ATKINS' PHYSICAL CHEMISTRY-ACCESS
ATKINS' PHYSICAL CHEMISTRY-ACCESS
11th Edition
ISBN: 9780198834700
Author: ATKINS
Publisher: OXF
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Chapter 7, Problem 7E.1P

(a)

Interpretation Introduction

Interpretation:

It has to be shown that in a diatomic molecule A-B, when an isotopic substitution is made for atom A, the vibrational frequency of A'-B can be expressed in term of vibrational frequency of A-B.

Concept introduction:

 Vibrational frequency is an important measurement that describes the information to identify phase, observe the bonding between atoms in a molecule and to study the relationships between vibrational frequency and phase transitions.

(a)

Expert Solution
Check Mark

Answer to Problem 7E.1P

It has been proved that when an isotopic substitution is made for atom A, the vibrational frequency of A'-B can be expressed in term of vibrational frequency of A-B.

Explanation of Solution

For a diatomic molecule A-B, the vibrational frequency is expressed as,

wAB=(KfμAB)12 (1)

Where,

  • wAB is the vibational frequency of molecule A-B.
  • Kf is the force constant.
  • μAB is the effective mass for the molecule A-B.

The effective mass for the molecule A-B is calculated by the formula,

  μAB=mAmBmA+mB                                                                                            (2)

Where,

  • mA is the mass of atom A.
  • mB is the mass of atom B.

When an isotopic substitution is made for atom A, its mass mA changes to mA'.  Hence, the effective mass μAB changes to μA'B and the vibrational frequency wAB changes to wA'B.

Therefore,

  wA'B=(KfμA'B)12                                                                                          (3)

Divide the equation (3) by equation (1).

  wA'BwAB=(KfμA'B)12×(μABKf)12=(μABμA'B)12

Or,

  wA'B=wAB(μABμA'B)12

Therefore, it has been proved that when an isotopic substitution is made for atom A, the vibrational frequency of A'-B can be expressed in term of vibrational frequency of A-B.

(b)

Interpretation Introduction

Interpretation:

Under the given conditions, the vibrational frequencies have to be calculated.

Concept introduction:

Vibrational frequency is an important measurement that describes the information to identify phase, observe the bonding between atoms in a molecule and to study the relationships between vibrational frequency and phase transitions.

(b)

Expert Solution
Check Mark

Answer to Problem 7E.1P

The vibrational frequencies for the diatomic molecules, H2Cl35 and H1Cl37 are 4.036×1014s-1_ and 5.626×1014s-1_, respectively.

Explanation of Solution

(i)

For a diatomic molecule H1Cl35, when an isotopic substitution is made for atom H1, its mass mH1 changes to mH2.  Hence, the effective mass μH1Cl35 changes to μH2Cl35 and the vibrational frequency wH1Cl35 changes to wH2Cl35.

Therefore, the vibrational frequency of wH2Cl35 can be expressed in term of vibrational frequency of wH1Cl35.

  wH2Cl35=wH1Cl35(μH1Cl35μH2Cl35)12                                                                             (1)

Where,

  • wH1Cl35 is the vibrational frequency for molecule H1Cl35.
  • wH2Cl35 is the vibrational frequency for molecule H2Cl35.
  • μH1Cl35 is the effective mass for molecule H1Cl35.
  • μH2Cl35 is the effective mass for molecule H2Cl35.

It is given that,

The vibrational frequency for H1Cl35 is 5.63×1014s1.

The effective mass of H1Cl35 is calculated as,

  μH1Cl35=mH1mCl35mH1+mCl35=1×351+35amu=3536amu=0.9723amu

The effective mass of H2Cl35 is calculated as,

  μH2Cl35=mH2mCl35mH2+mCl35=2×352+35amu=7037amu=1.892amu

Substitute the values of wH1Cl35, μH1Cl35 and μH2Cl35 in equation (1).

  wH2Cl35=5.63×1014s1(0.9723amu1.892amu)12=5.63×1014×0.7168s1=4.036×1014s-1_

(ii)

For a diatomic molecule H1Cl35, when an isotopic substitution is made for atom Cl35, its mass mCl35 changes to mCl37.  Hence, the effective mass μH1Cl35 changes to μH1Cl37 and the vibrational frequency wH1Cl35 changes to wH1Cl37.

