Dipole Moment of Dichlorobenzene
CHEM 366
MiaomiaoGu
Experiment date: Feb 24th, 2011
Student ID: 301100545
Submission date: Mar 10th, 2011
Abstract. The dipole moment of o- and m-dichlorobenzene in benzene at constant
temperature was estimated by determine the capacitance in order to obtain the
dielectric constant. The dipole moment values were obtained as 2.0(1) D and 1.5(1) D
for o- and m-dichlorobenzene by deduction method and 1.98(5) D and 1.45(5) D for
o-dichlorobenzene by Guggenheim’s method.
Purpose:
Obtain the dipole moment of polar o- and m-dichlorobenzene in benzene by the
heterodyne-beat frequency method. The results were extrapolated by Guggenheim’s
and deduction methods.
Introduction:
The permanent dipole moment  of a polar molecule, as a solute molecule in a
liquid solution in a non-polar solvent, can be determined experimentally from
measurements of the dielectric constant . The dielectric constant is also known as the
relative permittivity. The dielectric constant is determined with a capacitance cell. In
this experiment, by the heterodyne-beat frequency method, the capacitances of o- and
m-dichlorobenzene in benzene at closed and open positions were obtained. Then, the
dipole moment was extrapolated.
Theory
Based on use of an electrical oscillator incorporating an inductance L and a
capacitance in parallel, the frequency of such an oscillator is given by: (1)
1
𝑓 = 2∏√LC
(1)
The difference △C between the closed and open positions is independent of the
stray capacitance. Thus the dielectric constant of the liquid or solution is given by:
κ= △C(liq)/ △C(air)
(2)
The mole fraction of the dichlorobenzene solute X2 has linear relationship with
dielectric constant, solution density and the square refractive index n2:
κ= κ1 + aX2
(3)
ρ = ρ1 + bX2
(4)
n2 = n12 + cX2
(5)
By equation (3) and (4), it is possible to rearrange terms and obtain the limiting
expression:
Po2M =
3M1 a
ρ1(K1+2)2
+
k1−1
(M2
(k1+2)ρ1
−
M1b
ρ1
)
(6)
If the molar distortion polarization in an infinitely dilute solution is equal to that in
the pure solute, then:
Po2d =
n22 −1 M2
n22 +2 ρ2
(7)
The molar orientation polarization of the solute at infinite dilution can be obtained
from equation (6) and (7) two expressions:
Po2 = Po2M - Po2d
(8)
The dipole moment of solute is extrapolated from the molar orientation polarization:
 = 42.7 (Po2T)1/2 * 10-30 Cm
(9)
= 12.8 (Po2T)1/2 debye
The molar orientation polarization of the solute could also be derived from
Guggenheim’s method by experiment:
Po2 =
3𝑀1
ρ1
𝑎
[(κ1+2)2 −
𝑐
(𝑛12 +2)2
]
(10)
Experiment:
Most procedures were same as shown in the lab manual,
(2)
few details were
indicated in the following:
The 25ml solutions containing 1%, 2%, 3% and 4% mole fraction dichlorobenzene
in benzene were prepared at 23°C conditions.
Since the capacitance was very sensitive with temperature, the solutions were
placed into the 25°C bath for 7 minutes before the capacitance measurements.
Results and Calculation:
At room temperature, benzene and two series of o- and m-dichlorobenzene
solutions were prepared. The mass of solute, solvent and solution of each solution
were measured. From equation (1), the capacitance of each solution was measured by
an oscillator circuit at the open and close position of cell capacitor in a constant
temperature bath 25°C. Afterward, the refractive index of the solute of each solution
was obtained at 25°C, and the value of obtained capacitance, refractive index and
solution mass was shown in Table 1.
Mass(g)
Mass(g)
Empty
Vial
vial
+Solute
Mass(g)
Capacitance
Index of
Position
Position
refraction
Vial+solute+solvent
a
b

48.3097
291.9(1)
335.1(1)
1.4984
Benzene
26.4260
soln 1 o-dichloro
26.6947
27.0638
48.7667
291.1(1)
338(1)
1.4968
soln 2 o-dichloro
27.4328
28.2016
49.5891
289.23(6)
334.93(6)
1.4983
soln 3 o-dichloro
24.3517
25.4671
46.6317
287.67(6)
334.6(0)
1.4995
soln 4 o-dichloro
23.8428
25.3717
46.2399
285.73(6)
334.13(6)
1.5095
soln 1 m-dichloro
24.8318
25.2308
47.2023
291.03(6)
334.97(6)
1.4992
soln 2 m-dichloro
26.6153
27.3686
48.7539
290.43(6)
334.6(0)
1.4999
soln 3 m-dichloro
24.8233
25.9498
47.0115
298.77(6)
334.5(1)
1.5004
soln 4 m-dichloro
24.0412
25.5534
46.5949
289.5(1)
334.83(6)
1.5006
Air
320.7(5)
338(1)
Table 1. Estimated capacitance of dichlorobenzene solutions.
