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Problem Set11 Solutions

Problem Set11 Solutions - CHAPTER 2 I PRINCIPLESO F C...

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Unformatted text preview: CHAPTER 2 I PRINCIPLESO F C HROMATOGRAPHY A ND M ASS S PECTROMETRY 2 t-1. 2t-2. 2r-3. Eluenti s t he s olvent r g asg oing i nto a c olumn. E luatei s w hat c omeso ut. o Smallerp lateh eightg ives l essb and s preading:0 .1 m m. b If t he f low r ate i s t oo l ow, b andss pread y l ongitudinald iffusion. I f t he f low r ate t is t oo h igh, b andss pread ecausehe r ateo f m asst ransferb etweent he m obile b p i and s tationary hasess t oo s low t o k eepu p w ith t he r ate a t w hich t he m obile phasei s m oving. I n g eneral, herei s a n i ntermediatelow r ate a t w hich t he b est t f m i t tradeoffb etween heset wo b andb roadening echanismss o btained. 2r-4. (a) G asesd iffuse m uch f astert han l iquids. T hereforeg asesc an s preado ut a long the l engtho f a c olumn m uch f astert han c an l iquids. (b) B ecausel ongitudinald iffusion i s m uch f asteri n g as c hromatography han i n t m liquid c hromatography,he f low r ate i n g as c hromatography ust b e m uch t fastert o p reventb andsf rom b roadeningt oo m uch d uring t heir p assage throught he c olumn. 2t-5. c Silanization apsp olar h ydroxyl g roupsw ith l essp olar g roups. S trongh ydrogen bondingb etweenp olar s olutes nd t he h ydroxyl g roupsl eadst o t ailing. a Eliminatingt his h ydrogenb ondingr educes he t ailing. t 2t-6. g t For q ualitativea nalysis, he m asss pectrometer ivest he m asso f t he m olecular f ion a nd t he m olecularm asses f c haracteristicragmenti ons. F or q uantitative o t d c t analysis, he m asss pectrometer etector urrenti s p roportional o t he q uantityo f analytee luted. 2t-7. s a In s piking,o n a uthentic ampleo f a s uspected nalytei s a ddedt o a n u nknownt o p I seei f t he h eighto f t he c hromatography eak f or t he a nalytei ncreases. f a n ew peaka ppears,he a ddedc ompoundi s n ot i denticalt o t he a nalyte. I f t he a nalyte t peakg rows,t he a ddedc ompoundc ould b e t he s amea s t he a nalyte. I f t he s ame i resulti s o bserved n s everal ifferentc olumnsw ith d ifferentt ypeso f s tationary d phases,t i s l ikely t hat t he a ddeds amplei s i denticalt o t he a nalyte. W e d o n ot i expectt wo d ifferent c ompoundst o b e r etainedt o t he s amee xtento n s everal p t i b differents tationary hases, ecausehe r etentionm echanisms d ifferento n e ach p stationary hase. r 86 CHAPTER 2 I PRINCIPLESO F C HROMATOGRAPHY A ND M ASS S PECTROMETRY 2 t-1. 2t-2. 2r-3. Eluenti s t he s olvent r g asg oing i nto a c olumn. E luatei s w hat c omeso ut. o Smallerp lateh eightg ives l essb and s preading:0 .1 m m. b If t he f low r ate i s t oo l ow, b andss pread y l ongitudinald iffusion. I f t he f low r ate t is t oo h igh, b andss pread ecausehe r ateo f m asst ransferb etweent he m obile b p i and s tationary hasess t oo s low t o k eepu p w ith t he r ate a t w hich t he m obile phasei s m oving. I n g eneral, herei s a n i ntermediatelow r ate a t w hich t he b est t f m i t tradeoffb etween heset wo b andb roadening echanismss o btained. 