Therefore, the vibrational frequency of wH2Cl35 can be expressed in term of vibrational frequency of wH1Cl35.

  wH1Cl37=wH1Cl35(μH1Cl35μH1Cl37)12                                                                             (1)

Where,

  • wH1Cl35 is the vibrational frequency for molecule H1Cl35.
  • wH1Cl37 is the vibrational frequency for molecule H1Cl37.
  • μH1Cl35 is the effective mass for molecule H1Cl35.
  • μH1Cl37 is the effective mass for molecule H1Cl37.

It is given that,

The vibrational frequency for H1Cl35 is 5.63×1014s1.

The effective mass of H1Cl35 is calculated as,

  μH1Cl35=mH1mCl35mH1+mCl35=1×351+35amu=3536amu=0.9723amu

The effective mass of H1Cl37 is calculated as,

  μH1Cl37=mH1mCl37mH1+mCl37=1×371+37amu=3738amu=0.9736amu

Substitute the values of wH1Cl35, μH1Cl35 and μH1Cl37 in equation (1).

  wH1Cl37=5.63×1014s1(0.9723amu0.9736amu)12=5.63×1014×0.9993s1=5.626×1014s-1_

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Chapter 7 Solutions

ATKINS' PHYSICAL CHEMISTRY-ACCESS

Ch. 7 - Prob. 7D.1STCh. 7 - Prob. 7E.1STCh. 7 - Prob. 7E.2STCh. 7 - Prob. 7F.1STCh. 7 - Prob. 7A.1DQCh. 7 - Prob. 7A.2DQCh. 7 - Prob. 7A.3DQCh. 7 - Prob. 7A.4DQCh. 7 - Prob. 7A.1AECh. 7 - Prob. 7A.1BECh. 7 - Prob. 7A.2AECh. 7 - Prob. 7A.2BECh. 7 - Prob. 7A.3AECh. 7 - Prob. 7A.3BECh. 7 - Prob. 7A.4AECh. 7 - Prob. 7A.4BECh. 7 - Prob. 7A.5AECh. 7 - Prob. 7A.5BECh. 7 - Prob. 7A.6AECh. 7 - Prob. 7A.6BECh. 7 - Prob. 7A.7AECh. 7 - Prob. 7A.7BECh. 7 - Prob. 7A.8AECh. 7 - Prob. 7A.8BECh. 7 - Prob. 7A.9AECh. 7 - Prob. 7A.9BECh. 7 - Prob. 7A.10AECh. 7 - Prob. 7A.10BECh. 7 - Prob. 7A.11AECh. 7 - Prob. 7A.11BECh. 7 - Prob. 7A.12AECh. 7 - Prob. 7A.12BECh. 7 - Prob. 7A.13AECh. 7 - Prob. 7A.13BECh. 7 - Prob. 7A.1PCh. 7 - Prob. 7A.2PCh. 7 - Prob. 7A.3PCh. 7 - Prob. 7A.4PCh. 7 - Prob. 7A.5PCh. 7 - Prob. 7A.6PCh. 7 - Prob. 7A.7PCh. 7 - Prob. 7A.8PCh. 7 - Prob. 7A.9PCh. 7 - Prob. 