VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
OBJECT: The purpose of this experiment is to introduce you to molecular spectroscopy and to
the molecular parameters and thermodynamic properties which can be obtained by analyzing the
vibration-rotation spectrum of gaseous hydrogen chloride.
REFERENCES (in addition to the Chem 158a,b textbooks):
F. Daniels, R. A. Alberty, J. W. Williams, C. D. Cornwell, P. Bender, and J. E. Harriman,
Experimental Physical Chemistry, 7th. ed., McGraw-Hill, New York, 1970, pp. 247-256.
M. Karplus and R. N. Porter, Atoms and Molecules, Benjamin, Menlo Park, CA, 1971, Ch. 7.
EXPERIMENTAL:
You will measure fundamental and first overtone vibrational transitions of gaseous hydrogen
chloride on a Nicolet Fourier transform infrared (FTIR) spectrometer. The instructor will issue two
10.0 cm cylindrical cells, a blank (empty) and one containing a mixture of HCl and DCl. You will
only measure the spectra of the HCl species. When handling the cells, care must be taken to
avoid scratching the cell windows. Fingerprints will permanently damage the optical surfaces if
they are not washed off immediately with a good quality solvent. The FTIR is controlled by a PC
running under Windows 98. The software is all menu-driven and is straightforward to use if one
follows the prompts.
1) Preparation of the instrument. The MCT detector on the Nicolet must be cooled with liquid
nitrogen. Using the funnel provided, fill the trap for the detector. The fill hole is accessed by
opening the small circular door on the left side of the bench. There are two fill holes. Use the
one towards the back that is NOT taped shut. Do not overfill as liquid nitrogen spilling over the
top of the instrument might cause damage. Check to see that the neutral density filter labeled
“screen A” is installed. The detector is very sensitive and the infrared radiation from the
source must be reduced in the case of normal, fairly optically transparent samples. Otherwise,
the detector is blinded by excess radiation.
2) Start the software by clicking on the Omnic E.S.P. 5.1 icon (not the EZ Omnic icon). If the icon
is not on the desktop, go through the following sequence of mouse clicks: Start, Program,
Omnic E.S.P. 5.1 folder, Omnic E.S.P. 5.1. Once the program starts, a window will appear
that will allow you to select the methods file for the experiment. Select the method "HCl” and
click OK. You will probably not need to change the parameters stored in this file. For the
record, they are as follows: number of scans, 64; resolution, 0.5 cm-1; format, Absorbance;
correction, none; gain, Autogain; velocity, 1.8988; detector, MCT/A; beam splitter, KBr; range,
7500-1700; zero-filling, none; apodization, boxcar; phase correction, Mertz.
3) Initialize the bench for the method that you selected (i.e. HCl) by the clicking on “Collect” and
then “Experiment Setup”. The Collect menu that displays the values of the acquisition and
processing parameters will appear. The Diagnostic tab accesses useful diagnostic functions
that the instructor will demonstrate. You have the option now of changing parameters. If you
do so, please use a method name other than HCl. After you have viewed the values of the
parameters, click on the OK button to configure the bench.
4) Collect a background spectrum by loading the empty blank cell and clicking on the “Col Bkg”
button. While the instrument accumulates the data from the 64 acquisitions, the PC calculates
the spectrum from the accumulated interferogram on the fly. The sharp bands are due to
atmospheric carbon dioxide and water. Note that the cell heavily absorbs in certain regions of
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VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
the spectrum as it is fabricated from a form of glass and hence is infra-red absorbing. These
absorbing features in the spectrum will be removed by the computer via background
subtraction. This approach would not be possible on a conventional CW spectrophotometer.
Normally the cell windows must not be infra-red absorbing.
5) After the background spectrum has been measured, replace the blank cell with the sample cell
and click on the “Col Smp” button. When the interferogram of the sample spectrum has been
acquired, the difference spectrum will be calculated and displayed on the screen. We
recommend that you save the results at this point by clicking on File and Save As.
6) The final step is the measurement of the transition frequencies and the assignment of quantum
numbers to each peak. We recommend starting with the bands of the fundamental spectrum
of HCl. They are the strongest features in the spectrum and are located at ca. 3000 cm-1.
