Problem Set13 Solutions

Problem Set13 Solutions - C HAPTER 1 1 POLYPROTIC A CIDS A...

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Unformatted text preview: C HAPTER 1 1 POLYPROTIC A CIDS A ND B ASES a b o P ointA i s a s olution f a w eaka cid,H 2A,w hiche ffectively ehavessa H f p a monoprotic cidw hose H i s c omputedrom t he r eaction 2A + H A- + H +. p o PointB i s a m ixture f H 2A a ndH A-, w hichi s a b ufferw hose H i s c omputed P p e quation H : p Kr + l og([HA-]/[H2A]). oint fromt heH enderson-Hasselbalch p o p oint-a s olution f H A- w hose H i s g iven C i s t hef irste quivalence w o b yi(pfr + pK).Point D i s a m ixture f H A- a ndA 2-, hichi s a approximately e quation: H f p bufferw hose H i s c omputedrom a nother enderson-Hasselbalch p oint, hichi s a w e P pH: p Kz+ l og([Az-1ltHA-]).ointE i s t hes econd quivalence t f a A o solution f t hew eakb ase ,2-t hatc anb e t reated sm onobasicor c omputinghe + pH: A ,2- H 2O = : H A- + O H-. ll-1. tr-2. H SO; &r = 1 .03: l 0-, B f romA ppendix ) SO?- + H + ( Kazcomes # + H zCzOa, OH- KbZ: K wlK a l : 1 . 8 6 x l Q - I 3 HC2Oj + H zO B (Kar c omes rom A pPendix ) f l1-3. l Kat: f t : 7.09x o-3 Kat:#:4.2x l s -13 Kaz:#:6.33 x lo-8 tl-4. R +l H3l.{- c F{- c oz pK v alues pplyt o ]-NH 3 , - cqH a Kbl : K slKv2 : 5.38x 10-5 R c a nd,i n s ome ases, . 1l- 5 . N H+ HN \_,/ Hzo Kb2 : K *l K v 1 : 2. 1 5 x 1 0 9 HN \-J N H; + I O H- HN \-J N H7 + + + HzO -+ Kbl = K *lKu2 : 2. 5 6 x l O e H"N .\_J N H; + o HL J CO; L ,cozH O>co; -+ H zo cot 19 80 ChapterI I co2H CO; + H zO K V : K *l K s 1 : 8.93 10-12 " -.t(- co2H co2H 11-6. \+N , rcoa ' --/ \ H2 i;il +co; H Kaz +H + -o tt-7. + HzO: + o H- o- o- K* Kut : * * : 2 .49x l0-8 Kw Xuz : X uz : 5 .78x I Q -10 K* x Kb3 : K ^ : 1 .34 l0-l I NHr +NHr Kat -LL l1-8. CHCH2OH + H 2O --CO; +NHr I CHCH,,OH + O H- K Ur : K *lKu2 : 7 .62x l 0-> CO; +NHr Kaz I I cHCH2OH+H2O + CO; I l -9. I : : CHCH?OH + O H- K Uz K *lKul I . 54x l 0-12 c02H I I (a) W e t reat H zM a s a m onoprotica cid: H2M F-x u2 H + + H Mx x K1 : 1 .42x l 0-3 ''^ : K l ) y : l . l2 x l0 -2 0.100x - : 0.089 M [HzM] : 0 .10 0 x tHM-l : x : l . l2 x l 0 -2 M p H : - lo g x : 1.95 tM2-l _ [ HM-]K z : 2 .01x 1 0_6 M IHn] P olyprotic cidsa ndB ases A 8r (b) HM- i s t he i ntermediateorm o f a d iprotic a cid. T herefore, f : p H= * fp x, + p K z ): ) { z.t+ 7 + 5 .696)4.27 = [ H*]:5.3sx l 0- 5 M tH M-l = Q .l o o M _-- ^ _ K zIHM-l [ HzM ]: W : 3 .8x r o- 3M l M ' - l f f i : 3 . 