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) cos4 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 • • • • • • 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 • • • • • • • • 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.
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