Download Infrared Vibration-Rotation Spectroscopy of HCl and DCl

Chemistry 363
Spring 2010
JMS 1/05
DLC 1/10
Infrared Vibration-Rotation Spectroscopy of HCl and DCl
Experiment Objective: to obtain the equilibrium bond length (re) and vibration-rotation spectroscopic
constants from the FTIR spectra of the diatomic molecules HCl and DCl in the gas phase.
SECTION 1: THEORETICAL BACKGROUND
References
A basic introduction to the quantum mechanics and spectroscopy of the vibration-rotation states of
diatomic molecules can be found in any standard physical chemistry text. Some examples include:
Physical Chemistry, 2nd ed., T. Engel and P. Reid, Pearson, Chapter 19; Physical Chemistry, 1st ed., D.
W. Ball, Brooks/Cole, Pacific Grove, CA, 2003, Section 14.17. Physical Chemistry, 8th ed., P. W. Atkins
and J. de Paula, W. H. Freeman, NY, 2006, Chapter 13.
If you are not familiar with the vibrations and rotations of diatomic molecules, you should consult one of
the above references. Your instructor/TA will also provide a mini-lecture before you analyze the data.
Vibration-Rotation Spectroscopy - Harmonic Oscillator, Rigid Rotor Approximation
Both the vibrational and rotational motions of a molecule are quantized. Vibrational motion describes the
internal motion of an atom within a molecule relative to other atoms. In a diatomic molecule, this motion
occurs along the bond and is called a stretching. This motion depends largely on the strength of the bond,
which is proportional to the potential energy holding the atoms together. The vibrational motion of a
diatomic molecule may be treated ideally as if the potential energy were harmonic. This is called the
harmonic oscillator approximation. The quantum mechanical solution of this harmonic vibrational motion
introduces a vibrational quantum number v that correlates to the vibrational energy content (Ev) of the
molecule in such a particular vibrational state:
Ev = hνe(v + ½)
(1)
In equation (1), h is Planck’s constant and νe is the classical harmonic frequency.
Rotational motion describes the position of a molecule around an arbitrary set of spatial coordinate axes.
In a diatomic molecule, a simple approximation considers the molecule to be rigid at certain equilibrium
position of the atoms, such that vibrational motion is neglected. Such approximation is denoted as the
rigid rotor. Quantum mechanical treatment of the rigid rotor approximation introduces a rotational
quantum number J that correlates with the rotational energy content (EJ) of the molecule in such a
particular rotational state:
EJ = hcBeJ(J+1)
(2)
In equation (2), c is the speed of light and Be is the rotational constant. The expression for the quantized
combination of vibration-rotation energy levels of a molecule, Ev,J is:
E v, J = hν e ( v + 1 / 2) + hcBe J ( J + 1)
or in wavenumbers,
(3)
ω v, J =
E v, J
= ω e ( v + 1 / 2) + Be J ( J + 1)
hc
(4)
Recall that νe is the harmonic vibrational frequency, or in wavenumbers, ωe =νe / c, v is the vibrational
quantum number and J is the rotational quantum number. Be is the rotational constant, which is given by
Be =
h
8π 2 cI
(5)
where I is the moment of inertia, I = µre2 , µ is the reduced mass, and re is the equilibrium bond length. For
a diatomic molecule with formula AB, the reduced mass µ is defined as
µ=
m A mB
m A + mB
(6)
where mA and mB are the isotopic masses of atoms A and B.
The probability of a change in a particular state of a molecule is dictated by quantum mechanical
constraints known as selection rules. For instance, the selection rule for diatomic molecule rotational
transitions allows state changes in which ∆J = ±1. For vibrations in the harmonic oscillator
approximation, the selection rule is ∆v = ±1, though this selection rule is lifted when an anharmonic
system is considered (as in a real diatomic molecule), and so the so called overtone transitions, such as v
= 0 → 2, are allowed. The v = 0 → v = 1 transition is called the fundamental, and is the most intense (i.e
most probable) vibrational transition.
The light absorption spectrum of a molecule reflects the changes in the state of a molecule as it absorbs
energy as allowed by the transition rules for a particular type of motion. Let us consider a diatomic
molecule that absorbs light from the infrared region of the electromagnetic spectrum that corresponds to
the harmonic wavenumber of motion (ωe). Most molecules at room temperature will be in the ground
vibrational state (v” = 0) and will end up in the v” = 1. The molecules are originally distributed into
different rotational states (with J” rotational number) according to the temperature of the sample. Thus,
the absorption of IR light will reflect vibration-rotation transitions from (v" = 0, J") → (v' = 1, J').
