Expanded Choices for Vibration-Rotation Spectroscopy in the Physical Chemistry Teaching Laboratory Joel R. Schmitz and David A. Dolson Department of Chemistry Wright State University Dayton, OH

Traditional Vibration-Rotation Spectrum Experiment in the Teaching Laboratory  Quantum mechanical and spectroscopy theory is reinforced to third year Physical Chemistry students in the laboratory through laboratory experience with vibration-rotation spectroscopy.  Stafford et al. 1 introduced vibration-rotation spectroscopy of HCl vapor in teaching laboratories in  With time, many other molecular choices were demonstrated in the chemical education literature.  Gaseous hydrogen chloride (HCl) has remained the common molecule of choice due to its simple synthesis or availability, simple & resolvable P/R branch structure, isotopic variance, and strong infrared (IR) spectrum. 1. Stafford, F. et al., J. Chem. Educ. 1963,40,

Figure 1. Fundamental vibrational band 2 with rotational branches of HCl at 2860 cm Schwenz, R. et al., J. Chem. Educ., 1999, 76,

Selected Literature  Various analysis methods (difference methods, polynomial fits, multiple linear and nonlinear regressions, global analysis with multiple isotopomers) have been suggested by Schwenz et al. 2, Iannone 3, and Tellinghuisen 4.  Deuteration methods for HCl/DCl & HBr/DBr preparation have been suggested by Rieck et al 5, Ganapathisubramani 6 and Lehmann et al 7. 1.Stafford, F. et al., J. Chem. Educ. 1963,40, Schwenz, R. et al., J. Chem. Educ. 1999, 76, Iannone, M., J. Chem. Educ. 1998, 75, Tellinghuisen, J. J. Chem. Educ. 2005, 82, Rieck, D. F., J. Chem. Educ. 1989, 66, Ganapathisubramani, N. J. Chem. Educ. 1993, 70, Lehmann, E. et al., J. Chem. Educ. 2010, 87, 1402.

Improved Instrumental Resolution Offers New Choices for Molecular Samples  Choices include other linear molecules: HBr/DBr, HCN/DCN, C 2 H 2 /C 2 D 2, CO, CO 2, OCS and N 2 O...  HCl/DCl and HBr/DBr 1-0 & 2-0 vibration-rotation spectra (without halogen isotope resolution) can be obtained with 2 cm -1 resolution.  Increasingly improved instrumental resolution (to 0.25 and cm -1 ) is becoming available to academic teaching laboratories, which is sufficient to resolve H 79 Br/D 79 Br vibration-rotation lines.  Many 13 CO and 13 CO 2 lines may be resolved in fundamental IR spectra of natural abundance gas samples with resolutions of 0.5 cm -1 and better. (RC09 - Dolson & Anders)  Vibration-rotation lines of O 13 CS/O 12 CS may be resolved in the fundamental C=O stretching band of a natural abundance gas sample with a resolution of cm -1

Sample Preparation

Figure 2. HBr fundamental band.Figure 3. HBr overtone band.

Figure 4. Isotopic splitting of the R(1) peak of the HBr fundamental at cm -1 resolution. Figure 5. Isotopic splitting of the R(1) peak of the HBr fundamental at 0.25 cm -1 resolution.

Figure 6. DBr fundamental band.Figure 7. DBr overtone band.

Data Analysis 8. Dunham, J.L., Phys. Rev. 1932, 41,

Dunham Coefficient ParameterValue (cm -1 ) Literature Value 9 (cm -1 ) Y 10 ωeωe (2) (88) -Y 20 ωexeωexe 45.55(1) (70) Y 01 BeBe (1) (37) -Y 11 αeαe (8) (88) -Y 02 DeDe 3.434(5) x (18) x Y 12 βeβe 3.4(2) x (24)x Table 1. Vibration-rotational constants for H 81 Br. 9. Stocker & Goldman, J. Quant. Spectrosc. and Radiat. Transfer 1976, 16, Average Residual: cm -1 Maximum Residual: cm -1

Determination of CO Vibration-Rotation Constants 10. Mina-Camilde, N. et al., J. Chem. Educ. 1996, 73,

Figure CO fundamental band. Figure CO overtone band.

Figure 8. Expanded view of CO fundamental P-branch to show 13 CO lines.

Dunham Coefficient Parameter Value (cm -1 ) Literature Value 11 (cm -1 ) Y 10 ωeωe (5) (13) -Y 20 ωexeωexe (2) (774) Y 01 BeBe (7) (18) -Y 11 αeαe (3) x (130) x Y 02 DeDe 6.14(5) x (892) x Table 2. Vibration-rotational constants for 12 C 16 O. 11. Farrenq et al., J. Mol, Spectrosc. 1991, 149, Average Residual: cm -1 Maximum Residual: cm -1

Conclusions  Infrared vibration-rotation spectroscopy is used in the teaching laboratory to reinforce fundamental quantum concepts and spectroscopic theory.  Typically HCl/DCl is the chosen molecule for experiments, but higher resolution makes other options available.  HBr/DBr and CO were synthesized and the vibration-rotation constants for the various isotopomers were determined through non-linear regressions in terms of Dunham coefficients.  Experimentally determined spectroscopic constants are in satisfactory agreement with literature values.  Laboratory instructors have more choices of molecules to conduct vibration-rotation spectroscopy, as instrument resolution permits. ( 12/13 C isotopomers of CO, CO 2, OCS; 79/81 Br isotopomers of HBr/DBr)

Vibration-Rotation Analysis by Polynomial Fit of Frequency (cm -1 ) vs. m Plots  = 0 + (B+B  ) m + (B-B  ) m 2 – 4·D m 3  m = - J  for P-branch lines  m = J  +1 for R-branch lines  0 is the band center  B v = B e -  e (v+½) + · · ·  Examine residuals after cubic fit to determine if a quartic fit is warranted – redefines quadratic and cubic coefficients.  D v = D e -  e (v+½) + · · · Herzberg vol I, Eq III-139