is much shorter than that of 90Sr.

We can assume that Y90 formed from 90Sr and will be converted to Z90.

The energy changes in (a) refer to decay of individual nuclei.

In 0.0244 moles, the number of nuclei that have decay is:

0.0244 mol×6.022 ×10 23nuclei1mol=1.47×1022nuclei

There are two decay processes occurring, so we need to add the energy released for each process calculated in part (a).

So the heat released from 1 mole of 90Sr waste in a year is given by:

heat released =(1.47× 1022nuclei)×2.90×10-13J1nucleus=4.26×109J=4.26×109kJ

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Chapter 21 Solutions

Connect 1 Semester Access Card for General Chemistry: The Essential Concepts

Ch. 21 - Prob. 21.2QPCh. 21 - Prob. 21.3QPCh. 21 - Prob. 21.4QPCh. 21 - Prob. 21.5QPCh. 21 - Prob. 21.6QPCh. 21 - Prob. 21.7QPCh. 21 - Prob. 21.8QPCh. 21 - Prob. 21.9QPCh. 21 - Prob. 21.10QPCh. 21 - Prob. 21.11QPCh. 21 - Prob. 21.12QPCh. 21 - Prob. 21.13QPCh. 21 - Prob. 21.14QPCh. 21 - Prob. 21.15QPCh. 21 - Prob. 21.16QPCh. 21 - Prob. 21.17QPCh. 21 - Prob. 21.18QPCh. 21 - Prob. 21.19QPCh. 21 - Prob. 21.20QPCh. 21 - Prob. 21.21QPCh. 21 - Prob. 21.22QPCh. 21 - Prob. 21.23QPCh. 21 - Prob. 21.24QPCh. 21 - Prob. 21.25QPCh. 21 - Prob. 21.26QPCh. 21 - Prob. 21.27QPCh. 21 - Prob. 21.28QPCh. 21 - Prob. 21.29QPCh. 21 - Prob. 21.30QPCh. 21 - Prob. 21.31QPCh. 21 - Prob. 21.32QPCh. 21 - Prob. 21.33QPCh. 21 - Prob. 21.34QPCh. 21 - Prob. 21.35QPCh. 21 - Prob. 21.36QPCh. 21 - Prob. 21.37QPCh. 21 - Prob. 21.38QPCh. 21 - Prob. 21.39QPCh. 21 - Prob. 21.40QPCh. 21 - Prob. 21.41QPCh. 21 - Prob. 21.42QPCh. 21 - Prob. 21.43QPCh. 21 - Prob. 21.44QPCh. 21 - Prob. 21.45QPCh. 21 - Prob. 21.46QPCh. 21 - Prob. 21.47QPCh. 21 - Prob. 21.48QPCh. 21 - Prob. 21.49QPCh. 21 - Prob. 21.50QPCh. 21 - Prob. 21.51QPCh. 21 - Prob. 21.52QPCh. 21 - Prob. 21.53QPCh. 21 - Prob. 21.54QPCh. 21 - Prob. 21.55QPCh. 21 - Prob. 21.56QPCh. 21 - Prob. 21.57QPCh. 21 - Prob. 21.58QPCh. 21 - Prob. 21.59QPCh. 21 - Prob. 21.60QPCh. 21 - Prob. 21.61QPCh. 21 - Prob. 21.62QPCh. 21 - Prob. 21.63QPCh. 21 - Prob. 21.64QPCh. 21 - Prob. 21.65QPCh. 21 - Prob. 21.66QPCh. 21 - Prob. 21.67QPCh. 21 - Prob. 21.68QPCh. 21 - Prob. 21.69QPCh. 21 - Prob. 21.70QPCh. 21 - Prob. 21.71QPCh. 21 - Prob. 21.72QPCh. 21 - Prob. 21.73QPCh. 21 - Prob. 21.74QPCh. 21 - Prob. 21.75QPCh. 21 - Prob. 21.76QPCh. 21 - Prob. 21.77QPCh. 21 - Prob. 21.78QPCh. 21 - Prob. 21.79QPCh. 21 - Prob. 21.80QPCh. 21 - Prob. 21.81QPCh. 21 - Prob. 21.82QPCh. 21 - Prob. 21.83QPCh. 21 - Prob. 21.84QPCh. 21 - Prob. 21.85QPCh. 21 - Prob. 21.86QPCh. 21 - Prob. 21.87SPCh. 21 - Prob. 21.88SPCh. 21 - Prob. 21.89SPCh. 21 - Prob. 21.90SPCh. 21 - Prob. 21.91SPCh. 21 - Prob. 21.92SPCh. 21 - Prob. 21.93SPCh. 21 - Prob. 21.94SPCh. 21 - Prob. 21.95SPCh. 21 - Prob. 21.96SPCh. 21 - Prob. 21.97SPCh. 21 - Prob. 21.98SPCh. 21 - Prob. 21.99SP
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