Infrared Spectrum Analysis of Vibrational and Rotational Energy in Gaseous Hydrogen Chloride

Nathaniel J. Wise. Bob Jones University, Division of Science, Department of Chemistry

1700 Wade Hampton Blvd. Greenville, SC 29614

Abstract Using a FT-IR spectrometer, the lab group analyzed gaseous hydrogen chloride to determine

the portion of the spectra due to vibrational changes and the portion due to rotational changes in the

molecule. The moment of inertia was calculated and a bond strength force constant was also

determined, along with the centrifugal distortion constant. Sources of error are discussed and

calculated values are compared to literature values.

Introduction The vibrational and rotational IR spectrum of

HCl is well studied.1 By passing a beam of infrared

light through a sample, the frequency of the light that

coincides with the vibrational frequency of the

molecule can be used to calculate this vibrational

frequency.2 This spectrum, when used for a gas, can

be used to analyze interactions between the gas being

analyzed and the solvent gas molecules.34 In this

experiment, the gas being analyzed was HCl, diluted

with inert N2. Since chlorine exists as two isotopes, 35Cl and 37Cl, each individual peak on the IR spectrum

is split into two at the end; the higher energy of the

double peaks is that of H35Cl. Cl occurs naturally as

about 75% 35Cl and about 25% 37Cl.

For most diatomic molecules, a harmonic

oscillator model is appropriate. This enables

calculations of frequency types, zero point energy and

the like. However, for overtone spectroscopy, as in

this lab, the oscillatior is anharmonic; that is, it

doesn’t follow the harmonic oscillator model.5 A

harmonic oscillating model allows for vibrational

quantum number changes of -1 and +1, but the

anharmonic model has overtones; that is, Δν of ±1,

±2, ±3, etc.6 A vibrational-rotational spectrum has

two so-called “branches.” One, with simultaneous

excitation of both vibration and rotation, is labelled

the R branch. The branch with the opposite, that is,

a quantum of rotational energy lost while a quantum

of vibrational energy is gained, is labelled the P

branch.

Methods and Materials Setup

The experiment used a gas cell with NaCl

windows and filled with HCl for the IR spectrum.

The spectrometer was connected to a purge gas inlet

with N2 flowing into the tube throughout the

experiment; this gave a positive pressure for the gas

so that HCl did not leak into the sensitive interior of

the instrument. The sample cell was filled with the

HCl gas under a hood by connecting the gas canister

to the cell and allowing it to flow through for about

thirty seconds. A small amount (several seconds

worth) of N2 was added to the cell to ensure that the

HCl concentration in the tube was low enough that

the peaks in the spectrum were resolved sufficiently.

The glass cell was fitted into the spectrometer in

preparation for the procedure. The spectrometer

used was an Anasazi Eft60 FT-NMR Spectrometer,

and the software used to analyze the spectrum was

EZ-Omnic.

Procedure

We set the scan rate to 32 scans and took a

spectrum according to standard procedure for the

instrument. Following the measurement, the gas was

flushed from the cell under a fume hood using N2.

Results

The following spectrum (Figure 1) was

obtained. Figures 2 and 3 are sections of this

spectrum with J” values labelled at the top of the

image and m values at the bottom, along with the

wavenumber values for each peak, including the

double peak resulting from the isotopes.

Figure 1. Rotational-Vibrational Spectrum of HCl.

Figure 2. Rotational-Vibrational Spectrum of HCl – R Branch

Figure 3. Rotational-Vibrational Spectrum of HCl – P Branch

For each isotope of chlorine, the

quantum number m was paired with the

appropriate wavenumber value, tabulated

below in Tables 1 and 2. Wavenumbers are

reported in cm-1.

m -10 -9 -7 -6 -5 -4 -3 -2 -1 ν, 35H 2651.51 2677.24 2726.91 2751.34 2774.76 2798.68 2820.84 2843.01 2864.28

ν, 37H 2649.52 2675.2 2725.51 2749.78 2774.05 2797.09 2819.71 2841.78 2862.36

Table 1. m and ν values for R branch.

m 1 2 3 4 5 6 7 8 9 10 11 12 13

ν, 35H

2905.45 2925.12 2943.83 2962.24 2980.08 2997.3 3013.76 3029.51 3044.53 3058.8 3072.36 3085.17 3097.22

ν, 37H

2903.98 2923.85 2942.45 2960.74 2978.31 2995.41 3011.95 3027.48 3042.39 3056.64 3069.97 3082.56 3094.67

Table 2. m and ν values for P branch.

A plot of m vs. ν resulted in the

following plots, one each for 35H and 37H , with

both a 2nd order and 3rd order polynomial fit

for the trendline.

Figure 3: ν vs. m for 35HCl; 2nd order fit.

y = -0.3034x2 + 20.3599x + 2885.2703R² = 0.99997935

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ν35 vs. m

Figure 4: ν vs. m for 37HCl; 2nd order fit.

