Prelim_1_solutions

Prelim_1_solutions - COVER Chemistry 288 8—06 Thursday...

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Unformatted text preview: COVER Chemistry 288 8—06 Thursday, March 9, 2006 7:30 — 9:00 PM, Baker 219 Prelim I Print Your Name ‘2 ‘. Last J First Middle Initial Complete academic integrity is expected of all students of Cornell Unversity at all times, whether in the presence or absence of members of the faculty or teaching staff. Understanding this, I declare that I shall not give, use, or receive unauthorized aid in this examination. Your Signature: As soon as you are told to begin, check to see that your examination booklet is complete, and notify a proctor immediately if it is not. Your examination booklet should contain 13 numbered pages including one work sheet. You may leave when finished, but please do so quietly. Question A] _(17) Question C1 ___(12) A2____{12) CZ _ (6) ‘43 (14)l c3 (10) A4___(5) C4 (10) A5___(10) c5 __ (33) Question B1 __ (12) BZ___(6) 133 __ (15) TOTAL ............. __ (1 74) B4 (12) Chem. 288, 8-06 Prelim 1, March 9 A. B 0NDIN G AND MOLECULAR PROPER TIES ," 215i; P) l General ’ ; a) Write down the Hamiltonian for a system containing n electrons and N nuclei. 52? 5 The jth nucleus carries charge zje and mass m]; I rim] i" .f; ' l Ag “3 ,“. I, I up: i 3‘ i“? . 1 ' r f: a"! “J V J J i ’3: . . . v V b) How many nuclear (posrtlonal) coordinates are there? «- n" c) How many electron (positional ) coordinates are there? '4‘), I d) In setting out to solve Schroedinger’s Equation within the Born- Oppenheimer approximation (both nuclearcg‘orgirgtesgfldm J electrgggogrdinates are variables,<in¥§1§§1192£9§£§§1§£¢§ V‘ ‘ (arciyaltiahleshonly nuclear coordinates are variables). Under- 1: 5i line_best answers. ‘ .‘t . .‘ u l 7'] g. a /’ e) i) Label axes below and ii) sketch a reasonable potential energy curve for 5’ "lg; a stable diatomic molecule. iii) On it locate the equilibrium bond length, re J l and iv) the bond dissociation enegy, De. Then v) on the right briefly state how this curve is calculated. , a u» c r a ., fl “"gr'F‘ }; 1 a A “ if ' l , 7:: (35» ZN '7 “z . W-“ W Chem. 288, 8-06 Prelim 1, March 9 “it, t , i i x;- ., 2. X :1) Write the ground state configuration of N2 . ' f a n3 I ' H ,v; V 5t 675‘ ~' V 7" i; i I,” t ,2? ., i, (I, f e b) What is its bond order? ’ y ‘ Qtij L954“ — e 77' —' W‘- 3 J | 0) Consider the cation, 0: . What is its term symbol? ‘jir i J M f 9. hr—i oi, i J /( i: I, re?“ Lidia-g. M. d) Given the two choices of D9 (in eV): 6.48 and 7.38, assign these to la , , f; s V. 5t 0 V + a 2/ 2 02 Consider the planar CO;2 molecular anion. n ’ ‘7 _ A :d y ’ “.A rm ii 4 a) How many electrons does it have? 1‘ V +~~ L —~ “3 "V" 1 7w '3 .7, ,1,“ a ,. ‘u . . I t r MA 5» x , v Tl t': x . ' . I) n i i H r ~ ‘”-~_‘ . 1??!) b) Of these, how many are cme electrons. A X j + r ' ;___,\_‘:_,_,,, 2 [c) How many hybrid orbitals are there on the carbon and What are they called? 1 / j S ;’> 1 { d) How many cs bonds are there? 2 '7’ 5 /" i t < ' “‘2‘ a e) How npnngO‘s are made from the appropriate AO’s (includethen‘)? J l" > 17/ ~L i7" Q; 1) How many of these 7t MO’s are filled? 