2r-4. (a) G asesd iffuse m uch f astert han l iquids. T hereforeg asesc an s preado ut a long the l engtho f a c olumn m uch f astert han c an l iquids. (b) B ecausel ongitudinald iffusion i s m uch f asteri n g as c hromatography han i n t m liquid c hromatography,he f low r ate i n g as c hromatography ust b e m uch t fastert o p reventb andsf rom b roadeningt oo m uch d uring t heir p assage throught he c olumn. 2t-5. c Silanization apsp olar h ydroxyl g roupsw ith l essp olar g roups. S trongh ydrogen bondingb etweenp olar s olutes nd t he h ydroxyl g roupsl eadst o t ailing. a Eliminatingt his h ydrogenb ondingr educes he t ailing. t 2t-6. g t For q ualitativea nalysis, he m asss pectrometer ivest he m asso f t he m olecular f ion a nd t he m olecularm asses f c haracteristicragmenti ons. F or q uantitative o t d c t analysis, he m asss pectrometer etector urrenti s p roportional o t he q uantityo f analytee luted. 2t-7. s a In s piking,o n a uthentic ampleo f a s uspected nalytei s a ddedt o a n u nknownt o p I seei f t he h eighto f t he c hromatography eak f or t he a nalytei ncreases. f a n ew peaka ppears,he a ddedc ompoundi s n ot i denticalt o t he a nalyte. I f t he a nalyte t peakg rows,t he a ddedc ompoundc ould b e t he s amea s t he a nalyte. I f t he s ame i resulti s o bserved n s everal ifferentc olumnsw ith d ifferentt ypeso f s tationary d phases,t i s l ikely t hat t he a ddeds amplei s i denticalt o t he a nalyte. W e d o n ot i expectt wo d ifferent c ompoundst o b e r etainedt o t he s amee xtento n s everal p t i b differents tationary hases, ecausehe r etentionm echanisms d ifferento n e ach p stationary hase. r 86 a nd Principles f C hromatography M assS pectrometry o 18 7 2 t-8. (a) W e n eedt o e xpress r a nd w 12in t he s ameu nits,s o t heir u nits w ill c ancel. / Let's c onvert/ r t o s econds: r 'I t/ 5 .5 5 i ( s - -+ - 5 .55769.8)2 : 4 .3sxl oap tates ( 8.7 * r iz s )2 (b) H - ( 158 m m)/(4.3sx 1 04p lates): 3 .6 t rtm 2t-9. (a) w yz:0.8 a m m f or e thyl a cetate nd2.6 m m f or t oluene. (b) t r: | 1 .3 m m f or e thyl a cetate nd36.2m m f or t oluene. T he n umbero f a l theoreticalplatesisN:5.554 l *r?z : l .l x 1 03f orethyl a cetateand.l x 103f or t oluene. ,r_rn Lr-rv' l argeoad : ( lurg..olurn r udirl 2 l r s malll oad \ smallc olumn adius/ 250m g ( turg..otu*n r uditi2 n^g:(@ = l argec olumn r adius : 3 .42c m 6 The l argec olumn s houldb e a pproximately .8 c m d iameterx 2 5 c m l ong. i The v olume f low r ate s houldb e i ncreasedn p roportiont o t he c ross-sectional T herefore he f low r ate f or t he 2 50-mg s amples hould b . ( #:A)'z t (3.4't m\2 c times a s g reata s t he f low r ate f or t he l Z-mg s ample: [ gJs , ", ( 0.8 m L/min) : area( .c r \. 17 m Llmin. 2l-ll. 5.ss _ 5 .55 13.81 in) 2 ( m 4 _ 3 8 x 1o a : ( a) w y2:0.172 m in = , ly' --:'5 P lates * iz Q .l7zmiin)2 x (b) H : p late eight: ( 30.0x 1 03m m)/(3.58 l Oap lates): 0 .838m m h (c) w(measured): 0 . 3 m1 1 in : wlw12( measured)( 0.31 min) / ( 0.172): 1 .81 I 2l-12. : ( a) w lp ( heptane) 0 .126m in; w yz (Ca H+ F ): 0 . 1 l9m in 5 .55 ( m 4 - 5 . 