A study of the suspension effect observed in a Dowex-50 - water system by John Edward Robbins A THESIS Submitted to the Graduate Faculty in partial fulfillment of the requirements for the degree of Master of Science in Chemistry Montana State University © Copyright by John Edward Robbins (1961) Abstract: In this investigation, the distribution of ions in a Dowex-50-Water System, was considered. Within the limits of experimental error, the data support the ’’bound-water theory" as it relates to ion distribution. The actual distribution of Cl as determined with Cl36 was compared with the apparent distribution as determined potentiometrically with a Ag,AgCl-reference electrode pair. The discrepancy (corresponding to as much as 93 millivolts) was attributed to a liquid junction potential at the resin-salt bridge interface. The data are shown to provide qualitative, and to some extent quantitative, support to a theory proposed by Overbeek. Any potentiometric measurement made in an exchanger-water system and employing reference electrode with salt bridge is considered to be subject to error from this source. A STUDY OF THE SUSPENSION EFFECT OBSERVED IN A DOWEX-50 - WATER SYSTEM i by Jo h n E .R obbins A THESIS Subm it,ted to the. G ra d u a te F acu ljty in p a r t i a l f u l f i l l m e n t o f th e r e q u ir e m e n ts fo r. th e d e g re e o f M a s te r o f S c ie n c e i n C h em istry at M ontana S t a t e C o lle g e A pproved: H ead, M ajor DepdrEment / Bozeman, M ontana A u g u st, 1961 -3 - ACKNOWLEDGEMENT I w ish to e x p r e s s my s i n c e r e th a n k s to D r. R. A. O lse n f o r h i s g u id a n c e and h i s p a t i e n c e th ro u g h o u t t h i s w ork. I w ould l i k e to e x p r e s s my a p p r e c i a t i o n to Anaconda Copper Company f o r th e fu n d s to c a r r y on my r e s e a r c h and a l s o to th e chem­ i s t r y d e p a rtm e n t f o r th e a s s i s t a n t s h i p w hich e n a b le d me to c o n tin u e my w ork. I w ould a l s o l i k e to e x p re s s th a n k s to D r. Graeme B aker and D r. B ruce M urray f o r th e h e l p f u l c r i t i c i s m , and a l s o th e g r a d u a te s t u ­ d e n ts who gave h e l p f u l s u g g e s tio n s . To my w if e , P a t r i c i a , a h ig h n o te o f a p p r e c i a t i o n f o r h e r h e lp th ro u g h o u t t h i s tim e . -4- TAfiLE OF CONTENTS Page LIST OF TABLES............................................................ 5 LIST OF FIGURES. . . . ................................................... .............................................6 ABSTRACT ........................ I. II. III. INTRODUCTION ................... V I. .............................................. i . . . . . . . . . . . EXPERIMENTAL.................................... B. C. D. E. V. . . . . . . . . . LITERATURE REVIEW. . . . . . . . . . . A. IV. 7 8 10 17 C h a r a c t e r i s t i c S u sp e n sio n E f f e c t s o f S e le c te d Io n E xchange R e s in s ......................................................................... 17. . Io n D i s t r i b u t i o n i n Dowex-50 - W ater S y s t e m ......................... 20 D i s t r i b u t i o n o f' C1^6 i n a Dowex-50 - W ater System . . .. 2 7 S tu d y o f 3^+ by E s t e r H y d ro ly s is R a te s ....................... 29 P o te n tio m e tr ic D e te r m in a tio n i n Exch a n g e r-W a te r System . . 33 OVERfiEEK' S TREATMENT................................................................................. CALCULATION OFE j . . 36 ............................................................................... .4 3 SUMMARY AND CONCLUSIONS............................ ...................... .... ................................46 V II. SUGGESTION FOR FUTURE RESEARCH . . . . . . . . . . . . . . . . 47 V III, APPENDIX . ........... ......................................................................................... . . . . 48 A. B. C. D. IX. D e f i n i t i o n s and S y m b o l i s m .......................................... ... . . . . . T h ree P h ase S y s t e m ........................... Donnan S ystem ............................................................ . . . . . . . . P ro c e d u re s . . . . . . . ................... . ............................ LITERATURE CITED ...................... 48 49 50 51 .5 8 -5- LIST OF TABLES T a b le I. Page C h a r a c t e r i s t i c s o f Io n Exchange R e s in s - . . i , ............................ 19 ll a . "Bound W ater" D a ta .......................................................................... i . . . . ll b . "Bound W ater" D ata ( c o u n tin g d a t a ) ............................................................ 25 III. D i s t r i b u t i o n o f C l" ^ . . . ......................................................... ...................... 31 IV. C o n c e n tr a tio n o f C l 1 C o r r e c te d f o r "Bound W a te r" ............................ 32 V. V I. V II. V III. 24 C o m p a rativ e R a te s o f E s te r H y d r o ly s is o f E q u iv a le n t Amounts o f H+ P e r U n it V o lu m e ................... .......................... 32 .C om parisoh o f AEc a l and E0 o n n an ............................................................. 3 7 C om parison o f V a lu e s f o r E j w ith D i f f e r e n t E le c tr o d e P a i r s . . 44 Volumes o f th e S e p a r a t e .P h a s e s . ............................................................... 54 -6- LIST OF FIGURES F ig u r e Page 1. E l e c tr o m e tr ic O b s e rv a tio n s Made by D a v is .............................................. 12 2. C om parison o f th e S u s p e n sio n E f f e c t Between S tro n g A cid and Bash R e s in s and Weak A cid and B ase R e s in ..................................... 18 3. "Bound W ater" Theory* ................................. . . . . . . . . . . . . 4. H y d ro ly s is o f M eth y l A c e ta te H+- C a ta ly z e d .......................................... 30 5. S a l t C o n c e n tr a tio n v s . pH. .... ............................................................................ 38 6. C om parison o f 4 E c a l w ith- E U sin g 2.42% H+ M o n tm o r illo h ite . . . . . . . ? . . . . . . ................... .... 26 39 7. C om parison o f i w ith EDonnan U sin g 2.42% Na+ M o n tm o r illo n ite . . . . . 7 . . . .................................................................. 40 8. C om parison o f S E , w ith Evwiriar, U sing 5.86% Ca++ F o r t C o ll in s C la y . . . . . . . . D? n" a? . . . . . . . . . . . . . . 9." C om parison o f 2S1E , w ith Ennririari U sin g 2.42% Ca++ F o r t CojLlins C la y . . / . . . . . D?n? a ? ............................................................ 42 10 . C o m p o sitio n o f 11. T h ree P h ase S ystem . ' 12, ' 41 AEc a l o f Dowex-50 - W ater S ystem . . . . . . . 45 49 Donnan S ystem ..............................................................................................................50 13. The E f f e c t o f ■% R e s in on S u sp e n sio n E f f e c t . . . . . . . . . . 53 14. C l3 6 S e l f T A b s o r p t i o n . ............................ .... .................................... 