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
Question
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Chapter 11, Problem 11C.4AE
Interpretation Introduction

Interpretation:

The force constants of the hydrogen-halogen bonds 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.4AE

The force constants for H1F19H1C35l, H1B81r and  H1I127 are 958.71 N m1_,511.06 N m-1_,407.90 N m1_ and 311.098 N m1_ 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

Rearrange the above equation for force constant as shown below.

  ν˜=12πc(kfmeff)124ν˜2π2c2=kfmeff

Thus, the above equation reduces as shown below.

  kf=4π2c2ν˜2meff        (2)

The effective mass of H1F19 is calculated by the formula shown below.

  meff=mambma+mb        (3)

Where,

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

For H1F19, substitute the value of ma as 1 g/mol and mb as 19 g/mol in equation (3).

  meff=1 g/mol×19 g/mol1+19 g/mol=1920g/mol=0.95 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol0.95 g/mol=0.95 g/mol×103 kg6.022×1023 /mol=1.577×1027 kg

Substitute the value of ν˜ as 4141.3 cm1, meff as 1.577×1027 kg and c as 2.998×1010 cm s1 in equation (2).

  kf=4×(3.14)2×(2.998×1010 cms1)2×(4141.3 cm1)2×(1.577×1027kg)=4×9.8596×8.988×1020 cm2s2×17150365.69 cm2×1.577×1027kg=958.71 N m1_

Therefore, the force constant for H1F19 is 958.71 N m1_.

For H1C35l, substitute the value of ma as 1 g/mol and mb as 35 g/mol in equation (3).

  meff=1 g/mol×35 g/mol1+35 g/mol=3536g/mol=0.9722 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol0.9722 g/mol=0.9722 g/mol×103 kg6.022×1023 /mol=1.614×1027 kg

Substitute the value of ν˜ as 2988.9 cm1, meff as 1.614×1027 kg and c as 2.998×1010 cm s1 in equation (2).

  kf=4×(3.14)2×(2.998×1010 cms1)2×(2988.9 cm1)2×(1.614×1027kg)=511.06 N m1_

Therefore, the force constant for H1C35l is 511.06 N m1_.

For H1B81r, substitute the value of ma as 1 g/mol and mb as 81 g/mol in equation (3).

  meff=1 g/mol×81 g/mol1+81 g/mol=8182g/mol=0.9878 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol0.9878 g/mol=0.9878 g/mol×103 kg6.022×1023 /mol=1.64×1027 kg

Substitute ν˜ as 2649.7 cm1, meff as 1.639×1027 kg and c as 2.998×1010 cm s1 in equation (2).

  kf=4×(3.14)2×(2.998×1010 cms1)2×(2649.7 cm1)2×(1.64×1027kg)=4×9.8596×(8.988×1020 cm2s2)×(7.02×106 cm2)×(1.64×1027kg)=407.90 N m1_

Therefore, the force constant for H1B79r is 407.90 N m1_.

For H1I127, substitute the value of ma as 1 g/mol and mb as 81 g/mol in equation (3).

  meff=1 g/mol×127 g/mol1+127 g/mol=127128g/mol=0.9922 g/mol

Convert the effective mass in kg as shown below.

  1 g/mol =103 kg6.022×1023/mol0.9922 g/mol=0.9922 g/mol×103 kg6.022×1023 /mol=1.647×1027 kg

Substitute ν˜ as 2309.5 cm1, meff as 1.639×1027 kg and c as 2.998×1010 cm s1 in equation (2).

  kf=4×(3.14)2×(2.998×1010 cms1)2×(2308.5 cm1)2×(1.647×1027kg)=4×9.8596×(8.988×1020 cm2s2)×(5329172.25 cm2)×(1.647×1027kg)=311.098 N m1_

Therefore, the force constant for H1I127 is 311.098 N m1_.

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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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