AP-101 INFRARED SPECTROSCOPIC ANALYSIS OF HCL AND DCL

Introduction High resolution infrared spectroscopy is a valuable tool for the elucidation of physical properties ofmolecules. This experiment examines the vibrational and rotational spectra of HCl and DCl gas molecules from which several fundamental properties of these systems are determined.We may consider the total energy of the diatomic molecules HCl and DCl to be partitioned amongthe vibrational, rotational, translational, and electronic energies. Our discussion is confined to just one vibrational and a number of rotational transitions which are manifested in the mid infrared region of the spectrum. We begin with simplified models for these processes to show the physical basis for the interaction with infrared energy, and then elaborate on the models.For the vibration process to be infrared active, the molecule must undergo a change in dipolemoment. The selective rule for the rotation requires that the molecule possess a permanent dipole moment. This oscillating dipole may then interact with the oscillating electric field of the radiation. The selection rules are based upon solutions to the Schrodinger equations for the various process which we will see below. Discussion Assume the vibrating molecule is a simple harmonic oscillator. The harmonic oscillator modelpictures the two atoms connected by a perfect spring. The equilibrium distance for the spring is of lowest potential energy, and as the spring is either stretched or compressed the potential energy rises in a parabolic fashion. The potential energy for the harmonic oscillator is: PE = 1/2kr
2 Where:PE = potential energyk = the force constant for the bond r = the internuclear separationThis expression depicts the potential energy well as symmetric and continuous. Substitution of thepotential energy into the Schrodinger equation affords the following relation: d
2 ψ dr
2 + 8
Ï€ 2 µ /h
2 (E- 1/2k
χ x
2 ) = 0 and the solution is: E(v) = h
ν (v + 1/2) (1)where v = quantum number for the vibration having values of 0, 1, 2, ....
1