View
17
Download
1
Category
Tags:
Preview:
Citation preview
Studying the Oscillation of Hydrochloric Acid via Gas Phase Vibrational-Rotational Infrared
Spectroscopy
Josiah Matthew
Bob Jones University Chemistry Department
1700 Wade Hampton BLVD
Greenville, SC 29614
Abstract
The following experiment studies the oscillations of hydrochloric acid using vibrational
rotational infrared spectroscopy. The spectral data is fitted to a polynomial from which the
moment of inertia and inter-nuclear distance are both calculated. These data can be used to
analyze how well an anharmonic oscillator fits our data. Most of the data corresponds well to
literature data, except for values predicted for an anharmonic oscillator. This suggest that HCl
best fits the model of a harmonic oscillator rigid rotor, and demonstrates very little
anharmonicity.
Introduction
The purpose of this experiment is to
study the harmonic and anharmonic
oscillations of HCl. A quantum harmonic
oscillator is a quantum mechanical
approximation of a classical harmonic
oscillator which follows Hook’s law. In this
model, a chemical bond is treated like a
spring, where a restoring force acts upon a
molecule when it is displaced from
equilibrium. A harmonic oscillating
molecule is quantized and only has
specifically allowed energy levels. The
simplest model of a harmonic oscillator is
the rigid rotor, which assumes that atoms
are joined by a rigid weightless rod which
does not distort under rotational stress. A
chemical bond is not truly rigid and
therefore does stretch some when rotated.
Anharmonicity is a deviation from
harmonicity where the actual potential is
different from the harmonic potential and
the actual vibrational energy levels are not
as predicted by harmonic oscillation due to
centrifugal distortion. This experiment uses
vibrational-rotational infrared spectroscopy
to determine study the harmonic-oscillator
rigid rotor model as it applies to HCl gas.
Infrared rotational-vibrational
(rovibrational) spectroscopy is used
extensively in physical chemistry. The
rovibrational spectra of polycyclic aromatic
hydrocarbons (PAHs) have been studied
and PAHs are thought to be responsible for
some of the unidentified spectral bands in
interstellar emissions1. One study that is
similar to this current experiment uses
rovibrational spectroscopy on various
isotopologues of carbon monoxide in order
to test molecular rotor theories by
calculating rotational constants and
predicting the center of mass and center of
interaction of the molecule2. Rovibrational
spectroscopy has been important in
determining the structural properties,
reaction kinetics, and dynamics of radicals
such as the phenyl radical, which has a
variety of uses due to its high reactivity, and
is considered the most important aromatic
radical in all of chemistry3. In addition,
rovibrational spectroscopy has been used in
determining the presence of
dichlorodifluoromethane (CFC-12), a
significant greenhouse gas, in the
atmosphere4. The chemical and physical
properties of SiO have also been discovered
using rovibrational spectroscopy, and this
data is important to its role in interstellar
space5.
This experiment uses a gas phase
infrared rovibrational spectrum to
determine the harmonic properties of HCl
gas. Because chlorine exists in isotopes 35Cl
(~75 %) and 37Cl (~25 %), two resolved
features are observed for each absorption
peak. The spectrum shows absorbances for
vibrational transitions following the
selection rule for a change in value of the
rotational quantum number of ∆𝐽 = ±1.
The spectrum is divided into R and P
branches, where ∆𝐽 = 1 for the R branch,
and ∆𝐽 = −1 for the P branch. This
experiment is concerned with transitions
from the ground state J’’ values to the first
excited state J’. The quantity m is defined as
𝑚 = 𝐽′′ + 1 for the R branch, and 𝑚 = −𝐽′′
for the P branch. The spectrum acquired in
this experiment is labelled with m and J’’
values. The wavenumber of absorbance, ��,
is plotted vs. the m value it represents. This
plot can be fit to a second order polynomial
in order to determine the following values
from equation 1:6
𝜈0 =
𝑡ℎ𝑒 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑓𝑜𝑟𝑏𝑖𝑑𝑑𝑒𝑛 𝑡𝑟𝑎𝑛𝑠𝑖𝑡𝑖𝑜𝑛 (∆𝐽 =
0), 𝐵𝑒 =
𝑡ℎ𝑒 𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛𝑎𝑙 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑎𝑛𝑑 𝛼𝑒 =
𝑡ℎ𝑒 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛 −
𝑟𝑜𝑡𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑡𝑒𝑟𝑎𝑐𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
��(𝑚) = 𝜈0 + (2𝐵𝑒 − 2𝛼𝑒)𝑚 − 𝛼𝑒𝑚2 (1)
This data can also be fit to a third order
polynomial6 in order to include a correction
for anharmonicity due to centrifugal
stretching,
𝐷𝑒 =
𝑡ℎ𝑒 𝑐𝑒𝑛𝑡𝑟𝑖𝑓𝑢𝑔𝑎𝑙 𝑑𝑖𝑠𝑡𝑜𝑟𝑡𝑖𝑜𝑛 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡.
