5.1: Pre-lab Assignment
- Page ID
- 419788
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)- Develop an energy level diagram and relate that diagram to rotational-vibrational spectra.
- Identify, describe, and interpret the molecular constants that can be extracted from gas-phase IR spectra.
- Discover the impact of spectral resolution on precision of molecular constants derived from the spectral data.
- Use data to evaluate and refine quantum mechanical models.
In addition to the "general" prelab work expected for all experiments in the course (Introduction and Experimental Plan as described in the Orientation Module), please complete the following and submit the work prior to the lab meeting.
Read this entire manual and complete the following written assignment (to be turned in with the usual pre-lab assignment):
- Consider the types of molecular motions and their energies:
- What types of motion can gas-phase molecules exhibit?
- In general, what type of motion allows molecules to absorb infrared radiation?
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The frequency of electromagnetic radiation is often reported in units of wavenumbers (\(cm^{-1}\)). Consider the equation \(E=\frac{h c}{\lambda}\) and to determine whether wavenumbers (use units as your guide) are directly or inversely proportional to energy.
- Consider a hypothetical diatomic gas with a typical harmonic frequency of 2000 \(cm^{-1}\).
- Draw the energy level diagram corresponding to the vibrational energy levels for this molecule (assume harmonic oscillator).
- To which region of the electromagnetic spectrum do transitions between these energy levels belong?
- A sample of this diatomic gas is placed in a spectrometer capable of measuring absorbance in the range 1000 – 5000 cm-1. Predict the appearance of the spectrum (intensity of absorbance vs. frequency). Put frequency (in cm-1) on the x-axis and intensity of absorbance on the y-axis. Draw the spectrum and explain you reasoning.
- Go back to the energy level diagram you drew in 3A. Add an arrow to your energy level diagram from 3A to represent each transition drawn in your spectrum in 3C.
- Show which equations you would use to find: \(B_e\); \( \alpha_e\); \(\tilde{\nu_o}\).
Adapted from Beck, Jordan P., and Diane M. Miller. “Encouraging Student Engagement by Using a POGIL Framework for a Gas-Phase IR Physical Chemistry Laboratory Experiment.” Journal of Chemical Education 99, no. 12 (December 13, 2022): 4079–84. https://doi.org/10.1021/acs.jchemed.2c00314.
Additional reading: (available in the library)
- Part l. Instrumentation, Journal of Chemical Education, 1986, 63 (1), A5. (This is a description of how the Michaelson Interferometer is applied in FTIR spectroscopy. See also the video lined below.)
- Shoemaker, D.P., Garland, C.W., and Nibler, J.W. Experiments in Physical Chemistry, 6th ed., McGraw-Hill, New York, 1996, Chapter XIV, Experiment 37.
- McQuarrie, D.A. and Simon, J.D. "Physical Chemistry: A Molecular Approach", University Science Books, CA, 1997, Sections 13.2-13.4, 18.4-18.5); Atkins, P., Physical Chemistry, 5th ed., sections 16.8 – 16.11
- Silbey, R.J., Alberty, R. A. Bawendi, M.G., Physical Chemistry, 4th ed., Sections 13.4, 13.6 and 13.7, for a discussion of rotation-vibration spectroscopy of diatomic molecules.
Helpful videos
Dr. Welsher's P-Chem lectures are on YouTube!
In addition, the videos below provide a nice introduction and demonstration of the theory and techniques you will use.
Introduction to the Michaelson Interferometer in FTIR
Introduction to rotovibrational spectroscopy
Filling a gas cell