56 . . . . ABSTRACT In t h i s i n v e s t i g a t i o n , th e d i s t r i b u t i o n o f io n s in a Dowex-SG-Water S ystem , was c o n s id e r e d . W ith in th e l i m i t s o f e x p e r im e n ta l e r r o r , th e d a ta s u p p o r t th e ’’b o u n d -w a te r th e o ry " a s i t r e l a t e s to io n d i s t r i b u t i o n . The a c t u a l d i s t r i b u t i o n o f C l a s d e te rm in e d w ith C l ^ was com pared w ith th e a p p a r e n t d i s t r i b u t i o n a s d e te rm in e d p o t e n t i o m e t r i c a l l y w ith a Ag1A g C l - r e f e r e n c e e l e c t r o d e p a i r . The d is c r e p a n c y (c o r r e s p o n d in g to a s much a s 93 m i l l i v o l t s ) was a t t r i b u t e d to a l i q u i d . j u n c t i o n p o t e n t i a l a t th e r e s i n - s a l t b r id g e i n t e r f a c e . The d a ta a r e shown to p r o v id e q u a l i t a t i v e , and to some e x t e n t q u a n t i t a t i v e , s u p p o r t to a th e o ry p r o ­ p o se d by O v erb eek . Any p o te n tio m e tr ic m easurem ent made i n an e x c h a n g e r-w a te r sy stem and em ploying r e f e r e n c e e l e c t r o d e w ith s a l t b r id g e i s c o n s id e r e d to be s u b j e c t to e r r o r from t h i s s o u r c e . -8 - INTRODUCTION The c o n v e n ie n c e ' and a c c u ra c y o f th e e l e c t r o m e t r i c m ethod h as le d to i t s w id e s p re a d u s e f o r d e te r m in a tio n o f pH o f aqueous s o l u t i o n s . For th is p u rp o s e , th e g la s s e l e c t r o d e i s commonly u s e d w ith a r e f e r e n c e calo m el e le c tro d e . The p o t e n t i a l d i f f e r e n c e b etw een t h i s e l e c t r o d e p a i r i s r e l a t e d to th e pH by fh e e x p r e s s io n Eg l - Er e f = 0 .0 5 9 1 pH, E le c tric a l c o n t a c t b etw een th e c a lo m e l e l e c t r o d e and s o l u t i o n i s commonly made by means o f a KCl s a l t b r id g e . Inasm uch a s th e e q u i v a le n t c o n d u c ta n c e o f K+ and C l" a r e n e a r l y th e same (76 vs 79 m ho), th e l i q u i d j u n c t i o n p o te n t t i a l ( E j ) a t th e c a l o m e l - s o l u tio n i n t e r f a c e i s c o n s id e r e d to b e n e g l i g i b l y s m a ll (< 2 m v .). The o b s e rv e d p o t e n t i a l d i f f e r e n c e i s t h e r e f o r e c o n s id e r e d to b e a r e l i a b l e q u a n t i t a t i v e m easu re o f th e pH o f th e s o l u t i o n . The q u e s tio n o f a p p l i c a b i l i t y o f th e e l e c t r o m e t r i c m ethod to e x c h a n g e r-w a te r sy stem s h a s r e c e iv e d a t t e n t i o n i n r e c e n t y e a r s , A d iffe r­ en ce o f o p in io n s t i l l p e r s i s t s - r s o m e c o n te n d in g t h a t E 1 i n th e s e sy stem s i s n e g l i g i b l y s m a ll a s i t i s in t r u e s o l u t i o n s —o th e r s c o n te n d in g t h a t th e E j may be so l a r g e a s to c o m p le te ly i n v a l i d a t e th e d e te r m in a tio n . i s s u e may be b r i e f l y o u t l i n e d a s f o llo w s : The I f th e pH o f an a l i q u o t o f th e e q u i lib r i u m aqueous p h a s e o f an e x c h a n g e r i s d e te rm in e d e l e c t r o m e t r i c a l l y , i t i s commonly fou n d to d i f f e r from th e pH o f th e s l u r r y . phenomenon h a s b een term ed th e " s u s p e n s io n e f f e c t " . The In m a g n itu d e , it 'm a y ra n g e from z e ro to a s h ig h a s 4 pH u n i t s , d ep en d in g upon th e ty p e o f e x ­ c h a n g e r, e l e c t r o l y t e c o n te n t and o th e r c h e m ic a l p r o p e r t i e s o f th e sy stem . W ith r e s p e c t to th e aqueous p h a s e , th e pH o f th e r e s i n may be low er ( p o s i ­ t i v e s u s p e n s io n e f f e c t ) o r may be h ig h e r ( n e g a tiv e s u s p e n s io n e f f e c t ) . -9- The o r i g i n a l , and s t i l l p o p u la r , e x p l a n a tio n f o r th e p o s i t i v e su sp en d s io n e f f e c t a t t r i b u t e s th e low er pH o f th e r e s i n to th e e x i s t e n c e o f H+ io n "sw arm s" a t th e s u r f a c e o f th e p a r t i c l e s . B eing c o n s tr a i n e d f r o m ' f r e e d i f f u s i o n th r o u g h o u t th e e n t i r e s y ste m by th e o p p o s ite ly ch a rg e d exchange s i t e s , th e y a r e n e v e r t h e le s s c o n s id e r e d to be e f f e c t i v e i n i n ­ c r e a s i n g th e a c t i v i t y o f th e H+ io n n e a r th e p a r t i c l e s u r f a c e . A g la s s e l e c t r o d e p la c e d n e a r th e s u r f a c e o f th e p a r t i c l e a c c o r d in g ly i s exposed t o s o l u t i o n o f low er pH. • ■y R e c e n tly , e v id e n c e h a s b een p u b lis h e d w hich i s i n t e r p r e t e d to mean t h a t th e s u s p e n s io n e f f e c t may b e due to an e r r o r in h e r e n t i n th e e l e c t r o ­ m e tr ic m eth o d . A c c o rd in g to t h i s v ie w p o in t, an a p p r e c ia b le Ej a r i s e s a t th e c a lo m e l- s u s p e n s io n i n t e r f a c e upon b r in g i n g th e c a lo m e l i n c l o s e p ro x im ity to th e c h a rg e d p a r t i c l e s . Er e £ a c c o r d in g ly c a n n o t b e c o n s id e r e d a c o n s t a n t and E g i - Er e f i s a c c o r d in g ly n o t a r e l i a b l e m easu re o f th e pH i n e x c h a n g e r-w a te r s y s te m s . As i s r e a d i l y a p p a r e n t, t h e .m a t t e r o f d e te rm in in g th e o r d e r o f m a g n itu d e o f E j i s a c r u c i a l p ro b lem . I f i t a c c o u n ts f o r a l l o f th e s u s ­ p e n s io n e f f e c t , i t may b e l a r g e enough i n so m e-sy stem s t o c o m p le te ly i n ­ v a l i d a t e any e l e c t r o m e t r i c m easurem ents r e q u i r i n g th e u s e o f a s a l t b r id g e . I f E j i s low ( o f th e o r d e r o f m a g n itu d e o f s e v e r a l m i l l i v o l t s o r l e s s ) i t w i l l n o t b e o b j e c t i o n a b l e i n m ost e l e c t r o m e t r i c d e t e r m in a tio n s . m ary o b j e c t i v e s o f th e p r e s e n t i n v e s t i g a t i o n w ere to d e te rm in e E j i n a p a r t i c u l a r sy ste m and The p r i ­ (a ) q u a n t i t a t i v e l y (b ) t o s tu d y th e e f f e c t o f s e v e r a l c h e m ic a l p r o p e r t i e s o f th e s y ste m upon i t s m a g n itu d e . LITERATURE REVIEW The s u s p e n s io n e f f e c t was f i r s t r e p o r te d in d e p e n d e n tly by B r a d f ie ld (9) and W iegner (28) i n 1931. B r a d f ie ld o b s e rv e d t h a t th e p o te n tio m e tri* ? . c a I Iy m easu red pH o f a Hr -C la y s u s p e n s io n was a s much as 3 pH u n i t s low er th a n th e pH o f th e e q u i lib r i u m s u p e r n a ta n t s o l u t i o n . The s u s p e n s io n e f f e c t was o b s e rv e d r e g a r d l e s s o f w h e th e r a g l a s s , a h y d ro g en o r a q u in h y d ro n e e l e c t r o d e was u s e d , B r a d f ie ld s u g g e s te d t h a t th e c h e m ic a l p r o p e r t i e s o f th e H+-C la y w ere s i m i l a r to th o s e o f a weak a c i d . Inasm uch as th e n e g a t i v e l y c h a rg e d c la y p a r t i c l e s s e t t l e d o u t , th e a s s o c i a t e d H+ io n s a l s o s e t t l e d o u t i n o r d e r to m a in ta in e l e c t r i c a l n e u t r a l i t y th ro u g h o u t th e sy ste m . The c l a y s , b e in g weak a c i d s , a llo w e d some d i s s o c i a t i o n o f H+ io n s and e f f e c t i v e l y low ered th e pH o f th e s u s p e n s io n . The e x p l a n a ti o n by B r a d f ie ld was w id e ly a c c e p te d w ith l i t t l e m o d if i­ c a t i o n u n t i l a b o u t 1950. D u rin g t h i s tim e i n t e r v a l , Ej was c o n s id e r e d to b e n e g l i g i b l y s m a ll, as i t r e p o r t e d l y i s , i n t r u e s o l u t i o n s ( 1 9 ) . Jen n y e t a l , I n 195.0, ( 20) p u b lis h e d e v id e n c e w h ich was i n t e r p r e t e d to mean t h a t t h e s u s p e n s io n e f f e c t i s s o l e l y due t o E j . They i n t e r p r e t e d t h e i r r e s u l t s to mean t h a t th e m o b i l i t i e s o f K+ and C l" a r e changed ( in c r e a s e d and d e ­ c r e a s e d r e s p e c t i v e l y ) by t h e p r e s e n c e o f th e n e g a t iv e l y c h a rg e d ex ch an g er p a rtic le s . As. a r e s u l t , an a p p r e c ia b le d i f f u s i o n p o t e n t i a l a r o s e a t th e s u s p e n s i o n - s a l t b r id g e i n t e r f a c e . D avis (32) arid’ Du R e itz (33) hav e shown t h a t th e o b s e rv e d pH o f com par­ a b l e s u s p e n s io