Infrared Vibration-Rotation Spectroscopy of HCl and DCl

Transcription

1 Chmistry 363 JMS 1/05 Spring 010 DLC 1/10 Infrard Vibration-Rotation Spctroscopy of HCl and DCl Exprimnt Objctiv: to obtain th quilibrium bond lngth (r ) and vibration-rotation spctroscopic constants from th FTIR spctra of th diatomic molculs HCl and DCl in th gas phas. SECTION 1: THEORETICAL BACKGROUND Rfrncs A basic introduction to th quantum mchanics and spctroscopy of th vibration-rotation stats of diatomic molculs can b found in any standard physical chmistry txt. Som xampls includ: Physical Chmistry, nd d., T. Engl and P. Rid, Parson, Chaptr 19; Physical Chmistry, 1st d., D. W. Ball, Brooks/Col, Pacific Grov, CA, 003, Sction Physical Chmistry, 8 th d., P. W. Atkins and J. d Paula, W. H. Frman, NY, 006, Chaptr 13. If you ar not familiar with th vibrations and rotations of diatomic molculs, you should consult on of th abov rfrncs. Your instructor/ta will also provid a mini-lctur bfor you analyz th data. Vibration-Rotation Spctroscopy - Harmonic Oscillator, Rigid Rotor Approximation Both th vibrational and rotational motions of a molcul ar quantizd. Vibrational motion dscribs th intrnal motion of an atom within a molcul rlativ to othr atoms. In a diatomic molcul, this motion occurs along th bond and is calld a strtching. This motion dpnds largly on th strngth of th bond, which is proportional to th potntial nrgy holding th atoms togthr. Th vibrational motion of a diatomic molcul may b tratd idally as if th potntial nrgy wr harmonic. This is calld th harmonic oscillator approximation. Th quantum mchanical solution of this harmonic vibrational motion introducs a vibrational quantum numbr v that corrlats to th vibrational nrgy contnt (E v ) of th molcul in such a particular vibrational stat: E v = hν (v + ½) (1) In quation (1), h is Planck s constant and ν is th classical harmonic frquncy. Rotational motion dscribs th position of a molcul around an arbitrary st of spatial coordinat axs. In a diatomic molcul, a simpl approximation considrs th molcul to b rigid at crtain quilibrium position of th atoms, such that vibrational motion is nglctd. Such approximation is dnotd as th rigid rotor. Quantum mchanical tratmnt of th rigid rotor approximation introducs a rotational quantum numbr J that corrlats with th rotational nrgy contnt (E J ) of th molcul in such a particular rotational stat: E J = hcb J(J+1) () In quation (), c is th spd of light and B is th rotational constant. Th xprssion for th quantizd combination of vibration-rotation nrgy lvls of a molcul, E v,j is: or in wavnumbrs, E J = hν (v + 1/ ) + hcb J ( J 1) (3) v, +

2 Ev, J ω v, J = = ω (v + 1/ ) + B J ( J + 1) (4) hc Rcall that ν is th harmonic vibrational frquncy, or in wavnumbrs, ω =ν / c, v is th vibrational quantum numbr and J is th rotational quantum numbr. B is th rotational constant, which is givn by h = (5) 8π ci B whr I is th momnt of inrtia, I = µr, µ is th rducd mass, and r is th quilibrium bond lngth. For a diatomic molcul with formula AB, th rducd mass µ is dfind as m m A B µ = (6) ma + mb whr m A and m B ar th isotopic masss of atoms A and B. Th probability of a chang in a particular stat of a molcul is dictatd by quantum mchanical constraints known as slction ruls. For instanc, th slction rul for diatomic molcul rotational transitions allows stat changs in which J = ±1. For vibrations in th harmonic oscillator approximation, th slction rul is v = ±1, though this slction rul is liftd whn an anharmonic systm is considrd (as in a ral diatomic molcul), and so th so calld ovrton transitions, such as v = 0, ar allowd. Th v = 0 v = 1 transition is calld th fundamntal, and is th most intns (i. most probabl) vibrational transition. Th light absorption spctrum of a molcul rflcts