Atkins' Physical Chemistry
Atkins' Physical Chemistry
11th Edition
ISBN: 9780198769866
Author: ATKINS, P. W. (peter William), De Paula, Julio, Keeler, JAMES
Publisher: Oxford University Press
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Chapter 11, Problem 11C.4BE
Interpretation Introduction

Interpretation:

The fundamental vibrational wavenumbers of deuterium halides have to be stated.

Concept introduction:

The internal mode of vibration of molecule leads to a periodic change in the internal internuclear separation of a molecule.  Due to this change, the molecules are considered as harmonic oscillators.  The strength of a bond in a bond is measured by force constant. The force constant of a molecule is related to the effective mass and vibrational frequency.  The vibrational energy of a molecule is given by the equation as shown below.

  Eν=(ν+12)ω.

Expert Solution & Answer
Check Mark

Answer to Problem 11C.4BE

The fundamental vibrational wavenumbers of H2F19,H2C35l,H2B81r and H2I127 are 2997.568 cm1_,2141.949 cm1_,1883.851 cm1_ and  1638.390 cm1_ respectively.

Explanation of Solution

The wavenumber of a molecule is given by the equation shown below.

  ν˜=12πc(kfmeff)12        (1)

Where,

  • kf is the force constant.
  • meff is the effective mass.
  • c is the speed of light

It is assumed that the force constants of deuterium halides are same as that of hydrogen halides.

The effective mass of H2F19 is calculated as shown below.

  meff=mambma+mb        (2)

Where,

  • ma is the mass of first atom
  • mb is the mass of second atom

For H2F19, substitute the value of ma as 2 g/mol and mb as 19 g/mol and in equation (2).

  meff=2 g/mol×19 g/mol2+19 g/mol=3821g/mol=1.81 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol1.81 g/mol=1.81 g/mol×103 kg6.022×1023 /mol=3.01×1027 kg

Substitute kf as 958.71N m1, meff as 3.01×1027 kg and c as 2.998×1010 cm s1 in equation (1).

  ν˜=12×3.14×2.998×1010 cm s1(958.71 N m13.01×1027kg)12=12×3.14×2.998×1010 cm s1×5.644×1014 s1=2997.568 cm1_

Therefore, the fundamental vibrational wavenumber for H2F19 is 2997.568 cm1_.

For H2C35l, substitute the value of ma as 2 g/mol and mb as 35 g/mol and in equation (2).

  meff=2 g/mol×35 g/mol2+35 g/mol=7037g/mol=1.892 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol1.892 g/mol=1.892 g/mol×103 kg6.022×1023 /mol=3.142×1027 kg

Substitute kf as 511.06N m1, meff as 3.142×1027 kg and c as 2.998×1010 cm s1 in equation (2).

  ν˜=12×3.14×2.998×1010 cm s1(511.06 N m13.142×1027kg)12=12×3.14×2.998×1010 cm s1×4.034×1014 s1=2141.949 cm1_

Therefore, the fundamental vibrational wavenumber for H2C35l is 2141.949 cm1_.

For H2B81r, substitute the value of ma as 2 g/mol and mb as 81 g/mol and in equation (2).

  meff=2 g/mol×81 g/mol2+81 g/mol=16283g/mol=1.952 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol1.952 g/mol=1.952 g/mol×103 kg6.022×1023 /mol=3.242×1027 kg

Substitute kf as 407.90N m1, meff as 3.242×1027 kg and c as 2.998×1010 cm s1 in equation (1).

  ν˜=12×3.14×2.998×1010 cm s1(407.90 N m13.242×1027kg)12=12×3.14×2.998×1010 cm s1×3.548×1014 s1=1883.851 cm1_

Therefore, the fundamental vibrational wavenumber for H2B81r is 1883.851 cm1_.

For H2I127, substitute the value of ma as 2 g/mol and mb as 127 g/mol and in equation (2).

  meff=2 g/mol×127 g/mol2+127 g/mol=254129g/mol=1.9689 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol1.9689 g/mol=1.9689 g/mol×103 kg6.022×1023 /mol=3.269×1027 kg

Substitute kf as 311.098N m1, meff as 3.269×1027 kg and c as 2.998×1010 cm s1 in equation (1).

  ν˜=12×3.14×2.998×1010 cm s1(311.098 N m13.269×1027kg)12=12×3.14×2.998×1010 cm s1×3.085×1014 s1=1638.390 cm1_

Therefore, the fundamental vibrational wavenumber for H2I127 is 1638.390 cm1_.