n s does n o t depend upon th e p o s i t i o n o f th e g l a s s e l e c t r o d e b u t r a t h e r upon th e p o s i t i o n o f th e c a lo m e l e l e c t r o d e . T h e ir o b s e r v a tio n s -11- a r e d e p ic te d i n F ig u r e I . s e n t in v e s tig a tio n . C o n firm a to ry o b s e r v a tio n s w ere made i n th e p r e ­ F o llo w in g th e p u b l i c a t i o n s o f D av is (3 2 ) and D ujR eijte ( 3 3 ) , how ev er, a c o n tr o v e r s y a r o s e r e g a r d in g , th e i n t e r p r e t a t i o n o f th e s e o b s e r v a ti o n s . (1 ) The i n t e r p r e t a t i o n o f Jen n y e t a l . a p p e a rs to be a s f o llo w s : I f a g la s s - c a l o m e l e l e c t r o d e p a i r i s im m ersed i n th e s u p e r ­ n a t a n t l i q u i d a s i n ( a ) , th e Ej a t th e c a l o m e l - s o l u tio n i n t e r f a c e i s n e g l i g i b l y s m a ll ,(<2 m i l l i v o l t ) and th e o b s e rv e d pH i s a v a l i d i n d i c a t i o n o f th e ajj+ i n th e medium. (2) Em = 0 . , As shown i n ( c ) , th e ajj+ i n b o th p h a s e s i s e q u a l, assum ing t h a t (Em,. th e membrane p o t e n t i a l , r e p r e s e n t s t h e p o t e n t i a l d if f e r e n c e a c r o s s th e i n t e r f a c e b etw een s l u r r y and s u p e r n a ta n t s o l u t i o n . (See Appen­ d ix page ..4 9 .) (3) I f Em = 0 th e n , a s shown i n ( d ) , am . Ej o f 240 m i l l i v o l t s a r i s e s a t th e c a lo m e l- s u s p e n s io n i n t e r f a c e upon im m ersing th e c a lo m e l i n t o th e s u s p e n s io n . (4 ) The o b s e rv e d pH s h o u ld t h e r e f o r e depend o n ly upon th e p o s i t i o n , o f th e c a lo m e l e l e c t r o d e and i s u n a f f e c t e d by th e p o s i t i o n o f th e g la s s e le c tro d e . (f). T h is i s shown to be t r u e by o b s e r v a tio n s ( a ) , (b )» (e ) and A c c o rd in g to t h i s v ie w p o in t, th e o b s e rv e d EMF. f o r e a c h c e l l w ould be g iv e n by th e f o llo w in g : E(a ) = - E°a l + 0 .0 5 9 1 lo g E(W - EI l " Ec a l + 0 .0 5 9 1 lo g 4 + E(o ) = Eg l ‘ 0 .0 5 9 1 lo g a^+ - E ° ! E(d ) “ Ec a l - Ec a l + Ej = Ej + Ej ' + 0 .0 5 9 1 lo g a " + = 0 -1 2 - t f D. O mv 240 mv pH 2 .0 pH 6 .0 pH = 4 .0 Key; | Ui 240 mv. I e q u ilib r iu m s o l u t i o n s u s p e n s io n ( c o l l o i d a l p a r t i c l e s ) F ig u r e I . g la s s e l e c tr o d e IiJ c a lo m e l e l e c tr o d e E l e c tr o m e tr ic o b s e r v a tio n s made by D av is -1 3 - Il I E(e ) = Eg l - Ec a l + 0 '0 5 9 1 lo g aH+ Il lo g E ( f ) = Eg l ’ Ec a l + 0 .0 5 9 1 aH+ If III aH+ = a H+ . E r ik s s o n (17) and o th e r s have s u g g e s te d an a l t e r n a t i v e e x p la n a tio n o f th e o b s e r v a tio n s d e p ic te d p r e v io u s l y . From th e Donnan (15) th e o r y , ( s e e / 1A p pendix, p ag e 4 9 ) , one c a n o b ta in th e r e l a t i o n s h i p : V If m Em = 0.0591, lo g a H+ / a^+ . I n c lu d in g t h i s te rm i n th e e x p r e s s io n s f o r . th e c e l l p o t e n t i a l s w here n e c e s s a r y , we o b ta in f o r c e l l s a , b , c , d , e , and f th e f o llo w in g : E(a ) eI i " Ec a l + 0 .0 5 9 1 log. aH+ V ) E: i " Ec a l + 0 .0 5 9 1 lo g a " + E (c) = E(d) = EBl - Eg l + 0 .0 5 9 1 lo g a^+ / Ec a l “ Ec a l + Ej E(e ) Eg l " Ec a l E( f ) Eg l " Ec a l + Ej - Em +Em III + 0 .0 5 9 1 lo g a H+ + E. , + 0 .0 5 9 1 lo g a^+ - Em +Em Now i f we- s u b s t i t u t e i n t o th e above e x p r e s s io n s th e v a lu e o f Em, and m aking th e a ssu m p tio n th e E j = 0 w e'h av e: E(a ) Eg l - E° cal E (b) = Egl Ec a l E(c ) = 0 E(d) - Em E(e ) = Eg l E( f ) = Eg l - Ec a l “ Ec a l + 0 .0 5 9 1 lo g a™+ + 0 .0 5 9 1 !o g + 0 .0 5 9 1 lo g a H+ + III 0 .0 5 9 1 lo g aH+ -14- T h is tr e a tm e n t p r o v id e s an a l t e r n a t i v e e x p l a n a tio n f o r th e o b s e r v a tio n s made by Jen n y e t a l . , D av is (32) and Du R e itz ( 3 3 ) . They p o i n t o u t t h a t th e o b s e r v a tio n s can be e x p la in e d s a t i s f a c t o r i l y by assu m in g t h a t Ej i s n e g l i g i b l y s m a ll and Em c o r r e s p o n d in g ly l a r g e . The o b s e r v a tio n s may be e x p la in e d e q u a lly w e ll by th e e x i s t e n c e o f an Em o r a l t e r n a t i v e l y by th e e x i s t e n c e o f an E 1. I n 1952, M. P eech , G. H. B o lt and R. A. O lsen (27) r e p o r te d some a n o m a lie s t h a t th e y a t t r i b u t e d to a l i q u i d ju n c tio n p o t e n t i a l b etw een th e s a t u r a t e d KCl and c l a y s u s p e n s io n i n t e r f a c e . They m easu red th e membrane p o t e n t i a l o f s e v e r a l c la y s u s p e n s io n s by u s e o f two s a t u r a t e d c a lo m e l e l e c t r o d e s u s in g th e Donnan (1 4 ) e q u i lib r i u m m ethod f o r m e a su rin g io n a c t i v i t i e s i n s u s p e n s io n s . & Ec a ^ was g iv e n a p o s i t i v e s ig n when th e e l e c t r o d e i n th e d i a l y z a t e was p o s i t i v e w ith r e s p e c t to th e e l e c t r o d e i n s u s p e n s io n . T h is i s i n a c c o rd a n c e f o r a membrane p o t e n t i a l o f a n e g a ­ t i v e l y c h a rg e d c o l l o i d . A ^ ca r ="%n + E j. The s ig n o f A E ^ ^ was found to b e p o s i t i v e f o r s u s p e n s io n s o f many d i f f e r e n t c la y s s a t u r a t e d w ith H+ , Na+ and K+. However, when c e r t a i n c la y s w ere s a t u r a t e d w ith Ca"!"*", th e AEc a ^ was n e g a t iv e . One p o s s i b l e e x ­ p l a n a t i o n s f o r t h i s o b s e r v a tio n w ould b e th e r e v e r s a l o f s ig n on th e col"? I o id p a r t i c l e . ' T h is p o s s i b i l i t y was ch ec k ed in d e p e n d e n tly by z e t a p o te n ­ t i a l m e asu re m en ts. I t was found t h a t th e s ig n o f th e c h a rg e on th e p a r ­ t i c l e s h ad n o t b e e n r e v e r s e d . The r e v e r s a l o f s ig n was t h e r e f o r e a t t r i ­ b u te d to a n e g a t iv e Ej.. I n c o n ju n c tio n w ith th e above w ork, th e o sm o tic p r e s s u r e o f th e c la y -1 5 - s u s p e n s io n was d e te rm in e d by e x p e r im e n ta l m easurem ents and a l s o by c a lc u la tio n . The a c t i v i t i e s d e te rm in e d th e Dohnan m ethod w ere u se d i n c a l c u l a t i n g o sm o tic p r e s s u r e , Tf , by th e e q u a tio n : V = RT (Z + 2Y - 2X) ' Z = Na+ c o n c e n tr a ti o n ( d i s s o c i a t e d from c la y ) Y = NaA s a l t c o n c e n tr a ti o n i s th e s u s p e n s io n X = NaA c o n c e n tr a ti o n i n th e d i a l y z a t e . T hese v a lu e s w ere c a l c u l a t e d from th e fo llo w in g r e l a t i o n t o A Ec a p A Ec a l = RT In X F Y = F RT In Z + Y X The o sm o tic p r e s s u r e t h a t was c a l c u l a t e d showed s e r io u s d e v i a t i o n from th e o sm o tic p r e s s u r e t h a t was m e asu re d . The d is c r e p a n c y was a t t r i b u t e d to th e e r r o r in tr o d u c e d i n th e e x p e r im e n ta l e v a l u a ti o n o f Em, and th e r e s u l t a n t e r r o r i n c a l c u l a t i o n o f o sm o tic p r e s s u r e . I n 1953, O verbeek (26) p u b lis h e d a t h e o r e t i c a l tr e a tm e n t o f th e s u s p e n s io n e f f e c t . He c o n s id e r e d th e s u s p e n s io n e f f e c t and th e Donnan p o t e n t i a l to be i d e n t i c a l and made up o f th e sum o f E j and Em. A tte m p ts a t s e p a r a t e l y e v a l u a ti n g Ej and E ^ w ere c o n s id e r e d to ,be u n s a t i s f a c t o r y b e c a u se o f th e n e c e s s i t y o f a r b i t r a r y a s s u m p tio n s . He showed t h a t th e s u s p e n s io n e f f e c t ( r e f e r r e d to as Eq ) c a n be c a l c u l a t e d a p p ro x im a te ly from th e c o m p o s itio n o f th e sy ste m by th e r e l a t i o