Fourier-transform infrared spectroscopy has been very useful in helping scientists examining molecules of HCl and DCl. Because deuterium has a greater mass than hydrogen, the IR band shown for HCl is at a higher wavelength than DCl. The absorption of light in DCl was at lower frequency 1700-2200 cm-1 because D is bigger and heavier. That’s why the vibrations on the IR were shorter for DCl compared to HCl. The stretching of HCl on the IR region was around 2700-3100 cm-1. The constant vibration frequency is added to determine the bond length of isotope between HCl and DCl. From the ab-initio calculations it was showed that r = 1.29344 Ǻ for HCl.
The purpose of this experiment is to observe the absorption of light from the stretching of the diatomic linear molecules HCl and DCl. By using the Fourier-transform infrared, or FTIR, technique, we will be able to study and obtain information about the vibrations of the H–Cl and D–Cl bonds. The first part of the experiment consists of preliminary calculations with data obtained from Gaussview. Using Gaussview, draw an HCl molecule and obtain the length of the H–Cl bond. This will be used for r when finding the moment of inertia. It is important to note that the H–Cl and D–Cl bond are the same length even though the deuterium atom weighs twice as much as the hydrogen atom. Though the bonds lengths are equivalent, the spectrum shows that the HCl can obtain a lower transmittance percentage and that DCl vibrations take place at a lower frequency. Quantum mechanics gives us the following formula for a harmonic oscillator:
where [pic] is the vibrational frequency, h is Planck’s constant, and n is the vibrational quantum number. The rigid rotor model also applies to diatomic molecules. It can be solved in the equation below:
where J is the rotational quantum number.
Below is a simple picture of a chlorine atom bonded to a hydrogen atom. This is a pictorial example of the type of bond being measured in this experiment.
The method was almost exactly like the handout. The FTIR spectrometer is explained and discussed in detail in the book on page 693 of Experimental in Physical Chemistry.  In this lab, there are 3 parts:
a) Theoretical analysis of HCl using ab-initio methods obtained with GAUSSIAN b) FTIR technique and instrument operation
c) Collection of IR spectra from HCl and DCl gas.
Below are some of the equations used to calculate the reduced mass, frequency, and moment of inertia.
• I = μr2
• Be = h / (8πIc)
where μ is the reduced mass, I is the moment of inertia, and Be is the equilibrium rotational constant.
Below are tables and graphs of our recorded data. The large numbers in the tables are the frequency of those peaks. They are an expression of wave numbers (1/cm). The graphs are the frequencies, ν, as a function of m. We took seven degrees of m in both directions, for a total of fifteen m’s when counting peak m = 0. The negative m peaks, or peaks to the left of the center of the set of peaks, are a part of the “P” branch and the peaks m0 to m7 are a part of the “R” branch, which is on right hand half of the peaks. It is important to note that the spacing is greater for the R branch than the J branch for both graphs. For the P branches, ΔJ= –1. For the R branches, ΔJ=+1.