Concise Physical Chemistry

c18 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

296 EXPERIMENTAL DETERMINATION OF MOLECULAR STRUCTURE

PlottingPT, which we obtain from measured values ofε,against1/Tgives a linear

function with a slope of (4πNA/3)(μ^2 / 3 kB). This gives usμand enables us to subtract

the temperature-dependent term fromPTat any specific temperature to determine

4

3 πNAαand thusα. (Note thatμis not the reduced mass in this context.)

The valueμis the twistingmomenton a dipole in a field. The moment is the

sum of each charge times the lever arm separating it from the center of rotation of

the molecule

∑

iqir^1. In the simplest case of a diatomic molecule, the charges are

equal in magnitude andμis equal to the moment of one charge times the entire bond

length:

μ=|qr 1 |+|qr 2 |=q(r 1 +r 2 )=qr

Thepolarizabilityαis a proportionality constant telling how much of a dipole can

be induced in a given molecule by a given field. It is inversely related to the tightness

with which a system of nuclei hangs onto its electrons and is widely used in organic

chemistry to predict the ease with which electrons can be shifted to or away from a

reaction site in the course of a reaction.

18.7.1 Bond Moments

It is useful to break molecular moments into contributions from each bond. The dipole

moment of the molecule is, to a good approximation, the vector sum of individual

moments of its bonds. We expect that chlorine will draw electrons toward it and

constitute the negative end of CH 3 Cl. By the principle of bond moments, we predict

thatcis-1,2-dichloroethene has a permanent dipole moment while thetransisomer

has none. The values ofμgiven below the isomeric structures in Fig. 18.8 are

experimentally determined.

The definition of dipole moment gives us both a convenient unit to expressμand

a way of characterizing the polarization of bonds like the H–Cl bond. Sinceμ=qr

and we know that the electric charge isq= 4. 80 × 10 −^10 esu, a typical bond that is

C C

H H

Cl Cl

C C

H

Cl

Cl

H

D = 0

FIGURE 18.8 The total dipoles of two dichloroethene isomers.