8 x1 0 - 3 M (c) M2- + H 2O * F- x x2 H M- + O Hx x K ur : K yllKv2 : 4.9gx l 0-9 Ol00_r : K bl = . r: 2 . 2 3 x l. ^ E 0 -5 p H: - lo g ; : Kw 9.35 M [M2-] - 0 .100-x : 0 . 1 0 0 t HM-l : x : 2 . 2 3x l 0 -5M l-H+ll-HM-t * 'fr- [H z MJ : : 7.04x10-t2 l1-10. ( a) W e t reatB a si f i t w erea m onoprotic ase: b t otSto-t B + H 2o B H++ o HK al : K *rK62: r .00 x l 0-5 O . loo- x x2 x x Ka2:Kyy/K61:1.00x10-9 Kw 0100_, .^ A : K bt : > " r : 9 . 9 5x 1 0 -a = [ H* ] : ? : 1 . 0 1 x l 0 -ll M [B H*] : x :9.95x l 0 -4 M : ) p H: 1 1 . 0 0 0.0990M t B l : 0 . 1 0 0 -x : * , H 2 ; , : % | 4 : r.o o xlo - e M (b) B H+ i s t he i ntermediateorm o f a d iprotic a cid w ith a cid d issociation f constantsK 6 a ndK a2 c omputedi n p art ( a). : pH= * ox*+pKaz): ] ts.oo 9 .00) 7 .00 [ H*]: I . 0s x + = M [BH*] = S .100 l 0-7 M rBH2;,: {fl S 1 0 -3 M : r .ox10-3M : tBlffi:r.ox BH'; = 0 .1 0 0 x x2 0100_"{ : (c) W e t reatB H'; a sa m onoproticcid: a B H+ + H + x Kat = x r: [H*] : 9.95 x l 0-4M K at : l .o0 x l 0-5 P olyprotic cidsa ndB ases A 83 I l -14. ( a) D iprotics ystem: Ac idic Basic pKt PKz % (p K r+ p K2) PKt: %(pKt+ p K): PKz: (b) M onoprotic ystem: s Ac idic Basic lHzAl : [ HA-J lHzAl= 1 42-1 IHA-I: J 42-1 HAlepKu PKa: Triprotics ystem: Ac idic Basic lHAl: [ A- ] H:A HzA- HA2- 43- PKttpKztpKt %(p\ + p K) % (pKz+p K3) PKt: + Yr(pKr p K): PKz: + %(pKz p K3): pK:: ll-15. [H:A] = [ HzA-] lHgAl - [ HA2-] lHzA-J: [ HA2-] lHzA-l: J A3-1 : lHnz-1 J A3-1 ( a) A t p H : p Ka,the c oncentrationsf H A a nd A - are e qual. o A t a p H b elow pKa,H A i s t he d ominantf orm. (b) A t a p H a bovep Ka,A - i s t he d ominantf orm. (c) p H : PKa r A + ili^i + 7 .00 -r 7.0 : 0 7 .0 0 +t ogH IHA] - [ A-]ilHAl: 1 .0 6.00 : I l -16. ( a) 4 .00 rnl ' o*i rol : = [ A-]/[HA] 0 .10 (d) H A- (b) 8 .00 ( c) HzA (e) s 2- 84 lt-t7. H3PO4 H2PO4 Chapter l 1 HPOoz- Poo:- pH : pH 2 3,4 5,6,7 8,9 10,11 ,12 l3 2 .ts 4 7.20 A 9,77 12.38 4.6 7 predominantorm f H3POa H2POaH2POa' second ostp revalent orm m f H2POaH3POa HPOozH2POaPOo:HPOoz' HPooz' HPOozPO43- rr-18. ( a) e.00 ( b) 9 .00 ( c) B H+ t rr.f + [ B]/[BH+] 1 .0x 1 03 - (d) 1 2 .0 0 9 .0 0 1-l og t Bl - 1l-19. ( a) Kat= K y1lK62 = ) p Kat= p Kw7 KUZ: 1 4.00 7 .15: 6 .g5 Ka2= K y,lK61 + p KaZ: p Kw- p KUt= 1 4.00 4 .07: 9 .93 - 8. 3 9 (b) [ BH*] - [ B] a r p H e .e3 (c) [ BH*] = [ BHz;] a t p H 6 .85 (d) p H 4,5,6 7,8 9B H+B 10 B B H+ (e) A tpH 1 2.00, i s d ominant ndB H+ i s t he s econd osta bundant B a m s pecies. Therei s a n egligible mount f B H22+. heH enderson-Hasselbalch a o T e quation for B a ndB H+ i s p redominantorm f B H,; B H+ s econd ostp revalent orm m f B H+ B HT pH: pKa2l"g + ffi l2.oo=9.