5 J. Phys. Chm G Dtrmination of Vibrational and Elctronic Paramtrs From an Elctronic Spctrum of I 2 and a Birg-Sponr Plot 1 15 2 25 3 35 4 45 Dpartmnt of Chmistry, Gustavus Adolphus Collg. 8 Wst Collg Avnu, St. Ptr, MN, 5682. XXX@gustavus.du. Rcivd: March 31, 27. Abstract Using an lctronic spctrum of I 2, Dslandrs tabl and Birg-Sponr plots, vibrational and lctronic paramtrs wr calculatd. Th vibrational frquncy, anharmonicity constant, dissociation nrgy and th quilibrium dissociation nrgy for th ground stat wr found to b 221.13 cm -1,.119 cm -1, 12189 cm -1 and 123.2 cm -1, rspctivly. Th vibrational frquncy, anharmonicity constant, dissociation nrgy and th quilibrium dissociation nrgy for th xcitd stat wr calculatd to b 132.21 cm -1,.771 cm -1, 4351.29 cm -1 and 4284.93 cm -1, rspctivly. Th convrgnc limit, lctronic nrgy of th B stat and th nrgy of th xcitd iodin atom wr calculatd to b 1993.3 cm -1, 1544.8 cm -1 and 1174.89 cm -1, rspctivly. Th calculatd paramtrs for th xcitd stat wr in good agrmnt to tabulatd valus. It was concludd that th xcitd stat follows a harmonic oscillator bttr than th ground stat and that th bond lngth in th xcitd stat was longr than th ground stat. Introduction Upon hating, th xcitd vibrational lvls of th ground stat of I 2 bcom populatd. 1,2 Th vibronic spctrum that may b obtaind by monitoring ths xcitations provids vibrational constants and dissociation nrgis of ach lctronic stat. 3 Th lctronic transitions obsrvd in th spctrum ar th transitions btwn th lowr lvls, X 1 Σ + (v =), and various xcitd vibrational lvls of th B 3 Π (v ) lctronic stat. 2,4 In this invstigation, transitions from v =,1 and 2 stats to v =13, 14, 15,,47 ar invstigatd using an lctronic spctrum of I 2 and a Birg-Sponr plot. Exprimntal 3 A prpard 1 cm cuvtt containing iodin crystals was hatd until I 2 (g) was visibl. Th cuvtt was placd into a Cary UV-Visibl spctrophotomtr and I 2 (g) was scannd from 5-6 nm. Th sttings on th spctrophotomtr includd an avrag tim of 1 sc, avrag data intrval of.1 nm, a band width of.2 nm and a doubl bam mod. Th rsulting spctrum was analyzd yilding th vibrational and lctronic paramtrs ", x", D", D", ', x ', D ', D T ' and E(I*). Ths paramtrs wr calculatd using Equations 1-5 and a Birg-Sponr plot. Δ ( v') = 2 ' x '( v' + 1) Equation 1 D ' = Δ ( v' = ) + Δ ( v' = 1) + Δ ( v' = 2) +... = A Equation 2 1 1 D ' = D Evib v D ' + ( ' = ) = ' + ' ' x Equation 3 2 4
E* = v ( v' = b) + A' = Do ' + E( I*) Equation 4 T ' = D " + E( I*) D ' Equation 5 5 55 6 65 In ths quations, is th vibrational frquncy, x is th anharmonicity constant, D 'is th dissociation nrgy, A is th ara undr th Birg-Sponr plot, D ' is th quilibrium dissociation nrgy, E* is th convrgnc limit, E(I*) is th nrgy of th xcitd iodin atom, T ' is th lctronic nrgy of th B stat, v =b at th last transitions stat bfor th bands bcom continuous and A is th ara undr th Birg-Sponr plot from v =b to th convrgnc point. A Birg-Sponr plot of (v +1) vs. Δ (v ) was constructd to yild dsird valus in Equations 1-5. A two-point plot of (v +1) vs. Δ (v ) was constructd to compar a calculatd valu of E(I*) to th tabulatd valu of 763.15 cm -1 usd in Equation 4. 