Infrared rovibronic spectroscopy of HCl

 

��������� In this investigation we will record high resolution infrared absorption spectra of gaseous HCl and DCl.� This spectrum will focus on a single vibrational band (v = 0 � v = 1) and the rotational levels associated with this band.� There is a vibrational selection rule which states that the only allowed vibrational transitions are for Dv = +1.� As we have noted this rule does not apply for electronic transitions.� In the case of electronic spectrum I₂ (X � B) which we will record later, we will observe a large number of different vibrational transitions arising from only a few vibrational levels in the ground state.� There are a number of different rotational levels populated at room temperature, as indicated by a Boltzmann distribution, and each of these levels has an associated rotational quantum number, J.� In the infrared spectrum of HCl we will observe transitions corresponding to DJ = +/- 1.� The transitions corresponding to DJ = +1 are called the R-branch of the vibrational band and those corresponding to DJ = -1 are labeled the P-branch.� Isotopic species (³⁷Cl and ³⁵Cl) will result in different spectra.� Detailed analysis of these spectra will provide accurate values for the equilibrium bond length, the moments of inertia, and other molecular constants.

 

Methods

HCl gas is placed in a cell with KBr windows.� The KBr windows are used because glass absorbs strongly in the infrared region.� These windows are hydroscopic and thus the cell is kept in a dessicator.� We will use the Nicollet FT-IR to record the IR spectrum of HCl.� Before we start make a rough prediction of the spectrum we will observe using the physical constants of HCl.� To do this read Atkins section 16.9 � 16.13 (or equivalent section in Barrows). �Simulate four lines of this spectrum using a Gaussian function.

 

Key Equations

	(1)
	(2)
	(3)
	(4)
����	(5)
	(6)
	(7)
	(8)
	(9)
	(10)

Analysis

The detailed analysis of the spectrum will provide a very accurate value for the equilibrium bond length as well as several other important molecular constants.� The details of the vibrational spectra of diatomics are described in Barrow¹ sections 12-3 and 12-5 as well as in Hollas² (handout).� Other details can be found in several other books.³ As well the first link below gives a nice discussion.

�       Using the index, m (P branch: m = - J" ; R branch m = J" + 1), tabulate the values of m and the corresponding �(in wavenumber) of the transition.

�       Plot  against m using equation 5.  Look for outliers.

�       Use Sigmaplot or other program and equation 5 above to get n₀ , (2B - 2 a_e), and a_e for all isotopic species.

�       Repeat procedure for equation 6.

�       Calculate the moment of inertia for HCl.

�       Using the two isotopic peaks (H ³⁷Cl and H ³⁵Cl or H ³⁵Cl and D ³⁵Cl) compute the ratio of B_e for the two isotopes.� Use Table 1 for correct isotopic masses.� Remember that data reported in periodic table is for abundance weighted atomic mass.

�       Using a combination of equation 7, 8, 9, and 10; calculate k, the force constant, using isotopic data.� In particular, using equation 9 and 10 and solving for n_e and then using the second equation above to solve for k.

�       In a separate calculation, compute r_e based on B_e values.� Do they differ for the two isotopes?

�       Use uncertainty analysis to determine the error in r_e.

�       Determine r_e and compare this and your other constants to the latest data at NIST Webbase.

�       Determine the temperature of the sample using the Boltzmann equation and the peak in the rotational contour (what is J' max and how does this relate to the temperature).

�       Simulate a spectrum using 1 cm^-1 resolution and Gaussian functions to simulate the individual lines.� Do this at two temperatures 600 K and 300 K.� Use mathcad file gaussian_spectrum.mcd as a template for this calculation.

 

 

Table 1

	atomic mass (in amu)	isotopic abundance (%)
1H	1.007825	99.985
2H	2.0140	0.015
35Cl	35.968852	75.77
37Cl	36.965903	24.23
79Br	78.918336	50.69
81Br	80.916289	49.31

 

Links

Discussion of Analysis of Rovibronic Spectra of Heteronuclear Diatomics

Results of an ab initio calculation on HCl

 

References:

 

1. Barrow, G. M. Physical Chemistry; WCB McGraw-Hill: Boston, 1996.

2. Hollas, J. M. Modern Spectroscopy; 3 ed. John Wiley & Sons: New York, 1996.

3. Shoemaker, D. P.; Garland, C. W.; Nibler, J. W. Experiments in Physical Chemistry; 6 ed. McGraw-Hill: New York, 1996.