The dielectric constant, solution density, square of index refractive, and mole
fraction of each dichlorobenzene solution were computed and given in table 2.
Benzene
o-diCl 1
o-diCl 2
o-diCl 3
o-diCl 4
m-diCl 1
m-diCl 2
m-diCl 3
m-diCl 4
Air
ΔC(liq)(pF)
43.2
43.93
45.7
46.93
48.4
43.93
46.17
44.8
45.3
17
±
к
0.1
2.5
0.08 2.5
0.08 2.5
0.06 2.5
0.08 2.6
0.08
2.6
0.06
2.6
0.1
2.6
0.1
2.7
1
±
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
0.2
ρ(g/ml)
0.87
0.88288
0.886252
0.8912
0.895884
0.89482
0.885544
0.887528
0.902148
n2
2.245203
2.24041
2.244903
2.2485
2.27859
2.247601
2.2497
2.2512
2.2518
X2
0
0.008956
0.018743
0.027241
0.036807
0.009556
0.018372
0.027634
0.036783
Table 2. calculated к,ρ,ηand mole fraction of solute in different solutions.
ΔC was calculated from the difference capacitances between open and closed
positions. For the o-diCl 1 solution, the dielectric constant was extrapolated from
equation (2), where ΔCliq = 43.93 pF and ΔCair = 17. Then, the dielectric constant for
o-diCl 1 solution was obtained as 2.48 and shown in table 2. The difference
capacitance and dielectric constant of other solutions was computed by the same
method and given in table 2.
The density of each solution was calculated from ρ = mass of solution / volume of
solution, the obtained values were presented in table 2. The mole fraction X2 for
o-diCl 1 was calculated form X2 = # moles solute / (# moles solute + # mole solvent)
where solute was 0.002511mol and solvent was 0.27785 mol, thus, the mole fraction
X2 of o-diCl 1 solution was 0.008956 and recorded in table 2. The density and mole
fraction of other o- and m-dichlorobenzene solution were determined by the same
way.
The extrapolated dielectric constant, solution density and square of refractive index
n2 all had linear relationship with the mole fraction of the solute. Three curves for
each o- and m-dichlorobenzene were plotted to present this relationship and the
parameters a, b, c were obtained as shown in figure 1-6.
dielectric constant vs mole fraction
2.85
y = 6.2085x + 2.501
dielectric constant κ
2.8
2.75
2.7
2.65
2.6
2.55
2.5
2.45
2.4
2.35
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
mole fraction X2
Figure1. Relationship between dielectric constant and mole fraction of
o-dichlorobenzene in benzene.
density of solution Vs the mole fraction
0.905
y = 0.653x + 0.8733
0.9
density r (g/ml)
0.895
0.89
0.885
0.88
0.875
0.87
0.865
0.86
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
mole fraction X2
Figure
2.
Relationship
between
solution
density
and
mole
fraction
of
o-dichlorobenzene in benzene.
refraction index vs index refraction
2.253
y = 0.1401x + 2.2465
2.252
square of Index refraction n2
2.251
2.25
2.249
2.248
2.247
2.246
2.245
2.244
2.243
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
mole fraction X2
Figure3.
Relationship
between
o-dichlorobenzene in benzene.
index
refraction
and
mole
fraction
of
dielectric constant vs mole fraction
dielectric constant κ
2.72
2.7
2.68
2.66
2.64
2.62
2.6
2.58
2.56
2.54
2.52
2.5
y = 3.4942x + 2.5415
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
mole fraction X2
Figure4.
Relationship
between
dielectric
constant
and
mole
fraction
of
m-dichlorobenzene in benzene.
solution density vs mole fraction
0.9
0.895
y = 0.6214x + 0.8699
density ρ (g/ml)
0.89
0.885
0.88
0.875
0.87
0.865
0.86
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
mole fraction X2
Figure5.
Relationship
between
m-dichlorobenzene in benzene.
solution
density
and
mole
fraction
of
square of Index refraction n2
index refraction vs mole fraction
2.254
2.253
2.252
2.251
2.25
2.249
2.248
2.247
2.246
2.245
2.244
2.243
y = 0.1833x + 2.2457
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
mole reaction X2
Figure6.
Relationship
between
index
refraction
and
mole
fraction
of
m-dichlorobenzene in benzene.
Since dielectric constant, solution density and square of refraction index n2 had
linear relationship with mole fraction, by equation (3)-(5), κ1, ρ1 and n12 were the
intercepts and a, b and c were the slope values of the equation for o-dichlorobenzene
solutions in Figure 1- 3. Therefore, κ1, ρ1 and n12 were obtained as 2.501, 0.8733g/mL
and 2.2465; a ,b and c were obtained as 6.2085, 0.653 and 0.1401 and shown in table
3. By the same method, these values of m-dichlorobenzene were determined and
shown in table 3.