n s h i p : Eq = RTi In c o n d u c ta n c e o f e x ch a n g er F c o n d u c ta n c e o f e q u i lib r i u m l i q u i d O v e rb e e k 's tr e a tm e n t was t e s t e d e x p e r im e n ta lly by Bloksma ( 2 ) , u s in g m o b i l i t i e s o f th e a d s o rb e d io n s . He c o n c lu d e d t h a t th e ag ree m en t was s u f f i c i e n t l y good to be c o n f ir m a tiv e . —16" R e c e n tly , Bower ( 5 ) ( 6) s tu d ie d th e s u s p e n s io n e f f e c t w ith a g la s s e l e c t r o d e w hich i s s e l e c t i v e f o r Na+ . b e e k ’s th e o r y . Bower found good s u p p o r t f o r O v er- He a l s o ch eck ed th e e f f e c t o f th e c o n c e n tr a ti o n o f th e s a l t b r id g e on th e m a g n itu d e o f th e s u s p e n s io n h f f e c t . I t was found t h a t th e s u s p e n s io n e f f e c t became n e g l i g i b l e when th e c o n c e n tr a ti o n s o f s a l t i n th e s a l t b r id g e and e q u i lib r i u m l i q u i d a r e th e sam e. A t th e p r e s e n t tim e , t h e r e seems to b e , ju d g in g from th e p u b lis h e d in f o r m a tio n , two s c h o o ls o f th o u g h t r e g a r d in g E j i n c o l l o i d a l s y ste m s. I One s c h o o l (24) i s a p p a r e n tly o f th e o p in io n th e Ej i s n e g l i g i b l e . The o th e r ( 2 0 ) , i s a p p a r e n tly o f th e o p in io n th e Ej i s o f s u f f i c i e n t m agni­ tu d e to e n t i r e l y a c c o u n t f o r th e s u s p e n s io n e f f e c t . In th is in v e s tig a ­ t i o n , an a tte m p t h a s b een made to o b ta in a m ore r e l i a b l e e s ti m a t e o f E j th a n i s c u r r e n t l y a v a i l a b l e and th e re b y c o n t r i b u t e to o u r u n d e r ­ s ta n d in g o f th e s u s p e n s io n e f f e c t . -17" EXPERIMENTAL C h a r a c t e r i s t i c S u s p e n sio n E f f e c t s o f S e le c te d Io n Exchange R e sin s The i n i t i a l o b j e c t i v e was to s e l e c t an e x ch a n g er w h ich e x h i b ite d a l a r g e s u s p e n s io n e f f je c t. I t was r e a s o n e d t h a t i f th e e x ch a n g er ex­ h i b i t e d o n ly a s m a ll s u s p e n s io n e f f e c t , th e a c c u ra c y w ith w hich Ej c o u ld ■ be m easu red w ould b e c o r r e s p o n d in g ly low . So f a r a s i s knowny th e l a r g e s t s u s p e n s io n e f f e c t r e p o r te d in th e l i t e r a t u r e i s th e v a lu e o f 4 pH u n i t s r e p o r te d by Jen n y (20) f o r a Dow p r o d u c t c a l l e d lo n -X . A c c o rd in g ly , s e v e r a l s y n t h e t i c c a t i o n and a n io n e x c h a n g e rs w ere s e l e c t e d f o r c o m p ari­ so n . A ll r e s i n s w ere t r e a t e d i n th e f o llo w in g way: (1 ) A sam ple o f a p p ro x im a te ly 20 g . was p la c e d i n a B uchner f u n n e l under s u c tio n . (2 ) C a tio n e x c h a n g e rs w ere w ashed w ith 0 .1 N HCl and th e a n io n e x ­ c h a n g e rs w ere w ashed w ith 0 .1 N NaOH. (3 ) The r e s i n s w ere t r a n s f e r r e d to 500 m l. E rlen m ey e r f l a s k s and w ere e q u i l i b r a t e d w ith e x c e ss a c id o r b a s e f o r one h a l f h o u r on a w r i s t a c tio n sh a k e r. (4 ) The sam p les w ere th e n w ashed i n th e B uchner f u n n e l w ith o u t s u c ­ t i o n u n t i l i n d i c a t o r p a p e r in d i c a t e d t h a t th e e f f l u e n t h ad become a p p r o x i­ m a te ly n e u t r a l . P r i o r to th e d e te r m in a tio n o f th e s u s p e n s io n e f f e c t , t e n m i l l i l i t e r s o f w a te r w ere added to a p p ro x im a te ly two gram s o f r e s i n . The f l a s k was sh a k e n p e r i o d i c a l l y f o r t h r e e h o u rs and th e n a llo w e d to s ta n d over n ig h t. The s u s p e n s io n e f f e c t was m easu red w ith a g l a s s e l e c t r o d e and a s a t u r a t e d c a lo m e l e l e c t r o d e . V a lu e s , o b ta in e d f o r th e s u s p e n s io n e f f e c t -1 8 f o r th e v a r io u s r e s i n s , a r e shown i n T a b le I (p ag e 1 9 ) . t e r i s t i c s a r e a l s o l i s t e d in th e t a b l e . O th e r c h a r a c ­ T hese w i l l be d is c u s s e d l a t e r , As a r e s u l t o f th e f in d in g s h e r e , Dowex-50 was s e l e c t e d a s th e r e s i n to be u se d i n th e i n v e s t i g a t i o n . T h is p a r t i c u l a r r e s i n i s c h a r a c t e r i z e d by th e fo llo w in g ; 8% c r o s s - l i n k a g e ; p a r t i c l e s i z e 100-200 m esh. I n th e H+ form , i t was found to e x h i b i t a s u s p e n s io n e f f e c t o f a p p ro x im a te ly 3 pH u n i t s ; w hich was b e l ie v e d s a t i s f a c t o r y f o r th e p u rp o s e s o f t h i s i n v e s t i ­ g a tio n . A co m p ariso n o f th e s u s p e n s io n e f f e c t f o r a weak a c id and a s tr o n g a c id and o f a weak b a s e and s tr o n g b a s e i s d e p ic te d in f ig u r e 2 . A cid 0 Base F ig u re 2: C om parison o f th e S u sp e n sio n E f f e c t b etw een S tro n g A cid and Base R e s in s and Weak A cid and B ase R e sin s "19TABLE I C h a r a c t e r i s t i c s o f Io n E xchange R e s in s E x ch a n g ers . Wet R e s in C a p a c ity * S u s p e n sio n E f f e c t . A q u eo u s-R esin A cid o r Base S tr e n g th C a tio n Dowex-50 1 .7 meq/ml 3 .2 6 pH u n i t s s tr o n g Dowex-SOM 1 .7 meq/ml 2.6A pH u n i t s s tr o n g A m b e rlite IR -120 1 .9 meq/ml . 3 .0 5 pH u n i t s s tr o n g A m b e rlite IRC-SO 3 .5 meq/ml 0 .8 1 pH u n i t s weak 0 .5 5 meq/ml 2 .8 8 pH u n i t s D owex-I •1^33 meq/ml - 2 .7 9 pH u n i t s s tr o n g Dowex-2 1 .3 3 m eq/m l - 2 .0 5 pH u n i t s s tr o n g IR -45 2 .0 0 meq/ml - 0 . 7 0 , pH u n i t s weak !ER-400 1 .0 0 meq/ml - 3 ,0 7 pH u n i t s s tr o n g IRr-410 1 .2 0 meq/ml -2 .A 6 p H u n i t s s tr o n g D u o lite A-AO I . AO meq/ml - 3 .3 0 pH u n i t s s tr o n g D u o lite A2 1 .3 0 meq/ml - 2 ,5 3 pH u n i t s s tr o n g Mixed bed IR MB-3 A nion . *A11 ex ch an g e c a p a c i t i e s a r e r e p o r te d a s m i l l i e q u i v a l e n t s p e r m i l l i l i t e r o f w et r e s i n , w ith th e c a t i o n e x c h a n g e r in th e H+ form ; th e a n io n e x c h a n g e rs i n th e C l” form . F o r th e s u s p e n s io n e f f e c t , th e H+ and OH” form s w ere u s e d . -2 0 - Io n D i s t r i b u t i o n i n a Dowex-50 - W ater System A. Donnan T heory v e r s u s "Bound W ater" T heory In a r e c e n t l y p u b lis h e d t h e s i s , Moreno (34) h as c o n s id e r e d th e r e l a ­ t i v e m e r i ts o f th e Donnan th e o ry and o f th e "bound w a te r" th e o r y (15) f o r d e s c r ib i n g io n d i s t r i b u t i o n i n an e x c h a n g e r-w a te r sy stem . i s b a se d upon h i s tr e a tm e n t o f th e two t h e o r i e s . The fo llo w in g I n th e "bound w a te r" th e o r y , i t i s p o s t u l a t e d t h a t a c e r t a i n volum e o f w a te r , V^ 1 - is tig h tly a d so rb e d a t th e s u r f a c e o f an ex c h a n g e r so t h a t i t does n o t f u n c tio n as a s o lv e n t f o r an e l e c t r o l y t e . By m aking t h i s a s s u m p tio n , one c a n form u­ l a t e th e fo llo w in g : L e t X = am ount o f C l" * [ C l- - ) = c o n c e n tr a ti o n o f C l" Vb , Vr j Vt = volum e o f bound w a te r , volum e o f re m a in d e r o f w a te r , and th e t o t a l volum e o f w a te r r e s p e c t i v e l y . Then Xr V[ = Xt Vt - Vb : . and m u ltip l y in g by Vt we o b ta in , ^ tvt _ Vt (Vt -Vb ) ™ v r , t h i s may a l s o be w r i t t e n a s f c l T . = (Vt -V^) [ c l \j — ^ T hus, by k e e p in g Vt , Vr , Vb c o n s ta n t and v a r y in g Xt , we sh o u ld g e t a p l o t o f Xt /Vt v e r s u s Xr /Vr a s a s t r a i g h t l i n e w hich p a s s e s th ro u g h th e . o r i g i n and h as a s lo p e o f (Vt - Vb ) /V fc. d e te rm in e d from th