3 Rsults Each band on th I 2 lctronic spctrum was labld with its corrsponding initial and xcitd stat. Bcaus of th small ovrlap btwn th shiftd harmonic oscillator vibrational wav functions of th v = and v'= stats, tabulatd valus wr usd as a basis to start th band assignmnts. 3 Th I 2 spctra with labld transitions may b sn in Figur 1. A B 7 75 Figur 1: Elctronic spctrum of I 2 (g). Figurs A and B ar nlargd vrsions of th original spctrum. Figur A includs 5 nm to 55 nm and Figur B includs 545 nm to 6 nm. Transitions wr labld basd on valus Tabl 1. v = to v =1 and v 1 to v 2 transitions occurrd with incrasing wavlngth. v =13, 14, 15,,47 transitions occurrd with dcrasing wavlngth. Onc th transitions wr labld, a Dslandrs tabl was constructd (Tabl 1). Valus from this tabl wr constructd into a Birg-Sponr plot (Figur 2). Basd on Equation 1, th linar rgrssion of this plot, y = -2.397 x + 132.21, rvals a y-intrcpt qual to ', a slop qual to -2 x ' ' and an x-intrcpt qual to th convrgnc limit. Using this plot and Equations 1-5 th lctronic paramtrs
8 ", x", D", D", ', x ', D ', D T ' wr calculatd (Tabl 2). Th valus " and x" wr obtaind with Equation 1, using valus of v = and v =1 in plac of th v valus. An xprimntal valu of E(I*) was calculatd to b 1174.89 cm -1 using a twopoint Birg-Sponr plot (Figur 2). 85 Tabl 1:Dslandrs tabl of xprimntal data. v'/v'' 1 2 Avg 13. 16786.97331 (17.7724254) 17.77242 14. 1715.71 [21.9676] 16894.74573 (1.678) (1.4955984) 1.2817 15. 17421.6 [215.821645] 1725.78 [21.5398] 16995.24133 (97.66841) (98.257) (98.77576159) 98.23162 16. 17519.27 [215.2393589] 1734.3 [21.147] 1794.179 (95.66627) (99.37923) (96.97482622) 97.3411 17. 17614.94 [211.5263984] 1743.41 [212.4191] 1719.99192 (96.7168) (94.417) (98.8138544) 96.39996 18. 17711.65 [213.8414951] 17497.81 [28.7395] 17289.7331 (94.61354) (95.43142) (96.18399614) 95.4965 19. 1786.27 [213.23612] 17593.24 [27.9869] 17385.2573 (89.22253) (9.22177) 89.72215 2. 17895.49 [212.243771] 17683.47 (9.12117) (87.9938) 89.5713 21. 17985.61 [214.152474] 17771.46 (87.7664) (88.87317) 88.31978 22. 1873.38 [213.457122] 1786.33 (85.32919) (86.5454) 85.93711 23. 18158.71 [211.8298567] 17946.88 (82.8159) (84.1361) 83.47335 24. 18241.52 [21.543513] 1831.1 (83.56935) (81.64741) 82.6838 25. 18325.9 [212.4262943] 18112.66 (77.56294) (79.82) 78.32157 26. 1842.65 [21.9932] 18191.74 (78.22232) (79.77376) 78.9984 27. 1848.87 [29.3575886] 18271.51 (75.44613) (73.7434) 74.59459 28. 18556.32 [211.66756] 18345.26 (72.59365) 29. 18628.91 (73.16386) 3. 1872.8 (7.21617) Avg [212.483622] [21.1113]