The set of spectral bands in which ∆J = +1 is called an R-branch. In wavenumbers, each band of the R
branch corresponds to:
R( J " ) = ω e + 2 Be ( J "+1)
(7)
The set of bands originating associated to vibration-rotation transitions from (v" = 0, J") → (v' = 1, J') in
which ∆J = –1 is called a P-branch. In wavenumbers, each band of the P branch corresponds to:
P ( J " ) = ω e − 2 Be J "
(8)
As mentioned above, for a typical diatomic molecule, vibrational-rotational transitions fall in the infrared
region of the spectrum. In polyatomic molecules the transition corresponding to v" = 0, J" → v' = 1, J'
with ∆J = 0 is allowed and is called the Q branch. However, because of the selection rules for diatomic
molecules, the Q-branch transition is not allowed and thus no IR band is present. The position of the
missing Q-branch transition is called the band origin, denoted by σv”v’. In the harmonic oscillator, rigid
rotor approximation, the band origin in wavenumbers for the fundamental vibrational transition is equal to
ωe.
Corrections to the Harmonic Oscillator and Rigid Rotor Models
The harmonic oscillator and rigid rotor views of diatomic molecular vibrations and rotations is not an
accurate enough approximation to adequately describe all of the features of a vibration-rotation spectrum.
We may include additional terms in the energy expressions (Eqs. 1 and 2) to account for various effects
called vibrational anharmonicity, centrifugal distortion, and vibration-rotation coupling.
In wavenumbers, with these corrections included, Eq. (4) becomes:
ω v, J = ω e ( v + 1 / 2) − ω e xe ( v + 1 / 2) 2 + Be J ( J + 1) − D J J 2 ( J + 1) 2 − α e ( v + 1 / 2) J ( J + 1)
(9)
where xe is the anharmonicity constant, DJ is the centrifugal distortion constant, and αe is the vibrationrotation coupling constant. The other quantities are the same as defined for Eq. (4).
Each band of the R branch for the fundamental v" = 0 → v' = 1 vibrational transition (modified from Eq.
(7)) is given in wavenumbers by:
R( J " ) = ω e − 2ω e x e + ( B1 + B0 )( J "+1) + ( B1 − B0 )( J "+1) 2 − 4 D J ( J "+1) 3
(10)
B0 and B1 are rotational constants for the v = 0 and v = 1 vibrational levels, respectively. The general
constant Bv for vibrational state v is defined as:
B v = Be − α e ( v + 1 / 2 )
(11)
The P branch for the fundamental v" = 0 → v' = 1 vibrational transition (modified from Eq. (8)) is given
in
wavenumbers by:
P( J " ) = ω e − 2ω e x e − ( B1 + B0 ) J "+( B1 − B0 ) J " 2 +4 D J J "3
(12)
The band origin for the fundamental transition, σ0,1, in this case is given by:
σ 0,1 = ω e − 2ω e x e
(13)
In general, the band origin for any v" → v' vibrational band is given in general by the equation:
σ v",v' = ωe ( v'− v" ) − ωe xe [(v'+1 / 2) 2 − ( v"+1 / 2) 2 ]
(14)
Examples of typical vibration-rotation spectra for heteronuclear diatomic molecules can be found in the
references given on page 1. These spectra are similar to the spectra that you will obtain in this experiment.
Section 4, entitled "A Guide to the Calculations", will show you how to use the equations presented in
this section to obtain the equilibrium bond length, re, and the harmonic frequency (ωe) for each of the
diatomic molecules you study. In addition, for one of the molecules, you will carry out a complete
analysis of the spectrum to obtain the spectroscopic parameters ωe, xe, Be, DJ, and αe. For the other
molecule, you will carry out a simplified analysis to obtain only the most important spectroscopic
parameters, ωe and Be.
SECTION 2: EXPERIMENTAL PROCEDURE
Cell Evacuation
1. The instructor will assist you in setting up the vacuum line to purge and fill the IR cell. ALWAYS
PROCEED SLOWLY AND CAREFULLY WHEN USING WITH THE VACUUM LINE.
2. Once the vacuum manifold is evacuated, attach the IR cell to the line. Be careful handling the
cell; it is fragile and expensive. Do not touch the cell windows, which are made of sodium
chloride. Evacuate the cell by slowly opening the connecting stopcock on the manifold and then
the stopcock on the cell.
3. Close the stopcock on the cell and the connecting stopcock on the manifold. Carefully remove the
IR cell from the vacuum line.
Background Collection
1. Proceed to the FTIR spectrometer in room SLB 220 and place the evacuated IR cell in the sample
chamber.