��(𝑚) = 𝜈0 + (2𝐵𝑒 − 2𝛼𝑒)𝑚 − 𝛼𝑒𝑚2 −
4𝐷𝑒𝑚3 (2)
Once 𝐵𝑒 is known, the moment of inertia 𝐼𝑒
can be calculated using equation 3
(ℎ = 𝑝𝑙𝑎𝑛𝑐𝑘′𝑠 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡, 𝑐 =
𝑠𝑝𝑒𝑒𝑑 𝑜𝑓 𝑙𝑖𝑔ℎ𝑡).6
𝐼𝑒 =ℎ
8𝜋2𝐵𝑒𝑐 (3)
This is then used in equation 4 to calculate
the inter-nuclear distance, 𝑟𝑒:6
𝑟𝑒 = √𝐼
𝜇 (4)
where 𝜇 =𝑚1𝑚2
𝑚1+𝑚2 is the reduced mass. The
values for
𝜈�� =
𝑡ℎ𝑒 𝑓𝑢𝑛𝑑𝑎𝑚𝑒𝑛𝑡𝑎𝑙 𝑓𝑟𝑒𝑞𝑢𝑒𝑛𝑐𝑦 𝑜𝑓 𝑣𝑖𝑏𝑟𝑎𝑡𝑖𝑜𝑛
, and
𝜈��𝜒𝑒 = 𝑡ℎ𝑒 𝑎𝑛ℎ𝑎𝑟𝑚𝑜𝑛𝑖𝑐𝑖𝑡𝑦 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡 can
be determined by simultaneously solving
equations 5 and 6.6
𝜈0 = 𝜈�� − 2𝜈��𝜒𝑒 (5)
𝜈0∗ = 𝜈�� (
𝜇
𝜇∗)
1
2 − 2𝜈��𝜒𝑒
𝜇
𝜇∗ (6)
According to the rigid rotor prediction the
following equation6 is true:
𝐵𝑒∗
𝐵𝑒=
𝜇
𝜇∗ (7)
Therefore by calculating 𝐵𝑒
∗
𝐵𝑒, this will tell us
how close our data follows the rigid rotor
model.
Our results correspond well to
literature values, except for our values of
𝜈��and 𝜈��𝜒𝑒 . The experimental value of 𝐵𝑒
∗
𝐵𝑒 is
almost exactly the same as the theoretical
value. Inclusion of centrifugal distortion did
not significantly improve our data. This
suggests that HCl fits the rigid rotor model
very well, and that it does not demonstrate
much anharmonicity.
Materials and Methods
Materials
The HCl used in this experiment was
technical grade HCl gas obtained from
Matheson Tri-Gas, 4328 kPa at 21 ˚C. The
Infrared Spectrometer was a Nicolet 300 FT-
IR from Thermo Electron Corporation. A 10
cm cell was used with NaCl windows, similar
to the cell shown in figure 1.
Figure 1. Diagram of gas IR cell
Methods
Because HCl is highly corrosive, a
purge of N2 gas was flowing through the
spectrometer throughout the experiment.