^er + 't og I B I ''l f fi : ) [ B]/[BH+] 1 ,2 1 02 x - P olyprotic cidsa ndB ases A 85 (f) A t p H 2 .00,8H2; i s d ominanta nd B H+ i s t he s econdm ost a bundant pecies. s e quationf or There i s a n egligiblea mounto f B . T he H enderson-Hasselbalch BHz;a ndB H+i s pH : p Kat + f ogf 4 E 2.oo: 6 .85+ r on !* - t BHi l = [BH+]/[Bn']l : 1 .4x 10 -5 : 1vn2|1t1BH*l7 .1x t oa r 1-20. NHr pH 9 .00 pH 10.00 NH, I Predominantorm: f CHCH,CO; t" II CHCH,CO; + NHr CO; NHr Secondary orm: f CHCH?CO; tt" coi I CHCH, CO , CO; t" CO; pH 9 .00 pH 10.00 Predominant f orm: -ozc€or T "' - ozc€o" T "t -ozCfu-" ll-z1^ ( a) C alling t he t hreef orms o f g lutamineH 2G+,H G, a nd G -, t he f orm s hown i s w G-, w hich i s t he f ully b asicf orm. T reatingG - a s m onobasic, e w rite G-+HzO+ HG + O HF- x Kbl : K yllKa2: l .0o x 1 0-5 K b r= "Lrr-r: x: 9 .95x l 0-4 M = PH : K * lx : 1 1 . 0 0 86 I ChapterI (b) C alling t he f our f orms o f a rginineH 3A2+,H2A*, H A, a nd A -, t he f orm showni s H A. pH = i O* r+p K r ) : ) $ s s l + l 2 . t ) : 1 0 . 5 t t-2 2 . "-t{-Itr:", eY H is a Pyridoxal-5-phosphatet etraprotic o w system ith p Kuv alues f 1 .4,3.44,,6.01, t and8 .45.A t p H 7 .00, hep redominant h species asl ost3 o f t he4 p rotons. 1r-23. i", ,/ / frH, I ^cH-cH | 0H20H2NHC I LL' \ PK3: F or 3Arg2*Kt: 1.823 H P p Kz: 8.991 CO; N HZ 12.1 H2Arg- f ound i n A rginine ' HCl pH = * 6K r + pK ) I : 5 . 4 1 = [ H* ] : 3 . 9 , . 1 0 -6 M [ H3Arg-1 - W H3Are2+,: l o: r .3 x l 0-5M [HzArg+][H+] -T11,p*z+f : K t) K t) lHAre.l[H+l_ IH2Arg+] fArg-llH+l _ IHArg] ll-24. H 3Cit K23 [ HArg]:fi: f K3= [ Arg-]:ffi:3xlo-l2M H 2Citp KZ: 4 .761 € H Cir-- l .3xl o-sM pKt: 3.128 : : p K3 6 .396 ., =C ir'- At p H 5 .00, H Cit2-i s d ominant. l l-25. ( 100.0m L)(0.100 ) : M \_------------- m m ol H 2A V e{1.00M ) = \___________-v_ V et : 1 0.0m L mmol O H- Vez: 2 Vet : 2 0.0m L V6 pH 0 m L: 0 2 .51 5 .0 4 .0 0 1 0.0 6.00 1 5.0 8.00 2 0.0 2 2.0 10.46 t2.21 a a o T hisi s a s olution f H 2A,w hichw e t reat sa m onoproticcid. P olyprotic cidsa ndB ases A a VL 87 H A -+H+ x x HzA = 0 .1 0 0;r ffi- : K t: 1 9-a'oo l 0 -3 M = p H: 2 . 