Recall that for each vibrational transition, the R branch for which J increases by one lies to
higher frequency than the P branch for which J decreases by one. Also, the transitions for
HCl-35 and DCl-35 are more intense by a factor of 3:1 than those of HCl-37 and DCl-37,
respectively, and also lie to slightly higher frequency.
There are two options for expansion. One can draw a box around the region of interest by
holding down the left mouse button and dragging the mouse. Once the box enclosing the
region of interest has been drawn, move the cursor inside the box and perform one left mouse
click to expand the box. Alternatively, one can use the utilities of the View Finder at the bottom
of the Omnic window to expand the frequency scale and then clicking on “View” and “Full
Scale” in order to expand along the absorbance (y axis) to fill the screen. To display the full
spectrum after expanding it, double click in the white (displayed) portion of the View Finder
window.
Once a region has been expanded, you can automatically measure the frequencies of the
peaks in the window with the peak finder function. Click on “Analyze” and “Find Peaks” in the
Analyze submenu. You may need to lower the threshold to obtain the frequencies of weaker
peaks or raise the threshold to suppress annotation of noise. The threshold in indicated by a
horizontal black line across the spectral window. To raise the threshold, click just above the
black line; to lower it, click below. Alternatively, you can manually determine the frequencies
with the Annotation Tool symbolized by the large capital T at the bottom of the screen. To
enter annotation mode, click on the T. To annotate, move the cursor now labeled by a T so
that the arrow is above the peak. Hold down the shift key and perform a left mouse click. The
software will find the frequency of the peak closest to the position of the peak. If you simply
left-mouse click, the annotation tool will print the frequency of the exact location of the arrow
when you click.
Once you have annotated a section of the spectrum, you can create and print a report by
clicking on “Report” and then on “Preview/Print Report” in the Report submenu. Once the
report appears, click on the Print button to print the report. Alternatively, you can start up
Microsoft Word that is installed on the PC and use the Edit and Copy functions in Omnic to
transfer an image of the screen to the Windows Clipboard. Then enter Microsoft Word and
use the Edit and Paste function to transfer the contents of the Clipboard to the Word window
that can be saved as a .doc file. We recommend that you insert a page break after each
screen dump so that the image of each screen appears on a separate page.
7) Once you have analyzed the components of the fundamental spectrum for the two isotopic
species of HCl, turn your attention to the fundamental spectrum of DCl. You should be able to
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VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
predict its approximate location by using the well known dependence of the vibrational
frequency on reduced mass. Unfortunately, you will only obtain the transitions for the R
branch as the cell window is totally opaque in the region of the P branch.
8) Next turn your attention to the analysis of the first overtone spectrum of DCl whose position
can be predicted by the harmonic oscillator approximation.
9) Finally analyze the first overtone spectrum of HCl whose approximate location is also
predictable from the harmonic oscillator approximation. These bands partially overlap broad,
but fortunately weak, artifacts that should not be confused with authentic transitions.
CALCULATIONS:
As shown in Daniels et al. and in Karplus & Porter, the vibrational-rotational energy of a diatomic
molecule is given by equation (1):
E = (v + 0.5) - x(v + 0.5)2 + BJ(J + 1) - DJ2(J + 1)2 - (v + 0.5)J(J + 1) (1)
where the subscript e has been dropped from all of the parameters to simplify the format. Since E
and all spectroscopic parameters are given in wavenumbers, each energy difference, E, of each
allowed transition is given directly by a spectroscopic frequency in wavenumbers. For each
spectroscopic transition v"v', J"J' (" denotes the ground state where v" = 0; ', the excited
state), the following constraints on v' and J' apply: v' = v" + 1 for the fundamental transition and v"
+ 2 for the first overtone, J' = J" - 1 for a P band transition and J" + 1 for an R band transition. The
energy difference for each allowed transition is given by equation (2):
E(v',J',v",J") = E(v',J') - E(v",J")
= (v' - v") + x[(v" - v')(v' + v" + 1)] +
B[J'(J' + 1) - J"(J" + 1)] +
D[J"2(J" + 1)2- J'2(J' + 1)2] +
[(v" + 0.5)J"(J" + 1) - (v' + 0.5)J'(J' + 1)] (2).
