Application Note AN # 58 Analysis of the gas phase ... - Bruker

Application Note AN # 58Analysis of the gas phase spectrum of hydrogenchloride measured with the ALPHA FT-IR spectrometerAn experiment commonly performed in the physical chemistryteaching laboratory.IntroductionInfrared spectroscopy is a classical technique, whichdepends upon the interaction of infrared radiation withthe vibrating dipole moments of molecules. In the vaporphase, with the exception of homonuclear diatomics andnoble gases, a characteristic spectrum for each substanceis obtained. This individual spectrum is based on the uniquephysical properties of each investigated molecule. Infraredspectroscopy serves as an excellent tool for gaining thevalues of these physical properties, in particular the molecularstructure and force constants of the chemical bonds.The vapor phase spectrum of the heteronuclear diatomicmolecule hydrogen chloride (HCl) is an ideal example toillustrate the principles.When infrared radiation absorbed by a liquid or solid is measured,well-defined regions of absorption can be attributedto the vibrational transitions. The IR spectra of molecules inthe gas phase, assuming the resolution of the instrument isadequate, no longer show such smooth and structurelessabsorption bands but rather absorption regions of considerablecomplexity. The fine structure of these absorptionbands can be correlated to changes in the rotational energyof the molecule accompanied by a vibrational transition.FT-IR spectrum of hydrogen chloride in the gas phase. Insert: Thero-vibrational lines are split due to the chlorine 35 and chlorine 37natural isotopic ratio.Simple TheoryFor the description of molecular motions, one starts fromsimple physical models in which the atoms are thoughtto be points of mass kept together by weightless elasticsprings. The simplest molecule to be built this way has twomass points connected by a spring: the diatomic one. Thecorresponding vibrational equation of this molecule can be

obtained by classical mechanics; the solution is representedby a sinusoidal motion of two masses at a frequency determinedby their masses and the restoring force of the spring.During the vibration the potential and the kinetic energyof the system continually interconvert but the sum of bothenergies keeps constant as in a pendulum.V=1J=4J=3J=2J=1J=0J=4V=0J=3J=2J=1J=0Figure 1Energyv = 3v = 2v = 1E = 7/2 hνE = 5/2 hνE = 3/2 hνVibrational and rotational energy levels for a diatomic molecule suchas HCl. The spacing between V=0 and V=1 is much more thandepicted. The R branch ro-vibrational lines are shown on the left andthe P branch ro-vibrational lines are shown on the right. Only the firstfew J levels are shown.Where E v is the energy of the vibrational state with quantumnumber v, ν is the classical vibrational frequency and h isPlanck’s constant. v takes integer values starting from 0.Figure 2Figure 1: Mechanical model of the vibrating diatomic molecule. k thespring constant corresponds to the molecular binding force, m 1andm 2are the atomic mass and r 0the equilibrium distance.Figure 2: The potential energy of the two mass model can be assumedto be a parabola, that is harmonic. The further the masses aredisplaced from their equilibrium position, the higher the potentialenergy of the system.The resulting classical vibrational frequency of such an oscillatoris given by:For the description of the vibrational motion of a heteronucleardiatomic molecule, the quantum mechanical descriptionof the harmonic oscillator can be used. The quantizedenergy levels are given by:E v = hν (v+½)v = 0E = 1/2 hνBond length1 kν =2πµ being the reduced mass.m 1 .m 2µ = m 1 + m 2Under normal conditions, the vibrational transitions takeplace from the ground state (v=0) to the first excited state(v=1). This simple vibrational model predicts just one singlevibrational band for a diatomic molecule. However, we canobserve a series of closely spaced bands as for the spectrumof HCl shown in the figure. These lines are due to therotational sub- structure and a further quantum number Jfor the rotational energy is introduced. J also takes