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 14, Problem 14A.2ST
Interpretation Introduction

Interpretation:

The polarizability volume and the dipole moment of chlorobenzene have to be calculated.

Concept introduction:

The dipole forces are attractive forces between two permanent dipoles.  The interaction is between the positive end of one polar molecule and the negative end of another polar molecule.  The induced dipole interaction occurs when an ion or a dipole induces a temporary dipole in an atom or a molecule with no dipole.  The induced dipole forces are the attraction forces between molecules having temporary dipoles.

Expert Solution & Answer
Check Mark

Answer to Problem 14A.2ST

The dipole moment of chlorobenzene is 1.16D_.

The polarizability volume of chlorobenzene is 1.349×10-29m3_.

Explanation of Solution

The molar mass of chlorobenzene is 112.56g/mol.

The constant density, ρ of chlorobenzene is 1.11g/cm3.

The value of εο is 8.854×1012J1C2m1.

The value of Boltzmann constant is 1.38×1023J/K.

The value of Avogadro’s number is 6.022×1023mol1.

The relative permittivities of chlorobenzene at different temperatures are shown below.

(1) 5.71 at 20°C or 293K.

(2) 5.62 at 25°C or 298K.

According to the Debye equation, the polarization (Pm) of chlorobenzene at 293K and 298K is calculated by the expression given below.

    εr1εr+2=(ρPmM)Pm=(εr1εr+2)×Mρ        (1)

Where,

  • εr is the relative permittivity.
  • M is the molar mass of chlorobenzene.
  • ρ is the density of chlorobenzene.

Substitute the values of εr as 5.71 and ρ in equation (1) to calculate the polarization (Pm) at 293K.

    Pm(293K)=(5.7115.71+2)×112.56g/mol1.11g/cm3=(4.717.71)×101.4054=61.948cm3/mol×106m31cm3=61.948×106m3/mol

Substitute the values of εr as 5.62 in equation (1) to calculate the polarization (Pm) at 298K.

    Pm(298K)=(5.6215.62+2)×112.56g/mol1.11g/cm3=(4.627.62)×101.4054=61.482cm3/mol×106m31cm3=61.482×106m3/mol

The value of polarizability is calculated by the formula shown below.

    α+μ23kT=3εοPmNAα=3εοPmNAμ23kT        (2)

In the given case, the polarizability remains constant and the polarization varies with respect to temperature. Therefore, the dipole moment is calculated by the formula shown below.

    μ23k×(1T1T')=(3εοNA)×(Pm(298K)Pm(293K))μ2=(9εοkNA)×(Pm(298K)Pm(293K))(1T1T')μ2=(9εοk)×(Pm(298K)Pm(293K))NA(1T1T')        (3)

Now, Substitute the values of εο, k, NA, molar polarizations and temperatures in equation (3) to calculate the dipole moment.

    μ2=(9×8.854×1012J1C2m1×1.38×1023J/K)×(61.94861.482)106m3mol16.022×1023mol1(12931298)=1.099×1033×0.466×1066.022×1023×5.7×105C2m2=0.51213×103934.3254×1018C2m2=0.01492×1057C2m2

Simplify the above equation.

    μ2=0.01492×1057C2m2μ=0.01492×1057C2m2=3.8611×1030Cm

The conversion of C m to Debye is done as shown below.

    1Cm=2.997×1029D

Therefore, the conversion of 5.531×1030Cm to Debye is done as shown below.

    3.8611×1030Cm=3.8611×1030Cm×2.997×1029D=1.16D_

Therefore, the dipole moment of chlorobenzene is 1.16D_.

Substitute the value of μ2=0.01492×1057C2m2 in equation (2) to calculate the polarizability.

    α=3×8.854×1012J1C2m1×61.948×106m3/mol6.022×1023mol10.01492×1057C2m23×1.38×1023J/K×293K=1.645×1015J1C2m26.022×10230.01492×1057C2m21.213×1020=(2.732×10391.23×1039)J1C2m2=1.5×10-39J1C2m2

The formula to calculate the polarizability volume (α') is given below.

    α'=α4πε0

Substitute the value of α as 1.5×10-39J1C2m2 and εο in the above expression.

    α'=1.5×10-39J1C2m24×3.14×8.854×1012J1C2m1=1.5×1027m3111.206=1.349×10-29m3_

Therefore, the polarizability volume of chlorobenzene is 1.349×10-29m3_.