e s lo p e . S in c e Vfc i s known, Vb can be (S ee f i g u r e 3, p ag e 26 ) . *C l was ch o se n b e c a u se i t can be a n a ly z e d f o r by p o t e n t i o m e t r i c , r a d i o m e t r i c , and v o lu m e tr ic m eth o d s. - If th e Dohnan th e o r y p r o v id e s 21 th e m ost s a tis fa c to ry - ■ tr e a tm e n t o f c h l o r i d e d i s t r i b u t i o n in ah e x c h a n g e r-w a te r sy ste m , th e n t h e r e i s n o t a d e f i n i t e r e g io n i n w hich Cl™ i s e x c lu d e d , b u t r a t h e r an e x p o n e n tia l r e l a t i o n s h i p b etw een th e e l e c t r i c a l p o t e n t i a l and Cl™. A ppendix C, p ag e 4 9 ) . (S ec The n e a r e r one a p p ro a c h e s t h e ^ r e s i n s u r f a c e , th e low er th e (^C lwJ becom es. The one th e o ry r e q u i r e s a d i f f u s e d o u b le la y e r th e o th e r a d i s t i n c t d o u b le la y e r . i , A cc o rd in g to th e Donnan tr e a tm e n t f o r u n i - u n i v a l e n t e l e c t r o l y t e a' M+ x = a' G l­ and a l s o (a ' + X a" M+ x a" C l" , (1) a' . ) (a' ) Cl C l" ( 2) (ac i - y Where a" i s th e a c t i v i t y o f an io n i n th e s u p e r n a ta n t and a ' r e f e r s to th e s l u r r y and w here a x i s th e a c t i v i t y o f th e a d so rb e d c a t i o n . T h a t th e t o t a l c h l o r i d e in th e sy ste m e q u a ls th e sum o f th e c h l o r i d e i n th e p a r t s re q u ire s th a t, Xt = LCl"l' v' [c r j. M t (3 ) £ c i ~ ] " V" V' + qf crl " (4) S in c e V1 y' [c r n Vt and [C l" ] ’ ' _ fc i" I . L = [cl^ l' - - F c r l " V" Vfc [ c l" ] " V" ^ • = Fc l I t v t - (vt - v") [C l']-" '7" Vt (V ^ V nT (5 ) -2 2 ” A c c o rd in g to (2 ) ( a ^ - X a ^ .) + ( a ^ J 2 = (a ^ . ) 2 (» 6 i - ) 2 ♦ (= C l-) ( V and (%a x + a C l- ) 2 th u s (%a x + = S i-)" and + 4=x = = ( = S l- ) 2 (7 ) ( 8) ( = S i- ) 2 + « = * ) 2 + (9 ) %(=x) 2 ( 10) ( = S i- ) 2 + K = x ) 2 ( a " ) 2 + %(a ) 2 - %a Cl x x ( = c i- ) = ( 11) I f we assum e t h a t a ^ „ = C l" ' th e n we e q u a te (11) and ( 6) . ( a C l- ) 2 + X ax>2 - %ax = [ C l - J t Vfc - |c iJ " V " (Vt - V") Ca" ( r + - %a Cag1- ) 2 + %(axr f 31" ! = ( + "V" Ji (Vt - V") - %ax)(V t - V") + (13) P 1"] V") C l- InV" fi t t ( aC i- ) 2 + %(*x ) 2 “ %&J >(y t ~ vM) + Lc l ~ l "V" ( ( aC I- ) 2 + t ( a , ) 2 - %ax)(V fc - V") WJ' F V" (14) (15) (16) T As shown by e q u a tio n (16) one w ould n o t e x p e c t a l i n e a r r e l a t i o n s h i p b e ­ tw een [ C l J t and [ c r j " i f th e Donnan th e o r y i s a p p l i c a b l e to th e sy stem . ■ To ch e c k th e a p p l i c a b i l i t y o f th e s e two th e o r i e s to c h l o r i d e d i s t r i ­ b u ti o n i n a Dowex r e s i n - w a t e r sy ste m , a s e r i e s o f sam ples w ere e q u i l i ­ b r a te d f o r tw e n ty -f o u r h o u r s , w ith c o n c e n tr a ti o n o f H C l^ b e in g th e in d e ­ pendent v a ria b le . A one m i l l i l i t e r sam ple o f th e s u p e r n a ta n t s o l u t i o n was p i p e t t e d o u t, n e u t r a l i z e d w ith sodium h y d ro x id e , e v a p o ra te d to d ry n e s s and -23- c o u n te d w ith a G e ig e r-M u e lle r c o u n te r . S o lu tio n s o f e q u a l volum es o f w a te r and e q u a l am ounts o f c h l o r i d e b u t w ith no r e s i n w ere p r e p a r e d f o r eac h c o n c e n tr a ti o n and c o u n te d i n th e same m anner. The fo rm er m easurem ents w ere u se d a s a m easu re o f (X "/V ") and th e l a t t e r a s (XfcZVfc) . th e s e two v a lu e s was th e n made; ( s e e f i g u r e 3 , p a g e £ 6 ) . A p lo t of The l i n e a r i t y o b s e rv e d betw een (X11ZVm) and (XfcZVfc) i s c o n s id e r e d to c o n s t i t u t e e v id e n c e o f th e a p p l i c a b i l i t y o f th e "bound w a te r" th e o r y . A n o th er s u p p o r tin g p ie c e o f e v id e n c e f o r th e "bound w a te r" th e o ry was p u b lis h e d r e c e n t l y by A nderson and Low ( I ) . T h e ir s t u d i e s d e a l w ith th e d e n s it y o f w a te r n e a r th e s u r f a c e o f c la y p a r t i c l e s . They found t h a t w ith i n 10£ o f th e s u r f a c e o f a c la y p a r t i c l e t h a t th e d e n s it y d e c re a s e d c o n tin u o u s ly . The d e n s i t i e s a p p ro ac h ed 0 .9 7 gZcc. a s a lo w er l i m i t . T h is w ould s u g g e s t t h a t th e w a te r m o le c u le s a r e ta k in g on some ty p e o f o rd e re d a rra n g e m e n t p resu m ab ly s i m i l a r to w a te r o f h y d r a tio n . w a te r w ould p ro b a b ly c e a s e t o f u n c ti o n a s a s o lv e n t . T h is volum e o f The p r e s e n t i n ­ v e s t i g a t o r s f e e l t h a t t h i s i s th e same volum e ele m e n t t h a t i s o cc u p ie d by th e "bound w a te r " . -24- TABLE I I a Bound W ater D ata •• \ Sample W eight Volume o f H C l 36 . Volume o f H2O T o ta l Volume •la 1.0000 g. 5 m l. ' 5 m l. 10 m l. lb 0 .9 9 9 9 g. 5 m l. 5 m l. 10 m l. 5 m l.. 5 m l. 10 ml. b la n k - 2a 0 .9 9 9 6 g. 4 m l. 6 m l. 10 m l. 2b 1.0 0 0 3 g . . 4 m l. 6 m l. 10 m l." 4 m l. 6 m l. 10 m l. b la n k 3a 1.0001 g. 2 m l. 8 m l. 10 m l. 3b 0 .9 9 9 9 g. 2 m l. 8 m l. 10 m l. 2 m l. 8 m l. 10 m l. b la n k 4a 0 .9 9 9 7 g. I m l. 9 m l. 10 m l. 4b 0 .9 9 9 7 g. I m l. 9 m l. 10 m l. I m l. 9 m l. 10 m l. b la n k -5a* * 1 .0000 g . .5 m l. 5 m l. 10 m l. 5b 1.0000 g. 5 m l. 5 m l. 10 m l. 5 m l. 5 m l. 10 m l. b la n k Of: *The HCl u se d i n th e f i r s t f o u r sam p les was a 0 .0 0 7 6 9 N s o lu ti o n w h ereas th e H C l^ u se d f o r th e l a s t sam ple was a t e n f o l d d i l u t i o n o f th i s a c id . z I -2 5 TABLE I I b I "Bound W ater" D ata ( c o u n tin g d a ta from C l ^ ) Xt Zvt , c o u n ts Zmin. meqZml. x 1(H Xr Zvr c o u n t s Zmin. Xr Zv , meqZmin XH Xt Zvt Sam ple la 13,677 4 .1 0 lb 13,6 7 4 4 .1 1 2a 10,848 3 .3 5 2b 10,615 3 .2 8 3a 5 ,8 6 5 1 .7 8 3b 5,719 1 .7 4 4a 2,719 0 .8 3 4b 2 ,5 8 4 0 .7 8 5a 1,4 5 2 0 .4 4 5b 1,4 3 2 0 .4 3 b la n k b la n k b la n k b la n k b la n k 12,795 3 .8 4 9 ,9 6 7 3 .0 8 5 ,0 8 4 1 .5 4 2,-529 0 .7 7 1 ,3 4 5 0 .4 0 A l l c o u n ts a r e c o r r e c t e d f o r b ack g ro u n d . Sam ple c a l c u l a t i o n : Xr ZVr = 13,667 £ m in Xt ZVt = 5 .x 0.00769Z10 = 0 .0 0384 meqZml x 0 .3 0 0 1 meq min " m l c o u n ts x ' 1 0 = C a l c u la t io n s f o r V^ from th e s lo p e i n f i g u r e 3 = 0 .9 2 7 = — k \and Vt = 10 m l. s o lv in g f o r V^ Vb = 0 .7 3 m l. 0 .0 0 4 1 meqZml; x 10 -26- C I 2 3 x 10 F ig u r e 3: +3 Bound W ater T heory 4 -27 D is trib u tio n of C 6 i n a Dowex-50 - W ater System . The o b j e c t i v e o f t h i s s e c t i o n was to d e te rm in e th e a c t u a l d i s t r i ­ b u ti o n o f C l" i n th e r e s i n - w a t e r sy ste m . The v a lu e s o b ta in e d a r e l a t e r com pared w ith th e a p p a r e n t d i s t r i b u t i o n o f C l" a s d e te rm in e d p o t e n t i o m e tric a lly . Any d is c r e p a n c y b etw een th e a p p a r e n t and a c t u a l d i s t r i b u ­ t i o n w i l l be a t t r i b u t e d to an Ej a t th e c a l o m e l - r e s i n i n t e r f a c e . The r e s i n - w a t e r sy ste m i s d iv id e d i n t o th r e e a r b i t r a r y d i v i s i o n s w hich w i l l be r e f e r r e d to a s p h a s e s . s o lu tio n . P h a s e 1" r e f e r s to th e e q u ilib r iu m P h ase" r e f e r s to th e i n t e r s t i t i a l s o l u t i o n , i . e . , t i o n b etw een th e p a r t i c l e s . th e s o l u ­ P h a s e 1 r e f e r s to th e s o l u t i o n i n th e i n ­ t e r i o r o f th e r e s i n p a r t i c l e s . H+ r e s i n sam p les w ere e q u i l i b r a t e d w ith a l i q u o t s o f d i l u t e HCl ,tag g ed w ith C l ^ . A f te r e q u ilib r iu m was a t t a i n e d , th e t h r e e p h a se s w ere p h y s i c a l l y s e p a r a t e d u s in g th e