5 5 1 4 . 5 6 in )2 : 7. 41x l 0a p latesor h eptane f ,\:---:^, * t iz Q .126m in)2 : * p m H: p lateheigh t 3 0 . 0 m1 7 . 4 1 1 04 lates: 0 .404 m ly' : 5 .55( 14.77 . min)2 : u ' )) x l0a p latesor C 6HaF2 f g (0.11 ^tF a nd Principles f C hromatography M assS pectrometry o 18 7 2 t-8. (a) W e n eedt o e xpress r a nd w 12in t he s ameu nits,s o t heir u nits w ill c ancel. / Let's c onvert/ r t o s econds: r 'I t/ 5 .5 5 i ( s - -+ - 5 .55769.8)2 : 4 .3sxl oap tates ( 8.7 * r iz s )2 (b) H - ( 158 m m)/(4.3sx 1 04p lates): 3 .6 t rtm 2t-9. (a) w yz:0.8 a m m f or e thyl a cetate nd2.6 m m f or t oluene. (b) t r: | 1 .3 m m f or e thyl a cetate nd36.2m m f or t oluene. T he n umbero f a l theoreticalplatesisN:5.554 l *r?z : l .l x 1 03f orethyl a cetateand.l x 103f or t oluene. ,r_rn Lr-rv' l argeoad : ( lurg..olurn r udirl 2 l r s malll oad \ smallc olumn adius/ 250m g ( turg..otu*n r uditi2 n^g:(@ = l argec olumn r adius : 3 .42c m 6 The l argec olumn s houldb e a pproximately .8 c m d iameterx 2 5 c m l ong. i The v olume f low r ate s houldb e i ncreasedn p roportiont o t he c ross-sectional T herefore he f low r ate f or t he 2 50-mg s amples hould b . ( #:A)'z t (3.4't m\2 c times a s g reata s t he f low r ate f or t he l Z-mg s ample: [ gJs , ", ( 0.8 m L/min) : area( .c r \. 17 m Llmin. 2l-ll. 5.ss _ 5 .55 13.81 in) 2 ( m 4 _ 3 8 x 1o a : ( a) w y2:0.172 m in = , ly' --:'5 P lates * iz Q .l7zmiin)2 x (b) H : p late eight: ( 30.0x 1 03m m)/(3.58 l Oap lates): 0 .838m m h (c) w(measured): 0 . 3 m1 1 in : wlw12( measured)( 0.31 min) / ( 0.172): 1 .81 I 2l-12. : ( a) w lp ( heptane) 0 .126m in; w yz (Ca H+ F ): 0 . 1 l9m in 5 .55 ( m 4 - 5 . 5 5 1 4 . 5 6 in )2 : 7. 41x l 0a p latesor h eptane f ,\:---:^, * t iz Q .126m in)2 : * p m H: p lateheigh t 3 0 . 0 m1 7 . 4 1 1 04 lates: 0 .404 m ly' : 5 .55( 14.77 . min)2 : u ' )) x l0a p latesor C 6HaF2 f g (0.11 ^tF r88 H - p late eight: 3 0.0m / 8 .55x 1 04 lates: 0 .351 m h p m : (b) w ( heptane) 0 .214 in; w ( C6HaF) : 0 .202min m Chapter l 2 : w ^v : * ro.T4+ o . z o 2 ) o . 2 o g m in : resorurion * ")1 1 a Lr'rr' : 1 {hf1e : r .or 2 , a/ L argel oad : ( turg. . oturn r uOiril (,^\ S mallload_ ( @ ' 12 1 .50 m c ,. 2.4 m e ( = r a d iu s : 0 . 5 5 7 c m ( .m l0^ 0;;: = d iameter: l .l I c m ( Lengths u nchangedt 3 2.6c m.) i a (b) S cale olumei n p roportiono m ass f a nalyte v t o : = v olum. ( ## \v,' S mall f low r ate mllmin. 2l-14. ,^l ( o.5ooL): o .o6e L m m c I O.SSZ m/ 2 f . ,^\ L arge low r ate _ ( l"rg. . "lur" r .Oirl _ f t .SO *_) z \ small c olumn r adius/ Puttingi n l argef low r ate: 1 .85m llmin g ivess mallf low r ate: 0 .256 5 0 c m o f c olumn w ith a d iametero f 0 .25 m m h asa v olume o f x P x l ength: zr(0.0125 m)zx 5 0 c m : 0.0245 c m3 : 0.0245 m L. A f low r ateo f 0 .0245 m '-is c coffespondso ( 0.0245 m l/s)(60 s /min) : 1 .47m llmin. t A\ : fl 2 l - 1 5 . ( a ) r " i _ r,ffi!q ) = L.rr 3 473 : , ( ) 0222 \ , . 72m M )r 3 A? \l ^ N4 F :0. l 68a ( b ) t s l : W : 0 . 