th changs in th stat of a molcul as it absorbs nrgy as allowd by th transition ruls for a particular typ of motion. Lt us considr a diatomic molcul that absorbs light from th infrard rgion of th lctromagntic spctrum that corrsponds to th harmonic wavnumbr of motion (ω ). Most molculs at room tmpratur will b in th ground vibrational stat (v = 0) and will nd up in th v = 1. Th molculs ar originally distributd into diffrnt rotational stats (with J rotational numbr) according to th tmpratur of th sampl. Thus, th absorption of IR light will rflct vibration-rotation transitions from (v" = 0, J") (v' = 1, J'). Th st of spctral bands in which J = +1 is calld an R-branch. In wavnumbrs, ach band of th R branch corrsponds to: R( J") = ω + B ( J" + 1) (7) Th st of bands originating associatd to vibration-rotation transitions from (v" = 0, J") (v' = 1, J') in which J = 1 is calld a P-branch. In wavnumbrs, ach band of th P branch corrsponds to: P( J") = ω B J" (8) As mntiond abov, for a typical diatomic molcul, vibrational-rotational transitions fall in th infrard rgion of th spctrum. In polyatomic molculs th transition corrsponding to v" = 0, J" v' = 1, J' with J = 0 is allowd and is calld th Q branch. Howvr, bcaus of th slction ruls for diatomic molculs, th Q-branch transition is not allowd and thus no IR band is prsnt. Th position of th missing Q-branch transition is calld th band origin, dnotd by σ v v. In th harmonic oscillator, rigid

3 rotor approximation, th band origin in wavnumbrs for th fundamntal vibrational transition is qual to ω. Corrctions to th Harmonic Oscillator and Rigid Rotor Modls Th harmonic oscillator and rigid rotor viws of diatomic molcular vibrations and rotations is not an accurat nough approximation to adquatly dscrib all of th faturs of a vibration-rotation spctrum. W may includ additional trms in th nrgy xprssions (Eqs. 1 and ) to account for various ffcts calld vibrational anharmonicity, cntrifugal distortion, and vibration-rotation coupling. In wavnumbrs, with ths corrctions includd, Eq. (4) bcoms: v, J J + ω = ω (v + 1/ ) ω x (v + 1/ ) + B J ( J + 1) D J ( J + 1) α (v + 1/ ) J ( J 1) (9) whr x is th anharmonicity constant, D J is th cntrifugal distortion constant, and α is th vibrationrotation coupling constant. Th othr quantitis ar th sam as dfind for Eq. (4). Each band of th R branch for th fundamntal v" = 0 v' = 1 vibrational transition (modifid from Eq. (7)) is givn in wavnumbrs by: B0 )( J" + 1) + ( B1 B0 )( J" + 1) 4DJ ( " 1) R( J") = ω x + ( B J + (10) ω B 0 and B 1 ar rotational constants for th v = 0 and v = 1 vibrational lvls, rspctivly. Th gnral constant B v for vibrational stat v is dfind as: B α (v 1/ ) (11) v = B + Th P branch for th fundamntal v" = 0 v' = 1 vibrational transition (modifid from Eq. (8)) is givn in wavnumbrs by: 3 x ( B1 + B0 ) J" + ( B1 B0 ) J" + 4DJ " P( J") = ω ω J (1) Th band origin for th fundamntal transition, σ 0,1, in this cas is givn by: σ = ω x (13) 0,1 ω In gnral, th band origin for any v" v' vibrational band is givn in gnral by th quation: v ",v' = + σ ω (v' v") ω x [(v' + 1/ ) (v" 1/ ) ] (14) Exampls of typical vibration-rotation spctra for htronuclar diatomic molculs can b found in th rfrncs givn on pag 1. Ths spctra ar similar to th spctra that you will obtain in this xprimnt. Sction 4, ntitld "A Guid to th Calculations", will show you how to us th quations prsntd in this sction to obtain th quilibrium bond lngth, r, and th harmonic frquncy (ω ) for ach of th diatomic molculs you study. In addition, for on of th molculs, you will carry out a complt analysis of th spctrum to obtain th spctroscopic paramtrs ω, x, B, D J, and α. For th othr molcul, you will carry out a simplifid analysis to obtain only th most important spctroscopic paramtrs, ω and B.