2' ‘- n i \_/‘ i in g) How many 71: bonds exist in this molecular ion? ’) J l l l t I | 1 "“ Chem. 288, 3-06 Prelim 1, March 9 Enter a number from 1—5 for the following diatomics according to their dipole strength (5 is strongest, 1 is weakest). :2 L h \ Law J ‘I/ 17-131“””" gr: / a) Briefly state what quantities you would measure (not how) and tell how to plot the 5 data to measure the polarizability and the dipole moment of a molecule. f ~u‘» ' . J. ’ / f r ‘ j l i; i I 4‘“; [i r 7 77777777 Mr W b) The molecular polarizability of Kr is 2.48 X 10‘24cm3. f, g ’l i)? What is the induced dipole in the Kr atom if it is subjected to a DC field of i/ T}? 2 x 1 Odesu cm’z? ‘ _ i ‘ WV / ,‘ . iv v, V :x a \‘L g" v h H if i V r‘r‘ I; H “,1.‘ -' r M “(will "r {In (I ’ K . (l, .7 2/4, I) y , U, ‘ Qg is’ii) Express this induced dipole in Debye (D). I; — 3/ ' ,3? : v. V 0L 1 f n (f . A, ’ :~ Kr"; v) ‘ "Li ~ 1“" '"i‘i’l ~‘ ’ ‘” ' r”) ("a If," ‘7 f j": , l 5,3 I, , B. SPE C T ROSC OPIES — GENERAL Here is a list of common spectroscopies in alphabetical order. For use on the next pages a short- hand code is assigned to each one: Dm = dielectric measurements ESR = electron spin resonance IR = infrared spectroscopy v-MM»: microwave spectroscopy NMR = nuclear magnetic resonance RAM; Raman spectroscopy UV-n = near ultraviolet spectroscopy UV—v = vacuum ultraviolet spectroscopy Vis = visible spectroscopy X-. = soft x-ray spectroscopy Prelim 1, March 9 Chem. 288, 8-06 r: —4 2:52.“: .:w__nu:m.:o:w .5 com...— 2 .2: 2.0 :23... 1323...?» .:_.$ 3:35:29— ..Esuo—c... .2. Quiz—u a 3.235.. :2: 2.0 :23... 3:23.53 5?. 25.....5 2.3:. ho aura... a 32:3. 3.: 2.0 .:w=2 2:... 9...ng :3 2:: 2.0 32.. 2.2.9:: €2.99. 5. 31:5. :2: 3:. .- III-fl III-I..- .I.... ~\ 3182...: 2:. 2.8... 5 £5.62» 32.22:: 2: a: 3.52.3.0 .32 2: one... :3 2:: 2.0 3:529: .1. 953:5... 2.5.520 3:2...» 2: .59... .9: 9.; I...- fr 3.522... __.....m :c 2.2.5:. 22:: 2: 525.3... .5: 2.0 3282...: cu...— uc 2.2.5:. 233—. 2: 3.532: :2: 2.0 I II...— > \ ‘\ N. 3...: 7.553;? .2522: use... 2:: can. \, \ nu Ea— v—mfl >32 m—ZZ Ex: :4»: >->D mm> TX n. N» G. W 5:25.23... . :8 9.: a: :28 .8 Amvoismobmwam 22:3...5.“ #5.: 2: 5 $3.02? 32.— A KNFNQV. Chem. 288, 8—06 Prelim 1, March 9 The various spectroscopies are distinguished by the energy of the photons needed to /> probe resonances. For the following subset of six spectroscopies enter the relative rank according to photon energy used (6 is highest photon energy, 1 is lowest photon energy). Spectroscopy UV-n X—s r 3 There are many “energy” units used in spectroscopy. 'l y a) For each of the following units identify by the letter code one spectroscopy where the unit is commonly used. ‘ a in" ("j ‘ i ’ J b) Suppose the energy gap between two levels is 19.1 kJ mol". Convert this energy to: | ' (l) A temperature K ‘ , 2| . p . 4' . I) I’iv i :y w 5 r —. ii: :2 ’f)’ f it i: ‘I 1}! ‘4 a"; ‘ "'3'; I)“ 9 .. /i ,. v ‘ £3: ' “ ’3 FT g ' )1 (2) The energy of.the_phgtgn_needed for resonance in terms of r i) the freqency of the light a l s. i“ '1' ~ \a / ‘1 7 :1 77 I 4 (J “:7 ‘ i. (I! “ t i I : . r : /' L/ = my :7 ,A , A ,f ' ii) the wavelength of the light (in a vacuum) ' A V l i/ .3 ., \ , «:1 W ~‘ t - " l ' " f' z' T— i: :5" “or i /‘ ",i/J. t w ‘ iii) the wavenumber of the light (in a vacuum) V f Fur h fl .1: ,5“? .2 , _ 7 —— H—.