Molecular Vibration and Bond Length

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Vibration- Rotation Spectroscopy of HCl and DCl
Purpose: To determine the fundamental vibration frequency and bond length for H35Cl, H37Cl,
D35Cl, and D37Cl and to compare the isotope effects to theoretically predicted values.
Introduction
Vibration spectroscopy is one of the most important tools for the accurate determination of molecular structure. Vibration spectroscopy also plays an important role in environmental chemistry. For example, the albedo of the earth’s atmosphere is controlled by the absorption of infra-red light by green house gasses, which include CO2, H2O, and CH4. For normal modes that have a changing dipole moment, the vibrational spectrum of a molecule is observable using infrared absorption. Such modes are said to be IR active. Raman spectroscopy is used to observe normal modes that are not IR active. The fundamental vibration frequency of a normal mode is dependent on the isotopes of the atoms that are involved. Therefore, vibration spectroscopy is a very useful way to study isotope effects.
In this exercise we will determine the fundamental vibration frequency and bond length for
H35Cl, H37Cl, D35Cl, and D37Cl. The shift in fundamental vibration frequency and rotational constant with isotopic substitution will also be predicted and compared to the experimental values. Because of the natural abundance of 35Cl and 37Cl, the HCl spectrum will contain peaks for both isotopes H35Cl and H37Cl. Similarly, the DCl spectrum will contain peaks for both D35Cl and D37Cl. The isotopic abundance of 37Cl is 24.22%, so the peaks for the 37Cl containing molecules are one-third the height of the 35Cl containing molecules.
Theory
The vibrational energy of a diatomic molecule using the harmonic oscillator approximation is:
Eυ = hνo ( υ + 1/2)

(1)

where νo is the fundamental vibration frequency in s-1 and υ is the quantum number for the vibration, Figure 1. The rotational energy for a diatomic molecule using the rigid-rotor approximation is:
~

EJ = Bo hc



References: 1. D. P. Shoemaker, C. W. Garland, J. W. Nibler, Experiments in Physical Chemistry, 5th. ed., McGraw Hill, New York, N. Y., 1989. Experiment 38. 2. K.P. Huber and G. Herzberg, Molecular Spectra and Molecular Structure, v. 4, Constants of diatomic molecules, Van Nostrand, Toronto, Canada, 1945.

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