Problem Set9 Solutions

Problem Set9 Solutions - C HAPTER 1 8 LET T HERE B E L IGHT...

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Unformatted text preview: C HAPTER 1 8 LET T HERE B E L IGHT l8-1. l8 - 2 . ( a) d ouble ( b) h atve ( c) d ouble ( a) E = h v: h cl),=(6. 6 2 6 )x lQ -3 4 1 )e . 9 9 7 9 xl 0 8 ms -r; / 1 O S O0.-e m) l, = 3 .06x l Q-l9J/ p h o t o n = (3.00 l O-leJ /photon)(6.022 x l g23p hotons/mol) 1 .84 1 05 /mol x J ' ( x l 0) . 8a. ,^s J ) f l k J ) : t8 4 k r ll tr m orJ o oo-l t f fi (b) F or), : 4 00 n m, E : l8-3. (a) (b) (c) l8-4. w avelength 4 50 n m 5 50 n m 6 50 n m 4 .97 x l Q-l9J/photon- 2 99 k J/mol. c olor t ransmitted o range v iolet-blueo r v iolet b lue-green c olor a bsorbed b lue y ellow o r y ellow-green r ed T ransmittanaeD i s t he f ractiono f i ncidentl ight t hat i s t ransmitted y a ( b : P /Po,w hereP o i s i ncidentp ower a nd p i s t ransmifted substance: T p ower. Absorbance s l ogarithmically elatedt o t ransmittance: : - l og7. W hen a ll i r A light i s t ransmitted, bsorbances z ero. W hen n o l ight i s t ransmitted, bsorbance a i a is i nfinite. A bsorbance s p roportional o c oncentration. olar a bsorptivityi s t he i t M constant f p roportionality etween bsorbance nd t he p roductc b, w herec i s o b a a concentration nd b i s p athlength. a l8-5. 18-6. A bsorbance r m olar a bsorptivityv ersusw avelength o T he c olor o f t ransmittedight i s t he c omplement f t he c olor t hat i s a bsorbed.I f l o blue-green ight i s a bsorbed,he e ye p erceiveshe t ransmitted ed l ieht. l t t r V iolet-blue, ccordingo T able l 8-1. a t U singv : c lX, i v(hz) i(cm-t; J/photon kJ/mol : l l)\.and E : h v,we f ind 2 .5 p m t .20xl0la 4 000 7 .95 x 1 0-20 4 7.9 l8-7. l8-8. 250 n m l .20xl0ls 4 .00x10a 7 .95 x l O-le 4 79 158 I I I L et T hereB e L ight r 59 18-9. E : h v : h cl)":(6.626)x l g-3al ) Q.9979 x 1 08m s -l)/(10.6 1 0-6 ) m " : 1 .87ax l Q-20 /photon J 5 'o x l o r J /s = 2 J x l Q23p hotons/s( almost 5.0 k w : 5 .0 k J/s =t@ half a m ole o f p hotonsp er s econd) = l8-10. A = - log T . F ore xample, T = 0 .99, : - log ( 0.99) 0 .0044. if A Transmittance:.99 0 Absorbance: 0 .004 4 0.90 0 .046 0.50 0 .30 0.10 0.010 0.0010 0.0000 1 1 .00 2 .00 3 .00 4 .00 x ( e) l8-11. F ora m olara bsorptivity o f 1 .00 1 6214-l m-1, s : ( 100M -l c m-1 x 2 . 0c m)(0 . 0 0 2 4 0) : 0 . 4 8 0 A = e bc 0 M ( e) For a m olara bsorptivity o f 2 .00x l g2 V 1-ls r-1, A = ( 200M -l c m-1x2.00m)(0.00240 ) : 0 .960 c M Transmittanceo btained y r aisingl 0 t o t hep owero n e ach ideo f t hee quation: is b s logl: l6log7 ' : l0lo8ri s t he same s7 ' a ForA:0.480, T : ForA :0.960. T : : l g-0.480 0 .331 : 33.1% : l g-0.e60 0 .110 : 1 1.0% -A l 0-A Transmittances n ot l inearlyr elatedt o a bsorbance r c oncentration. oubling i o D the a bsorbance oesn ot d ecreaseransmittance y a f actoro f 2 . d t b 18-12. ( a) S PF: l /T. T herefore,: l /SPF: % :0.5: 5 0%.H alfo f t heU V-B T radiations t ransmitted i t hroughhes unscreen.hism akes ense, ecause t T s b y SPF: 2 i s s upposed p rotect ou f romt wicea sl onga n e xposuresy ou to a wouldn eed ithout unscreen. - log 7 : - log 0 .5: 0 .30 w s A: : (b) F orS P F 1 0,T : l / 1 0: l 0 % . A : - lo g T : - lo g (l/ 1 0:) l . ForS P F - 2 0,T : l l2 0 : 5 % . A : - lo g T: - lo g (l/ 2 0:) 1 . 