1. Measure the infrared spectrum of HCl in the region of 2600-3100 cm-1. This can be accomplished by:
The energy of a particular state (S(v,J)) is due to vibrational and
rotational energy contributions:
where v and J are vibrational and rotational quantum numbers, Bv is the rotational constant associated with the vibrational level having quantum number v, and n is the vibrational wavenumber.
An R transition corresponds to a DJ of +1, while a P transition denotes a DJ = -1 change. Energy expressions for the R and P bands can be found by taking the difference in energies found using the S(v,J) expression. This results in:
Because of the difference in rotational constants for the first two vibrational levels (B1< B0), the P transitions get further apart and the R transitions get closer together as J increases.
3. From a plot of R(J) vs J+1, and a plot of P(J) vs. J; determine n, B1, and B0 using a 2nd order linear regression analysis of the R(J) and the P(J) expressions above. Then calculate the moments of inertia and bond lengths for the first two vibrational states. Finally, calculate the force constant k for HCl.
4. Note: Since the highest available resolution
available on the FT-IR is 2 cm-1, you will not be able to measure
separate bands for HCl35 and HCl37.