The following experimental conditions were
used for the spectrometer: 32 sample
scans, 32 background scans, resolution
1.000, sample gain 1.0, mirror velocity
0.4747, and aperture 10.00. After taking the
background scans, the cell was filled with
HCl gas under a hood and 8 sample scans
were taken initially. The peaks were not
resolved into the two components because
the cell was too concentrated. The cell was
moved to a hood and a little N2 gas was
blown through the cell to dilute it. 8 sample
scans were taken and the peaks were
resolved into two components, so the full
32 sample scans were used.
Results
The gas phase spectrum of HCl is included below. The R and P branches are labelled, along with
values for m and J’’
Figure 2. Gas phase IR spectrum of HCl
R Branch
9 8 7 6 5 4 3 2 1 0 J’’ values
P Branch
1 2 3 4 5 6 7 8 9 10
m values 10 9 8 7 6 5 4 3 2 1
-1 -2 -3 -4 -5 -6 -7 -8 -9 -10
H35Cl data
The spectral data for H35Cl is tabulated below and then plotted as 𝜈 vs. m.
m 𝜈, 𝑐𝑚−1 10 3058.83
9 3044.58
8 3029.64
7 3013.93
6 2997.56
5 2980.53
4 2962.80
3 2944.43
2 2925.45
1 2905.79
-1 2864.65
-2 2843.15
-3 2821.09
-4 2797.87
-5 2775.00
-6 2751.40
-7 2727.25
-8 2702.53
-9 2677.25
-10 2651.40
Table 1. Tabulated spectral data for H35Cl
The graph of 𝜈 vs. m is fitted to a second order polynomial. The values of 𝜈0, 𝐵𝑒 , and 𝛼𝑒 are
determined from the polynomial fit using equation 1:
��(𝑚) = 𝜈0 + (2𝐵𝑒 − 2𝛼𝑒)𝑚 − 𝛼𝑒𝑚2
The values of 𝐼𝑒 and 𝑟𝑒 are also calculated. All values are tabulated and compared to literature
data.
Figure 3. Second order polynomial fit for spectral data of H35Cl
Value Experimental Literature7 Percent error
𝜈0, 𝑐𝑚−1 2,885.4205 2885.9775 0.0193 %
𝐵𝑒 , 𝑐𝑚−1 10.5264 10.593404 0.633 %
𝛼𝑒 , 𝑐𝑚−1 0.3030 -0.307139 1.35 %
𝐼𝑒 , 𝑘𝑔 𝑚2 2.65742 ∙ 10−47 2.64061 ∙ 10−47 0.637 %
𝑟𝑒 , 𝑝𝑚 127.815 127.455 0.283 %
Table 2. Values obtained from figure 3 compared to literature data
𝐼𝑒 and 𝑟𝑒 are calculated using equations 3 and 4 below.
𝐼𝑒 =ℎ
8𝜋2𝐵𝑒𝑐=
6.626 ∙ 10−34𝐽 𝑠
8𝜋2 ∙ 10.534 𝑐𝑚−1 ∙ 3 ∙ 1010 𝑐𝑚𝑠
= 2.65742 ∙ 10−47𝑘𝑔 𝑚2
𝜇 =𝑚1𝑚2
𝑚1 + 𝑚2=
1.007825 ∙ 34.968853
1.007825 + 34.968853= 0.979593
0.979593 ∙ 1.66054 ∙ 10−27𝑘𝑔 = 1.62665 ∙ 10−27𝑘𝑔
𝑟𝑒 = √𝐼
𝜇= √
2.65742 ∙ 10−47𝑘𝑔 𝑚2
1.62665 ∙ 10−27𝑘𝑔= 127.815 𝑝𝑚
y = -0.3030x2 + 20.4468x + 2,885.4205 R² = 1.0000
2600
2650
2700
2750
2800
2850
2900
2950
3000
3050
3100
-15 -10 -5 0 5 10 15
Wav
en
um
be
r, c
m-1
m
H35Cl, ṽ vs. m
H35Cl
Poly. (H35Cl)
The above calculations are repeated using a 3rd order polynomial fit in order to include the
centrifugal distortion constant, 𝐷𝑒, as seen in equation 2 below.
