The fundamental asymmetric CCl stretch (termed the v0 v1 stretch) of carbon tetrachloride (CCl4) in the gas phase has an absorption maximum in the infrared at 789.00 cm-1. Using values from the table as needed, answer the following questions about the vibrational spectra of carbon tetrachloride.

Isotope Isotopic mass (g/mol)

C 12.0107

Cl 35.453 13

C 13.00335 37

Cl 36.9659

a. How many total vibrational modes does CCl4 have?

b. Calculate the spring constant of the asymmetric stretch in part a (use the unit we discussed in class). Use the values in the table for C and Cl.

c. Using the spring constant from b, determine the natural vibrational frequency (m) of the asymmetric stretch of carbon tetrachloride for an atom containing just 13C and 37Cl in units of Hz (s-1). These are naturally occurring, stable isotopes of carbon and chlorine.

d. The energy of the absorbed radiation at 789.00 cm-1 represents the energy gap of the C-Cl stretch. Calculate the energy gap (in Joules) between the vo and v1 vibrational states for the C-Cl stretch (not the 13C - 37Cl stretch).

e. Since carbon tetrachloride does not have a center of symmetry (its a tetrahedron), some IR-active modes can also be observed in the Raman scattering spectrum. The asymmetric CCl stretch described above happens to appear in both IR and Raman spectra. From the observed IR absorption maximum (789.00 cm-1), determine the wavelengths (in nm) at which one would expect to observe the Raman Stokes and anti-Stokes scattered photons if a sample of carbon tetrachloride was probed with a Nd:YAG laser excitation source at 532.00 nm. In your answer, be sure to state which is the Stokes shift and which is anti-Stokes.