Rainey_Experiment 4

Rainey_Experiment 4 - Experiment 4: Rotational-Vibrational...

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Experiment 4: Rotational-Vibrational Spectroscopy of CO 2 Author: Ben Rainey Group 3 Section 1, M 1:25 PM – 4:25 PM Partner: Mark Kalata February 21, 2011 Abstract : In this experiment, vibrational-rotation spectroscopy of carbon dioxide (CO 2 ) was studied. The main objective was to experimentally determine the rotational constant for CO 2 , the average moment of inertia for CO 2 , and the internuclear distance for the carbon to oxygen bond in CO 2 . A Nicolet Magna 550 FTIR spectrometer was used to generate the IR spectrum for CO 2 . The data collected was analyzed by performing a linear least-squares fit to the spacings for the P-branch as a function of J”. The rotational constant was experimentally determined to be 0.381 cm -1 . The literature cites a rotational constant value of 0.3902 cm -1 . The average moment of inertia was experimentally determined to be 7.35*10 -39 g*cm 2 . The internuclear distance for the carbon to oxygen bond was experimentally determined to be 1.17*10 -8 cm -1 . The literature cites an internuclear distance value of 1.16*10 -8 cm -1 . The rotational-vibrational coupling constant was also calculated from the experimental data, and was determined to be 0.00406 cm -1 . The literature cites a rotational-vibrational coupling constant value of 0.00307 cm -1 . All experimentally determined values are consistent with literature values and there is no reason to believe that any experimental values are inaccurate. I. Introduction The main objective of this experiment was to use FT-IR spectroscopy to analyze the vibrational spectrum of carbon dioxide and determine key constants for CO 2 and the equilibrium internuclear distance for the carbon to oxygen bond in CO 2 . The majority of the theory behind the analysis and calculations is specific to a diatomic molecule. Carbon dioxide is a linear
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Experiment 4: Rotational-Vibrational Spectroscopy of CO 2 triatomic molecule. However, due to the symmetry of CO 2 , the majority of the theory is quite similar to that of a diatomic molecule, and can reasonably be applied to the analysis of CO 2 . The rotation of a diatomic molecule (and a symmetric linear triatomic molecule) can be simply described as a rigid rotor with two atoms, of two distinct masses, separated by a constant distance. This constant distance is equivalent to the equilibrium internuclear distance of the molecule. The quantum mechanical energy levels of the rigid rotor F(J) are given by: = + = + FJ h8π2IecJJ 1 BeJJ 1 (4-1) where h is Plank’s constant, I e is the average moment of inertia, c is the speed of light, B e is the rotational constant, and J is the rotational quantum number having integral values 0,1,2… . The moment of inertia for a symmetric linear triatomic (with structure YXY) molecule is given by: = Ie 2mYr2 (4-2) where m Y is the mass of the terminal atoms and r is the distance from the central atom (X) to either of the terminal atoms (Y). A real molecule vibrates and rotates simultaneously. However, a real molecule in not a perfect harmonic oscillator and a real molecule is not a perfect
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Rainey_Experiment 4 - Experiment 4: Rotational-Vibrational...

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