Electronic Spectra of Change Transfer Complexes
CHEM 366
Miaomiao Gu
Experiment date: Feb 03rd, 2011
Student ID: 301100545
Submission date: Feb 17th, 2011
Abstract. The absorbance at wavelength of a series of o-xylene, mesitylene and
organic complex solutions was measured by UV/Vis spectrometer and recorded. The
equilibrium constant and molar extinction coefficients were then extrapolated and the
values were: 0.075(0.003) M-1, 1250(20) M-1cm-1 and 0.08(0.002) M-1, 2000(13)
M-1cm-1 for o-xylene and mesitylene complexes. Moreover, the free energy was
extrapolated from equilibrium constant for each complex solution.
Purpose:
To determine the extinction coefficient and equilibrium constant corresponding to
the charge transfer complex by analysis the charge transfer absorption spectra of a
series of electron donor mixed with a same electron acceptor, teracyanoethylene.
Introduction:
In this experiment, the absorbance of each molecular complex in various
concentrations was measured by UV-vis spectra. This instrument provides directly
absorbance of each solution with no true unit. Further analysis between the same
common electron acceptor and different electron donor, the equilibrium constant,
molar extinction coefficient and free energy were determined. Therefore, in this
experiment, the relationship between the electron acceptor and donor of the formed
molecular complexes was studied and determined.
Theory:
The standard free energy is related to the equilibrium constant of the complex
through the expression :( 1)
ΔG0 = –RTlnK
(1)
At the desired wavelength, Beer-Lambert’s law relates the concentration to the
absorbance at wavelength according to:
OD = cl
(2)
A substitution of equations was re-arrangement leads to:
ODmax/ (l*[A]o) = AB*K*[B] 0/ (1+K [B] 0)
(3)
Equilibrium constant was converted from a linear equation in the series of
dilutions:
U= s/ [B] 0 + i
(4)
The observable transition energy related to the ionization potential of the electron
donor:
≈(Ib-P)/hc
(5)
Species A, B and the CT complex AB are in equilibrium with equilibrium constant:
[AB] ≈K[A]o[B]0/(1+K[B]0)
(6)
Relate ΔGo to Ib according to :
ΔGo=M-Q/(Ib-P)
(7)
Experimental procedure:
Same procedures were as referenced in lab manual. (1)
Result and Calculation:
At room temperature, two series of o-xylene and Mesitylene solutions, Benzene,
Toluene, and Hexa.MethylBenzene (HMB) solutions were prepared with electron
acceptor, teracyanoethylene (TCNE) in different concentrations. Their uv/vis spectra
were collected by Hp-8453 spectrophotometer. Each series was diluted by TCNE to
four solutions with different concentrations. The concentration value of the acceptor
and donor in each mixture was obtained and given in Table 1-3.
Mixture ID [B]0/M
±
[A]0/M
±
OD
±
max/cm
2.244
0.008
Benzene
0.00008
3E-07 0.13
0.002 0.372
1.882
0.007
Toluene
0.00008
3E-07 0.081 0.0007 0.398
o-Xylene
1.658
0.006
0.00008
3E-07 0.0981 0.0004 0.42
Mesitylene 1.437
0.005
0.00008
3E-07 0.1304 0.0003 0.448
0.01115
4E-05
HMB
0.0001
4E-07 0.1725 0.0001 0.527
Table 1. Donor and acceptor concentrations and measured data of mixture solutions.
cm-1
2.688172043
2.512562814
2.380952381
2.232142857
1.897533207
Mixture ID [B]0/M
±
[A]0/M
o-xylene
1.658
0.006
0.00008
B2
0.663
0.002
0.000092
B3
0.332
0.001
0.000096
B4
0.1989 0.0007 0.0000976
B5
0.0663 0.0002 0.0000992
Table 2. Donor and acceptor concentrations
different concentrations.
±
OD
±
max/cm
cm-1
3E-07 0.0981 0.0004
0.42
2.380952381
3E-07 0.1091 0.0003
0.426
2.34741784
3E-07 0.1004 0.0004
0.426
2.34741784
3E-07 0.0846 0.0003
0.425
2.352941176
3E-07 0.0612 0.0003
0.424
2.358490566
and measured data of o-xylene at
Mixture ID [B]0/M
±
[A]0/M
mesitylene 1.437
0.005
0.00008
B2
0.575
0.002
0.000092
B3
0.287
0.001
0.000096
B4
0.1725 0.0006 0.0000976
B5
0.0575 0.0002 0.0000992
Table 3. Donor and acceptor concentrations
different concentrations.