This is a complicated expression but it has some features which permit a direct calculation of all
the parameters for each isotopic species. Note that the expression for E depends linearly on
each of the parameters. The equation is simply a variation of the well known expression y = mx +
b with a few new twists: 1) the intercept is zero, 2) there are 5 rather than 1 independent variables,
and 3) each independent variable is a non-trivial, but well defined combination of the quantum
numbers v', J', v", and J". For example, the independent variable associated with the parameter B
is [J'(J' + 1) - J"(J" + 1)]. Therefore, the dependence of E on [J'(J' + 1) - J"(J" + 1)], holding the
other variables constant, yields the parameter B as the slope. In other words, the extraction of the
required parameters from the spectroscopic data is simply a logical extension of the method of
least squares to the case of several independent variables. The extension is referred to as
multivariate analysis.
The analysis of the spectral data consists of the following steps:
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VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
a) The data from the FTIR are in wavenumber and no correction of the raw data is required. The
moving mirror in the FTIR’s interferometer is tracked by a laser that provides an internal
calibration for the frequency data.
b) Separate the observed peaks into four sets, those for HCl-35, HCl-37, DCl-35, and DCl-37.
You will analyze each set separately.
c) Assign quantum numbers to the transitions for each isotopic species.
d) Calculate the spectroscopic parameters - , x, B, D, and  - for each isotopic species via a
multivariate analysis (vide infra) of the assigned transitions. Also calculate the bond length, re,
from B, the force constant, k, from , and an estimate of the bond dissociation energy from  and
x.
e) Using the molecular constants obtained, the published isotopic abundances (cf. CRC
Handbook), and standard statistical mechanical formulae, calculate the following thermodynamic
quantities for naturally occurring gaseous HCl at 25.0C: Cp and S.
ANALYSIS OF THE DATA USING NCSS:
This section discusses how to analyze the data using the NCSS software. This document
assumes familiarity with the handout on the use of NCSS and general spreadsheet techniques.
The first step is to prepare a spreadsheet for each isotopic species that contains the data and the
quantum numbers of the transitions. Each row of the spreadsheet contains information on a single
transition. Consider organizing the spreadsheet in blocks with sections for the P branch of the
fundamental, the R branch of the fundamental, the P branch of the overtone, and the R branch of
the overtone. The first column should contain the transition energies in wavenumbers. The next
four columns contain the quantum numbers in the order v", v', J", and J'. The task of entering the
quantum numbers can be simplified if one makes liberal use of copying and pasting. Use all your
data. For example, if you have the R branch transition and not the P branch, still use the R branch
datum. Once the data for the regression have been entered, save the spreadsheet.
In the next step, calculate using spreadsheet techniques the independent variables for the five
parameters to be determined from the spectroscopic data:
item
1
2
3
4
5
parameter
e
exe
Be
De
e
corresponding independent variable
(v'-v")
(v"-v')(v'+v"+1)
J'(J'+1)-J"(J"+1)
J"2(J"+1)2-J'2(J'+1)2
(v"+0.5)J"(J"+1)-(v'+0.5)J'(J'+1)
Consider checking a few entries with a result calculated manually so that you know that the
variables have been defined correctly. Once the full spreadsheet has been defined, re-save it and
prepare for the regression by clicking on the Regression/Correlation item in the Analysis menu and
selecting the Multiple Regression module. The handout on the use of the regression modules in
NCSS discusses how to use the procedure. The following special features apply to this
experiment. There is no intercept so the Remove Intercept option should be set to Yes. In
defining the independent variables, select all five which are located in columns 6-10. The
Correlations report is useful as it contains the full correlation matrix from which the full covariance
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VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
matrix can be calculated. Also pay very close attention to the table of residuals for each
regression calculation. The accuracy and precision of the FTIR is ca. 0.1 cm-1. Errors in excess of
this indicate some type of error, e.g. input error, incorrect assignment, mistake in setting up the
spreadsheet. The spectroscopic parameters are all positive. With the exception of exe and the
centrifugal distortion constant, the relative errors should be small. Large relative errors are
indicative of a calculational or measurement error. The table of residuals is often helpful in
locating the error.