Valus in [ ] ar vibrational stat sparations in th ground stat and valus in ( ) ar vibrational stat sparations in th xcitd stat. All units ar cm -1. Δ 12 1 8 dlta v' 6 4 2 A y = -2.397x + 132.21 R 2 =.994. 5. 1. 15. 2. 25. 3. 35. 4. 45. 5. v '+1 213 212.5 212 211.5 dlta v" 211 21.5 21 9 95 29.5 y = -2.3718x + 214.85.8 1 1.2 1.4 1.6 1.8 2 2.2 v"+1 B Figur 2: (A) Birg-Sponr plot of (v +1) vs. Δ (v ) and (B) a two-point Birg-Sponr plot of (v +1) vs. Δ (v ). Using Figur A and Equations 1-5 th dsird lctronic paramtrs wr calculatd. Using Figur B an xprimntal calculation of E(I*) was obtaind. Tabl 2: Calculatd lctronic paramtrs compard to tabulatd valus. " x " D " D " ' x ' D D (cm -1 ) (cm -1 ) (cm -1 ) (cm -1 ) (cm -1 ) (cm -1 ) (cm -1 ) (cm -1 ) Calculatd 221.13.119 12189 123.2 132.21.771 4351.29 4284.93 Tabulatd 125.69.68 4391. E* T ' E(I*) (cm -1 ) (cm -1 ) (cm -1 ) Calculatd 1993.3 1544.8 1174.89 Tabulatd 15768.3 763.15 Tabulatd valus wr obtaind from NIST Wbbook. 5 R 2 = 1 1 Discussion Calculatd constants wr in good agrmnt with tabulatd valus. D had th closst comparison to tabulatd data, with an approximat 1% rror. Tabulatd valus for th ground stat wr unabl to found. From Tabl 2, it may b sn that th valus
15 11 115 12 125 13 135 for, x, D and D wr gratr for th ground stat than for th xcitd stat. Th corrction for anharmonicity is gratr for th ground stat by.423 cm -1 bcaus th potntial nrgy wll for th xcitd stat follows th harmonic oscillator approximation bttr than th ground stat, giving it a narrowr wll on a potntial nrgy diagram. Evn though a majority of th data corrspondd wll with tabulatd valus, th calculatd valu of E(I*) did not. Th larg dviation in th two valus is du to th us of a two-point plot. If mor data points wr obtaind and usd in th calculation, th two valus would b in bttr agrmnt. Whn comparing th dissociation nrgy, th nrgy was 815.27 cm -1 gratr for th ground stat than for th xcitd stat. This diffrnc is associatd to th varying bond strngths of th diffrnt stats. Th bond in th ground stat is shortr and absorbs at shortr wavlngths. This indicats that th bond is strongr, thrfor rsulting in a highr bond dissociation nrgy. Whn th lctrons of I 2 ar promotd to an xcitd stat both thir nrgy and bond lngth incras. As sn in Figur 1, as th lctrons mov to highr nrgy lvls thy absorb at gratr wavlngths. This is bcaus as th bond incrass in lngth it dcrass in strngth. Thrfor, th bond lngth is gratr in B, th xcitd stat, than it is in X, th ground stat. Conclusion Calculatd paramtrs ", x", D", D", ', x ', D ', D T ' from an I 2 lctronic spctrum and Birg-Sponr plot yildd good rsults whn calculatd valus for th xcitd stat wr compard to tabulatd valus. E(I*), howvr, was obtaind using a two-point Birg-Sponr plot and did not corrspond wll to tabulatd rsults. Whn comparing th ground stat to th xcitd stat, th xcitd stat bttr rprsnts a harmonic oscillator and has a longr bond. This crats a smallr wll for th potntial nrgy and a smallr bond dissociation nrgy for th xcitd stat. Rsourcs (1) Univrsity, T. A. Absorption and Lasr Inducd Fluorscnc Spctra of Molcular Iodin, 24. (2) Chapman, D. Th Elctronic Spctrum of Iodin. In SOU Chm 445, 27. (3) Ninow, A. Lab #4: Spctrum And Dissociation Enrgis of I2, 27. (4) Stinfld, J. I.; Zar, R. N.; Jons, L.; Lsk, M.; W, K. J. Chm. Phys. 1965, 42, 25. (5) NIST. NIST Chmistry WbBook, 25; Vol. 27.