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Chapter 11 Solutions

Atkins' Physical Chemistry

Ch. 11 - Prob. 11E.2STCh. 11 - Prob. 11F.2STCh. 11 - Prob. 11A.1DQCh. 11 - Prob. 11A.2DQCh. 11 - Prob. 11A.3DQCh. 11 - Prob. 11A.1AECh. 11 - Prob. 11A.1BECh. 11 - Prob. 11A.2AECh. 11 - Prob. 11A.2BECh. 11 - Prob. 11A.3AECh. 11 - Prob. 11A.3BECh. 11 - Prob. 11A.4AECh. 11 - Prob. 11A.4BECh. 11 - Prob. 11A.5AECh. 11 - Prob. 11A.5BECh. 11 - Prob. 11A.6AECh. 11 - Prob. 11A.6BECh. 11 - Prob. 11A.7AECh. 11 - Prob. 11A.7BECh. 11 - Prob. 11A.8AECh. 11 - Prob. 11A.8BECh. 11 - Prob. 11A.9AECh. 11 - Prob. 11A.9BECh. 11 - Prob. 11A.10AECh. 11 - Prob. 11A.10BECh. 11 - Prob. 11A.11AECh. 11 - Prob. 11A.11BECh. 11 - Prob. 11A.12AECh. 11 - Prob. 11A.12BECh. 11 - Prob. 11A.1PCh. 11 - Prob. 11A.2PCh. 11 - Prob. 11A.3PCh. 11 - Prob. 11A.4PCh. 11 - Prob. 11A.5PCh. 11 - Prob. 11A.7PCh. 11 - Prob. 11A.8PCh. 11 - Prob. 11A.9PCh. 11 - Prob. 11A.11PCh. 11 - Prob. 11B.1DQCh. 11 - Prob. 11B.2DQCh. 11 - Prob. 11B.3DQCh. 11 - Prob. 11B.4DQCh. 11 - Prob. 11B.5DQCh. 11 - Prob. 11B.6DQCh. 11 - Prob. 11B.7DQCh. 11 - Prob. 11B.8DQCh. 11 - Prob. 11B.1AECh. 11 - Prob. 11B.1BECh. 11 - Prob. 11B.3AECh. 11 - Prob. 11B.3BECh. 11 - Prob. 11B.4BECh. 11 - Prob. 11B.5AECh. 11 - Prob. 11B.5BECh. 11 - Prob. 11B.6AECh. 11 - Prob. 11B.6BECh. 11 - Prob. 11B.7AECh. 11 - Prob. 11B.7BECh. 11 - Prob. 11B.8AECh. 11 - Prob. 11B.8BECh. 11 - Prob. 11B.9AECh. 11 - Prob. 11B.9BECh. 11 - Prob. 11B.10AECh. 11 - Prob. 11B.10BECh. 11 - Prob. 11B.11AECh. 11 - Prob. 11B.11BECh. 11 - Prob. 11B.12AECh. 11 - Prob. 11B.12BECh. 11 - Prob. 11B.13AECh. 11 - Prob. 11B.13BECh. 11 - Prob. 11B.14AECh. 11 - Prob. 11B.14BECh. 11 - Prob. 11B.1PCh. 11 - Prob. 11B.2PCh. 11 - Prob. 11B.3PCh. 11 - Prob. 11B.4PCh. 11 - Prob. 11B.5PCh. 11 - Prob. 11B.6PCh. 11 - Prob. 11B.7PCh. 11 - Prob. 11B.8PCh. 11 - Prob. 11B.9PCh. 11 - Prob. 11B.10PCh. 11 - Prob. 11B.11PCh. 11 - Prob. 11B.12PCh. 11 - Prob. 11B.13PCh. 11 - Prob. 11B.14PCh. 11 - Prob. 11C.1DQCh. 11 - Prob. 11C.2DQCh. 11 - Prob. 11C.3DQCh. 11 - Prob. 11C.4DQCh. 11 - Prob. 11C.1AECh. 11 - Prob. 11C.1BECh. 11 - Prob. 11C.2AECh. 11 - Prob. 11C.2BECh. 11 - Prob. 11C.3AECh. 11 - Prob. 11C.3BECh. 11 - Prob. 11C.4AECh. 11 - Prob. 11C.4BECh. 11 - Prob. 11C.5AECh. 11 - Prob. 11C.5BECh. 11 - Prob. 11C.6AECh. 11 - Prob. 11C.6BECh. 11 - Prob. 11C.7AECh. 11 - Prob. 11C.7BECh. 11 - Prob. 11C.8AECh. 11 - Prob. 11C.8BECh. 11 - Prob. 11C.2PCh. 11 - Prob. 11C.3PCh. 11 - Prob. 11C.4PCh. 11 - Prob. 11C.5PCh. 11 - Prob. 11C.6PCh. 11 - Prob. 11C.7PCh. 11 - Prob. 11C.8PCh. 11 - Prob. 11C.9PCh. 11 - Prob. 11C.10PCh. 11 - Prob. 11C.11PCh. 11 - Prob. 11C.12PCh. 11 - Prob. 11C.13PCh. 11 - Prob. 11C.15PCh. 11 - Prob. 11C.17PCh. 11 - Prob. 11C.18PCh. 11 - Prob. 11C.19PCh. 11 - Prob. 11D.1DQCh. 11 - Prob. 11D.2DQCh. 11 - Prob. 11D.3DQCh. 11 - Prob. 11D.1AECh. 11 - Prob. 11D.1BECh. 11 - Prob. 11D.2AECh. 11 - Prob. 11D.2BECh. 11 - Prob. 11D.3AECh. 11 - Prob. 11D.3BECh. 11 - Prob. 11D.4AECh. 11 - Prob. 11D.4BECh. 11 - Prob. 11D.5AECh. 11 - Prob. 11D.5BECh. 11 - Prob. 11D.6AECh. 11 - Prob. 11D.6BECh. 11 - Prob. 11D.7AECh. 11 - Prob. 11D.7BECh. 11 - Prob. 11D.2PCh. 11 - Prob. 11E.1DQCh. 11 - Prob. 11E.1AECh. 11 - Prob. 11E.1BECh. 11 - Prob. 11E.2AECh. 11 - Prob. 11E.2BECh. 11 - Prob. 11E.3AECh. 11 - Prob. 11E.3BECh. 11 - Prob. 11E.1PCh. 11 - Prob. 11E.2PCh. 11 - Prob. 11F.1DQCh. 11 - Prob. 11F.2DQCh. 11 - Prob. 11F.3DQCh. 11 - Prob. 11F.4DQCh. 11 - Prob. 11F.5DQCh. 11 - Prob. 11F.6DQCh. 11 - Prob. 11F.1AECh. 11 - Prob. 11F.1BECh. 11 - Prob. 11F.2AECh. 11 - Prob. 11F.2BECh. 11 - Prob. 11F.3AECh. 11 - Prob. 11F.3BECh. 11 - Prob. 11F.4AECh. 11 - Prob. 11F.4BECh. 11 - Prob. 11F.5AECh. 11 - Prob. 11F.5BECh. 11 - Prob. 11F.6AECh. 11 - Prob. 11F.6BECh. 11 - Prob. 11F.7AECh. 11 - Prob. 11F.7BECh. 11 - Prob. 11F.8AECh. 11 - Prob. 11F.8BECh. 11 - Prob. 11F.9AECh. 11 - Prob. 11F.9BECh. 11 - Prob. 11F.10AECh. 11 - Prob. 11F.10BECh. 11 - Prob. 11F.11AECh. 11 - Prob. 11F.11BECh. 11 - Prob. 11F.12AECh. 11 - Prob. 11F.12BECh. 11 - Prob. 11F.13AECh. 11 - Prob. 11F.13BECh. 11 - Prob. 11F.1PCh. 11 - Prob. 11F.2PCh. 11 - Prob. 11F.3PCh. 11 - Prob. 11F.4PCh. 11 - Prob. 11F.5PCh. 11 - Prob. 11F.6PCh. 11 - Prob. 11F.7PCh. 11 - Prob. 11F.8PCh. 11 - Prob. 11F.9PCh. 11 - Prob. 11F.10PCh. 11 - Prob. 11F.11PCh. 11 - Prob. 11F.12PCh. 11 - Prob. 11G.1DQCh. 11 - Prob. 11G.2DQCh. 11 - Prob. 11G.3DQCh. 11 - Prob. 11G.4DQCh. 11 - Prob. 11G.5DQCh. 11 - Prob. 11G.1AECh. 11 - Prob. 11G.1BECh. 11 - Prob. 11G.2AECh. 11 - Prob. 11G.2BECh. 11 - Prob. 11G.1PCh. 11 - Prob. 11G.2PCh. 11 - Prob. 11G.3PCh. 11 - Prob. 11G.4PCh. 11 - Prob. 11G.5PCh. 11 - Prob. 11G.6PCh. 11 - Prob. 11.1IACh. 11 - Prob. 11.5IACh. 11 - Prob. 11.8IA
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