— ’ V ' J I ( 5:th : ' / , l n . i ff" i I t 07.; Chem. 288, 8-06 L! i 1’)" I. i) a. 7. , t Prelim 1, March 9 l V and F is Faraday’s Constant: 96,487 Cmol'l, and 1 Volt C = 1 J). l 6 ; Z; (3) Electron—volts (Hint: 1 eV at molar level is just FCIJ with (I) = “t 7‘, t/x' i‘x "M I ~ 4, ‘. t 1'" F I 9 , if (4) In what spectral region is this resonance located? if; [gift Absorption a) The molar extinction coefficient of tyrosine is :1": X 103 mol'] L cm" at 280nm. i) What is the absorbance o tical density of 2157mm path of an 4. 00.x 4 1 p ~ J,“ 10‘ mol L' solution of this amino acid in water (water 18 transparent 4». 9 'r j, at this wavelength)? , p j! _ Ci 3‘ , :/ xx} )7 H f ’ [I4 I'm .‘ A ~ ‘~i’;’(i rrits- i»* .‘ ’l/m 11‘ J; 7‘ t : T/[L’ ("7 ‘ . ‘f t vr/ ii) What is the optical cross-section for this molecule at‘280nm? r . i] a «9% " v 1'" l —A‘ i, V ‘V‘ H 1'” F . 7 i . / ‘iit ~'i‘,., b) A diver experiences ai'iirtar'lé'er world the deeper hfilfiheflives. suppose for sea water the effective inverse optical depth for the visible region is, Z a jCJ- = 6 x 10'4 cm‘1 . The diver reaches a depth where only 1/20 j=l ‘7' w(! . ,. i- i ‘ 1 IN N u 7 MI 9 _t ,4 - i ‘z. w I L_ new, of light incident-at thesiurface seen. 77 A f\' \ \ I i) How deep is the diver from the sea levelitin meters)? g‘ 2‘ ii) What is the % transmittance, 100T , at this depth? p J / H II)‘ J Chem. 288, 8—06 Prelim I, March 9 C. SPECTROSCOPIES — SPECIFIC ( 1. Emission: ng/ l 4. at? a) fluourescense electron spin forbidden), (nuclear spin allowed; ninc‘lEzirishpinrforbiddamand normally decays in a time scale H~._._‘hw . of (femtosecoiidslnanoseconds”microseconds, milliseconds, seconds). Underline in 3 places. b) phosphorescence is (electron spin—allowed,relectr‘on’spin forbidden), (nuclear spin allowedéijfifilearuspinforbidden), and nonnally decays in a time scale of (femtoseconds, nanoseconds, microseconds, milliseconds, seconds) Underline in 3 places. I Raman scattering: A laser at 500nm Raman (inelastically) scatters 312 vibration at .2_1N3 crri‘l (the scattered light loses energy). What is the wave number of the: a) The incident (Rayleigh) scattered light? b) Raman scattered light? 7 3 ~ ~ I J . u‘fi‘ / (,5! , ‘ l "<7 ( {f ".ax’e ‘ % (550. ’- 3. Degrees of Freedom: Consider the nucleic acid base uracil, C4H4N202. 0 JL / \ I’ NH l l ago . . . N 21) Give the degrees of freedom that it has in: . H ? Maj i) translation l. v Q l 5 ii) vibration ( l’ l " iii) rotation LEI? §.:;12 b) How many normal modes does it have? How many vibrational frequencies? :v" A Chem. 288, 8—06 Prelim 1, March 9 sample must exhibit a differentlfindéiof refractioer extinction‘coefficient) for / 0 IS 4. OR and CD ‘ , 7,, ,, P . a) QR. Optical rotation involves (the electricl‘field only, lthe magnetic field only, . both fields) of the photon (the EM field) and the molecules of the sample must K have (a center of symmetry, a chiral syrmmetryg‘a plane of symmetry).. The ) / pi i/ (left and right circularly polarized lightx/iierpglidiigitlglilyNandlparallfilmpgmgd V Misti" iligllgmer), and it causes (circularly polarized light to become elliptically ’ V i ~“polarizetj, plane‘polarizedwlightto become elliptically polarized,,§l§n§‘pol§if5' ijefdilright to remafiiplangpo‘larized but in a different plane). Underline in 5 places. I L,» \ \k W‘. m,“ / b) CD. Circlar dichroism involvesd(tl’lfle,el_eg£lc ,fidflpnjfi the magnetic field only, both fields) of the photon (the Elylfield) and the /molecules of the sample must have (a center of symmetry,:'a chiral symmetryng plane of symmetry)?" The sample must exhibitma different (index of refractionfliéxtin'ct’mn coerfibiéd‘tji n. ...-,..,un—.—.. —...._..._. _ .. -...4.,..... for emindrightrrci'rcularlypolarized light, fperpendiciiliii‘lYE'i‘i‘)d parallel quggfiei light, neither) and it causes lrcirculally.Pflléfize‘djighthgmgpmer 7 Ellipticauxipmarm Plane polarized light'to become elliptically polarized, W V , plane polarized‘lié'h't’to remain plane polarized but in a different plane). Underline in 5 places. '. NMR a) The nuclear g factor of the proton is 5.585 and in a 10T magnetic field the ‘ resonance is at 425.7MHz. l > At this four figure precision this is true for (all protons, only some "Ml—z”, mum...— f )7 Protons,}depends’ ofi’the'Ehielding factor” K K “KW Underline best‘answerr“ ' “m “ A"! Chem. 288. 8—06 Prelim 1, March 9 4/ B L) b) Consider an A3X2 proton spin system in whch the A3 protons display a a-~—~—~~-—w—~ ~ —7 f weaker chemical shift than do the X2 protons. i) With an applied magnetic field in the z direction, Bo, but figment spin-Sniflflypling‘; ., ‘ KQHE the number of energy levels in 21 A3 system is: 1 . b . the number in the X2 system 15. Loan [L (mg Aw I (dim/‘12 J745 l :‘i‘ .x .‘T ii) Give the total spin quantum number in the z direction, M2, for each of the levels in the A3 system in left to right order from lowest to highest energy level: iii) ‘Consider exactly 1,00rA3X2 molecules at thermal equilibrium near T room temperature. To the nearest integer tell how many of these molecules will be found in each of the energy levels of the A3 MM 3 _ system (froPm _lo_\1vest tohilghest): "” C’ 5"“ m ’ :7 am i m 7' . 3'2: "— = x3; — Zéré’x/a‘" h rand 7"_S I 3 iii/H150 : 232 Y/p—Zf [1 ~M I? X 31.0 10 .. ~ rv I. . r , If". my- \em 3) WM‘ \H} x. V U \Vxl “ M 2114 ~ Ag- H n ,. 3 ‘ V ‘r W: L kmm 4* NW, Sign «wen ..; whk Java )1 L: w .. find :3- 133' *i ‘1’" _l/ -I"\ “J’TL’j/[E’ /1, M . “é NFL-a :1 -qy..a/ "/ r,“ W '1 {2,12, J» I _ n (3 WW gumngtqé,” I ,iz‘ l M12: “{2- 4 {2, {a . A ‘g __ / M23: 2 [V2 ‘ g [’ {17%2' .a-r/Q / I - t i/ ‘\ X [I f [:7 7 \T/g': Kp(\il fl '.e,4‘ F! wigw7fig f \—} / ”’ é ;. W“ 1" ‘A (’r\ ’ 3 (-- LDfOJ DP?“ Quam‘gun'} Numbm iv”. 7’73?” A} if . " J . T‘mz Sfjrn'irFO-Ii flack {7,34% W ’ a 3x2: '/2'»‘r’2:’/2<."/7=’£/21' , Am:it L.) /\ l )4 §\ —‘ ~~ a V {f / v 71;: — /I?- .’ l g .’ ,i f ‘ 1 3 D ¥ .. ; A I *1 M. . ~ ‘ «y- 5 0“ «fax— . 1 ‘ . ’ -v ’t a . v ‘f', , BW' Ci m1 is“! -?/‘L:\,€fiu filmy)" ) 32'Wr‘é'1k) L: — m’K 'J“~ 3m 312 \(gg‘”m¢1“’3“' T” 1 . '7‘ :— - \hf ‘ l: ‘ KI: M. 1 3”“, , n ' : 'va ‘ 9 MA" 13am - 1 MN “— ~ ‘fi? JU‘ "» 413>~3».