��(𝑚) = 𝜈0 + (2𝐵𝑒 − 2𝛼𝑒)𝑚 − 𝛼𝑒𝑚2 − 4𝐷𝑒𝑚3
Figure 4. Third order polynomial fit for spectral data of H35Cl
Value Experimental Literature7 Percent error
𝜈0, 𝑐𝑚−1 2,885.4205 2885.9775 0.0193 %
𝐵𝑒 , 𝑐𝑚−1 10.6047 10.593404 0.107 %
𝛼𝑒 , 𝑐𝑚−1 0.3030 -0.307139 1.35 %
𝐷𝑒 5.951 ∙ 10−4 −5.32019 ∙ 10−4 11.9 %
𝐼𝑒 , 𝑘𝑔 𝑚2 2.6378 ∙ 10−47 2.64061 ∙ 10−47 0.106 %
𝑟𝑒 , 𝑝𝑚 127.004 127.455 0.354 %
Table 3. Values obtained from figure 4 compared to literature data
𝐼𝑒 and 𝑟𝑒 are calculated using equations 3 and 4 below.
𝐼𝑒 =ℎ
8𝜋2𝐵𝑒𝑐=
6.626 ∙ 10−34𝐽 𝑠
8𝜋2 ∙ 10.6649 𝑐𝑚−1 ∙ 3 ∙ 1010 𝑐𝑚𝑠
= 2.62378 ∙ 10−47𝑘𝑔 𝑚2
𝑟𝑒 = √𝐼
𝜇= √
2.62378 ∙ 10−47𝑘𝑔 𝑚2
1.62665 ∙ 10−27𝑘𝑔= 127.004 𝑝𝑚
y = -0.0023804x3 - 0.3030x2 + 20.6034x + 2,885.4205 R² = 1.0000
2600
2650
2700
2750
2800
2850
2900
2950
3000
3050
3100
-15 -10 -5 0 5 10 15
Wav
en
um
be
r, c
m-1
m
H35Cl, ṽ vs. m
H35Cl
Poly. (H35Cl)
H37Cl data
The spectral data for H37Cl is tabulated below and then plotted as 𝜈 vs. m.
m 𝜈, 𝑐𝑚−1 10 3056.29
9 3042.23
8 3027.28
7 3011.63
6 2995.47
5 2978.42
4 2960.78
3 2942.46
2 2923.32
1 2903.80
-1 2862.64
-2 2840.73
-3 2818.82
-4 2795.87
-5 2773.03
-6 2749.44
-7 2725.00
-8 2700.56
-9 2675.00
-10 2649.00
Table 4. Tabulated spectral data for H37Cl
The graph of 𝜈 vs. m is fitted to a second order polynomial. The values of 𝜈0, 𝐵𝑒 , and 𝛼𝑒 are
determined from the polynomial fit using equation 1:
��(𝑚) = 𝜈0 + (2𝐵𝑒 − 2𝛼𝑒)𝑚 − 𝛼𝑒𝑚2
The values of 𝐼𝑒 and 𝑟𝑒 are also calculated. All values are tabulated and compared to literature
data.
Figure 5. Second order polynomial fit for spectral data of H37Cl
Value Experimental Literature7 Percent error
𝜈0, 𝑐𝑚−1 2883.3803 2883.8795 0.0173 %
𝐵𝑒 , 𝑐𝑚−1 10.5259 10.578 0.493 %
𝛼𝑒 , 𝑐𝑚−1 0.3063 -0.3035 0.923 %
𝐼𝑒 , 𝑘𝑔 𝑚2 2.65742 ∙ 10−47 2.64446 ∙ 10−47 0.495 %
𝑟𝑒 , 𝑝𝑚 127.722 127.455 0.209 %
Table 5. Values obtained from figure 5 compared to literature data
𝐼𝑒 and 𝑟𝑒 are calculated using equations 3 and 4 below.