5 1 =x:3.11x 5.0 m L: p H alfivay t o t he f irst e quivalence oint w e h ave a n e quimolarm ixture o f HzA a nd H A-, ( Aha! A b uffer!) w ith p H : p Kr : 4 .00 p 10.0m L: T he f irst e quivalence oint g ivesa s olutiono f H A-, t he i ntermediate form o f a d iprotic a cid w ith p H = ) @n + p Kz) : 6 .00 p 15.0m L: H alfivay t o t he s econde quivalence oint w e h ave a n e quimolar : p Kz - - 8 .00 mixture o f H A- a nd A 2-,w ith p H p 20.0 m L: A t t he s econde quivalence oint, w e h ave a s olutiono f A 2-, w hich w e treat a s m onobasic ith a f ormal c oncentration f F ' : 0.083 3 M w o becausehe o rieinal 1 00 m L s olutionh asb eend ilutedt o 1 20 m L. t + A2- Hzo 3 F ' -x (1 0 0m L )(0 .1 0 M ) 0 F ' :w :0 ' 0 8 3 3 M HA- + oHx x Kw : d.d$3., K bt:'fr = y2 x : 2 . 8 8 x l 1 -aM > K* p H: -lo g ; : 10.46 2 2 .0 m L : N o w t h e re a re 2 .0 m L o f e xcessO H - toH-l: W 12 10 8 :E o-6 4 2 : 1 .64 to-2 = p H : t 2.21 x M vb rr-26. ( I 0 0.0m L)(0.1 0 M ) : VerQ.0O ) = 0 M mmol H 2A m mol O H- V er : 1 0 . 0 L m VeZ- - 2 Vet : 2 0.0 m L 90 Chapter 1 l 80.0m L: B h asb een onvertetoBH]j' a t a f ormal oncentration c d c of (40.0 LX0.l00 ) m M: 0 .033 M 3 120.0 L m BHt 0 .0 3 3 - x 3 ., + Kat a B H- + x H+ x : K al + 0.033- x 3 x x: 3 .91 1 0-4M = + p H : 3 .41 xL 100.0 L: E xcessH*] : m [ 12 10 8 E6 o 4 2 ( 20.0 LX0.l00 ) m M + l40.0m l- p H_ 1 .85 20 40 va 60 80 100 tl-29. T he t itrationr eactions etweenhe t riprotica cida ndt he s trongb asea re b t H3P O4+OH-+HrP O o + H2 O (25.0 l)(0.0a00 ) _ Z e1(0.0500) = m M M HrPOj + O H- - + H PO?-+ H zO + HPO2; + O H- - + P O3o- H zO V er : 2 0.0m L V ez: 2 Vet : 4 0.0m L Vg _ 3 Vet = 6 0.0m L The d ominant pecies iagramor p hosphoric cidl ooksl ike t his: s d f a H3PO4 H2PO4 HPOoz- Poo:PKt pH: 0 m L: z .ls PKr 4.67 PKz t 7 .20 4 9.79 1 2.38 0 .0 4 0 -.r 0 W e h avea s olution f 0 .0400M H 3POa hichw e t reata sm onoprotic: o w ') Kr xH3P O4 + H 2 P O ; + H+ 0 . 0 4 0 -x - ^ l 0 x x x:0.0137M = p H_ 1.86 P olyprotic cidsa ndB ases A 91 10.0m L: H alfway t o t he f irst e quivalence oint, t here i s a I : I m ixture o f H rPOo p andH rPOi, s o p H : p Kl : 2 .15 20.0 m L: A t t he f irst e quivalence oint, H 3PO4h asb eenc onverted o H 2PO;, p t the f irst i ntermediateorm o f t he p olyprotica cid. T herefore, f pH = * ( p r r + p K z ) : I e t s + 7 . 2 0 ): 4 . 6 8 30.0m L: H alfuayt o t he s econd quivalence p oint,t herei s a l : I m ixture f e o : p Kz: 7 .20 H2PO;a ndH PO2a-, p H so 40.0m L: A t t hes econd quivalence p oint,H 3PO4 asb een onverteA H eO2o-, e h c to the s econdntermediate i f orm o f t he p olyprotic cid. T herefore, H = p a ll : : ,(pK z + p K r) r (7 . 2 0+ 1 2 . 3 8 ) 9 . 