Figure 5: ν vs. m for 35HCl; 3nd order fit.

y = -0.3166x2 + 20.3889x + 2884.0556R² = 0.99998611

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ν37 vs. m

y = -0.0020x3 - 0.3004x2 + 20.5643x + 2885.1431R² = 0.99999895

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Figure 6: ν vs. m for 37HCl; 3nd order fit.

y = -0.0017x3 - 0.3086x2 + 20.5226x + 2883.8209R² = 0.99999763

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ν37 vs. m

From the equations of the 2nd order polynomial fit trendlines for these graphs, and using the equation7

𝝂(𝒎) = 𝝂𝟎 + (𝟐𝐁𝒆 − 𝟐𝛂𝐞)𝒎 − 𝜶𝒆𝒎𝟐, the rotational constant Be as well as the frequency

at which m = 0 (ν0) and αe were obtained. Additionally, the moment of inertia Ie was calculated by8

Ie = (ℎ

8𝜋2𝐵𝑒𝑐),

where h is the Planck constant and c is the speed

of light in centimeters per second. For the 3rd order polynomial fit trendline, values

for Be, ν0, and αe were again calculated, along with De, the centrifugal distortion constant. To obtain these values, the equations for the trendlines were used in conjunction with9

𝒗(𝒎) = 𝝂𝟎 + (𝟐𝐁𝒆 − 𝟐𝛂𝐞)𝒎 − 𝜶𝒆𝒎𝟐 − 𝟒𝑫𝒆𝒎𝟑.

Finally, νe, the fundamental frequency of vibration, and νexe, the anharmonicity constant, were calculated using the equations10,11

𝜈0 = 𝜈𝑒 − 2𝜈𝑒𝑥𝑒 and

𝜈0∗ = 𝜈𝑒 (

𝜇

𝜇∗)

12

− 2𝜈𝑒𝑥𝑒 (𝜇

𝜇∗)

where ν0 and ν0* are the terms for 35HCl and 37HCl,

respectively. These were each taken from the equation for the trendline of a 3rd order fit on the graph, since the R2 value for each of those graphs was higher than the quadratic equation.

All of these values are tabulated below.

35H 37H

Experimental -- 2nd order fit

ν0 2885.2541 2884.0577

Be 10.4851 10.5098

αe 0.3035 0.3164

Ie 2.66813E-47 2.66185E-47

r 128.0724863 127.8250652

Table 3. Experimental Constants.

35H 37H

Experimental -- 3rd order fit

ν0 2885.1431 2883.8209

Be 10.4820 10.5020

αe 0.3004 0.3086

De 0.0005 0.000425

Ie 2.66891E-47 2.664E-47

r 128.0914234 127.9694

vexe 3.507860661

ve 2892.158821

Table 4. Experimental Constants.

Literature

ν0 2885.9775 2883.8705

Be 10.593404 10.5780

αe -0.307139 -0.3035

μ 1.62665E-27 1.62912E-27

De -0.000532019 -0.000530

r 127.455

Table 5. Literature12 Constants.

Discussion The spectrum does not have an absorption

feature at ν0 cm-1 since this is the frequency of the

forbidden transition from ν" = 0, J" = 0 to ν' = 1, J' =

0.

The anharmonic oscillator is a good fit for the

data, since the spectrum clearly shows overtones,

which would not be explained by the harmonic

oscillator model.

By including the centrifugal distortion term;

that is, by using the cubic polynomial fit, the results are

not improved. The experimentally derived constants

are closer to the expected values with the quadratic fit,

not the cubic.

Comparing the values for Be*/Be calculated from the

experimental values and from the equation Be

*/Be = μ/μ*,

we obtain

Be*/Be 1.0019

μ/μ* .9985

This suggests that, since the values are close

together, the rigid motor prediction is good model for

the system.

Potential sources of error include

contamination of the HCl gas cell during filling or

when diluting with N2 or during measurements. These

sources are not expected to be significant.

Author Information Corresponding Author

Nathaniel J. wise nwise501@students.bju.edu

Author contribution:

The report was written solely by Nathaniel Wise. See acknowledgements.

Notes

The author declares no competing financial interest.

Acknowledgments

The author thanks Dr. George Matzko for his assistance during the preparation and procedure of the experiment.. The experiment was done with equal participation by this author, Patrick S. Avery, Eddie C. Hicks, Emily R. Hummel, Mary E. Silos, W. Daniel Smith, and Micah E. Raab.

References 1 B. Roberts. "The HCl vibrational rotational spectrum." J. Chem. Ed. 1966, 43, 357. 2 Marianne L. McKelvy, Thomas R. Britt, Bradley L. Davis, J. Kevin Gillie, L. Alice Lentz, Anne Leugers, Richard A. Nyquist, and Curtis L. Putzig. "Infrared Spectroscopy." J. Anal. Chem. 1996, 68, 93R-160R. 3 Bret N. Flanders, Xiaoming Shang and Norbert F. Scherer. “The Pure Rotational Spectrum of Solvated HCl: Solute-Bath Interaction Strength and Dynamics.” J. Phys. Chem. A. 1999, 103, 10054-64. 4 A. Padilla, J. Perez, W. A. Herrebout, B. J. Van der Veken and M. O. Bulanin. "A simulation study of the vibration-rotational spectra of HCl diluted in Ar: Rotational

dynamics and the origin of the Q-branch." J. Molec. Struc. 2010, 976, 42-48. 5 K. Lim. "The Effect of Anharmonicity on Diatomic Vibration: A Spreadsheet Simulation." J. Chem. Ed. 2005, 82, 1263-64. 6 Carl Garland, Joseph Nibler, David Shoemaker. Experiments in Physical Chemistry. McGraw-Hill Higher Education. Boston. 2009. 417. Print. 7 Ibid. 420. 8 Ibid. 416. 9 Ibid. 419. 10 ibid. 418. 11 Ibid. 420. 12 Sime, R.J. Physical Chemistry: Methods, Techniques, and Experiments. Philadelphia, PA: Saunders College Publishing, 1990, 680.