2. Record the background spectrum of the empty cell. Refer to section 6 entitled "Instructions for
Operating the Perkin Elmer Spectrum One FTIR Spectrometer".
Filling the Cell
1. Return to the vacuum manifold and attach the IR cell to the line. Evacuate the line between the
cell and the manifold by slowly opening the connecting stopcock. Then, open the stopcock on the
IR cell.
2. Attach the bulb containing the diatomic gas to the vacuum line. Evacuate the connecting line
slowly by opening the stopcock.
3. Close the stopcock to the vacuum pump. Carefully open the stopcock on the gas bulb until the
pressure reads around 10 torr above the initial pressure. Close the stopcock to the gas bulb when
the desired pressure is reached.
4. Close the stopcock on the cell. Then, open the stopcock to the pump slowly to evacuate the
manifold.
5. Close the connecting stopcock to the gas bulb and remove it from the line. Then, close the
connecting stopcock to the IR cell and carefully remove it from the line.
Spectral Collection
1. Return to the FTIR spectrometer and place the IR cell in the sample chamber.
2. Record the infrared spectrum of the diatomic gas. Make sure that you label the peaks in the
spectrum in wavenumbers. Refer to section 6 entitled "Instructions for Operating the Perkin
Elmer FTIR Spectrometer" for more information.
3. Remove the IR cell from the spectrometer, proceed to the vacuum manifold, and attach the IR cell
to the manifold.
4. Evacuate the cell by slowly opening the connecting stopcock on the manifold and then the
stopcock on the cell.
5. When the spectrum has been recorded and the IR cell is evacuated, remove it from the vacuum
line and open the stopcock on the cell to the atmosphere. Place the cell in a dessicator for storage.
SECTION 3: A GUIDE TO THE CALCULATIONS
You should have obtained the IR spectra of HCl and DCl. Your instructor/TA will designate one of these
molecules as your primary molecule and one as your secondary molecule. For your secondary molecule,
you will carry out a simplified analysis to obtain the the spectroscopic parameters ωe and Be and the
equilibrium bond length, re. For your primary molecule, you will carry out a complete spectral analysis in
order to determine the spectroscopic parameters ωe, xe, Be, DJ, and αe, and the equilibrium bond length, re.
SECTION 3A: Analysis of the Infrared Spectrum of Your Secondary Molecule
1. The first step in the analysis is to assign rotational quantum numbers to the observed absorption
lines in the R and P branches. This can be easily done by comparing the observed spectrum to the
examples found in the references given in Section 1. The R branch lines, which are on the high
frequency and wavenumber side of the central gap, start with J" = 0. The P branch lines, which
are on the low frequency and wavenumber side of the gap, start with J" = 1.
2. To determine an approximate value for the spectroscopic constant, ωe you can use the central
band gap in the spectrum. Within the harmonic oscillator, rigid rotor approximation, the band
gap, ωe is the midpoint between R(0) and P(1).
3. The spacing between lines in the spectrum can be used to determine an estimate for to rotational
constant, Be. In the harmonic oscillator, rigid rotor approximation, the spacing between the two
central R and P branch lines is equal to 4 Be. Use this band gap distance to determine Be.
4. From your calculated value of Be and known isotopic masses, determine an experimental value
for the equilibrium bond length re for your secondary diatomic molecule.
SECTION 3B: Analysis of the Infrared Spectrum of Your Primary Molecule
1. The first step in the analysis of the spectrum of your primary molecule is to assign rotational
quantum numbers to the observed absorption lines in the R and P branches as you did in the
previous section for your primary molecule.
2. To obtain values of the spectroscopic constants and the equilibrium bond length for your diatomic
molecule, you will use all your experimental values for the R and P branch lines in a least squares
analysis, along with additional data given below for the overtone bands. This analysis may be
carried out on the Macintoshes or PCs in the departmental computer lab (JH 216), or on any other
computer with a least squares program, as long as the program provides errors in the calculated
slope and intercept. The suggested software package for performing least squares analysis is
Microsoft Excel. To begin, three different plots should be prepared:
A)
½[R(J”) + P(J”+1)] vs. (J”+1)2
B)
[ R( J " ) − P ( J " )]
vs. ( J "2 + J "+1)
( J "+1 / 2)
C)
[ R( J "−1) − P ( J "+1)]
vs. ( J " 2 + J " + 1)
( J "+1 / 2)
You should use Equations (10) and (12) to evaluate expressions A, B, and C above in terms of the
spectroscopic constants. Determine what the slopes and intercepts of these plots should be. (You
must complete this part of the analysis before going on to step 3.). Carry out the derivations in
your notebook; a copy of these must be included in your lab report.