integervalues starting from 0. So each vibrational level has astack of rotational levels and transitions occur from v=0 tov=1 with J changing by +1 (so called R branch lines) and Jchanging by –1 (so called P branch lines).The figure for the HCL spectrum shows a few exampleswhere lines are assigned and the number in brackets refersto the J number of the v=0 level. It turns out that the Qbranch line with no change in J and expected at the bandcentre is missing due to the operation of selection rules.This results in a gap between R(0) and P(1), see the figure.The rotational energies are given by BJ(J+1) where B isknown as the rotational constant. Knowledge of B leads tothe molecular structure determination or in this simple case,the bond length. To a first approximation, the rotationalconstants B of the v=0 (lower) and v=1 (upper) vibrationallevels are determined as follows. For each J, take the differencesin cm -1 positions of the pairs of lines shown on theleft side of the two equations and divide by (2J+1).R(J-1) – P(J+1) = 2B lower(2J+1)R(J) – P(J) = 2B upper(2J+1)

J R(J) P(J) R(J-1)-P(J+1)R(J)-P(J) 2J+1 2B(lower) 2B (upper) (2J+1)**20 2906.251 2925.9 2865.09 62.63 60.81 3 20.877 20.27 92 2944.92 2843.62 104.35 101.3 5 20.87 20.26 253 2963.29 2821.55 146 141.74 7 20.857 20.249 494 2981.01 2798.92 187.55 182.09 9 20.839 20.232 815 2998.05 2775.74 229 222.31 11 20.818 20.21 1216 3014.42 2752.01 270.29 262.41 13 20.792 20.185 1697 3030.1 2727.76 311.44 302.34 15 20.763 20.156 2258 3045.07 2702.98 352.39 342.09 17 20.729 20.123 2899 3059.32 2677.71 393.13 381.61 19 20.691 20.085 3612B estimateHCl-35 lower20.920.8520.820.7520.720.6520.620.550 100 200 300 400 500 600(2J+1)**210 3072.85 2651.94 433.6 420.91 21 20.648 20.043 44111 3085.66 2625.72 473.86 459.94 23 20.603 19.997 529Slope = -0.000530Intercept = 20.882212 2598.99J R(J) P(J) R(J-1)-P(J+1)0 2904.08R(J)-P(J) 2J+1 2B(lower) 2B (upper) (2J+1)**21 2923.71 2862.99 62.52 60.72 3 20.84 20.24 92 2942.7 2841.56 104.17 101.14 5 20.834 20.228 253 2961.05 2819.54 145.75 141.51 7 20.821 20.216 494 2978.74 2796.95 187.24 181.79 9 20.804 20.199 815 2995.76 2773.81 228.62 221.95 11 20.784 20.177 1216 3012.11 2750.12 269.84 261.99 13 20.757 20.153 1692B estimateHCl-35 upper20.320.2520.220.1520.120.052019.950 100 200 300 400 500 600(2J+1)**27 3027.76 2725.92 310.9 301.84 15 20.727 20.123 2258 3042.72 2701.21 351.76 341.51 17 20.692 20.089 2899 3056.92 2676 392.44 380.92 19 20.655 20.048 361Slope = -0.000524Intercept = 20.274010 3070.51 2650.28 432.79 420.23 21 20.609 20.011 44111 2624.13 23 529B = Rotational constant; Delta J = +1 is the R branch, Delta J = -1 isthe P branchThis can be done for both chlorine isotopes (Cl-35 and Cl-37), see next two tables.Extended theoryInspection of the B constants determined in this simple wayshows a distinct curvature with J number. This arises fromthe neglect of the centrifugal distortion of the HCl molecule,which increases with J rotational quantum number. Themolecule stretches at higher rotational energy causing itsmoment of inertia I to increase. B is inversely related to themoment of inertia, so B decreases with J.Also B has a slightly lower value in the upper (v=1) vibrationalstate.Note : I = µr 2 where µ= reduced mass and r = internucleardistanceµ = M HM Cl/(M H+ M CL) where M = atomic massesMore detailed theory leads to the revised equations:R(J-1) – P(J+1) = (2B lower– 3D lower)(2J+1) – D lower(2J+1) 3R(J) – P(J) = (2B upper– 3D upper)(2J+1) – D upper(2J+1) 3Where D = centrifugal distortion constant, which has asmall value2B estimateSlope = -0.000536Intercept = 20.84722B estimateHCl-37 lower20.920.8520.820.7520.720.6520.620.550 100 200 300 400 500(2J+1)**2HCl-37 upper20.320.2520.220.1520.120.052019.950 100 200 300 400 500(2J+1)**2Slope = -0.000530Intercept = 20.2422A plot of the previously determined 2B values versus (2J+1) 2 willresult in a straight line. The slope will be –D and the intercept (2B-3D).Calculation of the internuclear distanceExtrapolate the rotational constants to the equilibriumstate when the molecule would reside hypothetically at thebottom of the potential well.