𝐼𝑒 =ℎ
8𝜋2𝐵𝑒𝑐=
6.626 ∙ 10−34𝐽 𝑠
8𝜋2 ∙ 10.5259 𝑐𝑚−1 ∙ 3 ∙ 1010 𝑐𝑚𝑠
= 2.65755 ∙ 10−47𝑘𝑔 𝑚2
𝜇 =𝑚1𝑚2
𝑚1 + 𝑚2=
1.007825 ∙ 36.965903
1.007825 + 36.965903= 0.981077
0.981077 ∙ 1.66054 ∙ 10−27𝑘𝑔 = 1.62912 ∙ 10−27𝑘𝑔
𝑟𝑒 = √𝐼
𝜇= √
2.65755 ∙ 10−47𝑘𝑔 𝑚2
1.62912 ∙ 10−27𝑘𝑔= 127.722 𝑝𝑚
y = -0.3063x2 + 20.4392x + 2,883.3803 R² = 1.0000
2600
2650
2700
2750
2800
2850
2900
2950
3000
3050
3100
-15 -10 -5 0 5 10 15
Wav
en
um
be
r, c
m-1
m
H37Cl, ṽ vs. m
H37Cl
Poly. (H37Cl)
The above calculations are repeated using a 3rd order polynomial fit in order to include the
centrifugal distortion constant, 𝐷𝑒, as seen in equation 2 below.
��(𝑚) = 𝜈0 + (2𝐵𝑒 − 2𝛼𝑒)𝑚 − 𝛼𝑒𝑚2 − 4𝐷𝑒𝑚3
Figure 6. Third order polynomial fit for spectral data of H37Cl
Value Experimental Literature7 Percent error
𝜈0, 𝑐𝑚−1 2883.3803 2883.8795 0.0173 %
𝐵𝑒 , 𝑐𝑚−1 10.6086 10.578 0.289 %
𝛼𝑒 , 𝑐𝑚−1 0.3063 -0.3035 0.923 %
𝐷𝑒 6.28 ∙ 10−4 5.30 ∙ 10−4 18.5 %
𝐼𝑒 , 𝑘𝑔 𝑚2 2.63686 ∙ 10−47 2.64446 ∙ 10−47 0.287 %
𝑟𝑒 , 𝑝𝑚 127.223 127.455 0.182 %
Table 6. Values obtained from figure 6 compared to literature data
𝐼𝑒 and 𝑟𝑒 are calculated using equations 3 and 4 below.
𝐼𝑒 =ℎ
8𝜋2𝐵𝑒𝑐=
6.626 ∙ 10−34𝐽 𝑠
8𝜋2 ∙ 10.6086 𝑐𝑚−1 ∙ 3 ∙ 1010 𝑐𝑚𝑠
= 2.63686 ∙ 10−47𝑘𝑔 𝑚2
𝑟𝑒 = √𝐼
𝜇= √
2.63686 ∙ 10−47𝑘𝑔 𝑚2
1.62912 ∙ 10−27𝑘𝑔= 127.32 𝑝𝑚
y = -0.0025129x3 - 0.3063x2 + 20.6045x + 2,883.3803 R² = 1.0000
2600
2650
2700
2750
2800
2850
2900
2950
3000
3050
3100
-15 -10 -5 0 5 10 15
Wav
en
um
be
r, c
m-1
m
H37Cl, ṽ vs. m
H37Cl
Poly. (H37Cl)
The value of 𝜈0 was determined above to be 2,885.4205 cm-1 for H35Cl and 2883.3803 cm-1 for
H37Cl. The values for 𝜈�� and 𝜈��𝜒𝑒 can be determined by simultaneously solving equations 5 and
6 below:
𝜈0 = 𝜈�� − 2𝜈��𝜒𝑒
2.885.4205 𝑐𝑚−1 = 𝜈�� − 2𝜈��𝜒𝑒
𝜈��𝜒𝑒 =𝜈��
2− 1442.71 𝑐𝑚−1
and
𝜈0∗ = 𝜈�� (
𝜇
𝜇∗)
12
− 2𝜈��𝜒𝑒
𝜇
𝜇∗
2,883.3803 𝑐𝑚−1 = 𝜈�� ∙ 0.999242 − 1.99697𝜈��𝜒𝑒
𝜈��𝜒𝑒 = 𝜈�� ∙ 0.50038 − 1443.88 𝑐𝑚−1
Combining these two equations gives:
𝜈��
2− 1442.71 𝑐𝑚−1 = 𝜈�� ∙ 0.50038 − 1443.88 𝑐𝑚−1
𝜈�� = 3081.76 𝑐𝑚−1
𝜈��𝜒𝑒 = 𝜈�� ∙ 0.50038 − 1443.88 𝑐𝑚−1 = 98.17 𝑐𝑚−1
Value Experimental Literature7 % error
𝜈�� 3081.76 2990.97424 3.04 %
𝜈��𝜒𝑒 98.17 52.84579 85.8 %
Table 7. Experimental values of 𝜈��𝜒𝑒 and 𝜈�� compared to literature values.