te c h n iq u e s u g g e s te d by G re g o re t a l. (18) as s t a t e d i n A ppendix D, page 5 1 . The c o n c e n tr a ti o n o f C l" i n th e t h r e e p h a s e s was d e te rm in e d by means o f s ta n d a r d c o u n tin g te c h ­ n iq u e s . R e s u lts o b ta in e d f o r a s e r i e s o f 1.0 0 0 gram sam p les a r e l i s t ­ ed i n T a b le I I I . The mean v a lu e o b ta in e d f o r J jC l" ] " ' / [ c l^ ] " was 1 .3 2 and 1 .3 4 f o r th e 1.0000 gm. and 2 .0 0 0 0 gm. sam p les r e s p e c t i v e l y . The c o rre s p o n d in g v a lu e s o f [ c l 3 " ' [ 7 c l 3 ' w ere 6 .7 and 6 .4 . An a tte m p t was made to d o u b le ch eck th e s e v a lu e s in th e fo llo w in g way: u s in g a lambda p i p e t t e and c o v e r in g th e t i p w ith a t i s s u e (sw ip e) w hich was im perm eable to th e r e s i n p a r t i c l e s , a sam ple o f p h a s e ’" w ith d raw n from t h r e e d i f f e r e n t sa m p le s. was P h a s e " 1 was e x t r a c t e d w ith a -28- p ip e tte . [ C l ] '" T h ese w ere c o u n te d and th e r a t i o s com pared. The mean v a lu e f o r / [ C l ] " was 1 .1 7 , i n d i c a t i n g a r e l a t i v e l y s m a ll d i f f e r e n c e i n c h l o ­ r i d e c o n c e n tr a ti o n betw een th e s e two p h a s e s . W hether o r n o t th e la c k o f ag ree m en t ( 1 .3 2 and 1 .3 4 v s 1 .1 7 ) i s a t t r i b u t a b l e to e x p e r im e n ta l e r r o r i s n o t known. A cc o rd in g to th e "bound w a te r" th e o r y , c h l o r i d e i s e x c lu d e d from th e "bound w a te r " a t th e p a r t i c l e s u r f a c e ; th e [ c l" " ] th ro u g h o u t th e r e ­ m a in d er o f th e sy ste m i s c o n s t a n t . I f we now th in k o f t h i s d i s t r i b u t i o n a p p lie d to th e sy ste m d e p ic te d i n A ppendix B, page 4 9 , th e n i t would seem a s tho u g h ' = I C l" ] " = ^ C l f l ' p ro v id e d p h a s e " and p h a s e ' a r e c o r r e c t e d f o r th e lo s s o f s o lv e n t to "bound w a te r " . We have s e e n t h a t [c l] T h e r e f o re one _ | ] l ] N " a c c o r d in g to th e r a d io m e tr i c d a ta . m ig h t e x p e c t th e "bound w a te r " to a f f e c t th e amount o f w a te r a v a i la b l e , as s o l v e n t i n p h a s e ' to th e g r e a t e s t e x t e n t . 'A c o r r e c t i o n c a n be made f o r th e volum e o f w a te r a c t i n g a s a s o lv e n t f o r C l" i n p h a s e 1 i f we assum e a l l th e "bound w a te r" volum e, V^, to b e c o n ta in e d i n t h i s p h a s e . [ c l] The a c t u a l 1 w ould be c a l c u l a t e d by s u b t r a c t i n g V^, a s d e te rm in e d from f i g u r e 3, p a g e f r o m th e t o t a l volum e o f. p h a s e 1. A c tu a l [ c l ] 1 = a p p a r e n t f c l~ J ] 1 x volum e o f phase* volum e o f p h ase" - V j 3. , U sing th e v a lu e s from T a b le I I I th e a c t u a l [ c l ] 1 was c a l c u l a t e d f o r ea c h sam ple. T hese v a lu e s a r e l i s t e d i n T a b le IV a lo n g w ith th e co n ce n ­ t r a t i o n s f o r p h a s e 1" . S t a t i s t i c a l tr e a tm e n t o f th e d a ta i n d i c a t e s no s i g n i f i c a n t d i f f e r e n c e a t th e 5% l e v e l b etw een ^ C l ] '" when c o r r e c t e d f o r "bound w a te r " . and j j l l " ] ' The r e s u l t s , t h e r e f o r e , p ro v id e -2 9 - s u p p o r tin g e v id e n c e f o r th e a p p l i c a b i l i t y o f th e bound w a te r th e o ry to th e r e s i n - w a t e r sy stem u n d e r c o n s i d e r a t i o n . S tu d y o f a^.+ By E s te r H y d ro ly s is R a te s The r a t e o f h y d r o ly s is o f an e s t e r i s r e p o r t e d l y a f u n c tio n o f th e a ^ + in th e medium ( 2 2 ) . P resu m ab ly th e m easu red r a t e o f h y d r o ly s is o f an e s t e r c o u ld t h e r e f o r e be u se d to d e te rm in e a^,+. The p u rp o s e o f th e s tu d y r e p o r te d h e r e was to d e te rm in e a^+ i n Dowex-50 r e s i n i n t h i s way. The v a lu e o b ta in e d c o u ld th e n be com pared w ith th e a p p a r e n t a + a s d e t e r H X m ined p o t e n t i o m e t r i c a l l y . Any d is c r e p a n c y c o u ld be a t t r i b u t e d to th e E . • J in v o lv e d i n th e pH d e te r m in a tio n . W ith t h i s o b j e c t i v e i n m ind, a s e r i e s o f h y d r o c h lo r ic a c id s o l u t i o n s o f v a r y in g pH w ere u se d to s tu d y th e r e l a t i o n betw een pH and r a t e o f h y ­ d ro ly s is . F o r a m ore d e t a i l e d a c c o u n t o f th e e x p e r im e n ta l p ro c e d u re se e A ppendix D, pag e 57. page 30. The r e s u l t s from t h i s s tu d y a r e p l o t t e d i n f i g u r e 4 , R e s in sam p les w ere e q u i l i b r a t e d w ith enough w a te r to make th e volum es o f th e s o l u t i o n s c o m p arab le. th e s e sam ples was m e asu re d . Then th e r a t e o f h y d r o ly s is f o r The t r i a n g u l a r p o i n t on th e g ra p h i n f i g u r e 4 shows th e r e s t i l t s , o f th e s e d e te r m in a tio n s . A second s e t o f d e te rm in a ­ ti o n s was made u s in g HCl s o l u t i o n s and Dowex-50 o f co m p arab le e q u iv a le n ts o f H+ p e r u n i t volum e o f s o l u t i o n . T hese d e te r m in a tio n s in d i c a t e d t h a t th e H+ r e s i n was s l i g h t l y more e f f e c t i v e th a n HCl c o n t a in in g e q u a l p e r u n i t volum e i n c a t a l y z i n g th e h y d r o ly s is r e a c t i o n . l i s t e d v i n T a b le V, page 32. meq H+ The r e s u l t s a r e From th e s e o b s e r v a tio n s i t seems a s th o u g h th e r a t e o f h y d r o ly s is i s in f lu e n c e d by o th e r f a c t o r s , p o s s i b ly th e a b s o r p tio n o f th e e s t e r by th e r e s i n . I t was c o n c lu d e d t h a t . t h e r a t e b f . h y d r o ly s is -3 0 - c o u Id n o t be u se d ps a r e l i a b l e m easu re o f a ^ + in th e r e s i n - w a t e r sy stem . The r e s u l t s o f M cA u liffe and Coleman (22) a l s o h e lp s u b s t a n t i a t e t h i s c o n ­ pH u n i t s c lu sio n . R esin R ate (m eq/m in) x 10* F ig u r e 4: H y d ro ly s is o f M e th y l- a c e ta te H+ c a ta ly z e d -3 1 -. TABLE I I I D is trib u tio n of C l^ . Sam ple W eight (gram s) la 1.0002 c/m in (C orr« f o r B ,G .) c /m in /m l 1260 810 132 1219 853 180 1352 914 184 1269 857 165 1305 851 174 1260 900 152 1219 948 206 1352 1013 212 1269 956 190 1305 946 201 7 .8 4 5 .6 0 0 .9 5 7 .5 8 5 .9 0 1 .2 8 8 .4 3 6 .3 0 1 .3 3 7 .8 0 5 .8 7 1.1 7 8 ; 02 5 .8 3 1 .2 3 1123 6 .9 9 1410 1085 211 1350 1060 225 1341 978 216 1401 1021 204 1392 1063 211 1419 993 230 8 .3 4 6 .4 3 1 .2 6 8 .0 0 6 .2 8 1.3 3 7 .9 2 5 .7 8 1 .2 8 , 8 .1 2 5 .9 0 1 .1 8 8 .0 6 6 .1 7 1.22 8 .2 1 5 .7 5 1 .3 3 B lank f o r sam ples l"i3 1188 6 .9 9 B lank f o r sam p les 4 -6 1207 6 .9 9 P h ase Ift It I 1.0006 2a I I I rt ■ I 3a ■ M 1 . 0 0 0 I 0 Tl I ‘ 4a 1.0003 I Il ' , If I 5a 1 .0 0 0 4 I I I M I B lank 2 .0011 lb I 11 ft I 2.0 0 0 6 2b f I I M I 3b 2.0001 - ‘ T ft Il I 4b ' 2 .0 0 0 4 I I I If I 5b 2.0001 I I I ft I 6b 2 .0 0 0 3 M l 1 Il I 1410 1846 367 1350 1808 391 1341 1679 376 1401 1787 355 1392 1809 367 1419 1688 400 C o n c e n tr a tio n meq/ml x IO^ -32- TABLE IV C o n c e n tr a tio n o f C l' C o r r e c te d f o r "Bound W ater" [crj Sample x IO4 i n p h a s e '" as d e te rm in e d from Cl^G d a ta [ C l - ] ' x 10^ in p h a s e 1 a s c a l c u l a t e d by c o r r e c t i n g f o r "bound w a te r" la 7 .8 4 meq/ml 5 .9 0 meq/ml 2a 7 .5 8 7 .9 5 3a 8 .4 3 8 .2 6 4a 7 .8 0 7 .3 0 5a 8 .0 2 7 .7 7 8 .3 4 7 .8 4 2b 8 .0 0 8 .2 6 3b 7 .9 2 7 .9 7 4b 8 .1 2 7 .3 4 5b 8 .0 6 7 .5 9 6b 8 .2 1 8 .2 6 mean 7 .9 0 * 7 .6 8 * lb . ' *No s i g n i f i c a n t d i f f e r e n c e a t 5% l e v e l . TABLE V - C o m p arativ e R a te s o f E s te r H y d ro ly s is of E q u iv a le n t am ounts o f H* P er U n it Volume HCl Dowex-50 1 .0 2 8 x lO '^rneq/m in. 1.263 x IC ^ rn e q /m in . 