The values determined from the calibration curves were used in calculating the
limiting molar polarization of the solute in solution (Po2M). For o-dichlorobenzene, by
equation (6) where M2 was the molar mass of solute 147 g/mol, M1 was the molar
mass of solvent benzene 78.11 g/mol, a = 6.2085, b= 0.65299, k1 = 2.501, and ρ1 =
0.878326 g/ml. Thus, the limiting molar polarization of solute for o-dichlorobenzene
was extrapolated as 116.065 cm3/mol and shown in table 3. The limiting molar
polarization of solute for m-dichlorobenzene was obtained by the same method and
presented in table 3.
The molar orientation polarization could be approached by two methods. The first
one was derived from the expression of Po2M and Po2d, the other one was expressed by
Guggenheim’s method. Thus the two values of molar orientation polarization were
obtained, as well as the dipole moment, and they were listed in table 3.
o-dichlorobenzene
m-dichlorobenzene
o-dichlorobenzene
m-dichlorobenzene
a
6.208
3.494
0.004
b
0.7
0.621
0.004
к1
±
2.501
2.5415
0.0008
Po2M
0.001
c
0.14
0.1833
0.0005
ρ1 (g/ml)
±
n12
±
0.873
0.87
0.02
2.247
2.25
0.001
0.1
0.06
±
0.04
0.02
Po2
Po2d
(cm3/mol)
116
5
36.077
80
5
81
5
35.8054
45
2
±
D)
±
(D)
±
80
6
2.0
0.1
1.98
0.05
43
3
1.5
0.1
1.45
0.05
Po2
(cm3/mol)
o-dichlorobenzene
m-dichlorobenzene
0.0008
±
±
(cm3/mol)
o-dichlorobenzene
m-dichlorobenzene
±
±
±
(cm3/mol)
Table 3. the estimated dipole moments by two different methods.
The molar distortion polarization of o-dichlorobenzene was determined from
equation (7) where n2 was the literature index of refraction 1.550, ρ2 was the density
for the solute in the pure state 1.3g/cm3 and M2 was the mole mass of the solute
147g/mol, thus, the molar distortion polarization of o-dichlorobenzene was obtained
as 36.077 cm3/mol and given in table 3. The molar distortion polarization of
m-dichlorobenzene was extrapolated in the same way and shown in table 3.
From equation (8) where Po2M and Po2d were calculated and listed in table 3, then, the
molar orientation polarization of o-dichlorobenzene was obtained as 79.988 cm3/mol
and shown table 3. On the other hand, the molar orientation polarization could also
extrapolated by Guggenheim’s method. Thus, by equation (10) where M1 was the
mole mass of benzene as 78.11g/mol, ρ1, к1 n12, a and c were the computed values
from the experiment and listed in table 3. Therefore, the molar orientation polarization
of o-dichlorobenzene was obtained as 80.1482 cm3/mol and given in table 3. The
molar orientation polarization of m-dichlorobenzene were obtained by these two
methods and shown in table 3.
From equation (9), the dipole moment of o-dichlorobenzene for both methods was
calculated at temperature 298K as 6.59247E-30 Cm and 6.59907E-30 Cm and
reported in unit D in table 4. The dipole moment of m-dichlorobenzene was obtained
by the same method as E-30 Cm and 4.83359E-30 CD and given in unit D in
table 4.
Error Analysis:
The average capacitance at the closed position of o-diCl 1 solution was calculated
as 291.1 pF and the standard deviation on this capacitance has been calculated from
σ =√(Σ(xi-xave)2/(n-1)) where xave= 291.1 pF and n=3, thus, σC = 0.1. The result
should be reported as 291.1(1) pF and shown in table 1. By the same method, the
error of average capacitance of other solutions was calculated and shown in table 1.
The difference capacitance between the closed and open position of o-diCl 1
solution was calculated as 47.3pF. The error on this capacitance has been determined
from the error of capacitance at closed and open position where e△C = √(ea2 + eb2) ,
thus, e△C = 1. The result should be reported as 47(1) pF and shown in table 2. By the
same method, the error of △C of other solutions was determined and given in table 2.
The dielectric constant of o-diCl 1 solution was extrapolated as 2.764706 and the
error on this dielectric constant has been calculated from %e = √( (%eliq)2 + (%eair)2)
where %eliq and %eair were percent relative error of the solution and air, thus , the
error of dielectric constant was 0.02. Then, the result of dielectric constant error of
o-diCl 1 was shown in table 2 as 2.41(2). The dielectric constant error of other
solutions was calculated by the same method and given in table 2. In addition, the
error of Po2M, Po2and of o- and m-dichlorobenzene were also obtained by this
method and listed in table 3.