HCL-35 Literature HCL-37B lower 10.442 10.440254 10.424B upper 10.138 10.136228 10.122D lower 0.00053 0.00052828 0.000536D upper 0.000524 0.00052157 0.00053Values in cm -1Literature values for HCl-35 taken from very high resolution spectroscopy –Journal of Molecular Spectroscopy, vol. 17, 1965, p. 122.B lower= B equilibrium– 0.5 αB upper= B equilibrium– 1.5 αHCL-35HCL-37B equilibrium 10.594 10.576alpha 0.304 0.302Where α = vibration – rotation interaction constant (α =alpha in the table)The moment of inertia I is given by:I = 16.8575/B where B is in units of cm -1 and I has units ofamu Angstroms 2 (1 Angstrom = 10 -8 cm). The number inthis equation derives from the quantity h/8π 2 c where c =velocity of light.Assuming an harmonic oscillator, the band origins forHCl-35 and HCl-37 are related by:V 0-1(HCl-37) = V 0-1(HCl-35) * √ (reduced mass HCl-35/reduced mass HCl-37)Using values of the reduced mass for HCl-35 and HCl-37from the table, the prediction for HCl-37 is 2883.78 cm -1compared with the experimental value of 2883.84 cm -1 .ConclusionsHCL-35HCL-37eqn 1 2885.97 2883.84eqn 2 2885.97 2883.84Values in cm -1 , literature value for HCl-35 is 2885.9775 cm -1 , J. Mol.Spectroscopy vol. 17, 1965, p.122The ALPHA is a compact and affordable FT-IR spectrometerthat makes it ideal for teaching applications as well as QA/QC. With the high resolution option for the ALPHA, excellentspectra of HCl vapor measured in a gas cell can beobtained. Analysis of the HCl spectrum, making full use ofthe OPUS peak pick software installed on the ALPHA PC orLaptop, yields molecular constants entirely consistent withvalues published in the spectroscopic research literature.These excellent experimental results are possible becauseof the good line shape, signal to noise and precise frequencyregistration of the ALPHA FT-IR spectrometer line.The literature value for the HCl equilibrium bond length measuredby microwave spectroscopy is 1.27455 Angstroms(Phys. Rev., vol 136, A1229, (1964)). Theoretically thesebond length values for HCl-35 and HCl-37 should be theHCL-35HCL-37B equilibrium 10.594 10.576I (amu Angstroms**2) 1.5912 1.594Reduced mass (amu) 0.979569 0.981054Internuclear distance(Angstroms)1.2745 1.2747same. This experiment with the ALPHA FT-IR spectrometershows excellent agreement with these facts.Derivation of the vibrational band origin V 0-1V 0-1= R(0) – (2B upper– 4D upper) equation 1V 0-1= P(1) + (2B lower– 4D lower) equation 2The effect of D can be neglected.Prediction of the vibrational isotopic shiftwww.bruker.com/optics Bruker Optics Inc.Bruker Optik GmbHBruker Hong Kong Ltd.Billerica, MA · USAPhone +1 (978) 439-9899Fax +1 (978) 663-9177info@brukeroptics.comEttlingen · GermanyPhone +49 (7243) 504-2000Fax +49 (7243) 504-2050info@brukeroptics.deHong KongPhone +852 2796-6100Fax +852 2796-6109hk@brukeroptics.com.hkBruker Optics is continually improving its products and reserves the right to change specifications without notice.© 2011 Bruker Optics BOPT-4000353-01