Food Quality Evaluation Techniques Beyond the Visible Spectrum
Iodine visible spectrum - lab report
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Transcript of Iodine visible spectrum - lab report
Silvia BobeicaCHEM 382
Absorption Spectra of Iodine VaporAbstract:
This experiment involved the calculation of several diatomic constants for iodine in the vapor
phase using absorption spectroscopy in the visible region of 500 to 620 nm. The transitions were
assigned in the visible spectrum and from this the equilibrium wavenumber of the excited and ground
state was calculated to be 134 cm-1 and 230 cm-1 in good agreement with literature values. The
dissociation energy from the v=0 and the equilibrium dissociation energy for the excited state were
estimated 4328 and 4395 cm-1 respectively, reasonably close to literature values. The experimental bond
force constant was 67.5 N/m while the equilibrium radius of the iodine molecule in the excited state was
3.235 A, both these values comparing favorably to accepted values. The parameter β’ was also
calculated to be 1.965 A-1, in very good agreement with the literature value. The diatomic constants for the
ground state were not as accurate as those of the excited state. The experimental dissociation energy
from the v=0 state and the equilibrium dissociation energy were 8855cm-1 and 8964 cm-1, compared to
literature values of approximately 12000 cm-1. The bond force constant of the ground state 178 N/m was
in good agreement with the literature value. The parameter β’’ was estimated at 2.237 A -1 compared to
the literature value of 1.901 A-1. This experiment shows that while a good estimations can be obtained for
the excited state of the vapor phase iodine with this model, the ground state calculations are inaccurate
and do not provide a reliable information about the diatomic constants of a homonuclear halogen.
Introduction:
The visible spectrum of iodine has found applications as a convenient tool for the study of the
differential rotation of the Sun, or the improved efficiency of dye-sensitized solar cells when used to dope
titanium dioxide crystals.1,2 Spectra of small molecules in gas phase offer information on the potential
energy curves of the ground and excited electronic states. The absorption spectrum of iodine will be used
to deduce vibrational frequencies, and bond energies. Figure 1 represents some of the features this
experiment will analyze, such as the difference in energy between the minimum of the potential energy
curve and dissociated atoms, D’e and the dissociation energy from the ground vibrational level of the
potential D’0.
1
The internal energy of a diatomic molecule is given by the equation:
E∫¿=Eel+E v+Er(1)¿
where Eel is the electronic energy which designates the minimum value of the potential curve for a given
electronic state, Ev is the vibrational energy and Er is the rotational energy.4 Dividing by the quantity hc
with c expressed in cm/s, and changing notation of Ev/hc and Er/hc to G and F respectively, the term
value is obtained:
T∫¿ (cm−1)=
E∫ ¿
hc=T el+G+F (2 )¿¿
This equation allows for frequency expressed in reciprocal centimeters to be written as:
3
2
ν=T ' el−T' 'el+G (ν ' )−G (ν ' ' )+F (J ' )−F (J ' ' )=νel+G (ν ' )−G (ν ' ' )(3)
by considering the rotational term difference to be very small as this experiment will not resolve it.4
Therefore the transition frequency written as a function of the quantum numbers ν’ and ν’’ will be given by
the equation:
ν (v ' , v ' ' )=νel+ν ' el(v '+ 12 )−ν ' e x 'e(v '+ 12 )2
−ν ' ' e(v ' '+ 12 )+ν' 'e x ' ' e (v ' '+12 )❑2
(4)
or in a different form:
Δν (v ' )≅ ν (v '+1 , v ' ' )−ν (v ' , v ' ' )≈ ν ' e−2ν ' e x'e (v '+1 )(5)
From which, a Birge-Sponer plot with a slope of −2ν ' e x'e and an intercept of ν 'e−2ν
'e x
'e can be made.