7A.10PCh. 7 - Prob. 7B.1DQCh. 7 - Prob. 7B.2DQCh. 7 - Prob. 7B.3DQCh. 7 - Prob. 7B.1AECh. 7 - Prob. 7B.1BECh. 7 - Prob. 7B.2AECh. 7 - Prob. 7B.2BECh. 7 - Prob. 7B.3AECh. 7 - Prob. 7B.3BECh. 7 - Prob. 7B.4AECh. 7 - Prob. 7B.4BECh. 7 - Prob. 7B.5AECh. 7 - Prob. 7B.5BECh. 7 - Prob. 7B.6AECh. 7 - Prob. 7B.6BECh. 7 - Prob. 7B.7AECh. 7 - Prob. 7B.7BECh. 7 - Prob. 7B.8AECh. 7 - Prob. 7B.8BECh. 7 - Prob. 7B.1PCh. 7 - Prob. 7B.2PCh. 7 - Prob. 7B.3PCh. 7 - Prob. 7B.4PCh. 7 - Prob. 7B.5PCh. 7 - Prob. 7B.7PCh. 7 - Prob. 7B.8PCh. 7 - Prob. 7B.9PCh. 7 - Prob. 7B.11PCh. 7 - Prob. 7C.1DQCh. 7 - Prob. 7C.2DQCh. 7 - Prob. 7C.3DQCh. 7 - Prob. 7C.1AECh. 7 - Prob. 7C.1BECh. 7 - Prob. 7C.2AECh. 7 - Prob. 7C.2BECh. 7 - Prob. 7C.3AECh. 7 - Prob. 7C.3BECh. 7 - Prob. 7C.4AECh. 7 - Prob. 7C.4BECh. 7 - Prob. 7C.5AECh. 7 - Prob. 7C.5BECh. 7 - Prob. 7C.6AECh. 7 - Prob. 7C.6BECh. 7 - Prob. 7C.7AECh. 7 - Prob. 7C.7BECh. 7 - Prob. 7C.8AECh. 7 - Prob. 7C.8BECh. 7 - Prob. 7C.9AECh. 7 - Prob. 7C.9BECh. 7 - Prob. 7C.10AECh. 7 - Prob. 7C.10BECh. 7 - Prob. 7C.1PCh. 7 - Prob. 7C.2PCh. 7 - Prob. 7C.3PCh. 7 - Prob. 7C.4PCh. 7 - Prob. 7C.5PCh. 7 - Prob. 7C.6PCh. 7 - Prob. 7C.7PCh. 7 - Prob. 7C.8PCh. 7 - Prob. 7C.9PCh. 7 - Prob. 7C.11PCh. 7 - Prob. 7C.12PCh. 7 - Prob. 7C.13PCh. 7 - Prob. 7C.14PCh. 7 - Prob. 7C.15PCh. 7 - Prob. 7D.1DQCh. 7 - Prob. 7D.2DQCh. 7 - Prob. 7D.3DQCh. 7 - Prob. 7D.1AECh. 7 - Prob. 7D.1BECh. 7 - Prob. 7D.2AECh. 7 - Prob. 7D.2BECh. 7 - Prob. 7D.3AECh. 7 - Prob. 7D.3BECh. 7 - Prob. 7D.4AECh. 7 - Prob. 7D.4BECh. 7 - Prob. 7D.5AECh. 7 - Prob. 7D.5BECh. 7 - Prob. 7D.6AECh. 7 - Prob. 7D.6BECh. 7 - Prob. 7D.7AECh. 7 - Prob. 7D.7BECh. 7 - Prob. 7D.8AECh. 7 - Prob. 7D.8BECh. 7 - Prob. 7D.9AECh. 7 - Prob. 7D.9BECh. 7 - Prob. 7D.10AECh. 7 - Prob. 7D.10BECh. 7 - Prob. 7D.11AECh. 7 - Prob. 7D.11BECh. 7 - Prob. 7D.12AECh. 7 - Prob. 7D.12BECh. 7 - Prob. 7D.13AECh. 7 - Prob. 7D.13BECh. 7 - Prob. 7D.14AECh. 7 - Prob. 7D.14BECh. 7 - Prob. 7D.15AECh. 7 - Prob. 7D.15BECh. 7 - Prob. 7D.1PCh. 7 - Prob. 7D.2PCh. 7 - Prob. 7D.3PCh. 7 - Prob. 7D.4PCh. 7 - Prob. 7D.5PCh. 7 - Prob. 7D.6PCh. 7 - Prob. 7D.7PCh. 7 - Prob. 7D.8PCh. 7 - Prob. 7D.9PCh. 7 - Prob. 7D.11PCh. 7 - Prob. 7D.12PCh. 7 - Prob. 7D.14PCh. 7 - Prob. 7E.1DQCh. 7 - Prob. 7E.2DQCh. 7 - Prob. 7E.3DQCh. 7 - Prob. 7E.1AECh. 7 - Prob. 7E.1BECh. 7 - Prob. 7E.2AECh. 7 - Prob. 7E.2BECh. 7 - Prob. 7E.3AECh. 7 - Prob. 7E.3BECh. 7 - Prob. 7E.4AECh. 7 - Prob. 7E.4BECh. 7 - Prob. 7E.5AECh. 7 - Prob. 7E.5BECh. 7 - Prob. 7E.6AECh. 7 - Prob. 7E.6BECh. 7 - Prob. 7E.7AECh. 7 - Prob. 7E.7BECh. 7 - Prob. 7E.8AECh. 7 - Prob. 7E.8BECh. 7 - Prob. 7E.9AECh. 7 - Prob. 7E.9BECh. 7 - Prob. 7E.1PCh. 7 - Prob. 7E.2PCh. 7 - Prob. 7E.3PCh. 7 - Prob. 7E.4PCh. 7 - Prob. 7E.5PCh. 7 - Prob. 7E.6PCh. 7 - Prob. 7E.7PCh. 7 - Prob. 7E.8PCh. 7 - Prob. 7E.9PCh. 7 - Prob. 7E.12PCh. 7 - Prob. 7E.15PCh. 7 - Prob. 7E.16PCh. 7 - Prob. 7E.17PCh. 7 - Prob. 7F.1DQCh. 7 - Prob. 7F.2DQCh. 7 - Prob. 7F.3DQCh. 7 - Prob. 7F.1AECh. 7 - Prob. 7F.1BECh. 7 - Prob. 7F.2AECh. 7 - Prob. 7F.2BECh. 7 - Prob. 7F.3AECh. 7 - Prob. 7F.3BECh. 7 - Prob. 7F.4AECh. 7 - Prob. 7F.4BECh. 7 - Prob. 7F.5AECh. 7 - Prob. 7F.5BECh. 7 - Prob. 7F.6AECh. 7 - Prob. 7F.6BECh. 7 - Prob. 7F.7AECh. 7 - Prob. 7F.7BECh. 7 - Prob. 7F.8AECh. 7 - Prob. 7F.8BECh. 7 - Prob. 7F.9AECh. 7 - Prob. 7F.9BECh. 7 - Prob. 7F.10AECh. 7 - Prob. 7F.10BECh. 7 - Prob. 7F.11AECh. 7 - Prob. 7F.11BECh. 7 - Prob. 7F.12AECh. 7 - Prob. 7F.12BECh. 7 - Prob. 7F.13AECh. 7 - Prob. 7F.13BECh. 7 - Prob. 7F.14AECh. 7 - Prob. 7F.14BECh. 7 - Prob. 7F.1PCh. 7 - Prob. 7F.4PCh. 7 - Prob. 7F.6PCh. 7 - Prob. 7F.7PCh. 7 - Prob. 7F.8PCh. 7 - Prob. 7F.9PCh. 7 - Prob. 7F.10PCh. 7 - Prob. 7F.11PCh. 7 - Prob. 7.3IACh. 7 - Prob. 7.4IACh. 7 - Prob. 7.5IACh. 7 - Prob. 7.6IA
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