Experiment 4, RotationalVibrational Spectroscopy of CO
2
Author:
Daniel Wurst
Group 4
Section 4, T 11:00 AM – 2:00 PM
Partners: Scott Kwarsick & Michael Minor
2/8/2011
Abstract:
In this experiment, the principle objective was to use the FTIR spectroscopy to determine experimentally
the bond length of the Carbon Oxygen bond in a CO
2
molecule. This was done by measuring the infrared
released by the bonds vibration and rotation. The data was then used in equations that were derived (as
shown in the lab report) or by a least linear fit of the data that was used to solve for the main constants.
One of these constants , the rotational constant, was found to be between 0.387 cm
1
and 0.438 cm
1
with
the former being from equations and the later from least linear squares model. These values were then
used to find the moment of inertia , ,and provided, once again, a range from 7.23 x 10
46
kg m
2
to 1.33 x
10
45
kg m
2
. From there the bond length was found to be 1.16653 x 10
10
m for the equation method and
1.58375 x 10
10
m for the least linear squares fit. These values when compared to the literary value of 1.16
x 10
10
m were determined to be relatively close and therefore trusted as accurate values for this
experiment’s error.
Introduction:
Wurst
Page 1
2/8/11
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Experiment 4: RotationalVibrational Spectroscopy of CO
2
The purpose of this experiment was to use spectroscopy to determine key constants and intermolecular
bond radii. This was done by analyzing the rotations and vibrations of a diatomic (and symmetric linear
triatomic) molecule. In order to take both of these properties into consideration, each one needed to be
able to be calculated differently using different equations. The vibration of such a molecule can be
described best in terms of a quantummechanical harmonic oscillator. The quantized energy levels are
given by the equation:
(41)
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 Spring '11
 James
 Chemistry, Atom, RotationalVibrational Spectroscopy, Daniel Wurst

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