Lab 9. Analysis (Questions to Answer in Your Report).

Part A. CO₂

• How many vibrations does this molecule have and which ones you see in the IR spectra
• Explain (without calculations) why some vibrations appear to have all three branches, P,Q, and R, while others have only P and R
• What are the hot bands and overtones? Did you observe either of them and how did you identified them as such?

Part B. HCl and DCl

• Plot the experimental spectra
• Label the peaks in your spectra by m values. (Remember: m = J" + 1 for the R branch and m = - J" for the P branch.) Use a spreadsheet to tabulate the m values and their corresponding Dn (m) values, separating the peaks corresponding to the different isotopes. Use the highest precision possible in all numbers. Calculate Dn (m) for adjacent peaks and plot these values against m. Make sure that you are calculating n_e for adjacent peaks of the same isotope (That is, do not calculate the difference in wavenumber between the H³⁵Cl and H³⁷Cl peaks. Do calculate the difference between, for instance, the P(1) and P(2) peaks, the P(2) and P(3) peaks, etc. ).
• Use the linear least-squares function to fit the data (you can do this manually, if you prefer, but it might get ugly). From the linear least-squares data, calculate the intercept, which is (2B_e - 3a_e), and the slope, which is (-2a_e). Most spreadsheets have functions to give the linear least-squares intercept and slope directly from the data; check the manuals or online help of your spreadsheet. (Read pages 74-79 in SGN for discussion of this option in Excel). Use the intercept and slope to calculate a_e and B_e. Using these values and the appropriate equation, calculate n_o for m = 1 to 4; average the result. For each isotope of each molecule, present tables containing your calculated values of a_e, B_e, and n_o in wavenumbers.
• Alternatively, use Eq.(8) to get n_o, a_e and B_e from a quadratic fit:

• Calculate the reduced mass, moment of inertia, and bond length for each isotope. Important: When calculating the reduced mass of a molecule, use the exact mass of the particular isotope of interest for each element. Do not use the atomic mass given on a periodic table, since that value is weighted to account for the natural abundance of the various isotopes. There are two primary isotopes of bromine: ³⁵Cl and ³⁷Cl. These two isotopes make up more than 99.99% of chlorine. In other words, if the two isotopes of HCl are resolved in your spectrum, you should consider them separately. However, if the H³⁵Cl and H³⁷Cl peaks are not resolved, you will have to use a weighted average atomic mass to calculate the reduced mass.

Isotopes^*

^*Source: CRC Handbook of Chemistry and Physics, 73^rd ed., Ed. D. R. Lide, Boca Raton, FL: CRC Press, 1992.

• Comment on obtained values of n_o and B_e for different isotopes and explain the isotope effects demonstrated in your spectra. Should the values depend on masses?
• Comment on the values of J' and J'' with maximum intensity, what it depends on and how it agrees with your spectra.

Part C. C₂H₂ and C₂D₂ (if you did these measurements, will be treated as extra credit)