1.1 1 3 x 10"^m eq/m in. 1.2 3 3 x IO- ^meqZmin. * --33- P o te n t io m e tr ic D e te r m in a tio n i n E x ch an g er-W ater System t Some o f th e c e l l s to be c o n s id e r e d i n t h i s s e c t i o n a r e d e p ic te d below C e ll #1. g la s s e l . / H C l ^ / K C l ^ ^ ^ H g 2C l2 , Hg C e ll #2. g la s s e l . /H C l^ C e ll #3. Ag, AgCI / H G I / /NH4NO3 (10% )//K C I ( s a t . ) A g C l ( s a t . ) / AgCI , Ag C e ll #4. Ag, AgCI/H G I^ and r e s i n / / K C l ( s a t . ) / Hg2C lg , Hg and r e s i n / /NH^NO^CIO?.) / /K C l ( s a t .) A g C l( s a t.) / / AgCI , Ag C e ll #5. / Hg, H g g C lg /K C lC sa t.)/ / H C l ^ / HCl and r e s i n / / K C l ( s a t . ) / / Hg2C l2 , Hg See f i g u r e I . D, page 12. / C e l l # 6 . g l a s s e l./H C l( m ) / H C l(m ), r e s i n / g l a s s e l . J - See f i g u r e I . C, p a g e ,12. Where / / i n d i c a t e s a l i q u i d j u n c t i o n , / ‘. and / i n d i c a t e s a membrane o r o th e r m e c h a n ic a l means o f s e p a r a t i o n . The / p o t e n t i a l s o f th e c e l l s , a s d e p i c te d , w i l l b e r e f e r r e d to a s E^. \ E2 , Eg e t c . T hese p o t e n t i a l s may b e e x p r e s s e d by th e f o llo w in g ; E1 = E°1 - e C=I - e JX1KCD - ° - 0591 l ° s ='% E2 - EgX ' Ec a l - e JCKCD ' ° - 0591 loE 'll. E3 = EAg9AgCl “ Er e f ‘ Ej (NH4NO3) E- = E. 4 "A g,AgCI “re f EL = E E 6 , + E "' - E" ^j(NH4NO3) - E__! + E'! = E0 1 - 0 .0 5 9 1 lo g a ' gi . I + 0 .0 5 9 1 lo g a ^ . + 0 .0 5 9 1 lo g a 1' Cl * E„ Et 1 + 0 .0 5 9 1 lo g a"+ - E11 S As r e p o r te d i n m o st p h y s ic a l c h e m is tr y t e x t s , Ej a t a r e f e r e n c e - 34- e l e c tr o d e - s o l u t i o n i n t e r f a c e i s n e g l ig ib l y , s m a ll ( x ( 2 m i l l i v o l t s ) . cause of t h i s , and E j ^nh Be­ ^ w i l l be n e g le c te d and we s h a l l r e ­ f e r to EY a s E 1. J j The s u s p e n s io n e f f e c t , i s d e f in e d by th e d if f e r e n c e betw een E1 and Eg. E1 - Eg = E j(K c l) “ 0 .0 5 9 1 lo g a ”^ / a " + . Now i f th e . e J(NH4NO3) , Ej(KQ1) ' th e n El , " E2 = E3 ‘ E4 ‘ E3 " E4 = e J(NH4NO3) * 0 .0 5 9 1 lo g a ^ „ E5 r e p r e s e n t s / a^ . Efia l = Ej (KQ1) + Em E , = -0 .0 5 9 1 lo g - a " - E 6 H+ m I f a " ' x a M _ = a " , x a" _ , a s e x p e c te d from t h e iDonnan th e o ry (14) and H+ Cl HT Cl s i n c e , Em = 0 .0 5 9 1 lo g a^'+ = 0 .0 5 9 1 lo g a j ^ _ / a ^ _ , th e . above e x p r e s s io n s become e I " e 2 “ e J(K C I) + Em E3 " E4 = e J(NH4NO3) * Em E5 = e J(K C I) + Em E6 = 0 The e x i s t i n g l i t e r a t u r e i n d i c a t e s t h a t t h e r e a r e two s c h o o ls o f th o u g h t on th e e x p la n a tio n o f th e s u s p e n s io n e f f e c t . One s c h o o l i s o f th e o p in io n t h a t Ej i s n e g l i g i b l y s m a ll ( ^ 2 m v.) ( 4 ) ( 2 3 ) ( 2 4 ) ( 2 5 ) and th e o th e r i s o f th e o p in io n t h a t Ej may be la r g e enough to. c o n s t i t u t e a s e r i o u s e r r o r ( a s g r e a t a s 240 m v.) ( 2 ) ( 3 ) ( 5 ) ( 6 ) ( 2 6 ) ( 2 7 ) . Some f e e l t h a t Ej a c c o u n ts f o r th e e n t i r e s u s p e n s io n e f f e c t ( 2 0 ) . I n t h i s s e c t i o n o f th e t h e s i s , i t was p ro p o se d t h a t th e s i z e o f Ej =35- b e q u a n t i t a t i v e l y d e te rm in e d f o r Dowex-50 - w a te r s y s te m s . To do t h i s , ' a s p r e v io u s l y m e n tio n e d , we h av e s t u d i e d th e d i s t r i b u t i o n o f HCl-30 th ro u g h o u t th e s y ste m by two in d e p e n d e n t m eans. The a c t u a l d i s t r i b u t i o n i s c o n s id e r e d t o b e th e d i s t r i b u t i o n a s d e te rm in e d by C l* ^ . The p o t e n t i - o m e tric m easurem ents a r e ta k e n a s m easu res o f th e a p p a r e n t d i s t r i b u t i o n . The d i f f e r e n c e b etw een th e a p p a r e n t and th e a c t u a l d i s t r i b u t i o n makes p o s s ib le a c a lc u la tio n o f Ej. I n o r d e r to c o n s id e r th e r a d i o l o g i c a l d a ta as th e a c t u a l d i s t r i b u t i o n , th e a s s u m p tio n i s made t h a t th e a c t i v i t y c o e f f i c i e n t f o r C l" i s th e same i n a l l p h a s e s . The a ssu m p tio n t h a t th e a c t i v i t y c o e f f i c i e n t o f th e a d so rb e d c a t i o n and t h a t o f th e c a t i o n i n s o l u t i o n w ere th e same h a s p r e v io u s l y b e e n s u g g e s te d a s b e in g v a l i d (13) ' '. i ( 3 ) . The a s s u m p tio n made f o r th e C l a c t i v i t y c o e f f i c i e n t s i s e q u a lly re a s o n a b le . The a ss u m p tio n t h a t th e r a d i o l o g i c a l d a ta r e p r e s e n t s th e a c t u a l d i s t r i b u t i o n e n a b le s u s to c a l c u l a t e a v a lu e f o r Em. The a s s u m p tio n o f a c t i v i t y c o e f f i c i e n t o f C l b e in g th e same i n a l l p h a s e s means t h a t th e a c t i v i t y c o e f f i c i e n t i s one f o r d i l u t e s o l u t i o n s , i . e , i n th e o r d e r o f 10“% . T h is a ss u m p tio n a p p e a rs to b e c o n s i s t e n t w ith th e "bound w a te r " th e o r y . th e n Q c r ] ,M [C l-] = ac l - . th e n = ^C l ] " I f th e "bound w a te r" d i s t r i b u t i o n h o ld s , = Q C l ^ J 1. T h e r e f o re a'** - . = a ^ = i f th e s o l u t i o n s a r e d i l u t e , th e n = a^« and s i n c e a g ^ - = )f„ ^ p l ] j &V. U sing th e above e x p r e s s io n g iv e n f o r Em, th e s e a s s u m p tio n s i n d i c a t e I t h a t Em = 0 , From th e r a d i o l o g i c a l d a t a i t i s s e e n t h a t Em a s c a l c u l a t e d h as a maximum v a lu e o f a p p ro x im a te ly 7 m i l l i v o l t s . -3 6 O v erb eek 1s T re a tm e n t (26) O verbeek t h e o r e t i c a l l y t r e a t e d th e fo llo w in g c e l l ; I II / III Hg, HggClg / K C l(s a t) / e q u ilib r iu m s o l u t i o n / c o l l o i d s l u r r y / / 2 K C L (sat) / HggCIg, Hg. The e .m .f . , E, o f th e c e l l i s g iv e n by -EF = d^ i (17) By m a n ip u la tio n o f t h i s e q u a tio n i n o r d e r to a v o id s i n g l e io n a c t i v i t i e s and in c lu d in g th e membrane p o t e n t i a l , O verbeek o b ta in e d th e e q u a tio n E = S i C -->■ ti 4£i Zl + ^ r 11- zY r 111 f ^ V:______ R______ V V B i (18) J ■~v C E q u a tio n (18) now in c lu d e s E = Ej ( l ) + E ^(2 ) + R j ( 3 ) ’ an<^ a s shown by O v erb eek 1 th e p o t e n t i a l may b e e x p re s s e d a p p ro x im a te ly by th e fo llo w in g e q u a tio n : E_ = RT In c o n d u c ta n c e o f s u s p e n s io n S — c o ----------------------------------------n d u c ta n c e o f e q u i lib r i u m s o l u t i o n (19) T a b le I p ro v id e s some i n t e r e s t i n g f a c t s th a t,s h o w m e r i t i n e q u a tio n (1 9 ). The s tr o n g a c i d e x c h a n g e rs hav e a muph g r e a t e r s u s p e n s io n e f f e c t th a n weak a c i d e x c h a n g e rs . The s tr o n g b a s e ex c h a n g e rs hav e a much g r e a t e r n e g a tiv e s u s p e n s io n e f f e c t th a n th e weak b a s e e x c h a n g e rs . T h is i s as e x p e c te d a c c o r d in g to e q u a tio n ( 1 9 ) , s i n c e th e c o n d u c ta n c e o f th e d o u b le la y e r o f a s tr o n g a c id o r b a s e e x ch a n g er is. much g r e a t e r th a n t h a t o f th e weak a c id o r b a s e ex c h a n g e r ( s e e T a b le I , page 19 and f i g u r e 2, page 1 8 ) . “ 37 “ The c o n d u c ta n c e o f th e d o u b le la y e r o f th e c o l l o i d p a r t i c l e s does n o t i n c r e a s e s i g n i f i c a n t l y w ith i n c r e a s i n g c o n c e n tr a ti o n o f e q u ilib r iu m e le c tro ly te . Thus one w ould e x p e c t from e q u a tio n (19) t h a t th e conduct= a n c e o f th e e q u i lib r i u m e l e c t r o l y t e , a s i t s c o n c e n tr a ti o n was in c r e a s e d , w ould become e q u a l to t h a t o f th e s l u r r y . P eech e t a l . T h is o b s e r v a tio n was made by ( 2 7 ) , Bower (5 ) ( 6) f o r c l a y - w a te r sy stem s and by th e p r e ­ s e n t i n v e s t i g a t o r s f o r Dowex-50 - w a te r s y s te m s . (S ee F ig u r e 5 , page5 / ) A number o f r e s i n sam p les w ere e q u i l i b r a t e d w ith s o l u t i o n s o f NaCl f o r . tw e n ty - f o u r h o u r s . 