±
OD
±
max/cm
cm-1
3E-07 0.1304 0.0003
0.448
2.232142857
3E-07 0.1698 0.0003
0.449
2.227171
3E-07 0.1415 0.0003
0.45
2.222222
3E-07 0.1313 0.0003
0.448
2.232143
3E-07 0.0859 0.0002
0.449
2.227171
and measured data of mesitylene at
The absorbance at wavelength of each mixture was obtained by uv/vis spectra.
Equilibrium constant and free energy were computed and given in table 4.
Mixture ID
Benzene
Toluene
o-Xylene
Mesitylene
HMB
[AB]
5.43E-05
6.43E-05
8.85E-06
7.93E-08
6.75E-05
±
b-P
ΔG0/J
3E-07
4E-07
5E-08
4E-10
4E-07
9.66707E-38
1.07082E-37
1.39584E-38
1.17301E-40
8.48279E-38
149.7087
-1885.59
6267.202
6111.05
-12643.8
equilibrium
K/M-1
AB/M-1cm
0.075(0.003)
0.08(0.002)
1250(20)
2000(13)
-1
Table 4. Extrapolated values of complex solutions.
The equilibrium constant K and molar extinction coefficient of o-xylene and
mesitylene mixtures were calculated in turn of a calibration line which was plotted U
versus 1/ [B]o. The K and values were extrapolated from the calibration equation, as
shown in figure 1 and 2.
U Vs 1/[B]0
0.0018
y = 6E-05x + 0.0008
0.0016
U
0.0014
0.0012
0.001
0.0008
0
2
4
6
8
1/[B]0 (M-1)
10
12
14
16
Figure 1. Calibration curve as U against 1/ [B] 0 of o-xylene mixture solution.
U vs 1/[B]0
0.0012
y = 4E-05x + 0.0005
0.0011
0.001
U
0.0009
0.0008
0.0007
0.0006
0.0005
0
5
10
15
1/[B]0 (M-1)
Figure 2. Calibration curve as U against 1/ [B] 0 of Mesitylene mixture solution.
20
By equation (4), i=1/AB where i=0.0005 in figure 2. Thus, AB= 2000M-1cm-1.
Also, as s=1/ (AB*K) where s=4E-05
AB=
2000M-1cm-1, then K=0.08M-1 for
mesitylene solutions. Therefore, the values of equilibrium constant and molar
extinction for mesitylene solutions were 0.08M-1 and 2000M-1cm-1 as shown in Table
6. The equilibrium constant and molar extinction coefficients of o-xylene mixture
were determined by the same method and the values were shown in Table 4.
The free energy of mesitylene mixture was extrapolated from equation (1), where R
is the gas constant 8.3145 J/mol/K, T is temperature at 291K and equilibrium constant
K=0.08M-1. Therefore, the free energy ΔGo of mesitylene mixture was obtained with
value of 6110.68J and shown in Table 6. Same as mesitylene mixture, the free energy
ΔGo of o-xylene mixture was obtained and shown in Table 4.
By equation (6) where K=0.08M-1, [A]0= 0.00008M, and [B]0= 1.437M, the
mesitylene complex concentration was extrapolated as 8.248547033E-08M and
shown in Table 6. The other concentration of each complex was obtained by the same
method and given in Table 4.
According to ΔGo related to Ib, the provided data complex solution could
extrapolate an equation for the measuring complex solution. The relationship was ΔGo
against Ib-P and shown in Figure 3.
ΔGo Vs 1/Ib-p
0
-1000 0
2
4
6
8
10
12
-2000
-3000
y = 1369.9x - 14300
-4000
ΔGo /J
-5000
-6000
-7000
-8000
-9000
-10000
-11000
-12000
-13000
1/Ib-P E+36
Figure 3. Calibration curve of ΔGo Vs 1/Ib-p.
From equation (7), ΔGo value could be extrapolated from Ib where (Ib-P) was
obtained from equation (5). Thus, ΔGo values were determined as 83777.14351J and
11656529.75J for o-xylene and mesitylene complexes.