This will allow for easy calculation of v’e and x’e and an analogous calculation can be used to obtain v’’e
and x’’e
The convergence limit is the energy at which the spacing between the absorption bands is too
small to be distinguished. Beyond this energy, called the dissociation energy, the molecule is split into its
constituent atoms. Knowing ν 'e x'e, the dissociation energy of the excited state can be calculated from:
De=G (vmax❑)=ν e(
1xe
−xe)
4(6)
The dissociation energy D0 to dissociate from the v=0 level is smaller than De by the zero point
energy G(0) and is therefore given by:
D0=νe(1xe
−2)
4(7)
A harmonic force constant ke for both the excited and the ground vibrational level can also be
obtained from the following equation near the minimum in the potential energy curve, where the harmonic
oscillator model holds well:
k e=μ (2 πc νe)2(8)
where μ is the reduced mass. 4
At large displacement from the equilibrium bond length, the Morse potential is used to replace the
harmonic oscillator model. The parameter β in the Morse potential is obtained by equating ke to the
curvature of the Morse potential r=re from:
β=(ke
2hc De)2
(9)
3
The transition of greatest intensity ν(v*’) can be obtained from the spectrum and used in the
following equation to obtain the difference between the equilibrium radius of the ground state and that of
the excited state:
U ' (r ' ' e−r 'e)=D 'e{exp [−β ' (r ' 'e−r 'e )]−1 }2+νel=ν (v ¿' )+ 1
2ν ' 'e−
14ν ' 'e x
' 'e(13)
Experimental:
A few crystals of iodine were placed in a 1.0 cm path length quartz cuvette, heated to 32oC to
obtain more iodine in vapor phase, and the spectrum between 500 and 620 nm was acquired using an
Ocean Optics HR 4000CG-UV-NIR High Resolution spectrometer running 40 counts. The experimental
values for the diatomic constants were compared to the values obtained by McNaught.3
Results:
The absorption spectrum of iodine in the vapor phase is represented in Figure 2. The quantum
numbers of the ground electronic state are also represented on the spectrum. Notable features include
the decreasing separation between the transitions when approaching the convergence limit as well as
variable intensities of the signals for each transition. The transition with maximum absorbance occurs at
535 nm (18691 cm-1).
Figure 2. Absorption spectrum of I2 vapor with the ground quantum numbers assigned.
Table 1. Deslandres table of PN bands with band-head frequencies in cm-1. Differences between energy levels used in the excited state calculations are in bold font, while differences between energy levels used in the excited state calculations are between brackets [ ].
4
v''Average Differences
between energy levels for the excited state
calculation (cm-1)0 1 2
5
v'
Average separation between energy levels for
the ground state calculation (cm-1)
215.5464268
Average separationbetween energy levels
for the groundstate calculation (cm-1)
208.1200221
11 16549.71534
128.3479984
12 16678.06334
106.9375799
13 16785.00092
104.0380905
14 17099.8632 [210.8241874] 16889.03901
99.99920001 99.27302764 99.63611382
15 17422.81692 17199.8624 [211.5503598] 16988.31204
99.52406372 98.18291978 101.323095 99.67669282
16 17522.34098 17298.04532 [208.4101846] 17089.63514
95.6998891 99.00761835 96.9249737 97.21082705
17 17618.04087 17397.05294 [210.4928292] 17186.56011
92.98601148 94.33255341 105.5028331 97.60713267
18 17711.02689 17491.38549 [199.3225495] 17292.06294
98.09494686 93.81480279 95.95487483
19 17809.12183 [223.9215368] 17585.2003
86.36850423 99.82932699 93.09891561
20 17895.49034 [210.460714] 17685.02962
94.00379899 92.11607906 93.05993903
21 17989.49414 [212.3483339] 17777.1457
76.70040136 94.9969897 85.84869553
22 18066.19454 [194.0518456] 17872.14269
97.45999051 80.2117601 88.8358753
23 18163.65453 [211.300076] 17952.35445
86.85192426 81.26020644 84.05606535
24 18250.50645 [216.8917938] 18033.61466
77.93929625 82.65556456 80.29743041
25 18328.44575 [212.1755255] 18116.27022
87.76051371 78.11862819 82.93957095
26 18416.20626 [221.817411] 18194.38885
74.23418078 78.12745774 76.18081926
27 18490.44044 [217.9241341] 18272.51631
73.80111562 82.84345683 78.32228623
28 18564.24156 [208.8817929] 18355.35977
71.61382785 69.5302902
29 18635.85539
78.47043065 78.4704307
30 18714.32582
6
60.08091233 68.0457493
31 18774.40673
69.6960093 69.690093
32 18844.10274
66.63856301 66.638563
33 18910.7413
62.0706594 62.0706594
34 18972.81196
60.3056642160.30566421
35 19033.11762
57.77411089 57.7741108936 19090.89174
53.3602028 53.360202837 19144.25194
57.71434299 57.7143429938 19201.96628
50.27660495 50.2766049539 19252.24289
51.65843216 51.6584321640 19303.90132
52.31105791 52.3110579141 19356.21238
44.68782541 44.6878254142 19400.9002
10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 420
10
20
30
40
50
60
70
80
90
100
110
120
v'+1
v (c
m-1
)Δ
Figure 3. Birge- Sponer plot used to determine v’e and x’ e. Difference in wavenumber is ploted as a function of v’+1.