Use your experimental values and the linear least squares program to obtain three linear least
squares slopes and intercepts for the graphs above. If any points are clearly off of the line in these
analyses, make sure that you throw them out when determining the slopes and intercepts (if you
throw out points, include in your report a discussion of possible reasons for these deviations).
Make sure that you get hard copies of the plots to include in your lab report.
3. From the analysis in step 2, you should be able to determine the adjusted rotational constants, B1
and B0. Due to the resolution of the spectrometer, there may be significant scatter in plots B and
C, which may make it difficult to determine reliable values for B1 and B0. If this is the case, see
the instructor before proceeding. Use the definition of the adjusted rotational constants, Eq. (11),
along with the information in Table 1a to determine values of Be and αe if your primary molecule
is HCl. If your primary molecule is DCl, use the information in Table 1b to determine values of
Be and αe. You should perform another linear least squares analysis in this step.
Table 1a. Rotational constants for H35Cl (in cm–1)
B2
B3
9.835
9.535
Table 1b. Rotational constants for D35Cl (in cm–1)
B2
B3
5.168
5.058
4. From your calculated value of Be and known isotopic masses, determine an experimental value
for the equilibrium bond length re for your primary diatomic molecule.
5. Using the band origin obtained for the v” = 0 → v’ = 1 transition from the linear least squares
analysis in step 2, along with the data in Table 2a or Table 2b below for the 0–2 and 0–3 band
origins (for HCl and DCl respectively), determine ωe and xe. For this calculation, you should use
Eq. (14) make v” = 0 and then rearrange it so that
σ 0, v '
v'
plot will then yield the desired spectroscopic constants.
is on the left side. A linear least squares
Table 2a. Overtone band origins for H35Cl (in cm–1)
σ0,2
σ0,3
5667.98
8346.78
Table 2b. Overtone band origins for D35Cl (in cm–1)
σ0,2
σ0,3
4128.43
6112.46
6. If there is not too much scatter in plots B and C from step 2 above, you can use the remaining
information from the least squares analysis to determine a value for the centrifugal distortion
constant DJ.
SECTION 4: ITEMS TO INCLUDE IN THE LAB REPORT
1. The report should be in the informal (data) format. Refer to the report guidelines for complete
information.
2. Include a tabulation of your experimental values for R(J”) and P(J”) for both molecules, along
with the infrared spectra. Make sure to include any pertinent experimental conditions.
3. For your primary molecule, include the plots generated in Section 3, along with the least squares
slopes and intercepts and their associated errors.
4. Prepare a table containing the results for the equilibrium bond length re and the spectroscopic
parameters ωe, Be, xe, αe, and DJ for your primary molecule. Make sure to report the uncertainty in
each quantity. Prepare another table containing the results for the equilibrium bond length re and
the spectroscopic parameters ωe and Be for your secondary molecule (no uncertainties are needed
for the secondary molecule results).
5. Answer the questions and complete the discussion given in Section 5 below.
6. Include sample calculations, error analysis, and derivation of the slopes and intercepts from
Section 3 in the Treatment of Data section. The only sample calculations required are the
calculation of ωe and Be for your secondary molecule, along with the reduced mass µ and the
equilibrium bond length re for one of the molecules. For your primary molecule, you should also
show the determination of xe from your graphs. Most of the uncertainties in the spectroscopic
constants come directly from or are proportional to the uncertainties in the slopes and intercepts
from the linear regressions. Therefore, the only propagation of error calculations that are required
are for the equilibrium bond length re and the anharmonicity constant xe.
SECTION 5: QUESTIONS AND DISCUSSION
1. Compare your experimental values of the equilibrium bond length and the spectroscopic
constants to literature values. Discuss possible reasons for any discrepancies.
2. Explain in detail the reason for the intensity pattern seen in the experimental spectrum. That is,
why do the intensities of the peaks on either side of the center appear to grow to a maximum and
then fall off to zero? [Hint: You may want to consult your physical chemistry textbook]
3. Describe how the harmonic frequency ωe would change for H37Cl relative to the value that you
obtained for H35Cl. How would this affect the infrared vibration-rotation spectrum of H37Cl
compared to the spectrum of H35Cl? [Hint: Think about how the harmonic frequency is related to
the reduced mass. Check your textbook for the relation. Then, consider how the harmonic
frequency is related to the peak position in the spectrum.]
