Problem Set10 Solutions

Problem Set10 Solutions - C HAPTER 1 9 SPECTROPHOTOMETRY: I...

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Unformatted text preview: C HAPTER 1 9 SPECTROPHOTOMETRY: I NSTRUMBNTS A ND A PPLICATIONS 19-1. I n a s ingle-beam pectrophotometer,e f irst p lacea c uvet c ontaininga b lank s w reference olutioni nto t he s ingles ampleh oldera nd s ett he d etectorr eadoutt o s indicate1 00%t ransmittance. his c orrespondso t he r adiantp ower P g r eaching T t the d etector.T hen w e p lacet he s amples olutioni n t he h oldera nd t he r adiant power r eachingt he d etectori s t aken a s P . T ransmittance s t he q uotientP lPg. I n i a d ouble-beam pectrophotometer, s amplea nd r eferencec uvetsa re b oth i n s t he the i nstrument. A r otating b eam c hoppera lternatelyd irects l ight f rom t he monochromator o t he s ampleo r r eference. R adiantp ower r eachingt he d etector t from t he r eferencei s t aken a s P 6 a nd r adiantp ower r eachingt he d etectorf rom the s amplei s t akena s P . T he s ingle-beamnstrument roduces ffors i f t he i p e sourcei ntensityo r d etectorr esponse rifts b etweenm easurement f t he b lank d o and t he s ample. T his e rror i s a bsenti n t he d ouble-beamnstrument, hich i w measuresight p assing hroughb oth c uvetss everal imes p er s econd. l t t l9-2. D euteriuml amp l9-3. Advantage-increased a bilityt o r esolve losely paced pectral eaks c s s p Disadvantage-moreoiseb ecause l ightr eachesetector n l ess d (a) n ). : d (sin0 + s in g ) 1.600x l 0-em : d (s in 4 0 " + s in (-3 0 ' )) d : 4 . 2 0 x 1 0 -6 m > : l l(4.20x l 0-4c m) : 2 .38x 1 03l ines/cm Lines/cm (b) l :1(l000cm-l): l 0 -3 c m > d : 7 . 0 0 x 1 0 -3 c m = 1 4 3l in e s / c m t9-4. 19-5. (a) nlv: d (sin0+sinf) Inserting v alues : - 1 , l . : 6 3 3 n m: 0 . 6 3 3V m, : 1 . 6p m,a n d0 : 0 o t he n d allowsu s t o s olvef or $ : (-1X0.633 m) : ( 1.6p m)(sin o+ s in g ) = 0 : - 23" p 0 * 1, 0 : + 23o . o rn - + 2 , 0 : + 5 2 ' . Forn F (b) For t he 3 'do rderd iffracted eam, e f ind b w nlv: d (sin0+sinQ) (3)(0.633m) : ( 1.6p m)(s in ' + s in0 ) = s in0 : 1 . 1 9 p 0 But t hes ineo f a n a ngle annot xceed , s ot hed iffraction ondition annot c e 1 c c bes atisfied n :3. f or r68 a I nstrumentsndA pplications S pectrophotometry: r69 19-6. b i A n e lectrone jectedf rom t he p hotocathodes a ccelerated y a p ositive v oltage s o it s trikest he f irst d ynodew ith h igh k inetic e nergy. E ach e lectronf rom t he cathodel iberatesm any e lectronsf rom t he f irst d ynode. E ach o f t hesee lectrons, b in t urn, i s a ccelerated y a p ositive v oltage s o i t l iberatesm any e lectronsf rom t he e secondd ynode. A fter s everals uch s tages, ache lectronl iberateda t t he c athode s resultsi n - 106 e lcctrons trikingt he a nodea t t he e nd o f t he c hain. lg-7. t m T he p hotodiode a ftay s pectrophotometer easureshe e ntire s pectruma t o nce, a e because achd etectore lemento f t he d iode a rraym easures d ifferent, n arrow band o f w avelengths. T he s pectrumi s r ecordedr apidly r elative t o t hat o f a o w dispersives pectrophotometer, hich m easures ne w avelengtha t a t ime. T he i a o disadvantage f t he p hotodiode rray i nstrument s t hat i ts r esolutioni s n ot a s t great a s t hat o f t he d ispersivei nstrument,b ecause here c an o nly b e a s m any different w avelengthsr esolveda s t here a re d etectore lementsi n t he a rray. l9-g. c