Figure 3 presents a Birge-Sponer plot with the difference in energies between the excited levels
as a function of the excited state quantum number v’. The best-fit line has a slope of -2.0203 and an
intercept of 130.24 which lead to calculated values of 134 cm-1 for v’ e and 1.1015 cm-1 for v’ e x’ e
(Table 2).
7
0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 2.1 2.3 2.5208.5
209
209.5
210
210.5
211
211.5
212
212.5
213
213.5
v''+1
v'Δ
Figure 4. Birge- Sponer plot used to determine v’’ e and x’’ e. Difference in wavenumbers is ploted as a function of v’’+1.
Figure 4 shows a Birge-Sponer plot used in the calculations v’’ e and x’’ e with the ground state
vibrational level as an independent variable and the difference in energies between transitions
starting at different ground levels. The slope of the line is -2.658 and the intercept is 215.64, which
lead to calculated values of 230 cm-1 for v’’e and 1.329 cm-1 for x’’e v’’e (Table 2).
Table 2 has a list of the experimental and calculated values for diatomic constants of iodine.
The calculated values for the excited state are in better agreement with literature values than the
experimental values for the ground state. The energy required to dissociate the molecule into atoms
was also calculated for the excited and the ground state to be 4395 cm-1 and 8964 cm-1, respectively.
The energy required to dissociate the molecule from the v=0 state was estimated at 4328 cm-1 for
the excited state and 8855cm-1 for the ground state. The harmonic bond force constant was
calculated to be 67.5 N/m for the excited state and 178 N/m for the ground state. The Morse
potential parameter β was calculated using the values for the force constant and the dissociation
energy to be 1.965 A-1 for the excited state and 2.237 A-1 for the ground state.
Table 2. Experimental and literature values for diatomic constants of iodine vapour. Literature values are those reported by McNaught.5
Calculated Literature5
x’e v’ e 1.1015 cm-1 0.735 cm-1
v’ e 134 cm-1 126 cm-1
D’ e 4395 cm-1 3805 cm-1
D’ 0 4328 cm-1 3742 cm-1
k’ e 67.5 N/m 59.5 N/mβ’r’ e
1.965 A-1
3.235 A1.982 A-1
3.025 Ax’’ e v’’ e 1.329 cm-1 0.67 cm-1
v’’ e 230 cm-1 214 cm-1
D’’ e 8964 cm-1 11973 cm-1
8
k’’ eD’’ 0β’’r’’ e
178 N/m8855 cm-1
2.237 A-1
2.666 A
172 N/m11866 cm-1
1.901 A-1
2.666 A
Using the wavenumber of maximum absorbance (18691 cm-1) and equation 13, the difference in
radii was calculated to be 0.57 A between the excited state and the ground state. Using the accepted
literature value for r’’e of 2.666 A, the value for r’ e was calculated to be 3.235 A. Using the calculated
r’ e, the literature value for r’’ e and the calculated values for the parameter β of the excited state and
the ground state the Morse potential curves for the excited and the ground state were plotted in
Figure 5.
Figure 5 shows the bond dissociation energies for the ground state and the excited state at 4395
and 8964 cm-1 respectively, where the energy reaches a plateau, as well as the minimum in energy
when the internuclear distance is equal to the equilibrium radius for both states.