‘~54‘-='\»3 ~‘ ., 1 : .. “A I: ’- JJ ‘ ’ cgt‘?‘ mvfgxfmlf Q. ~ ‘ . Cin— 1 .u. ca“ “any: ’ New ’L J I ‘ g :‘f. _. 2 “M vii) “ :2 ("La "flit ‘Li» tfigq XI~J } 7‘ , ‘ h 33’ 2.3' '" Lu hum-5", ‘t'wfi‘tid .3“ 2 “graft: ’ .w 1 - - ~ - «r -‘ ‘3 “.3 ~ “Art; ~ _ _ ’3 3 Aug”- I'LHJQX37 X T- k w :4 'V‘GV MkQ‘Wfl) E v ‘23 r u (i v r " .9 s§ i 3 3f“? Kw S 7 .. z ‘ C1 ‘ ":3? 4k) :7? l M fin. is, ~ 23% m, A L": N=m~ (u. fl. ' “ YflD Q 4/) {£53 " exf J‘s, . . . "x ? i U] ‘1‘ 3 i‘ ; (30.611 (ingj‘uc. ‘4‘ r a.) & <. (2'... A t « | ‘l ‘i 4.- a {i «L f1. m 7 a , 1 '2 N992 ’39. w) r 5:59: :1 v3 -h‘- k‘ ». Chem 288, 8—06 Prelim I, March 9 5 iv) For a classical NMR instrument (not an FT—NMR), sketch below 5 a zeroth order NMR spectrum of the A3X2 system, include a 0) small amount of TMS. Label clearly, and indicate how the total ' areas from the A3X2 are related: v) Next we “turn on” the spin-spin coupling constant, J Ax, which is much less than the difference between the resonant frequencies of a A3 and X2. Draw the correct “first order” NMR spectrum of the 2 A3 and X2 system (in registry with your answer in iv): i. y . t/ 1/ ll Chem. 288, 8-06 Prelim 1, March 9 c) As an example of a simple analysis, draw below the high resolution NMR spectrum of ethyl acetate. In doing so, label the bands according to protons a,b, and c and indicate the relative intensities of the fine structure within each band, and also the relative total areas of each band. Assume that Jac=Jab = 0, ch ¢ 0.: ethyl acetate O A. [I in AC- a”? M Li rJ/ J binppm d) Consider a modern 900 MHz FT-NMR machine. Its superconducting magnet is such that the free proton would resonate at 880 MHz. I 7[ i) What is its magnetic field (in Tesla)? )7 V7432 10‘ were res/a 7 (cf J, ii) What frequency is absorbed by a 13 C resonance (the 13C nuclear g 730 f . factor is 1.405). '3‘ ~! '1 P. i r i “ . % _, —- . ;./l‘ :M‘ : ? ‘tv"~ 2n r . it as H:- c 111) An FT machine (scans the magnetic field, scans the spectrum ($04,, of “light” being absorbed, uses pulsed ‘li ht’, shgflsEID). ‘ / Underline best answer(s). f [I i b A ChemNMR H-1 Estimation Estimation Quality‘ blue = good. magenta = medium, red = rough 6.» PPM Protocol of the H—1 NMR Prediction: Node Shift Base + Inc. Comment (ppm rel. to TMS) CH3 2.01 0.86 methyl 1.15 1 alpha —C(=O)OC CH2 4.12 1.37 methylene 0.00 1 alpha —C 2.75 1 alpha —oc(=o) —c CH3 1 . 30 0 . 86 methyl 0.44 1 beta ~OC(=O)C Chem. 288, 8—06 Prelim 1, March 9 13 Chem. 288, 8-06 Prelim 1, March 9 NA = 6.0221 1023 mol ‘1 AE=hv, Vl:c,n=-{C; h = 6.6262 10-34 Js k3 = 1.38066 10”] K" c =2.99792 103 m s" 00:5.2917710—11171 e = 1.60219 10'” C 4.80298 10 '10 esu 1 1' m, _ 9.1095x10-3’ kg ’v m 1.67265x10“27 kg . n—j).... ( I) [m'kjnzizfifla]; Il 6=;;%Q(EL—ek)=3.3x103g ...
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This note was uploaded on 09/28/2008 for the course CHEM 2880 taught by Professor Freed, j during the Spring '06 term at Cornell.

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Prelim_1_solutions - COVER Chemistry 288 8—06 Thursday...

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