I f t he s pectrao f t wo c ompoundsw ith a c onstantt otal c oncentration rossa t a ny w wavelength,a ll m ixtures w ith t he s amet otal c oncentration ill g o t hrough t hat p o p samep oint, c alleda n i sosbestic oint. T he a ppearance f i sosbestic oints i n a b t chemicalr eactioni s g ood e vidence hat w e a re o bservingo ne m ain s pecies eing convertedt o o ne o ther m ajor s pecies. : x - ( 3870)(3990)l9 .01s l Q7 rg-g. b (ex, v-rv r x ) : ( 1.000)t(r6440)(6420) txl : * @tI - A " ti ) : - - 4 - 42xo- sM l ( 0'55ex'6#;?l tyt: ;(A"'x-A',i): ; (ry 19-10. I A - 5 .e6x M r 0-5 D E B C o ric Spreadsheetbr s pectrophotome a nalysis f a m ixtulg ( AbsorptivityM^- c m ^ - l rl ) 3 4 6 7 8 9 l0 ll ( nm) Compound X Wavelensth 16440 272 CompoundY o Absorbance f mixture 0.957 3870 6420 0.559 l" ( Pathlength b, c m): 327 3990 r.000 D: [X t: l Yl = t2 9 .0 10E + 07 4 .4 18E -05 5.9628-05 B l 0:6gx1C 5xD 6-D 5xC 6) B l I : ( E 5xD 6 E 6* D 5)/B l 0 ( E 6* C 5 E 5* C 6yB l 0 B l 2: l Chapter9 19 - 1 1 . I A 2 3 4 5 rl B C D E f Spreadsheetor s pectrophotometric nalvsis f a m ixtrre a o ( M^-l c m^-l Absorptiviry Waveleneth 266 1"" Pathleneth( b. c m) Permanganate Dichromate Absorbanceo f 420 l 6 80 1.000 4100 mixture 0.766 6 7 8 9 l0 ll 320 r 5 80 0.422 D: IPermanganate] = lDichromatel 4.2248+06 8.353E -05 1.7838-04 B l 0 : c 8* (c5xD 6_ D 5* C 6) B l I : ( E 5* D 6- E 6* D 5)/B I0 B 72: ( E 6* C 5 E 5* C 6)/B0 l t2 l g - 1 2 . ( a) , : 4 : - - 0 '463 - l . I ls x l o -4M : 8 .99g lL : 8 .99m g t ransferrinlmL x g p [Fe] : 2 .22s l 0-4M : 0 .0124 lL: 1 2.4 glmL. (b) T hes preadsheet ( TRF)]: 7 .30' l 0-5 M a nd s howshat[ transferrin t ( DFO)]: 5.22 x l 0-5 M . T hef raction f i ron i n t ransferrin o [desferrioxamine (whichinds F e3+ i , i ons) b t wo A I f fi C : n .7%. D E B f Spreadsheetor s pectroph tomelric a nalysiso f a n ixture o 2 3 4 J 1l Waveleneth ( AbsorptiviwM^-l c m^-l Absorbanceo f Transferrin Desferrioxamine mixture 428 3540 2730 0.401 4170 6 7 8 9 l0 ll 1," ( Pathlenethb, c m) = D: ITRFI : [DFO]= 470 2290 0.424 1.000 B l 0 = C 8* (C 5* D 6 D 5* C 6) B l I : ( E 5* D 6- E 6* D 5)/B l 0 B l 2: ( E 6* C 5 E 5* C 6)/B0 l t2 -3.278E+06 7.299E-05 5.224E-05 + l9-13. (a) A - - 2 0 80[HIn] 1 42 00[rn-] x (b) [HIn]: x ; [ n-] : 1 .84 1 0-4 x x + I : 0 .868: 2 080x 1 4 2 0 0 (1 . 8 4t 0 -a -x ) = x : 1 .44x l 0-4M :ppKHrn H 'o, # hl : 6.23- tog@ t0- 4)( t.44 " t o- a) x 1.44 l }-a _1 Spectrophotometry: I nstrumentsndA pplications a t7l C D A - A (H In) A (l n-)- A 0.1 0 7 0.287 0.41l 0.562 0.670 E 19-14. I A 2 3 4 J B Spreadsheetor f indins p Ka f rom s pectrald ata f Absorbanceo f pH A los(column D ) In- a t h ish n H = 0 .8 1 8 Absorbanceo f HI n a t l ow p H : 6 7 8 9 l0 0.006 3.35 3.65 3.94 4.30 4.64 0.253 0529 0.995 2.t72 4.486 -0.597 -0.276 -0.002 0.337 0.652 s 4 = ( C 4- $ A$ 8 X $ A $5 C 4) Fromt hee quation f t he o line,t hex -intercept is I < C I 0 .2 pH : 3.903 ^ -A %2 3 .95. p ThereforeKHln:3.95. 3i2 -0.2 3 .4 3 .6 I o) o -0 .6 -0 .8 pH 19-15. F irstc onvert t o A : - log T a ndthenonve rt to r : + : - 4 T c A bt:W Absorbance E ( M-l c m-l ) 2 022 A B 0.s08 6 0.0rr 4 4 | 9 93c m-l 2 022 A B l 9 93 c m-l 0 .098 4 5 0 .699 0 r 0 1 70 228.8 1 971 1 39 80 : : Fort hem ixture, zozz:- log ( 0.340) 0 .468 a ndA Dgt: - log(0.383) A 5 0.416 . U singE quations 8 l 9-5,w e f ind [ A] : 0 .009 I M a nd[ B] : 0 .004 8 M . I 6 ...
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