4 SECTION : EXPERIMENTAL PROCEDURE Cll Evacuation 1. Th instructor will assist you in stting up th vacuum lin to purg and fill th IR cll. ALWAYS PROCEED SLOWLY AND CAREFULLY WHEN USING WITH THE VACUUM LINE.. Onc th vacuum manifold is vacuatd, attach th IR cll to th lin. B carful handling th cll; it is fragil and xpnsiv. Do not touch th cll windows, which ar mad of sodium chlorid. Evacuat th cll by slowly opning th conncting stopcock on th manifold and thn th stopcock on th cll. 3. Clos th stopcock on th cll and th conncting stopcock on th manifold. Carfully rmov th IR cll from th vacuum lin. Background Collction 1. Procd to th FTIR spctromtr in room SLB 0 and plac th vacuatd IR cll in th sampl chambr.. Rcord th background spctrum of th mpty cll. Rfr to sction 6 ntitld "Instructions for Oprating th Prkin Elmr Spctrum On FTIR Spctromtr". Filling th Cll 1. Rturn to th vacuum manifold and attach th IR cll to th lin. Evacuat th lin btwn th cll and th manifold by slowly opning th conncting stopcock. Thn, opn th stopcock on th IR cll.. Attach th bulb containing th diatomic gas to th vacuum lin. Evacuat th conncting lin slowly by opning th stopcock. 3. Clos th stopcock to th vacuum pump. Carfully opn th stopcock on th gas bulb until th prssur rads around 10 torr abov th initial prssur. Clos th stopcock to th gas bulb whn th dsird prssur is rachd. 4. Clos th stopcock on th cll. Thn, opn th stopcock to th pump slowly to vacuat th manifold. 5. Clos th conncting stopcock to th gas bulb and rmov it from th lin. Thn, clos th conncting stopcock to th IR cll and carfully rmov it from th lin. Spctral Collction 1. Rturn to th FTIR spctromtr and plac th IR cll in th sampl chambr.. Rcord th infrard spctrum of th diatomic gas. Mak sur that you labl th paks in th spctrum in wavnumbrs. Rfr to sction 6 ntitld "Instructions for Oprating th Prkin Elmr FTIR Spctromtr" for mor information. 3. Rmov th IR cll from th spctromtr, procd to th vacuum manifold, and attach th IR cll to th manifold. 4. Evacuat th cll by slowly opning th conncting stopcock on th manifold and thn th stopcock on th cll. 5. Whn th spctrum has bn rcordd and th IR cll is vacuatd, rmov it from th vacuum lin and opn th stopcock on th cll to th atmosphr. Plac th cll in a dssicator for storag.

