Experiment #5

Molecular Dipole Moment

Ha, I am in a dipole moment!

Dipole Moment

Permanent dipole moment arises from an asymmetric distribution of electrical charge in the molecule, hence polar molecules

A separation of one electronic charge (1.60 10-19 C) of 1.00 Å from an equal and opposite charge gives a dipole moment of 1.60 10-29 C·m or 4.80 Debyes (D, a CGS unit, not an SI unit)

r r d

Peter Debye

Peter Joseph William Debye (March 24, 1884 –November 2, 1966) was a Dutch physicist and physical chemist, and Nobel laureate in Chemistry.

From 1934 to 1939 Debye was director of the physics section of the prestigious Kaiser Wilhelm Institute in Berlin. From 1936 onwards he was also professor of Theoretical Physics at the Frederick William University of Berlin. These positions were held during the years that Adolf Hitler ruled Nazi Germany and, from 1938 onward, also over Austria.

In 1939 Debye traveled to the United States of America to deliver the Baker Lectures at Cornell University in Ithaca, New York.

After leaving Germany in early 1940, Debye became a professor at Cornell, chaired the chemistry department for 10 years, and became a member of Alpha Chi Sigma.

Debye remained at Cornell for the remainder of his career. He retired in 1952, but continued research until his death.

Experimental Measurements

The dipole moment of individual solute molecules can be related to the dielectric constant (er) and refractive index (n) of the total solution

In a parallel plate capacitor, the external electric field causes the bound charges to be distorted such that a layer of induced negative charge will reside next to the positively charged plate and vice versa

Net Charges

Permanent dipole (): specific alignment Induced dipole: polarizability (a)

HARD: H2O, OH-, CH3COO-, F-, NH3, oxalate (-OOC-COO-), en.

SOFT: Br-, I-, SH-, (CH3)2S, S=C(NH2)2 (thiourea), P(CH3)3, PPh3, As(CH3)3, CN-, -S-C≡N (thiocyanate S-bound)

INTERMEDIATE: C6H5N (pyridine), N3- (azide), -N=C=S (thiocyanate, N-bound), Cl-

+

Polarizability

Relationship between the polarization of the sample (P), the applied field (E), and the sample dielectric constant (er) is

0 1rP Ee e

ero

C

C

net dipole moment per unit volume

(depending on both polarizability and

permanent dipole)

vacuum permittivity constant eo = 8.85 10-12 C2 N-1m-2 J-1

Clausius-Mossotti Equation

Local field (F) at the site of the molecule

03

PEF

e

0

PE

1r

e e

03 1

2

r

r

P Fe e

e

FM

NP 0

a

As

0 03 1

2

r

r

N

M

e e a

e

0

0

3

NM

2

1

eee a

r

r

Molar Polarization, PM

Molecular polarizability

Polar Molecules

kT32aa o

kT33

NM

2

1P 2

0

0M a

ee

e

o

r

r

distortion polarizability

PN

d

o

o

o3e

a PN

kT

o

o

e

9

2

DistortionPolarization

OrientationalPolarization

, permanent dipole

e

9 o

o

kT

NP

Polarizability

If high frequency AC is applied to the capacitance cell, then the permanent dipole of the molecules cannot rotate fast enough to follow the applied field and only the distortion term contributes to the molecular polarizability. Under these conditions the molar polarization only comes from distortion, Pd.

Measurement of the refractive index (n2 = er) of the substance at optical frequencies allows calculation of Pd.

In principle, measurement of PM at two temperatures allows ao and to be determined.

Polarizability

The equations derived above apply best to substances in gas phase where intermolecular interactions are weak

Experimentally we may apply them to very dilute solutions

Dilute Solutions

The constants “a” and “c” can be determined from knowledge of how dielectric constant and refractive index depend on solution composition.

X2 is the mol fraction of solute, er is the dielectric constant of the solution and n2 is the square of the refractive index of the solution

Linear regressions lead to the quantification of “a” and “c”

1

2 22

1 1 1

3

2 2r

M a cP

n

e

e

9 o

o

kT

NP

21

aXrr

ee

2

2

1

2 cXnn

Experimental Procedure

Capacitance meter

Capacitance dielectric constant (er)

Refractometer

Refractive index (n)

solution # Chlorobenzene (g) cyclohexane (g)

1 0.5 64

2 1 64

3 2 64

4 3 64

solution

#

o-dichloro-

benzene (g) cyclohexane (g)

5 0.5 64

6 1 64

7 2 64

8 3 64

Mol fraction (X2) εr n n2

ero

C

C

Data Analysis

X2

er

x

x x

x

X2

n2

xx

x

x

21 aX rr ee2

2

1

2 cXnn

0 0

er1

n12

Data Analysis

1

2 22

1 1 1

3

2 2r

M a cP

n

e

e

9 o

o

kT

NP

M1 = molar mass of cyclohexane in kg/mol1 = density of cyclohexane in kg/m3er1 = dielectric constant of cyclohexane (no units)n1 = refractive index of cyclohexane (no units)

http://macro.lsu.edu/howto/solvents/Dipole%20Moment.htm