8 4 7m M (c) Av ^ , l :I[ts i l = Lx - (l s) ( J4? s 42s: 0 ' 1 6 8 a t 04 43t n\, , M ] = : 6 ' 1 6 m M [x] IXf (d) T he o riginal c oncentration f [ X] w as t wice a s g reata s t he d iluted o concentration, o [ X] : 1 2.3m M. s 2l-16. F irst f ind t he r esponse actor f rom t he k nown m ixture: f Ag : , (D 4 .42 : - r J .sz ) : n [ tD, = n 6 t tst^L F lzn r g^t1 = F t 't4:q lq Then f ind t he c oncentration f C i n t he u nknown m ixture: o P rinciples f C hromatography M assS pectrometry o a nd r 89 t cl : 6 4.5a t rtglmL : 1 61 p glmL 3.33 -: tcl I . 1434 ( 2.22 il 230p g125.00 L m 1)= ) : [C] i n o riginal u nknown 2l-17. ( a) T he s preadsheetnd g raphb elow s how t hat m inimum p lateh eight o ccursa t a a f low r ate o f 3 1.6 m Llmin. A B A + B /u+ C ul C I 2 3 4 5 van D eemter c alcu ati ons[ H : A (m m ): B( m m * m l- / m i n ) : Flow r ate ( u. m llmin) H (mm) 1.5 25 C( m m * m in/ m l ) : 2 5 l0 20 30 3l . 6 40 80 t20 r4 .050 6.625 4.250 3.250 3.083 6 8 9 l0 ll 0.025 3.081 3.125 3.81 3 4.708 l3 l4 15 + C 4 : $ A $ 4+ $ ,4$6/84 $ A $8* B 4 12 H(mm)= A +Blu+Cu A =1'50mm C=0.0250mm'minlm ge -c .9 E e6 g o o -3 3 1.6 | 10 20 44.7 + 50 60 I = 5 0.0m m'ml/min A 40 B = 2 5.0m m'ml/min 70 80 90 1 00 1 10 1 20 30 Flow r ate ( mL/min) (From c afculus,he m inimum o ccursw hen d Hldu: 0 . t dHldu: - Blu2 + C: uoptimum 0 = E :\e: 25.0 : 3 1.6m l/min 0.025 0 (b) I f t he r ateo f l ongitudinald iffusion i s i ncreased, e m ust r un t he c olumn w fasters o t hat t he b andsd o n ot s pread oo m uch. T he o ptimum f low r ate t shouldi ncrease nd t he o ptimum p lateh eightw ill b e l arger( worse)t han a with t he s lowerl ongitudinal iffusion. T he g rapha boves howst hat d oubling d 1 90 C hapterl 2 B i ncreaseshe o ptimum f low r atet o 4 4.7m llmin. t (c) I f t he r ateo f e quilibration etweenp hasess i ncreased, e c an r un t he b i w column f asterw ithout s preadinghe b andst oo m uch. T he o ptimum f low r ate t shouldi ncrease nd t he o ptimum p lateh eightw ill b e s maller( better)t han a with t he s lowere quilibration etweenp hases. b 2l-18. ( a) l {mm) : A +B/u+Cu = ( l.50mm)+ 25.0m m.mllmin + ( 0.025 m m.minlmL)(20.0 0 m llmin) 20.0 m Llmin = 3 .25 m m (b) H : L IN ( Z: c olumn l ength,.A/: n umbero f p lates) ly' : L IH : 2 .00 m /0.0032 5 m : 6 15 p lates 5 .5 5 2 (c) / v: I *2 wiz ) r tt2: tr 5 . 5 5: ( 8.00 in) m il 5 . 5 5: m 6 1 5 0 .760 in 2l-19- M olecular m ass i s a w eighteda veragem assb asedo n t he n atural a bundance f a ll o isotopes n t he m olecularf ormula. T o c omputem olecularm ass,w e s um t he i atomic m assesistedi n t he p eriodict able,w hich a re w eighteda verages f t he l o isotopeso f e ache lement. N ominal m assi s t he i ntegerm asso f t he s peciesw ith the m ost a bundant f e acho f t he i sotopesn t he f ormula. o i : CoHom olecularmass 6 x 1 2.010 + 6 x I . 0079 4 : 7 g.l I I g 7 CoHonominal ass:6x 1 2+6 x l :78 m 2l-20. A tomic m asso f c l : I (atomic m assx n aturala bundance) = ( 34.9685X0.757+ ( 36.9650X0.242 3 5.453 8 S) 9 2 ): Happily, v aluen r he eriod t he i p t ables a lso3 5.453. i 2 t- 21. C+H11N3S+:4 t2C:4x ll l H: l l x 1 .007 25= 8 3 l 4N:3 x 14.003 7 : 0 329: subtractI e lectron sum +48 ( exact) +l 1.086 75 0 +42.009 l 2 +31.972 7 0 5 - 0 .000 49 r3 3 . 0 6 6 1 8 ...
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