5 SECTION 3: A GUIDE TO THE CALCULATIONS You should hav obtaind th IR spctra of HCl and DCl. Your instructor/ta will dsignat on of ths molculs as your primary molcul and on as your scondary molcul. For your scondary molcul, you will carry out a simplifid analysis to obtain th th spctroscopic paramtrs ω and B and th quilibrium bond lngth, r. For your primary molcul, you will carry out a complt spctral analysis in ordr to dtrmin th spctroscopic paramtrs ω, x, B, D J, and α, and th quilibrium bond lngth, r. SECTION 3A: Analysis of th Infrard Spctrum of Your Scondary Molcul 1. Th first stp in th analysis is to assign rotational quantum numbrs to th obsrvd absorption lins in th R and P branchs. This can b asily don by comparing th obsrvd spctrum to th xampls found in th rfrncs givn in Sction 1. Th R branch lins, which ar on th high frquncy and wavnumbr sid of th cntral gap, start with J" = 0. Th P branch lins, which ar on th low frquncy and wavnumbr sid of th gap, start with J" = 1.. To dtrmin an approximat valu for th spctroscopic constant, ω you can us th cntral band gap in th spctrum. Within th harmonic oscillator, rigid rotor approximation, th band gap, ω is th midpoint btwn R(0) and P(1). 3. Th spacing btwn lins in th spctrum can b usd to dtrmin an stimat for to rotational constant, B. In th harmonic oscillator, rigid rotor approximation, th spacing btwn th two cntral R and P branch lins is qual to 4 B. Us this band gap distanc to dtrmin B. 4. From your calculatd valu of B and known isotopic masss, dtrmin an xprimntal valu for th quilibrium bond lngth r for your scondary diatomic molcul. SECTION 3B: Analysis of th Infrard Spctrum of Your Primary Molcul 1. Th first stp in th analysis of th spctrum of your primary molcul is to assign rotational quantum numbrs to th obsrvd absorption lins in th R and P branchs as you did in th prvious sction for your primary molcul.. To obtain valus of th spctroscopic constants and th quilibrium bond lngth for your diatomic molcul, you will us all your xprimntal valus for th R and P branch lins in a last squars analysis, along with additional data givn blow for th ovrton bands. This analysis may b carrid out on th Macintoshs or PCs in th dpartmntal computr lab (JH 16), or on any othr computr with a last squars program, as long as th program provids rrors in th calculatd slop and intrcpt. Th suggstd softwar packag for prforming last squars analysis is Microsoft Excl. To bgin, thr diffrnt plots should b prpard: A) ½[R(J ) + P(J +1)] vs. (J +1) B) [ R( J") P( J")] vs.( J" + J" + 1) ( J" + 1/ ) [ R( J" 1) P( J" + 1)] " C) vs.( J" + J + 1) ( J" + 1/ ) You should us Equations (10) and (1) to valuat xprssions A, B, and C abov in trms of th spctroscopic constants. Dtrmin what th slops and intrcpts of ths plots should b. (You

6 must complt this part of th analysis bfor going on to stp 3.). Carry out th drivations in your notbook; a copy of ths must b includd in your lab rport. Us your xprimntal valus and th linar last squars program to obtain thr linar last squars slops and intrcpts for th graphs abov. If any points ar clarly off of th lin in ths analyss, mak sur that you throw thm out whn dtrmining th slops and intrcpts (if you throw out points, includ in your rport a discussion of possibl rasons for ths dviations). Mak sur that you gt hard copis of th plots to includ in your lab rport. 3. From th analysis in stp, you should b abl to dtrmin th adjustd rotational constants, B 1 and B 0. Du to th rsolution of th spctromtr, thr may b significant scattr in plots B and C, which may mak it difficult to dtrmin rliabl valus for B 1 and B 0. If this is th cas, s th instructor bfor procding. Us th dfinition of th adjustd rotational constants, Eq. (11), along with th information in Tabl 1a to dtrmin valus of B and α if your primary molcul is HCl. If your primary molcul is DCl, us th information in Tabl 1b to dtrmin valus of B and α. You should prform anothr linar last squars analysis in this stp. Tabl 1a. Rotational constants for H 35 Cl (in cm 1 ) Tabl 1b. Rotational constants for D 35 Cl (in cm 1 ) B B B B From your calculatd valu of B and known isotopic masss, dtrmin an xprimntal valu for th quilibrium bond lngth r for your primary diatomic molcul. 5. Using th band origin obtaind for th v = 0 v = 1 transition from th linar last squars analysis in stp, along with th data in Tabl a or Tabl b blow for th 0 and 0 3 band origins (for HCl and DCl rspctivly), dtrmin ω and x. For this calculation, you should us Eq. (14) mak v = 0 and thn rarrang it so that is on th lft sid. A linar last squars v' plot will thn yild th dsird spctroscopic constants. Tabl a. Ovrton band origins for H 35 Cl (in cm 1 ) σ 0,v' σ 0, σ 0, Tabl b. Ovrton band origins for D 35 Cl (in cm 1 ) σ 0, σ 0,