7 9 42.0m L: W e h avep assed s econd quivalence t he p ointb y 2 .0 m L, w hichi s 1 /10 e of t hew ay f romt hes econdo t het hirde quivalenceoint. W e h ave p t converte I l l0 o f H PO2;i ntoP O34-, d l eavingg ll0 i n t he f orm U YO2; . We h avea b ufferm adeo f H PO2a- P O3o-overned y t he g a nd b Henderson-Hasselbalch e quation pH : p K 3 + lo g Po34-l tHPo?-l : 1 2.38 + f #fi : n .43 ' o, The s ix p oints i n t he g raphb elow a re t he o nesw e j ust c alculated.T he solid l ine w as c omputedb y s preadsheetsing e xacte quations or t he u f titration. T hesee quations o n ot m ake t he s implifying a pproximationshat d t we h aveb eenu sing. T he a pproximate oint w e c omputeda t l 0 m L p (halfwayt o V s1)h asa s mall e rror b ecause 3POai s a r elativelys tronga cid. H Our a pproximations nderestimated f ractiont hat i s d issociatedo H 2PO; u t he t There i s a m uch m ore s eriouse rror f or t he p H c omputeda t 4 2 m L, which i s b eyond 2 .2. H Po?- i s s ucha w eak a cid ( pK3 : 1 2.38) hat i t h ardly t reactsw ith O H-. I t t akesa g reatd eal o f 0 .05 M O H- a ddedt o t he e xisting volume o f s olutiont o r aiset he p H t oward 1 2. F or e xample,i f w e a dded2 mL o f 0 .05M O H- t o 6 5 m L o f p lainw ater,t he p H w ould b e I 1.17. Y er w e computedhatt he p H a t 4 2 m L i n t he t itrationw ould b e 1 1 .43. O ur t approximate ethodsf ail c ompletelyi n t his e xampleb eyondt he s econd m p equivalenceoint. 92 ChapterI I 13 11 o oi Ll I I o_ . *o t - i I ,r I J o 1 40 V ol ume o f b ase ( mL) bU 11-30. H 'T H'- , - N H f r YN H H: 1 'li I t rNH t.orcA=-(N2 - - - o2c4./h, \ H * H ozc)YJ!-.) T"; I N H HHis H 2His+ H3His2+ (25.0 LX0.0500 ) : Z s1(0.0500) = m M M Ve2: 2 Vet : 5 0.0m L V et : 2 5.0 L m The e quilibriao f t he t riprotic a cid H 3His2+c an b e w ritten a s H3Hi52+ + 0 m L: ^Kt Kz Ki H 2His+ = H His = His- H His i s t he s econdi ntermediateorm d erivedf rom H 3His2+. f : pH = j {vxr+ p K:) : } tt . e7 e .2B) 7 .62 + 12.5 m L: H alfivay t o V "1t herei s a n e quimolarm ixture o f H His a nd H 2His+,s o pH: p K2:5.97 25.0 m L: H His h asb eenc onverted o H 2His+,w hich i s t he f irst i ntermediate t form d erivedf rom H 3His2+, o s p H = ) @xt + p Kz): * 11.6 s .s7): 3 .8 + 50.0 m L: H istidineh as b eenc onverted o H 3His2+a t a f ormal c oncentration t F:ffi :0 . 0 1 6 7 M H3Hi52+ = 0.016 - x 7 xx (25.0 LX0.050 M ) m 0 + H 2His+ H + K t:0.025 ...
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This note was uploaded on 04/06/2011 for the course CHEM 2011 taught by Professor Buhlman during the Spring '10 term at Minnesota.

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