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Chapter 14 Solutions

Atkins' Physical Chemistry

Ch. 14 - Prob. 14A.3DQCh. 14 - Prob. 14A.1AECh. 14 - Prob. 14A.1BECh. 14 - Prob. 14A.2AECh. 14 - Prob. 14A.2BECh. 14 - Prob. 14A.3AECh. 14 - Prob. 14A.3BECh. 14 - Prob. 14A.4AECh. 14 - Prob. 14A.4BECh. 14 - Prob. 14A.5AECh. 14 - Prob. 14A.5BECh. 14 - Prob. 14A.6AECh. 14 - Prob. 14A.6BECh. 14 - Prob. 14A.7AECh. 14 - Prob. 14A.7BECh. 14 - Prob. 14A.8AECh. 14 - Prob. 14A.8BECh. 14 - Prob. 14A.9AECh. 14 - Prob. 14A.9BECh. 14 - Prob. 14A.1PCh. 14 - Prob. 14A.2PCh. 14 - Prob. 14A.3PCh. 14 - Prob. 14A.4PCh. 14 - Prob. 14A.5PCh. 14 - Prob. 14A.6PCh. 14 - Prob. 14A.7PCh. 14 - Prob. 14A.8PCh. 14 - Prob. 14A.10PCh. 14 - Prob. 14A.12PCh. 14 - Prob. 14A.13PCh. 14 - Prob. 14B.1DQCh. 14 - Prob. 14B.2DQCh. 14 - Prob. 14B.3DQCh. 14 - Prob. 14B.4DQCh. 14 - Prob. 14B.5DQCh. 14 - Prob. 14B.1AECh. 14 - Prob. 14B.1BECh. 14 - Prob. 14B.2AECh. 14 - Prob. 14B.2BECh. 14 - Prob. 14B.3AECh. 14 - Prob. 14B.3BECh. 14 - Prob. 14B.4AECh. 14 - Prob. 14B.4BECh. 14 - Prob. 14B.5AECh. 14 - Prob. 14B.5BECh. 14 - Prob. 14B.6AECh. 14 - Prob. 14B.6BECh. 14 - Prob. 14B.1PCh. 14 - Prob. 14B.2PCh. 14 - Prob. 14B.3PCh. 14 - Prob. 14B.4PCh. 14 - Prob. 14B.5PCh. 14 - Prob. 14B.6PCh. 14 - Prob. 14B.7PCh. 14 - Prob. 14B.8PCh. 14 - Prob. 14B.10PCh. 14 - Prob. 14C.1DQCh. 14 - Prob. 14C.2DQCh. 14 - Prob. 14C.1AECh. 14 - Prob. 14C.1BECh. 14 - Prob. 14C.2AECh. 14 - Prob. 14C.2BECh. 14 - Prob. 14C.3AECh. 14 - Prob. 14C.3BECh. 14 - Prob. 14C.4AECh. 14 - Prob. 14C.4BECh. 14 - Prob. 14C.1PCh. 14 - Prob. 14C.2PCh. 14 - Prob. 14D.1DQCh. 14 - Prob. 14D.2DQCh. 14 - Prob. 14D.3DQCh. 14 - Prob. 14D.4DQCh. 14 - Prob. 14D.5DQCh. 14 - Prob. 14D.1AECh. 14 - Prob. 14D.1BECh. 14 - Prob. 14D.2AECh. 14 - Prob. 14D.2BECh. 14 - Prob. 14D.3AECh. 14 - Prob. 14D.3BECh. 14 - Prob. 14D.4AECh. 14 - Prob. 14D.4BECh. 14 - Prob. 14D.5AECh. 14 - Prob. 14D.5BECh. 14 - Prob. 14D.6AECh. 14 - Prob. 14D.6BECh. 14 - Prob. 14D.8AECh. 14 - Prob. 14D.8BECh. 14 - Prob. 14D.9AECh. 14 - Prob. 14D.9BECh. 14 - Prob. 14D.2PCh. 14 - Prob. 14D.3PCh. 14 - Prob. 14D.4PCh. 14 - Prob. 14D.6PCh. 14 - Prob. 14D.7PCh. 14 - Prob. 14D.8PCh. 14 - Prob. 14D.9PCh. 14 - Prob. 14D.10PCh. 14 - Prob. 14E.1DQCh. 14 - Prob. 14E.2DQCh. 14 - Prob. 14E.3DQCh. 14 - Prob. 14E.4DQCh. 14 - Prob. 14E.5DQCh. 14 - Prob. 14E.1AECh. 14 - Prob. 14E.1BECh. 14 - Prob. 14E.1PCh. 14 - Prob. 14E.3PCh. 14 - Prob. 14.1IACh. 14 - Prob. 14.2IACh. 14 - Prob. 14.6IACh. 14 - Prob. 14.8IA
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