hcl lab

HCl Rovibrational Spectral Analysis Lab

In this lab you will measure the rovibrational infrared spectrum of HCl and use spectral information to determine rotational constants, moments of inertias and bond lengths for each of the first two vibrational states of HCl.

1. Measure the infrared spectrum of HCl in the region of 2600-3100 cm^-1. This can be accomplished by:

Collecting a background spectrum with the gas cell in place.
Placing a drop of concentrated HCl in the cell, letting it evaporate for a few minutes before collecting the spectrum.
Examining the 2600-3100 cm^-1region. HCl infrared absorptions occur there, while water bands are found in other parts of the spectrum.

2. R and P branch transitions are due to energy differences between rovibrational states.

The energy of a particular state (S(v,J)) is due to vibrational and rotational energy contributions:

S(v,J) = (v+1/2) n + B_v J (J+1)

where v and J are vibrational and rotational quantum numbers, B_vis 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:

R(J) = n + (B₁+ B₀) (J+1) + (B₁-B₀) (J+1)² P(J) = n - (B₁+ B₀) J + (B₁-B₀) J²

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.