7 6. If thr is not too much scattr in plots B and C from stp abov, you can us th rmaining information from th last squars analysis to dtrmin a valu for th cntrifugal distortion constant D J. SECTION 4: ITEMS TO INCLUDE IN THE LAB REPORT 1. Th rport should b in th informal (data) format. Rfr to th rport guidlins for complt information.. Includ a tabulation of your xprimntal valus for R(J ) and P(J ) for both molculs, along with th infrard spctra. Mak sur to includ any prtinnt xprimntal conditions. 3. For your primary molcul, includ th plots gnratd in Sction 3, along with th last squars slops and intrcpts and thir associatd rrors. 4. Prpar a tabl containing th rsults for th quilibrium bond lngth r and th spctroscopic paramtrs ω, B, x, α, and D J for your primary molcul. Mak sur to rport th uncrtainty in ach quantity. Prpar anothr tabl containing th rsults for th quilibrium bond lngth r and th spctroscopic paramtrs ω and B for your scondary molcul (no uncrtaintis ar ndd for th scondary molcul rsults). 5. Answr th qustions and complt th discussion givn in Sction 5 blow. 6. Includ sampl calculations, rror analysis, and drivation of th slops and intrcpts from Sction 3 in th Tratmnt of Data sction. Th only sampl calculations rquird ar th calculation of ω and B for your scondary molcul, along with th rducd mass µ and th quilibrium bond lngth r for on of th molculs. For your primary molcul, you should also show th dtrmination of x from your graphs. Most of th uncrtaintis in th spctroscopic constants com dirctly from or ar proportional to th uncrtaintis in th slops and intrcpts from th linar rgrssions. Thrfor, th only propagation of rror calculations that ar rquird ar for th quilibrium bond lngth r and th anharmonicity constant x. SECTION 5: QUESTIONS AND DISCUSSION 1. Compar your xprimntal valus of th quilibrium bond lngth and th spctroscopic constants to litratur valus. Discuss possibl rasons for any discrpancis.. Explain in dtail th rason for th intnsity pattrn sn in th xprimntal spctrum. That is, why do th intnsitis of th paks on ithr sid of th cntr appar to grow to a maximum and thn fall off to zro? [Hint: You may want to consult your physical chmistry txtbook] 3. Dscrib how th harmonic frquncy ω would chang for H 37 Cl rlativ to th valu that you obtaind for H 35 Cl. How would this affct th infrard vibration-rotation spctrum of H 37 Cl compard to th spctrum of H 35 Cl? [Hint: Think about how th harmonic frquncy is rlatd to th rducd mass. Chck your txtbook for th rlation. Thn, considr how th harmonic frquncy is rlatd to th pak position in th spctrum.] 4. How is th rotational constant B diffrnt for H 37 Cl compard to th valu for H 35 Cl? What ffct would this diffrnc hav on th infrard vibration-rotation spctrum of H 37 Cl rlativ to th

8 spctrum of H 35 Cl? [Hint: Considr how th rotational constant is rlatd to th rducd mass and th part of th spctrum that is affctd by B ] 5. Discuss th spcific ffcts that th constants x, D J, and α hav on th spctra of HCl and DCl. SECTION 6: INSTRUCTIONS FOR OPERATING THE PERKIN ELMER SPECTRUM ONE FTIR SPECTROMETER You will obtain th vibration-rotation spctrum of gas phas molculs using a Prkin Elmr Spctrum On FTlR spctromtr locatd in SLB 0. Opning th Softwar Log into th computr using an ADILSTU account. To start up th FTIR softwar, click on th Start bar, go to All Programs, thn PE Applications, doubl click th Spctrum icon. A window will opn indicating what instrumnt to us, mak sur to slct th Spctrum On and click OK. Paramtr and Instrumnt Stup Th softwar may rqust