Error Analysis:
The equilibrium constant and molar extinction coefficient of o-xylene were
extrapolated from the calibration curve in figure 1 where y= 6E-05x+0.0008. AB was
obtained from the intercept as 1250M-1cm-1. The standard deviation of AB was
determined from σAB = 0.0008/√ (σy2Σ (xi2)/D). (2) Thus, σAB= 19.54268602, and
σAB should recorded as 1250(20) M-1cm-1 and shown in Table 4. The error of σAB of
mesitylene was determined by the same way and given in table 4.
Same as AB, equilibrium constant K was determined from the slope of the
calibration curve in figure 1 for mesitylene. By equation (4) where K= i/s, K was
extrapolated as 0.075M-1. The uncertainty of equilibrium constant K was computed
from standard deviation of the slope and intercept %e = √((%es)2+(%ei)2), where %es=
7.62 and %ei= 4.69. The uncertainty was obtained as 0.003 and the equilibrium
constant K was recorded as 0.075(0.003) M-1 in Table 4. The uncertainty of
equilibrium constant K of o-xylene was extrapolated and shown in table 4 as well.
From equation (1), the uncertainty of free energy ΔGo is equal to the relative
uncertainty in equilibrium constant K for mesitylene complex where ey= ex/x.
Therefore, the uncertainty was extrapolated as 3 and the free energy ΔGo was
recorded as 6267(3) J in table 4. And the obtained ΔGo uncertainty of o-xylene was
shown in table 4.
The uncertainty of calibration curve in figure 1 was determined from the vertical
deviation di and the standard deviation of this slope was calculated from σy = √ (Σ di2/
(n-2)). By calculations, the uncertainty of the calibration curve was σy = 0.01. By the
same method, the uncertainty for other figures was extrapolated.
As the concentration of [A] 0, [B] 0 and [AB] were not treated as final values, their
uncertainties were not calculated particularly, but they were still shown in Table 1-4.
Discussion:
For Benzene, Toluene and HMB complexes which did not measured equilibrium
constants, their computed free energy and 1/ (Ib-P) values were consistent with the
linear equation (7). By this linear equation, the computed free energy for o-xylene and
mesitylene complexes were much bigger than the free energy which directed
computed from equilibrium constant. Therefore, free energy determined from the
experimental measurement was not consistent with the equation (7). This might
because the equilibrium constant was determined from a series of dilutions. As the
concentration of the complexes was already very small, the concentration of the
dilutions might too small to close to the limit detection of the UV/vis spectra.
Therefore, the noise of the spectra might cause the error in the extrapolation from the
absorbance.
As an electron acceptor, TCNE substituted benzenes, electron donor to form
molecular complexes TCNE-Benzene.
C6H5R + C3N2C3N2→ C6H5R-C3N2C3N2
Although, TCNE is the most powerful organic electron acceptors, being a prototype
for other cyano-based electron acceptors, hexacyanobutandiene (HCBD) also can
substitute benzenes to form molecular complexes. While TCNE is a basic constituent
in charge transfer compounds with either magnetic or conducting properties, HCBD
has been used in building hybrid organic-inorganic molecular magnets.
Conclusion:
By the measurement of absorbance at wavelength of benzene aromatic organics and
dilution with various concentrations, equilibrium constant K and molar extinction
coefficient of o-xylene and mesitylene complexes with TCNE was obtained and
compared with literatures. Moreover, the free energy could obtain from equilibrium
constant or the related Ib, the equilibrium constant method was more accurate. As a
result, the UV/vis spectrum was a good instrument of determining equilibrium
constant, but not good for measuring low concentration complexes.
Reference:
1) Physical Chemistry lab manual. Pg.V-1-V-11.
2) Daniel C.Harris; Quantitative Chemical Analysis, 7thed; W.H.Freeman and
Company, New York, 2007.P39-71.
3) Carl W. Garland; David P. Shoemaker; Experiments in Physical Chemistry, 8th
edition; McGraw-Hill Higher Education, New York, 2009. P106-118
4) Daniel C. Harris; Quantitative Chemical Analysis, 6th edition; W. H. Freeman and
Company, New York, 2003. P51-P56.