9.1: FTIR spectrum of HCl

Later in this semester, you will use a Fourier Transform Infrared (FT-IR) Spectrometer to investigate the coupling between the vibrational and rotational motions of a diatomic molecule, using hydrogen chloride (HCl) as the example. The FT-IR spectrum of HCl gas is a classic demonstration of quantum behavior. The diatomic, HCl, has only one IR-active vibrational mode. Yet, a close look at its IR spectrum shows interesting structure that can only be explained by quantization and coupling of the molecule's rotations to the vibrational motions.

This activity will help you get acquainted with MatLab, and it will also serve as a template for how you can approach data analysis later this semester. So, after you complete this, save your work and plan to use it again later!  

Be sure that the supporting files provided by our instructors are in your MatLab working directory. Using MatLab, open the "FTIR_StudentGuide.mlx" live script file, and follow the instructions in the document. 

Below is an FT-IR spectrum of HCl gas (Figure \(\PageIndex{1}\)). Since chlorine has two naturally-abundant isotopes, \(\ce{^{35}Cl}\) and \(\ce{^{37}Cl}\), the spectrum is actually the spectrum of \(\ce{H^{35}Cl}\) and \(\ce{H^{37}Cl}\). The taller set of peaks is from \(\ce{H^{35}Cl}\), while the shorter set of peaks is from \(\ce{H^{37}Cl}\).

FT-IR Spectrum of a mixture of  \(\ce{HCl^{35}}\) and \(\ce{HCl^{37}}\)

Figure \(\PageIndex{1}\): FTIR Spectrum of HCl. (CC-NC-BY; DUKE CHEM)

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 Table of Peak Energies in wavenumbers:

Table \(\PageIndex1: \tilde{\nu}_{(m)} ( {cm}^{-1})\) for HCl from m = 4 to -4

\( \tilde{\nu}_{(m)} ( {cm}^{-1})\)	m	isotope \(\ce{HCl^{35}}\) or \(\ce{HCl^{37}}\)
2963.01
2960.84
2944.57
2942.52
2925.65
2923.48
2906.00
2903.95
2864.78
2862.85
2843.33
2841.40
2821.27
2819.34
2798.61
2796.80

1. Determine from Figure \(\PageIndex{1}\) which peaks arise from H³⁵Cl and which peaks arise from H³⁷Cl and give each pair of peaks an appropriate m value.
2. Enter the peak positions \( \tilde{\nu}_{(m)}\) for H³⁵Cl and H³⁷Cl as two separate vectors into Matlab.
3. Create a corresponding vector of m values from +4 to –4.
4. For each isotope, use Matlab to calculate the separation between adjacent peaks \( { \Delta \tilde{\nu}}_{(m)}=\tilde{\nu}_{(m+1)}-\tilde{\nu}_{(m)}\).

   Note

   \({ \Delta \tilde{\nu}}_{(m)}\) cannot be calculated for m = –1 since there is no peak for m = 0

5. For each isotope, H³⁵Cl and H³⁷Cl, do a separate plot of \( {\Delta \tilde{\nu}}_{(m)} ( {cm}^{-1})\) (y-axis) versus m (x-axis) with each data point indicated by a small circle.

   Note

   When plotting an x-y graph, the vectors x and y must be the same length. If \({ \Delta \tilde{\nu}}_{(m)}\) cannot be calculated for a particular m value (see step (4)), then that value of m must be deleted from the vector of m values.

6. Perform a linear least-squares regression analysis and determine the slope, y-intercept, and standard deviation in the slope and intercept.
7. Create a final plot for each isotope, H³⁵Cl and H³⁷Cl , that includes the raw data and the least-squares fitting.

Save your work!

When you have completed the steps above and have created a final plot, it is a good idea to get feedback from your instructors to confirm that you have successfully created a "full-credit" plot. Then, please export your work, inlcuding the final plot, as a pdf file and move to the next section.