Molecular Spectroscopy of Acetylene

Molecular Spectroscopy of
Acetylene
Summer 2014
Chris Kruppe
[email protected]
5424 SES
Outline
• What is FTIR and why should we use it?
• Experimental purpose
• Theory
• Notes on performing the experiment
What is FTIR?
• Fourier Transform Infrared
Spectrometry
• A math function to transform
from time to frequency domain
• Near-IR: 14000-4000 cm-1
• Mid-IR: 4000-400 cm-1
• Far-IR: 400-10 cm-1
Near-IR: overtone or harmonic vibrations
Mid-IR: fundamental vibrations and
associated rotational-vibrational structure
Far-IR: rotational
Why FTIR?
• Fast analysis to determine structure and concentration of a chemical
in a sample
• Accurate and Precise
• Easy to use, relatively low maintenance
• Used for quality control, dynamic measurement, monitoring
applications
Instrumental Setup
• Source: Blackbody emitter- SiC (Silicon
Carbide Glowbar)
• Michaelson Interferometer
• Sample
• Detector
http://faculty.sdmiramar.edu/fgarces/LabMatters/Instruments/FTIR/FTIR.htm
Instrument Output
• Instrument records interferogram
• Performs fourier transform (FT), produces the single beam spectra:

 
 S ( x)  cos4  x    x

• Take sample/background, what is left gives absorbance plot
http://www.gascell.com/htmls/primer.htm
What’s in a spectrum?
Infrared radiation induces vibrations and
rotations that have characteristic frequencies
for specific molecules.
Within each vibrational level, there are a
number of allowed rotational levels.
(rotational levels are smaller than vibration)
http://hyperphysics.phy-astr.gsu.edu/hbase/molecule/vibrot2.html
Born Oppenheimer Approximation
• Each frequency that appears corresponds to a specific transition
(rotation, stretch, wag, etc.)
• Vibrations and rotations are very different phenomena! (time scale
for vibrations: 10-10 s / rotations 10-13 s)
• If a molecule is rotating, this can also impact its vibration mode (that’s
physics!). Thus, we must separate to get the specific mode.
• We can do this because the time scales vary drastically and…
• Mass of nuclei are much greater than the mass of an electron
• The two models we use are rigid rotor and harmonic oscillator
http://www.nature.com/nature/journal/v343/n6260/abs/343737a0.html
Harmonic Oscillator
• Describes vibrational energy
changes from the change in
distance between two atoms
(diatomic).
• G() = (u + ½) · e
• u = 0,1,2,3
• e= oscillator vibrational
wavenumber
0 to 1  fundamental
0 to 2  overtone
http://hyperphysics.phy-astr.gsu.edu/hbase/quantum/imgqua/qhar.gif
Vibrations
• For vibrations, the characteristic
frequencies are normal modes.
• For a linear molecule:
• Normal modes = 3N-5
• Acetylene:
• 7 normal modes
• 5 different IR bands
• Vibrations – single degenerate (3
modes)
• Bending – double degenerate (2 x 2
modes)
http://www1.lsbu.ac.uk/water/vibrat.html
Frequencies for C2H2/C2D2
• Study 4 + 5 band
• Combination of
bending modes
• IR active due to
symmetry of
molecule
http://upload.wikimedia.org/wikipedia/commons/8/8b/Acetylene-CRC-IR-3D-balls.png
Rigid Rotor
• A model where the nuclei are set
at a fixed distance to isolate the
rotational energy of a molecule
• Rotational selection rule
F(J)  B˜ J(J + 1)
• ΔJ = + 1
• B = rotational constant
 =
ℎ
8 2 
Moment of Inertia
• Resistance to change in rotational movement
Ie = 2 mRH2 + 2 mRC2
Ie = 1/2 mCrCC2 + 2 mH(rCH + 1/2rCC)2
H.O. & R.R. Corrections
• When adding the two models
together, the molecular vibrations
become anharmonic when the
distance between two atoms
becomes large
G ( v)  ( v +1 / 2 )~e  ~
xe~e ( v +1 / 2 ) 2
• Rotational motion is not perfect
and does cause centrifugal
distortion
• Distortion is important at much
higher values of J.
• We will neglect this and
anharmonicity in our final equation.
http://www.scielo.br/scielo.php?script=sci_arttext&pid=S0103-50532003000200006
H.O. + R.R. = Total Energy
• Rotations and vibrations are ‘coupled’ (happening at the same time
and impacting each other)
~
~
T ( v, J )  G ( v) + F ( J )  ( v + / 2 ) e + Bv J ( J + 1)
1
• ae = ro-vibrational constant
• Bu = Be - ae(u + ½)
Maxwell Boltzmann Distribution
• Distribution of the population
of molecules in each state
• Concentration of molecules in
each energy level correlate to
band intensity
• Experimentally the pressure
determines peak intensity
Nuclear Spin Statistics & the Pauli Principle
• (2I+1)(I+1) – symmetric wave functions
• (2I+1)I - antisymmetric wave functions
•
•
•
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•
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For yns , symmetric (+)
antisymmetric (-)
I = ½ (hydrogen)
3 symmetric, 1 antisymmetric
I = 1 (deuterium)
6 symmetric, 3 antisymmetric
C2H2
total elec vib rot ns
J=Even + + + J=Odd + + - +
C2D2
total elec vib rot ns
J=Even +
+ + + +
J=Odd +
+ + - -
Theoretical IR spectra C2H2
• Intensity ratio of odd:even J
values
• 3:1 for C2H2
• 1:2 for C2D2
• Figure shows spectra with and
without spin statistics
V0 = 1041.49 cm-1
R(0) ~1043 cm-1
P(1) ~ 1039 cm-1
Actual Spectra
Contamination from C2H2 can affect NS states
Contamination of H2O can affect NS states
Performing the Experiment
• Follow all directions precisely
• Do NOT use excess CaC2 !!!
• Make sure no water is in flask
before adding CaC2
• 50-100/150-200 Torr is needed for
C2H2/ C2D2 (gas)
• Pressure is correlated to peak
height or concentration of gas in
cell
CaC2 + 2 H2O --> C2H2 + Ca(OH)2
N2 Purge High Pressure IR Chamber
Using the instrument
• Why wait 5-10 minutes before taking
a scan?
.002
• Follow instructions in laboratory
handout
• Make sure you are printing to right
printer
Initial Scan after purge
changed from Dry Air to N2
44 minutes after purge initiated
72 minutes after purge initiated
115 minutes after purge initiated
141 minutes after purge initiated
1000
1500
2000
2500
wavenumbers, cm-1
3000
3500
4000
Short Lab Report and Notebook Guidelines
• Abstract (1/2 – 3/4 Page)
• Intro (~300 words)
• Short Experimental – Give amount of CaC2
used and pressure values
• Don’t copy from lab manual
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Results
Discussion
Be concise!
Plots for f and g functions
Calculations including uncertainties
Questions from lab manual
Any references
Copies of Lab Notebook pages
• Notebook
• Prelab (Short description of FTIR, pertinent
equations, experimental procedure)
• Inlab (Initial pressure of manifold, CaC2 used,
exact pressure of IR cell)
• Postlab (Plots of f and g functions, sample
calculations, small table of results, short
conclusion) - Do calcs in notebook first.