5.1: Pre-lab Assignments

📅 Due: Each part of this assignment must be completed before 1:00 PM on each scheduled lab meeting day (see syllabus schedule).

• Part I is due prior to the first week's meeting.
• Part II is due prior to the second week's meeting.

🕒 Time: Plan at least two hours to complete this assignment each week. 

🎯 Purpose: These pre-meeting assignments are designed to help you arrive to each week's meeting prepared to engage in thoughtful discussion and to conduct the experimental work.

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This module has two parts and is usually completed over two laboratory meetings.  Each meeting includes Wet Lab work, thus you should prepare for both meetings by dressing appropriately for lab and bringing your own safety eyewear.  Wear PPE and gloves when handling hazardous materials. 

For both meetings meetings, there is a written pre-lab assignment as described below.  Complete the GENERAL PRE-LAB ASSIGNMENT for both meetings as well as the specific assignment for each meeting.  Part I corresponds to the first meeting, and Part II corresponse to the second meeting.

Specific Pre-Lab Assignment for Part I: What can FTIR tell us about a molecule? 

📅 Due before Meeting 1 

Read sections 5.1 through 5.3 of this manual and complete the GENERAL PRE-LAB ASSIGNMENT for this part of the module.  Then complete the following written assignment and submit your work before the deadline.

1. Consider the types of molecular motions and their energies:
   1. What types of motion can gas-phase molecules exhibit?
   2. In general, what type of motion allows molecules to absorb infrared radiation?

2. 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.

3. Consider a hypothetical diatomic gas with a typical harmonic frequency of 2000 \(cm^{-1}\).
   1. Apply the Harmonic Oscillator Model: Draw the energy level diagram corresponding to the vibrational energy levels for this molecule (assume an ideal harmonic oscillator).
   2. Energies of Molecular Motion: To which region of the electromagnetic spectrum do transitions between these energy levels belong?
   3. Predict a spectrum: 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.
   4. Link your prediction to the model: 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.

Specific Pre-Lab Assignment for Part II: How does the instrument resolution affect the results? 

📅 Due before Meeting 2  

Review the group discussion guide worksheets that you completed during the first meeting, the data you collected, and your data analysis. Read section 5.4 of this module and complete the GENERAL PRE-LAB ASSIGNMENT for this part of the module, and the items below.

4. Find the rotovibrational models that you derived and fit to the experimental data in the previous meeting.  Write the expression for each.  Then define each one of the parameters (with units).
5. Describe how you can identify each of the parameters' values from theory or calculate it using the experimental data you collected.
   • m
   • \(\tilde{\nu}\)
   • \(\alpha\)
   • \(\tilde{B}\)
   • \(\tilde{D}\)
   • Moment of Inertia (\(I_e\))
   • Equilibrium bond length (\(r_e\))
6. Show the equations by which you would find uncertainty in each parameter using the results of nonlinear fitting (\(\Delta\tilde{\nu}, \; \Delta\alpha, ;\ \Delta\tilde{B}, \; \Delta\tilde{D}, ;\ \Delta I_e, \; \Delta r_e \)).
7. Predict the effect of resolution:  What will happen to the FTIR spectrum and the derived molecular parameters as instrument resolution is changed from 8 cm^-1 to 0.5 cm^-1?  Show your prediction by sketching the spectrum for at least three different resolutions.  Describe the trend you expect in the molecular parameters as resolution is varied.

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, Duke students click here)

• 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.

 

Optional 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