The uncertainty of the calibration curve in Figure 1 of o-dichlorobenzene was
determined from the vertical deviation di and the standard deviation of this slope was
calculated from σy = √(Σ di2/(n-2)), by calculations Σ di2 =9.43665E-07 and n= 4.
Therefore, the uncertainty of the calibration curve was σy = 0.0007. By the same
method, the uncertainty for other figures was extrapolated.
The dielectric constant κ1 of o-dichlorobenzene was extrapolated from the
calibration curve in figure 1, y = 5.3066x + 2.3708. The standard deviation of κ1 was
determined from σκ1 =√(σy2Σ(xi2)/D) where the calculated values were 4.9E-7,
0.002528337, and 0.001695837 for σy2, Σ(xi2) and D. Therefore, σκ1 = 0.0008. Then
the k1 was reported as 2.3708(8) in table 3. The error of dielectric constant κ1 n12 and
ρ1 values of o-dichlorobenzene and m-dichlorobenzene were obtained by the same
method and given in table 3 as well.
Value a of o-dichlorobenzene in equation (3) was also extrapolated from the
calibration curve in figure1. The standard deviation of a was determined from σa =
√(σy2n/D) where the computed values were 4.9E-7, 4 and 0.001695837 for σy2, n and
D. As a result, σa = 0.03. The a value should be recorded as 5.31(3) in table 3. The
errors of a, b and c values of o- and m-dichlorobenzene solutions were obtained by the
same way and shown in table 3.
As the density, molar fraction and index refraction were not treated as the final
values, their uncertainties were not calculated particularly.
Discussion:
The uncertainty of molar distortion polarization was considered as no error because
the index of refraction, density and molar mass of dichlorobenzene were from
literature (3) with no uncertainty.
Compared
the
results
of
dipole
moment
of
dichlorobenzene
with
monochlorobenzene, the dipole moment of monochlorobenzene is bigger than
m-dichlorobenzene, but smaller than o-dichlorobenzene. This is because the two
carbon-chloride bonds of o-dichlorobenzene have a 60o angle, then, the sum
carbon-chloride bond moment of o-dichlorobenzene calculated from the vector was
equal to √3 carbon-chloride bond moment and bigger than the monochlorobenzene
bond moment. In addition, the carbon-chloride bonds of m-dichlorobenzene have a
120o angle; its sum bond moment is smaller than the carbon-chloride bond which is
around 0.5 carbon-chloride bond moment. Therefore, the experiment results of dipole
moment were consistent with the physical vector determination which the dipole
moment of monochlorobenzene is bigger than m-dichlorobenzene, but smaller than
o-dichlorobenzene.
There were two methods to obtain the molar orientation polarization of the solute, by
equation (10); a more precise result was given than equation (8) did, as the uncertainty
indicated. For the results obtained from equation (10), a 2 decimal places uncertainty was
given where as the other method from equation (8) gave accuracy to only one decimal place.
Thus, the dipole moment obtained from Guggenheim’s method gave more accurate value.
Conclusion:
By the measurement of the capacitance of o- and m-dichlorobenzene in benzene
with various concentrations at open and closed positions, the dipole moment was
extrapolated by two calculating methods. These two methods determined very close
and no significant difference values, but the Guggenheim’s method gave more
accurate result.
Reference:
1. Carl W. Garland; David P. Shoemaker; Experiments in Physical Chemistry, 8th
edition; McGraw-Hill Higher Education, New York, 2009. P106-118
2. Physical Chemistry lab manual.
3. Handbook of Chemistry and Physics. 91st Edition, 2010-2011.
4. Daniel C.Harris; Quantitative Chemical Analysis, 7thed; W.H.Freeman and
Company, New York, 2007.P39-71.
Appendices:
Capacitance
closed (b)
O1
291.2
291.1
291
Capacitance
closed (b)
O3
287.6
287.7
287.7
Capacitance
closed (b)
M1
291
291
291.1
M3
289.7
289.8
289.8
Capacitance
closed (b)
Benzene
291.8
292
292
(pF)
open (a)
339.2
337
339
(pF)
open (a)
334.6
334.6
334.6
(pF)
open (a)
334.9
335
335
334.4
334.6
334.6
(pF)
open (a)
335
335.2
335.2
O2
O4
M2
M4
Air
Capacitance
closed (b)
289.2
289.2
289.3
Capacitance
closed (b)
285.7
285.8
285.7
Capacitance
closed (b)
290.5
290.4
290.4
289.4
289.5
289.6
Capacitance
closed (b)
320.4
321.2
320.4
(pF)
open (a)
334.9
334.9
335
(pF)
open (a)
334.1
334.1
334.2
(pF)
open (a)
334.6
334.6
334.6
334.8
334.8
334.9
(pF)
open (a)
339.2
337
339