• Plot your experimental spectra
• Vibrational assignments and fundamental frequencies.
  1. Examine your survey spectra for C₂H₂ and C₂D₂ and note the striking difference between parallel and perpendicular bands. Determine the frequencies of as many of the transitions shown in introduction as your data allow. In doing this, take the Q branch maximum of each expanded spectrum of the n₅, n₁ - n₅, n₂ - n₅, and n₃ - n₄ perpendicular bands as a measure of these vibrational frequencies. The Q branch of the C₂D₂ n₂ - n₅ band may be difficult to detect since it overlaps some of the rotational structure of the n₄ + n₅ band of C₂HD, an inevitable impurity in C₂D₂.
  2. The parallel bands are expected to show a gap between the P and R branches at the position of the missing Q branch, but in fact such a gap is not seen for the acetylenes owing to overlap with combination and difference bands. For example, in the expanded trace of the n₃ region of C₂D₂, a weak feature seen at the Q branch position is not a consequence of a violation of selection rules but rather is due to overlapping R (J" =2) branch lines of the difference bands (n₃ + n₄) - (n₄) and (n₃ + n₅) - (n₅) [10]. This line happens to be the one of minimum intensity between the P and R branches and may be taken as a good approximate value of the harmonic frequency of the n₃ mode of C₂D₂. The corresponding n₃ region for C₂H₂ is more complicated [11] owing to additional overlapping absorption by a combination band n₂ + n₄ + n₅, and the n₃ value given in Table I can be used for subsequent calculations.
  3. Use your data to obtain as many of the fundamental transition frequencies of acetylene as possible and compare the results with the literature values listed in Table 1. Use these values to assign other combination or difference bands that you observe in the C₂H₂ spectra, using band shapes and symmetry arguments as a guide. Draw a vibrational energy level diagram from 0 to 4000 cm^-1 and show all the vibrational transitions you observe for C₂H₂. For C₂D₂, such an assignment task is more difficult because of C₂HD impurities, for which all the fundamental transitions are allowed because of the lower symmetry. One clue serving to identify the transitions of the latter species is the absence of intensity alternation in the P and R branches, since there is no longer exchange symmetry for the protons.
• Rotational analysis.
  1. The n₄ + n₅ parallel combination bands of C₂H₂ and C₂D₂ should be analyzed to obtain the ground state B values for each species. {The n₃ band of C₂D₂ and the n₅ perpendicular bands for both isotopic species are also suitable for analysis.} Note the alternation of line intensities and use the intensity predictions from the nuclear spin statistics as an aid in assigning an m value to each line in the P and R branches. The feature that appears at the Q branch position is due to overlapping R lines of the difference bands (2n₄ + n₅) - (n₄) and (2n₅ + n₄) - (n₅) [11,12]. These overlapping branches also cause the alternating intensity ratios to differ somewhat from the values of 3:1 and 6: 3 predicted for C₂H₂ and C₂D₂
  2. Tabulate the transition frequencies and fit them to Eq. (25) using a least-squares method. Since this is a parallel transition between two states, l' and l" are zero in this equation. (If a perpendicular fundamental such as n₅ is to be analyzed, a value of l' = l" = 1 should be substituted.) Compare your rotational constants for the ground state with the literature values B"(C₂H₂) = 1.176608 cm^-1, B"(C₂D₂) = 0.847887 cm^-1 cited in Refs. 1 and 2. Assume that the structure is unchanged by deuteration and, using Eqs. (23) and (24), calculate the C-H and C-C bond lengths. Use the uncertainties from the least-squares analysis to calculate the uncertainty in these bond lengths and compare your results with values of R_CH = 1.0625 , R_CC= 1.2024 that correspond to the equilibrium positions of the atoms on the potential energy surface [2].

• Force-constant determination.
  1. Calculate the force constants for acetylene using Eqs. (21) with the fundamental frequencies and the C-H and C-C bond lengths that you have determined. The bending force constants k_d and k_dd have units of energy, N m, when the angular displacements are in (dimensionless) radians. Compare values of k_d and k_dd obtained with C₂D₂ frequencies with those calculated for C₂H₂; how good is the assumption that the force constants are independent of isotopic substitution?
  2. Compute the stretching force constants [k_r, k_R, k_rr, and k_rR] and discuss their magnitudes in terms of the strengths of the chemical bonds and the likely interactions among these. Two independent determinations of the quantity k_r - k_rr are obtained using the isotopic data and Eq. (21c) but the calculation of k_r + k_rr, k_R, and k_rR requires the combined solution of Eqs. (21a) and (21b) for both isotopic species. In fact, Eq. (21b) for C₂D₂ is redundant and places no new constraint on the force constants since these factor out of the ratio of Eq. (21b) for the two isotopes:

Equation above is an example of a relation derived from a general product rule [5,8] that provides a useful method of checking frequency assignments without doing a detailed normal-coordinate analysis.

Last updated on 05/12/09