ATKINS' PHYSICAL CHEMISTRY-ACCESS
ATKINS' PHYSICAL CHEMISTRY-ACCESS
11th Edition
ISBN: 9780198834700
Author: ATKINS
Publisher: OXF
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Chapter 7, Problem 7E.6P
Interpretation Introduction

Interpretation:

The force constants of the bonds in HCl, HBr, HI, CO, and NO have to be calculated. The molecules, HCl, HBr, HI, CO, and NO have to arranged in increasing order of stiffness.

Concept introduction:

A molecule is made up of atoms that are bonded together by covalent bonds.  These bonds undergo a to and fro movement to vibrate.  The vibrational frequency of a bond is given by the expression shown below.

    v=12πckfμ

Expert Solution & Answer
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Answer to Problem 7E.6P

The table for the force constant of the bond is shown below.

Molecule1H35Cl1H81Br1H127I12C16O14N16O
Force constant (kgs2)512.1262408.7319311.96021902.62091380.2479

The arrangement of given molecules in increasing order of their stiffness is shown below.

    1H127I<1H81Br<1H35Cl<14N16O<12C16O

Explanation of Solution

The Data table for the wavenumber number of the molecules is shown below.

Molecule1H35Cl1H81Br1H127I12C16O14N16O
Wavenumber (cm1)29902650231021701904

The mass of hydrogen atom is 1u.

The mass of hydrogen atom in kg is converted as shown below.

    mH=(1u)(1.66054×1027kg1u)=1.66054×1027kg

The mass of chlorine atom is 35u.

The mass of chlorine atom in kg is converted as shown below.

    mCl=(35u)(1.66054×1027kg1u)=58.1189×1027kg

The mass of bromine atom is 81u.

The mass of bromine atom in kg is converted as shown below.

    mBr=(81u)(1.66054×1027kg1u)=134.50374×1027kg

The mass of iodine atom is 127u.

The mass of iodine atom in kg is converted as shown below.

    mI=(127u)(1.66054×1027kg1u)=210.8886×1027kg

The mass of carbon atom is 12u.

The mass of carbon atom in kg is converted as shown below.

    mC=(12u)(1.66054×1027kg1u)=19.9265×1027kg

The mass of oxygen atom is 16u.

The mass of oxygen atom in kg is converted as shown below.

    mO=(16u)(1.66054×1027kg1u)=26.5686×1027kg

The mass of nitrogen atom is 14u.

The mass of nitrogen atom in kg is converted as shown below.

    mN=(14u)(1.66054×1027kg1u)=23.2476×1027kg

The reduced mass of a molecule (μ) is given by the expression as shown below.

  μ=mAmBmA+mB                                                                                                 (1)

Where,

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

Substitute the values of the mass of hydrogen atom and chlorine atom in the equation (1).

  μHCl=(1.66054×1027kg)(58.1189×1027kg)(1.66054×1027kg)+(58.1189×1027kg)=1.6144×1027kg

Substitute the values of the mass of hydrogen atom and bromine atom in the equation (1).

  μHBr=(1.66054×1027kg)(134.50374×1027kg)(1.66054×1027kg)+(134.50374×1027kg)=1.6403×1027kg

Substitute the values of the mass of hydrogen atom and iodine atom in the equation (1).

  μHI=(1.66054×1027kg)(210.8886×1027kg)(1.66054×1027kg)+(210.8886×1027kg)=1.6476×1027kg

Substitute the values of the mass of carbon atom and oxygen atom in the equation (1).

  μCO=(19.9265×1027kg)(26.5686×1027kg)(19.9265×1027kg)+(26.5686×1027kg)=1.1387×1026kg

Substitute the values of the mass of nitrogen atom and oxygen atom in the equation (1).

  μNO=(19.9265×1027kg)(23.2476×1027kg)(19.9265×1027kg)+(23.2476×1027kg)=1.073×1026kg

The wavenumber (v¯) for the corresponding vibrational frequency of a bond is given by the expression shown below.

    v¯=12πckfμ

Where,

  • kf is the force constant of the bond.
  • μ is the reduced mass of the molecule.
  • c isthe speed of light with value of 2.997945×1010cms1.

Rearrange the above equation for the value of kf.

    kf=μ(2πcv¯)2                                                                                                (2)

Substitute the value of wavenumber of the corresponding vibrational frequency of HCl bond and reduced mass of HCl in the equation (2).

    kf(HCl)=(1.6144×1027kg)(2π(2.997945×1010cms1)(2990cm1))2=(1.6144×1027)((1.8837×1011)(2990))2kgs2=512.1262kgs2

Substitute the value of wavenumber of the corresponding vibrational frequency of HBr bond and reduced mass of HBr in the equation (2).

    kf(HBr)=(1.6403×1027kg)(2π(2.997945×1010cms1)(2650cm1))2=(1.6403×1027kg)((1.8837×1011)(2650))2kgs2=408.7319kgs2

Substitute the value of wavenumber of the corresponding vibrational frequency of HI bond and reduced mass of HI in the equation (2).

    kf(HI)=(1.6476×1027kg)(2π(2.997945×1010cms1)(2310cm1))2=(1.6476×1027kg)((1.8837×1011)(2310))2kgs2=311.9602kgs2

Substitute the value of wavenumber of the corresponding vibrational frequency of CO bond and reduced mass of CO in the equation (2).

    kf(CO)=(1.1387×1026kg)(2π(2.997945×1010cms1)(2170cm1))2=(1.1387×1026kg)((1.8837×1011)(2170))2kgs2=1902.6209kgs2

Substitute the value of wavenumber of the corresponding vibrational frequency of NO bond and reduced mass of NO in the equation (2).

    kf(NO)=(1.073×1026kg)(2π(2.997945×1010cms1)(1904cm1))2=(1.073×1026kg)((1.8837×1011)(1904))2kgs2=1380.2479kgs2

Therefore, the table for the force constant of the bond is shown below.

Molecule1H35Cl1H81Br1H127I12C16O14N16O
Force constant (kgs2)512.1262408.7319311.96021902.62091380.2479

The stiffness of the bond increases with increase in force constant of the bond.  Therefore, the arrangement of given molecules in increasing order of their stiffness is shown below.

    1H127I<1H81Br<1H35Cl<14N16O<12C16O

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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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