3 0 The S PFI 0 s unscreen a bsorbs 0%o.ndS PF2 0 a bsorbs 5%o f U B-B 9 a 9 radiation. 18-13. e : A lbc: 0 .8221 1 (l. 0 0 c rn )(2 .l3 1 M)l : 3 . 5 6 x l 0 4 M-l c m-l " 0 -5 t 60 Chapter8 l 1 8 - 14. ( a) c : A leb: 0 .244/ [ (s . 8 3l 0 4 M-t c m-lx 0 . l0 0 c m)]: 2 . 7 6 x l 0 -5 M x (b) ( 2.76 l 0-5 m ot/L)(8l0 00g /mol) : 2 .24g tL ' : 18-15. ( a) C oncentration @ 5 x l 0 -3 L ':7'80 x l 0 -3 M (b) O net enth ilution= 7 .80, . l 0-4M d (c) e : A lbc:0.634/[(0 . 5 0 0 c m)(7 . 8 0 x -a M)] : l0 1 . 6 3 x l 0 3 M-1c m-l l8-16. ( a) A bsorbance easuredn t heg raph t 3 50n m i s 0 .052. m o a : = (b) T : 1 0-A 1 9-0'0s20 .89. 8 9%o f t he l ightp asses t hroughhes unscreen. t 18-17. ( a) A : - log P lPs : - logT: - log ( 0.45): 0 .347 (b) T hea bsorbanceill d ouble o 0 .694,giving : l 0-A : 1 g-0.6ea 0 .202 : w t T o /oT:20.2%. = e : 18-18. o riginalconcentration Q '267i ll(3-17Q9 lmol\ : 7 ' 9 1 x l o -3 M (o l o o 0 L ): / 2'ooom L\ Q .91 x l 0-r M ) : I . 58x t 0-4M Diruted on c centration ( .f O On LJ , e: A: bc @ 0 .728 = 2 . 3 0x l Q 3l \ 4 -lg m-l 18-19. ( a) I dealg as l aw: P V: n RT. M olarc oncentrat L = L i on: V RT. To c onvert .3 p bar:4.3 x 1 0-6 art o m ol/L,w e w rite 4 b n V: P 4 .3 x 1 0-6 ar b R r:ffi:l'74x1 0 -7 M r 45 10.083f fi,J(2es K ) Relationb etweena bsorbance nd t ransmittance: : _ los.T a A = 83.8%Tc orresponds = - 1og0.838 0 .0768 t oA I t I -l L et T hereB e L ight l6l ( T ransmittance%o) Absorbance ( ( Pressurepbar) C oncentrationpM) +.) A1 0.174 0.460 0.807 1.22 2.45 4.02 5.43 83.8 61.6 39.6 24.4 5.76 0.857 0.147 11.4 20.0 30.3 60.7 99.7 134.5 (b) e : 0.0768 0.210 0.402 0.613 1.24 2.07 2.83 f ;. f n"pathlength, D , i s 3 .00 c m. T he q uotientA lc i sthe s lopeo f t he graphb elow, w ith c oncentration hanged rom p M t o M . c f 5 . 2 3x l g s M -l : A x e : 6 r: 1 . 7 4 l Q 5\ 4 -l s m-l 3 J 0 c m3.0 -0026 : Srope0 .s23 # ' ft* : s .23 l g5 -r xv (D o C 2.0 | € 1.5 , o 1 .0 r 0.5 l 0.0 .A ( pM) C oncentral i on n /l 18-20. ( a) r (b) c (c) c cb A 0.624 0 .029 = 1 .50x l Q3 y -l s m-l ( 3 . 9 6 l 0 -4M )(1 . 0 0 0 m) * c 0 .37s 0 .029 2 . 3 1x l 0 -4M 4 . 6 9 x l 0 -4 M = M d i l A_ 0 . 7 3 3 -0 . 0 2 9 x ( 1 . 5 0 1 0 3 -l . r-lX 1 . 0 0 0c m) xb M (d) M OirV atl : M .on. Z .on. : r M .on. M air #: : s .87 ( .6e,10-4 )(rJ'*12!-q9IL)\ t o-rM M L et T here e L ight B t67 18-29. ( a) T hec oncentration p hosphate s olution i s L l96 x l Q-31 4. of in A When .140 L o f A i s d ilutedo 5 .00m L, 0 m t : e] [phos ph a(tl. le 6 x l 0 - 3 m g m ) : 3 . 3 4 e xg - s M l x e : A lbc : ( 0.829- 0 .017y[(1.00 m)(3.34e 1 0-5 )] : c M 2.425x 1 6414-lg m-I. (b) [ phosphate]n a nalyte: i * : : 3 .29,,| 0 _s M But t hisp hosphateadb een iluted rom0 .300 L t o 5 .00m L. T herefore h d f m the o riginalc oncentrationf p hosphate as o w : M oitZait M.on.Z.on. : x Mconc(0.300 : ( 3.29 l 0-5M X5.00 L) 3 M conc 5 .485 l 0-4M m L) m " Theo riginal olume f d igested v o f erritinw as 1 .00 L, w hichc ontains1.00x ( m : 5 .4g5 l 0-7m olphosphorus: .69e t 0-5g p x x x l0-3L X5.485 l 0-4M ) 1 wt%phosphorus: l 00x L69qx l 0-5ephosphorus f fi: 1 .26?o ...
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