Test Bank Answers Chapter 11 Infrared Spectroscopy

Problem 11.5: Using Table 11.1 and Example 11.1 as a guide, analyze the following spectrum:

Problem 11.7: In Example 11.3, we saw that the symmetric vibrational mode resulting from the trans-orientation of the two C=O bonds in CO₂ results in the symmetric vibrational mode being IR-inactive. Based only on symmetry arguments, determine which of each pair of molecules below will have the greatest number of IR active vibrations and therefore the most complicated IR spectrum.

Problem 11.8: A Michelson interferometer generates a beat pattern for a monochromatic radiation source. The frequency of the resulting interferogram is recorded below. Determine the frequency of incident radiation that created that interferogram given the fact that the mirror was pulsing over a distance of 3 cm at a frequency of 1 Hz.

Problem 11.9: A He-Ne laser in an FTIR instrument emits light having a wavelength of 632.8 nm. What is the expected frequency of the interferogram of the laser, assuming the moving mirror is oscillating over a distance of 3 cm at a frequency of 1 Hz?

Problem 11.10: What is the maximum distance the moving mirror in a Michelson interferometer would need to travel to be able to distinguish between (a) 1,000 and 1,004 cm^-1 in an FTIR spectrum?

(b) Between 1,000 and 999.5 cm^-1 ?

The relevant equation is,

Problem 11.12: Speculate on the reasons why it is more common to report UV-vis spectra using absorbance, whereas it is more common to report IR spectra using trans­mittance (recall that absorbance = –log(T)).

Problem 11.13: Using the peak at 1,220 cm^-1–1, in the transmittance spectrum of Figure 11.18, estimate the percent error in the percent T reading if your spectrometer has a ± 2 cm^-1 variance in its precision.

Problem 11.14: Define the term evanescent wave.

Problem 11.15: Under what conditions would an ATR accessory be ill suited? In other words, under what conditions might you get better data by using one of the trade tional sample introductory modes (KBr pellet or Nujol mull)?

EXERCISE 11.1: Determine the number of vibrational modes for each of the following molecules.

EXERCISE 11.2: Convert each of the following frequencies into wave numbers.

(a) 5.01 × 10¹³ Hz (d) 1.5 × 10¹⁴ Hz

(b) 6.7 × 10¹³ Hz (e) 8.97 × 10¹³ Hz

(c) 1.5 × 10¹³ Hz (f) 3.1 × 10¹³ Hz

EXERCISE 11.3: Convert each of the following wave numbers into (i) units of hertz (s^–1) and then (ii) into wavelength in unit of micrometers.

(a) 2,970 cm^–1 (c) 1,699 cm^–1 (e) 756 cm^–1

(b) 43,810 cm^–1 (d) 2,120 cm^–1 (f) 1,597 cm^–1

EXERCISE 11.4: Convert each of the following wavelengths into wave numbers.

(a) 3.12 mm (c) 6.85 mm (e) 11.99 mm

(b) 2.97 mm (d) 3.76 mm (f) 5.71 mm

EXERCISE 11.5: Why are deviations from Beer’s law more common in IR spectroscopy than in UV-vis spectroscopy?

EXERCISE 11.6: Determine the number of vibrational modes in each of the following molecules.

(a) SO₂ (d) SO₃^–2 (g) H₂O

(b) NO₂⁺ (e) HCN (h) CO₂

(c) NO₂^– (f) CO (i) NO₃^–

EXERCISE 11.7: In your own words, discuss the considerations one must make when selecting a suitable source for FTIR spectroscopy?

EXERCISE 11.8: Explain the relationship between the use of a Michelson interferometer and the time constant of the detector in FTIR spectroscopy.

EXERCISE 11.9: Explain why a thermal detector is not suitable for use in an FTIR instrument.

EXERCISE 11.11: In your own words, describe how a pyroelectric detector works.

EXERCISE 11.13: Construct a suitable circuit diagram for a pyroelectric detector. Be sure to include a means to drive an output reading device.

EXERCISE 11.15: Unless the solvent used is rigorously dry, the ketone group in the compound [Pt(DPK)2Cl2][PF6]2 undergoes hydrolysis to a stable enol (see Figure 11.1). Suppose you wanted to study the kinetics of this hydrolysis

reaction using IR spectroscopy. Propose a suitable solvent for this study and discuss how you would introduce the sample into the spectrometer. Defend your recommendations.

EXERCISE 11.16: Review your answer to Exercise 11.5 and comment on why it is more common to use UV-vis spec­troscopy for quantitative work than IR spectroscopy. You might also want to review the definition of sensitivity. See Figure 11.22.

EXERCISE 11.17: Determine the number of IR active vibrational modes in each of the following molecules. Note: You will have to use symmetry arguments to determine which vibrations result in a net change in the molecular dipole moment.

(a) SO₂ (d) SO₃^-2 (g) H₂O

(b) NO₂⁺ (e) HCN (h) CO₂

(c) NO₂^- (f) CO (i) NO₃^-

EXERCISE 11.19: Program a spreadsheet and perform a Fourier transform on the data set created by Exercise 11.18.

EXERCISE 11.20: The ketone peak in Figure 11.1 is centered at 1,714.8 cm–1. What is the force constant for the C=O bond? Predict the wave number of the carbonyl peak if the carbon atom is a ¹⁴C isotope and the oxygen atom is an ¹⁷O isotope.

EXERCISE 11.21: Calculate a theoretical absorption frequency in wave numbers for a C–H bond, assuming a force constant of 4.89 × 10² N/m. How would the frequency change if you substituted deuterium for hydrogen?

EXERCISE 11.23: Using Table 11.1 and Example 11.1 as a guide, analyze the following spectra.