a background collction; click Cancl bcaus you nd to st up th instrumnt to th conditions rquird by your xprimnt. Bfor any spctral collction you must st th rang, rsolution and numbr of scans to b collctd. Go to th mnu bar and click on Instrumnt, thn Scan. Click Cancl if a window rqusting a background collction pops up. A window with diffrnt tabs will opn. Th dfault tab is Sampl. Typ th nam of th fil you will giv to th background (bkg) and rcord som commnts (lik rsolution, sampl prssur, tc.). Nxt slct th Scan tab and st th spctrum typ to Background (units st automatically to EGY) and th scan numbr to 16. Nxt slct th Instrumnt tab and st th rsolution to 1.0 cm -1. Click Apply. A background collction window will opn. Click Cancl. Collcting a Background and Spctrum To obtain a spctrum of your sampl, you must first collct a background spctrum with no sampl in th cll, and thn collct th spctrum of your sampl. Th computr will automatically corrct and subtract for any background paks from th spctrum of your sampl. Th stps for collcting a background and sampl spctrum ar: 1. With th mpty cll positiond in th sampl compartmnt click Scan in th Instrumnt Stup window that is alrady opn. A window displaying a graph with th background nrgy spctrum and a scan status bar (indicating numbr of scans) will b shown. Th background spctrum taks a fw minuts to complt. Th background will b autosavd although if a fil with th nam you providd is alrady thr a window will pop up. You may ovrwrit th fil. A window will pop up on th scrn displaying th background nrgy spctrum.. In ordr to collct th sampl spctrum, carfully plac th gas cll in th FTIR spctromtr sampl compartmnt. Slct th Instrumnt option in th mnu. Th Instrumnt Stup window will opn. Provid a nam for your Sampl fil and ntr som commnts. Go to th Scan tab and slct th Absorbanc units (A). Click Apply, thn Scan. A window displaying th FTIR spctrum of th sampl and a scan status bar will b shown. If th spctrum is displayd in Transmittanc units convrt it to Absorbanc units by clicking on th icon with th big A. Th computr automatically subtracts th background data and adjusts th baslin. Whn th data collction is complt, you may b askd whthr you want to ovrwrit th fil or crat a fil with a Nw Nam. Provid a Nw Nam (suggstd nam DCl_HCl.sp) and sav your spctrum. Labling, Printing and Saving th Spctrum 1. First dlt th background spctrum from th window. Slct th bkg.sp fil nam at th bottom lft of th scrn. Thn go to th mnu bar and click on Edit, thn Dlt.

9 . Now slct th spctrum filnam in th bottom lft sction of th scrn. Us th AutoY icon to display th whol spctrum in th scrn. Sinc you hav usd DCl as th sampl, you will hav two intns bands. On corrsponds to DCl and th othr to HCl (which is a contaminant of DCl). First you nd to nlarg on of th rgions of th spctrum corrsponding to th absorption of on of thm. In ordr to do this, dprss th lft mous button and draw a rctangl around th rgion of th spctrum that you would lik to nlarg. Thn doubl click in th rgion you hav highlightd to nlarg it to full scrn. 3. To labl th paks go to th mnu and click on Viw, thn Labl Paks. You can also gnrat a list of paks by going to th mnu and click on Procss, thn Pak Tabl. A nw window with a list of paks will b displayd. B awar that ach band is a doublt du to th natural prsnc of th lss abundant 37 Cl isotop. Thus only labls on th mor intns band of ach doublt should b usd in your rport. 4. To print, slct th window you want to print and thn go to Fil, thn Print. Mak sur you slct th propr printr (in Print Stup) bfor you submit your print job. Suggstd printr is th on in SLB Rpat th procdur abov (stps -4) for th othr band. 6. Finally sav you may want to sav your spctrum as a txt fil (xtnsion.asc) for your rcords. Go to Fil, thn Sav As, thr slct from th typ fil, th ascii (*.asc) option, brows to th Foldr indicatd by th instructor/ta and Sav th fil. You will b abl to opn this fil in Excl in cas you nd it whn working on your rport. Finishing Up On th computr, slct Exit or Clos from th Fil mnu, this will clos th program. Carfully rmov th gas cll from th spctromtr. Your instructor will assist you with mptying th cll.