REPORT:
Include the following with your short report: the report sheets, all spectra with assigned transitions,
the NCSS spreadsheets and regression reports, notebook entries, all relevant printouts, and
sample calculations. Report all spectroscopic parameters and their associated 95% confidence
intervals to the correct number of significant digits. Do not calculate the random error of the bond
dissociation energy. Systematic errors in the calculation are much larger than the random errors
that your analysis would address. Similarly do not calculate uncertainties for S and Cp.
However, use a propagation of errors analysis to calculate an uncertainty for r e and k for each
isotopomer.
LONG REPORT. If you select this experiment for a long report, write it in the style of a short
paper in the Journal of Physical Chemistry. The report should contain the following elements:
a) A brief introduction. What have you done and what will you discuss?
b) Experimental. What sample was used? which instruments? Do not go into detailed
procedures, but provide instrumental details that one would need to repeat the experiment.
c) Results. Provide a table of the assigned frequencies and give a brief (few sentences) rationale
for the assignment. An appropriately labeled figure of the spectrum (cut and paste and label) with
a well chosen caption might make the point better than extensive text. Briefly describe how the
spectroscopic parameters were obtained. Briefly comment on the errors in the results and the
internal consistency of the results (i.e. can you estimate one parameter from the others). Don't go
into great detail on the theory of quantum mechanics and molecular spectroscopy. You are writing
a paper on HCl, not a monograph on physical chemistry.
d) Discussion. This is the most important section of the paper. Discuss what you have learned
about the molecule HCl. How stable is the molecule? Your data provide tests for the harmonic
oscillator, rigid rotor, and Born-Oppenheimer approximations (all 3) and this is worthy of
discussion.
e) Literature. Compare your spectroscopic parameters with comparable results from the chemical
literature. Use of the JANAF Thermochemical Tables and Huber and Herzberg’s compilation will
ease your work.
f) A brief conclusion. With this, you have all the elements of effective communication: tell them
what you're going to tell them, tell them, and tell them what you told them.
hcl_2001.doc, FJG, revised 3 Jan. 2002
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VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
REPORT SHEET
Date expt. completed: _____________
Date report due:
_____________
NAME:_________________________________
Date report submitted: _____________
I) Spectroscopic parameters for the isotopomer H35Cl
Experimental
Literature Values
Be (cm-1)
___________________
___________________
e (cm-1)
___________________
___________________
De (cm-1)
(cent. dist. constant)
___________________
___________________
e (cm-1)
___________________
___________________
exe (cm-1)
___________________
___________________
De = e2/4exe (cm-1)
(bond dissn.energy)
___________________
___________________
re (Å)
___________________
___________________
k(N/m)
___________________
II) Spectroscopic parameters for the isotopomer H37Cl
Experimental
Be (cm-1)
___________________
e (cm-1)
___________________
De (cm-1)
(cent. dist. constant)
___________________
e (cm-1)
___________________
exe (cm-1)
___________________
De = e2/4exe (cm-1)
(bond dissn.energy)
___________________
re (Å)
___________________
k(N/m)
___________________
N.B. ADDITIONAL INFORMATION IS REQUESTED ON THE BACK OF THIS FORM!
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VIBRATION-ROTATION SPECTRUM OF GASEOUS HCl
III) Spectroscopic parameters for the isotopomer D35Cl
Experimental
Literature Values
Be (cm-1)
___________________
___________________
e (cm-1)
___________________
___________________
De (cm-1)
(cent. dist. constant)
___________________
___________________
e (cm-1)
___________________
___________________
exe (cm-1)
___________________
___________________
De = e2/4exe (cm-1)
(bond dissn.energy)
___________________
___________________
re (Å)
___________________
___________________
k(N/m)
___________________
IV) Spectroscopic parameters for the isotopomer D37Cl
Experimental
Be (cm-1)
___________________
e (cm-1)
___________________
De (cm-1)
(cent. dist. constant)
___________________
e (cm-1)
___________________
exe (cm-1)
___________________
De = e2/4exe (cm-1)
(bond dissn.energy)
___________________
re (Å)
___________________
k(N/m)
___________________
V) Molar thermodynamic parameters (naturally occurring mixture of HCl35 and HCl37) at 25C.
Literature Values
S (J/K-mole) ________________________
___________________________
Cp (J/K-mole) _______________________
___________________________
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