Potential sources of error could be differences in instrumentation used in literature values or
calibration errors.
Discussion
There is no absorption feature at the
𝜈0 value because this represents a
forbidden transition. This transition is from
𝐽′′ = 0 to 𝐽′′ = 0 which violates the
selection rule of allowed transitions being
Δ𝐽 = ±1.
An anharmonic oscillator does not
fit well to our data because the value of
anharmonicity constant 𝜈��𝜒𝑒 is not close to
the literature value. We can determine
from this that the molecule does not
demonstrate much anharmonicity.
The inclusion of centrifugal
distortion does not significantly improve
our results. Comparing tables 2 and 3, the
values of 𝐵𝑒 and 𝐼𝑒 are improved slightly by
including centrifugal distortion, but the
value for 𝑟𝑒 is slightly better without
including it. A slight improvement is seen in
all three values when comparing table 5 and
6. None of these differences however are
significant, therefore we can determine that
centrifugal stretching does not play an
important role.
Our data give the value for 𝐵𝑒
∗
𝐵𝑒=
0.999632. According to the rigid rotor
prediction, equation 7 is true, 𝐵𝑒
∗
𝐵𝑒=
𝜇
𝜇∗ =
0.999242. Our experimental value is very
accurate with only 0.0390 % error, which
suggests that our data corresponds very
well to a rigid rotor. The very small error
suggests that our data is very precise.
Acknowledgements
Thanks are given to Bob Jones
University Dr. George Matzko for his
supervision of laboratory procedures, and
to my 4 lab partners Eric Boley, Liz Chu,
Erica Cosmos, and David Maloney for their
assistance in experimental procedures.
Author Information Corresponding Author
jmatt655@students.bju.edu
Bob Jones University, Box 40343
References
1. Calvo, F.; Basire, M.; Parneix, P.
Temperature Effects on the Rovibrational
Spectra of Pyrene-Based PAHs. J. Phys.
Chem. A, 2011, 115, 8845–8854.
2. Fajardo, M. E. High-Resolution
Rovibrational Spectroscopy of Carbon
Monoxide Isotopologues Isolated in Solid
Parahydrogen. J. Phys. Chem. A, 2013, 117,
13504−13512.
3. Buckingham, G. T.; Chang, C.; Nesbitt, D.
J. High-Resolution Rovibrational
Spectroscopy of Jet-Cooled Phenyl Radical:
The ν19 Out-of-Phase Symmetric CH
Stretch. J. Phys. Chem. A, 2013, 117,
10047−10057.
4. Robertson, E. G.; Medcraft, C.;
McNaughton, D.; Appadoo, D. The Limits of
Rovibrational Analysis: The Severely
Entangled ν1 Polyad Vibration of
Dichlorodifluoromethane in the
Greenhouse IR Window. J. Phys. Chem. A
2014, 118, 10944−10954.
5. Muller, H. S. P.; Spezzano, S.; Bizzocchi ,
L.; Gottlieb, C. A.; Esposti, C. D.; McCarthy,
M. C. Rotational Spectroscopy of
Isotopologues of Silicon Monoxide, SiO, and
Spectroscopic Parameters from a Combined
Fit of Rotational and Rovibrational Data. J.
Phys. Chem. A 2013, 117, 13843−13854.
6. Garland, Carl W.; Nibler, Joseph W.;
Shoemaker, David P.; Experiments in
Physical Chemistry. McGraw-Hill: New York,
2009; p. 416-23.
7. Sime, R. J.; Physical Chemistry: Methods,
Techniques, and Experiments. Philadelphia,
PA: Saunders College Publishing, 1990, 680.
Recommended