4. How is the rotational constant Be different for H37Cl compared to the value for H35Cl? What effect
would this difference have on the infrared vibration-rotation spectrum of H37Cl relative to the
spectrum of H35Cl? [Hint: Consider how the rotational constant is related to the reduced mass and
the part of the spectrum that is affected by Be]
5. Discuss the specific effects that the constants xe, DJ, and αe have on the spectra of HCl and DCl.
SECTION 6: INSTRUCTIONS FOR OPERATING THE PERKIN ELMER SPECTRUM
ONE FTIR SPECTROMETER
You will obtain the vibration-rotation spectrum of gas phase molecules using a Perkin Elmer Spectrum
One FTlR spectrometer located in SLB 220.
Opening the Software
Log into the computer using an ADILSTU account. To start up the FTIR software, click on the Start bar,
go to All Programs, then PE Applications, double click the Spectrum icon. A window will open
indicating what instrument to use, make sure to select the Spectrum One and click OK.
Parameter and Instrument Setup
The software may request a background collection; click Cancel because you need to set up the
instrument to the conditions required by your experiment. Before any spectral collection you must set the
range, resolution and number of scans to be collected. Go to the menu bar and click on Instrument, then
Scan. Click Cancel if a window requesting a background collection pops up. A window with different
tabs will open. The default tab is Sample. Type the name of the file you will give to the background (bkg)
and record some comments (like resolution, sample pressure, etc.). Next select the Scan tab and set the
spectrum type to Background (units set automatically to EGY) and the scan number to 16. Next select the
Instrument tab and set the resolution to 1.0 cm-1. Click Apply. A background collection window will
open. Click Cancel.
Collecting a Background and Spectrum
To obtain a spectrum of your sample, you must first collect a background spectrum with no sample in the
cell, and then collect the spectrum of your sample. The computer will automatically correct and subtract
for any background peaks from the spectrum of your sample. The steps for collecting a background and
sample spectrum are:
1. With the empty cell positioned in the sample compartment click Scan in the Instrument Setup
window that is already open. A window displaying a graph with the background energy spectrum
and a scan status bar (indicating number of scans) will be shown. The background spectrum takes
a few minutes to complete. The background will be autosaved although if a file with the name
you provided is already there a window will pop up. You may overwrite the file. A window will
pop up on the screen displaying the background energy spectrum.
2. In order to collect the sample spectrum, carefully place the gas cell in the FTIR spectrometer
sample compartment. Select the Instrument option in the menu. The Instrument Setup window
will open. Provide a name for your Sample file and enter some comments. Go to the Scan tab and
select the Absorbance units (A). Click Apply, then Scan. A window displaying the FTIR
spectrum of the sample and a scan status bar will be shown. If the spectrum is displayed in
Transmittance units convert it to Absorbance units by clicking on the icon with the big A. The
computer automatically subtracts the background data and adjusts the baseline. When the data
collection is complete, you may be asked whether you want to overwrite the file or create a file
with a New Name. Provide a New Name (suggested name DCl_HCl.sp) and save your spectrum.
Labeling, Printing and Saving the Spectrum
1. First delete the background spectrum from the window. Select the bkg.sp file name at the bottom
left of the screen. Then go to the menu bar and click on Edit, then Delete.
2. Now select the spectrum filename in the bottom left section of the screen. Use the AutoY icon to
display the whole spectrum in the screen. Since you have used DCl as the sample, you will have
two intense bands. One corresponds to DCl and the other to HCl (which is a “contaminant” of
DCl). First you need to enlarge one of the regions of the spectrum corresponding to the
absorption of one of them. In order to do this, depress the left mouse button and draw a rectangle
around the region of the spectrum that you would like to enlarge. Then double click in the region
you have highlighted to enlarge it to full screen.
3. To label the peaks go to the menu and click on View, then Label Peaks. You can also generate a
list of peaks by going to the menu and click on Process, then Peak Table. A new window with a
list of peaks will be displayed. Be aware that each band is a doublet due to the natural presence of
the less abundant 37Cl isotope. Thus only labels on the more intense band of each doublet should
be used in your report.
4. To print, select the window you want to print and then go to File, then Print. Make sure you
select the proper printer (in Print Setup) before you submit your print job. Suggested printer is the
one in SLB319.
5. Repeat the procedure above (steps 2-4) for the other band.
6. Finally save you may want to save your spectrum as a text file (extension .asc) for your records.
Go to File, then Save As, there select from the type file, the ascii (*.asc) option, browse to the
Folder indicated by the instructor/TA and Save the file. You will be able to open this file in Excel
in case you need it when working on your report.
Finishing Up
On the computer, select Exit or Close from the File menu, this will close the program. Carefully remove
the gas cell from the spectrometer. Your instructor will assist you with emptying the cell.