Figure 5. Morse potential curves for the excited state (red) and the ground state (blue). Harmonic
oscillator (green)
Discussion:
The absorption spectrum of iodine (Figure 2) approaches the convergence limit around 500 nm
(approximately 20000 cm-1). The different intensities of the bands is explained by the Franck-Codon
principle which states that the intensity of an electronic transition is proportional to the overlap of the
wavefunctions of the two states.4 The calculated diatomic constants were in better agreement with
literature values for the excited state of iodine. The calculated wavenumber of 134 cm -1 was in good
9
agreement with the literature value of 126 cm-1. The dissociation energy of 4395 cm -1 was also
reasonably close to the accepted value of 3805 cm-1. The dissociation energy from the zero
vibrational level was reasonably close to the literature value of 3742 cm -1. The force constant for the
excited state was estimated to be 67.5 N/m, close to the literature value of 59.5 N/m. The parameter
β’ 1.965 A-1 was also very close to the literature value of 1.982 A-1.
The values for the diatomic constants of the ground state do not agree so well with the literature
values and one reason for this is the low number of data points used in the linear regression. The
equilibrium wavenumber was 230 cm-1, reasonably close to the literature value of 214 cm-1 with a 7.5
percent difference. The dissociation energy for the ground state was calculated to be 8964 cm-1, a
value far from the literature value of 11973 cm-1. The dissociation energy from the v=0 level of 8855
cm-1 was also not very accurate compared to the literature value of 11866 cm-1. The lack of accuracy
of these results can also be attributed to the fact that the wavelengths used in the linear regression
were estimated from the plot. The spectrometer resolution was not high enough to allow for
unambiguously discerning the signals of the spectrum. The literature value of the iodine equilibrium
radius was used instead of an experimental one. The differences in Table 1 used in each of the
calculations should be relatively constant, but upon a closer look a variation in these differences can
be observed. The source of this variation is the use of the band-head frequencies rather than the
band origins.4
Figure 5 confirms that the dissociation energy of the ground state iodine is much higher than that
of the excited that and that the minimum in energy is reached at radius equal to the equilibrium
radius of the respective state. The equilibrium radius of the ground state is also smaller than the
equilibrium radius of the excited state. The experimental estimate for the excited state radius of
3.235 is reasonably close to the literature value of 3.025 A. Figure 5 also shows that a harmonic
oscillator model would have been inadequate for the iodine molecule.
The calculations in this experiment depend largely on how many data points were included in the
linear regressions and how these data points were chosen from the visible spectrum of iodine, thus
leaving the possibility for large sources or error, especially for the ground state. For example, if the
transitions between v’’ 0 or 1 to v’ 15,16,17,18 were included, the best-fit line for the ground state
calculation would have had a slope of approximately -7 which would have afforded values
significantly different from the literature values. For the excited state calculations, at least three data
points were adjusted to not be the wavelengths on the short wavelength side of each peak, in order
to get decreasing separation between the excited state transitions as the convergence limit was
approached, as some of the estimations were skewing the best-fit line.
Conclusion:
The absorption spectrum of iodine could generate reasonably accurate results for the diatomic
constants of the excited state, but failed to afford good estimations for the constants of the ground
state. The results of this experiment depend heavily on the choice of the wavelengths and data
10
points to be used in the linear regression and are therefore more inaccurate than analogous
calculations for smaller molecules with simpler spectra such as HCl.
Works Cited:
1. Takeda, Y., Ueno, S. Solar Physics, 2011, 270, p. 447-461. Iodine cell spectroscopy Applied to
Investigating Differential Rotation of the Sun.
2. Hou, Q.Q., Zheng, Y.Z., Chen, J.F., Zhou, W.L., Deng, J., Tao, X. Journal of Materials
Chemistry 2011, 21, p. 3877-3883. Visible-light-response iodine-doped titanium dioxide
nanocrystals for dye-sensitized solar cells
3. Stafford, F.E. J. Chem. Educ. 1862, 39, p. 626. Band Spectra and Dissociation Energies – A
Physical Chemistry Experiment
4. Handout – Experiment 39. Absorption and Emission Spectra of Iodine. February 26th 2013.
5. McNaught, I.J. J. Chem. Educ. 1980, 57, p. 101. The electronic spectrum of iodine revisited.
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