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SOLUTIONSMANUAL TO ACCOMPANY ATKINS' PHYSICAL CHEMISTRY 499
In this case µ1 = µ2, so
C = 2µ41
3(4πε0)2kT
=
2 × [(2.5 D) × (3.3356 × 10−30 Cm)/(2.5 D)]4
3×(4π × (8.8542 × 10−12 J−1 C2m−1))2×(1.3806 × 10−23 JK−1)×(273 K)
= 6.90... × 10−77 Jm6
Hence ⟨V⟩ = − C
r6
= −6.90... × 10
−77 Jm6
(1.0 × 10−9 m)6
= −6.9 × 10−23 J . �is energy
corresponds, a�er multiplication by NA, to −41 Jmol−1 . �is is very much
smaller than the average molar kinetic energy of the molecules which, as ex-
plained in Section 2A.2(a) on page 37, is given by
3
2RT = 3
2 × (8.3145 JK−1mol−1) × (273 K) = 3.4 kJmol−1
E14B.5(b) �e energy of the dipole–induced dipole interaction between a polar molecule
such as water and a polarizable molecule such as CCl4 is given by [14B.6–597],
V = −µ21α′2/4πε0r6. From the data in the Resource section the dipole moment
of water is 1.85 D and the polarizability volume of CCl4 is 10.3 × 10−30 m3.
V = − µ
2
1α′2
4πε0r6
= −
[(1.85 D) × (3.3356 × 10−30 Cm)/(1 D)]2 × (10.3 × 10−30 m3)
4π × (8.8542 × 10−12 J−1 C2m−1) × (1.0 × 10−9 m)6
= −3.52... × 10−24 J
�is interaction energy corresponds, a�er multiplication by Avogadro’s con-
stant, to −2.1 Jmol−1 .
E14B.6(b) �e London formula for the energy of the dispersion interaction is given by
[14B.7–598]
V = − C
r6
C = 3
2α′1α
′
2
I1I2
I1 + I2
In the case that the two interacting species are the same, with polarizability
volume α′ and ionisation energy I, this expression becomes
C = − 32α′2
I2
2I
= 3
4α′2I hence V = −3α
′2I
4r6
Table 14A.1 on page 585 in the Resource section gives the polarizability volume
of argon as α′ = 1.66 × 10−30 m3 and Table 8B.4 on page 325 gives the �rst
ionisation energy as I = 1520.4 kJmol−1, so
V = −3α
′2I
4r6
= −3×(1.66 × 10
−30 m3)2×(1520.4 × 103 Jmol−1)
4 × (1.0 × 10−9 m)6
= 3.1 Jmol−1