Experiment 4 INFRARED SPECTROSCOPY

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1 Experiment INFRARED SPECTROSCOPY Infrared (IR) spectroscopy is one tool for the study of molecular structure. In the case of diatomic molecules, one can extract bond lengths and bond force constants from the IR spectrum. In this experiment these molecular parameters will be determined for HC1 and DC1. Theory At the atomic level, energy is quantized. The internal energy (E) of independent molecules, as in a gas, is restricted to certain discrete values called molecular energy levels. By "internal energy" is meant (1) overall rotation of the molecule, () vibration of its atoms against one another, and () motion of the electrons about the nuclei. To a good approximation, E may be separated into rotational levels, vibrational levels, and electronic levels. The pattern of energy levels of a gas molecule and its connection with molecular parameters is given by a theory called quantum mechanics. The levels are specified by a set of quantum numbers. When a quantum of radiation is absorbed by the molecule, its set of quantum numbers changes, since the molecule is forced to occupy a higher energy state. The energy change is related to ω, the wavenumber (cm -1 ) of the absorbed radiation, by the Planck relation: E = hcω where h is Planck's constant and c is the velocity of light. Infrared spectroscopists commonly use wavenumber to represent energy in the IR spectrum. The energy level separation is roughly 00 kj/mol for electronic energy, 0 kj/mol for vibration, and 0.0 kj/mol for rotation. This turns out to mean that, in the normal IR region (00 to 000 cm -1 ), a molecule can absorb a quantum of energy by increasing its vibrational energy or its vibrational and rotational energy simultaneously. The pure electronic transition is too large and the pure rotational transition too small. Since the average thermal energy of a molecule at room temperature is on the order of kj/mol, most molecules will be, by the Boltzmann distribution law, in the lowest vibrational and electronic levels (the ground states) but will be distributed over a number of rotational levels. The transition following absorption of a quantum of radiation is limited by certain rules known as selection rules. The simplest model for a vibrating, rotating diatomic molecule is the rigid-rotor-harmonic-oscillator. The bond is assumed to be a Hooke's law spring with a 1

2 force constant, k. The vibrational levels are found by quantum mechanics to be a function of the vibrational quantum number, v, by the relation E(v) = (v+½)(h/π)(k/µ) ½, v = 0, 1,,... v = ± l (selection rule) where µ is the reduced mass, which is related to the masses of the two atoms by 1/µ = 1/M 1 + 1/M. If the selection rule is applied to absorption (v v+1), the frequency in wavenumbers of the quantum absorbed is It is customary to write this as ω o. ω = E/hc = (πc) -1 (k/µ) ½ For rotation, the molecule is assumed to be spinning about its center of mass with a fixed moment of inertia, even though the molecule is actually vibrating. The rigid-rotor model, therefore, substitutes an average moment of inertia, I = µr, where R is the average bond length. The rotational levels are given as a function of the rotational quantum number, J, as E(J) = (h /8π I)J(J+l), J = 0, 1,,... = hcbj(j+1) J = ±1 (selection rule) where B = (h/8π ci) is called the rotational constant. An additional restriction for radiative vibrational-rotational transitions in diatomics is that the molecule be polar (i.e. heteronuclear). Since the molecule is almost certainly in its vibrational ground state, the transitions in the IR will be limited to the following. V = 0 1 J J+1 or J-1 By combining the two energy level formulae the IR absorption features (in wavenumbers) can be found. The J-values of the final states are denoted by primes. E(v,J) = hcω o (v+½) + hcbj(j+l) ω = {E(v',J') - E(v,J)}/hc = ω o (v'-v) + B'J'(J'+1) - BJ(J+1)

3 Note the different values of B for initial and final states. It is necessary to assume that the rotational moment of inertia is slightly different in the two vibrational states to fit experiment. Transitions in which J = -1 belong to the P branch and J = +1 belong to the R branch, the whole forming a vibration-rotational band. The frequency formula is conveniently written for each branch in terms of the larger of the two J values. P branch (J' = J-1): ω(p) = ω o - (B'+B)J + (B'-B)J R branch (J' = J+1): ω(r) = ω o + (B'+B)JN + (B'-B)JN The first few transitions are shown below. The Q branch ( J = 0), which appears in certain cases, but not in HC1, is included for completeness. 7 6 JN = 0 1 Upper vibrational state J = 0 frequency Lower vibrational state P branch R branch Q branch The intensity distribution is an indication of the population distribution among the rotational levels at the experimental temperature. To analyze the spectrum, label each line with the larger of the two J values, as was done above, i.e., number the lines in each branch 1,,,... starting at the middle of the band.

4 Call this label "j". Now select a line from each branch with the same j label and both add and subtract their frequencies to obtain two equations. ω(r) + ω(p) = ω o + (B'-B)j ω(r) - ω(p) = (B'+B)j Plot the sum versus j and the difference versus j to determine ω o, B, and B'. The Spectrophotometer A Nicolet 0 Magna FTIR Spectrophotometer will be used. The 0 is computer controlled with peak labeling to 0.01 wavenumber. Spectral expansion may be used to improve a weak signal. There is a instrument operation tutorial available on CD and/or instruction will be provided by the TA. Experimental Procedure The IR cell is a Pyrex cylinder fitted with a teflon stopcock and having o-ring joints on the two ends. Salt windows are sealed across the ends making the cell reasonably gas tight. The windows may be NaCl or KBr. These are hydroscopic and fragile. If the windows are too cloudy they will have to be polished. Take care not to handle the optical surfaces with bare skin. Do not overtightened the window clamps during assembly. After assembly test the cell by pumping it down and leak testing. The vacuum line should be assembled as shown below, using a minimum amount of vacuum grease on the ball-and-socket joints but not on the teflon stopcocks. Pump the line and check for leaks. Bulb DO -way stopcock PCl air To pump IR cell

5 Now remove the reaction vessel and add the reactants: About 1 ml PC1 (corrosive liquid!) in the vessel and about 0. ml D O in the side arm. Reclamp the vessel on the vacuum line, reevacuate, and close the stopcock to the pump. Let a few drops of D O drip into the PCl. The reaction is D O + PC1 = DCl + D PO. The reaction is exothermic and it is possible to feel the vessel warming near where the mixing occurs. There will certainly be isotopic exchange with traces of ordinary water in the system so that the final gas mixture contains both DCl and HCl. When the pressure has risen enough to partially fill the small rubber bulb, shut off the IR cell, remove it quickly, and pump air through the line to avoid escape of noxious fumes. Place the IR cell in the holder in the sample cavity of the spectrophotometer and obtain a spectrum for the HCl and DCl mixture. Treatment of Data Plot the proper combinations (sum and differences) of peak frequencies as explained above, and determine ω o, B and B'. Then calculate bond lengths and force constants from these parameters. Because there is about a factor of two change in mass between H and D there is a very large shift in the vibration energy between HCl and DCl. But the chlorine naturally occurs as a mixture of two major isotopes. Is it therefore possible to apply the analysis above to four separate spectra (H Cl, H 7 Cl, D Cl, and D 7 Cl)? Illustrative Problem Below are the first four lines (in cm -1 ) of the P and R branches of H C1. Determine ω o, B, B', R and R'. 799, 8, 8, 86/ /906, 96, 9, 96 Following the scheme outlined above these lines should be labeled thusly:,,, 1 / / 1,,, Answers: 886 cm -1, 10.7 cm -1, 10.1 cm -1, 1.88D, and 1.0D, respectively