0 .0 0 0 5 N t o 0 .2 N, The c o n c e n tr a ti o n o f th e s o l u t i o n s v a r ie d from The ApH o r AEc a ^ o f e a c h sam ple was d e te rm in e d and th e v a lu e p l o t t e d v e r s u s c o n c e n tr a ti o n o f NaCI . Some c o n d u c ta n c e s t u d ­ i e s made on c l a y - w a te r sy ste m s (35) a r e a l s o in c lu d e d . T hese 4uchranbe4vai^|§/Lw.e^e'':iised^to;;c a !d e la te J%^n]i^n '^f-6qua:tidh) -lBfoese.-Yalu£sv @ 'fi% 0- ^ a ^ ;:a n 4 j - ^ E e a d g mp a r e ^ . . a r e d e p ic te d by F ig u r e s 6 , 7 , 8 , and 9. T h ese co m p ariso n s A s i m i l a r s tu d y was made by th e p r e s e n t i n v e s t i g a t o r s f o r Dowex-50, Dowex-SOW and Dowex-I . s u l t s a r e l i s t e d i n T a b le V I. Tmi f-*; I" „ ,I-. ", T hese r e ­ . TABLE VI C om parison o f ^ E c a l and EDonnan E 1 cal ./•®Donnan - Dowex-50 125 mv. 80 Dowex-SOW 160 mv. 79 74 mv. 68 D o w ex -I C o n c e n t r a t i o n NaCI . 0 .0 1 0.02 0 .0 3 0 .0 4 0 .0 5 F ig u re 5. 0 .0 6 0 .0 7 e q / l i t e r of so lu tio n 0 .0 8 0 .0 9 S a l t C o n c e n tr a tio n v s . 0 .1 pH D ia ly z a te Poharrhltil - -Log S p e c i f i c C onductance C la y -S lu rry Donnan — ^ Legend: Q — D ia ly z a te + — C lay S lu r ty & ~ ^E cal 0 “ - l o g K+C l - F ig u r e 6 . C om p arison o f V nnan m o le s/lite r A E c g l w it h E0on n an u s i n g 2 .4 2 7 , H+ M o n t m o r illo n it e Legend: Q + A A B caI ^Donnan PoV enfiaI - lo g S p e c i f i c C on d u ctan ce ® D ia ly z a te C lay S lu r r y F ig u r e 7 . C om p arison o f A E c a l w it h E0on n an u s i n g 2.42% Na+ M o n t m o r illo n it e Legend: Q -f- ■ 70 D ia ly z a te C lay S lu r r y "Fol-BTvt-V pecif ic ConJa<-4dnce. Donnan -lo g F ig u r e 8 . (jCaCl^j m o l e s / l i t e r C om p arison o f A E c g l w it h Elj0n r5n u s i n g 5.86% Ca F o r t C o l l i n s C la y Legend: q D ia ly z a te + C lay S lu r r y ^ ^ Er a l Po+ er\+ \a.| - lo g S p e c i f i c C on d u ctan ce onnan -lo g F ig u r e 9 . CaClg m o le s/lite r C om p arison o f A E c g l w it h E0on ngn u s in g 2.42% Ca"*+ M o n t m o r illo n it e -4 3 The r e s u l t s o b ta in e d q u a l i t a t i v e l y s u p p o r t O v erb eek ' s th e o ry a l ­ th o u g h th e v a lu e s a r e n o t i n good q u a n t i t a t i v e ag re e m e n t. The same co n ­ c l u s i o n was r e a c h e d by Bloksma (2 ) and more q u a n t i t a t i v e s u b s t a n t i a t i o n was. o b ta in e d by Bower ( 6) , I t i s i n t e r e s t i n g to n o te th e v a lu e s o b ta in e d f o r th e Ca++-M ontm o ri I I o n i t e and th e Ca-^+ - F o r t C o ll in s c l a y s . A n e g a tiv e AEc a ^ (27) i s o b s e rv e d and a n e g a t iv e Donnah i s c a l c u l a t e d by e q u a tio n ( 1 9 ) . Com­ p a r is o n o f th e m o b i l i t i e s and th e c o n d u c ta n c e s o f H"1", K+ , Na+ and Ca++ r e v e a l s no a p p a r e n t r e a s o n f o r th e ch an g e i n s ig n o f th e p o t e n t i a l . The s u s p e n s io n e f f e c t a p p a r e n tly c a n n o t be a f u n c ti o n o f c o n d u c ta n c e a lo n e , b u t o th e r f a c t o r s m u st be in v o lv e d . C a l c u l a t i o n o f Ej To c a l c u l a t e E j th e f o llo w in g e q u a tio n was u se d ; ■E; + E_ 1C a l - - J w here Ejn = ,5 9 .1 lo g a ^ _ / a " ^ _ and No. I and No. 2. AEc a ^ was d e te rm in e d a s i n c e l l s The d a ta f o r Em w ere ta k e n from T a b le I I I . I t was p o in te d o u t p r e v io u s l y t h a t i f th e "bound w a te r" th e o ry h e ld th e n Em w ould e q u a l z e r o . Thus th e v a lu e s c a l c u l a t e d f o r Em w ould b e a maximum v a lu e and t h e r e f o r e th e v a lu e o b ta in e d f o r E . by th e above ' J ■ e x p r e s s io n w ould be a minimum. A E re j^ was a l s o u s e d . d e te rm in e d by c e l l s l i k e No. 3 and No. 4 . The v a lu e s w ere A n o th e r e l e c t r o d e c o m b in a tio n u s e d was an A g,AgCI i n c o n ju n c tio n w ith a s a t u r a t e d c a lo m e l e l e c t r o d e . The Ag9AgCl e l e c t r o d e was p r e p a r e d by th e m ethod o f Brown ( 1 1 ) . A ll o f th e s e d a ta a r e l i s t e d i n T a b le V I I 9 p ag e 4 4 , s e e a l s o f i g u r e IO9 page 45. !I '. io ■, I". ■ ^ L ' ' v. . : •; j. •'>. ; „• -4 4 - I t s h o u ld be n o te d t h a t AEr g f and th e p o t e n t i a l a s m easu red by th e A g ,A g C l-s a tu ra te d c a lo m e l p a i r d i f f e r i n t h a t th e r e f e r e n c e e l e c ­ tr o d e s a r e d i f f e r e n t and th e s a l t b r id g e s o l u t i o n s a r e d i f f e r e n t co n A c e n t r a t i o n s . The fo rm er h a v in g a more d i l u t e b r id g e s o l u t i o n . The d i f f e r e n c e o b ta in e d i n E . i s a t t r i b u t e d to two f a c t o r s : J . (a ) th e m o b i l i t i e s o f th e NH^+ and NO^" a r e more n e a r l y e q u a l th a n th o s e o f K+ and Cl"", and (b ) th e d i f f e r e n t c o n c e n tr a ti o n s o f s a l t b r id g e s o lu tio n (3 ). TABLE V II C om parison o f V alu es f o r Ej w ith D i f f e r e n t E le c tr o d e P a ir s Sample ' AEc a l la 9 8 .0 * AEr e f Em fj 8.6 8 9 .4 102 9 3 .4 fj (EAg1AgCl Ec a l ) !i 2a 100.0 6.1 9 3 .9 103 9 6 .9 3a 112.0 7 .4 1 0 5 .6 108 100.6 4a 9 5 .8 7 .3 8 8 .5 82 7 4 .7 5a 88.6 8.0 • 8 0 .6 77 6 9 .0 lb 7 7 .5 6.6 7 0 .9 82 7 5 .4 8 4 .0 6.2 7 7 .8 81 7 5 .8 i : 2b . I 3b 9 7 .5 8.0 8 9 .5 79 7 1 .0 4b 11 8 .2 8.0 110.2 80 7 2 .0 5b 12 4 .0 6.8 1 1 7 .2 83 7 6 .2 6b 10 1 .5 9 .1 9 2 .4 *A11 r e a d in g s a r e i n m i l l i v o l t s r. -4 5 - L 1 20 HO- eH, 100EI» EJ \ \ w w \ \ \ % ,\\\ s s \ \W f 90- X I I I I I I I Ej X / X m X E j 0 X X X 3a 4a 5a Sam ples □ F ig u r e 10. C o m p o sitio n o f AEc y l o f Dowex-50 - W ater System -4 6 “- SUMMARY and conclusions The d i s t r i b u t i o n o f HCl i n a Dowex-50 - w a te r s y ste m r e c e iv e d a t t e n ­ tio n in th is in v e s tig a tio n . The d i s t r i b u t i o n c o u ld b e a d e q u a te ly d i s - c r i b e d , w i t h i n l i m i t s o f e x p e r im e n ta l e r r o r , by th e s o - c a l l e d "bound w a te r" th e o r y . A c c o rd in g to t h i s th e o r y , th e r e s i n p a r t i c l e s a r e c o a te d w ith a t h i n f i l m o f "bound w a te r " ( I ) . T h is w a te r h a s a c h a r a c t e r i s e :1 - ...Lj t i c a l l y low d e n s it y and i s presum ed to h av e s t r u c t u r a l c h a r a c t e r i s t i c s s i m i l a r to i c e . T h is th e o ry demands t h a t f r e e io n s b e e x c lu d e d from t h i s "bound w a te r " , w h ich a c c o u n ts f o r n e g a t iv e a d s o r p ti o n o f a n io n s ( 1 5 ) . D a ta o b ta in e d i n t h i s i n v e s t i g a t i o n i s c o n s i s t e n t w ith , and p r o v id e s some s u p p o r tin g e v id e n c e f o r th e "bound w a te r" th e o r y . The e l e c t r i c a l d o u b le l a y e r a t th e r e s i n s u r f a c e i s t h e r e f o r e v i s u a l i s e d a s a d i s t i n c t r a t h e r th a n a d i f f u s e l a y e r . The s o l u t i o n i n th e Dowex-50 - w a te r s y ste m b e ­ yond th e "bound w a te r " f i l m i s a c c o r d in g ly c o n s id e r e d to b e hom ogeneous. I n an e q u i l i b r a t e d Dowex-50 - w a te r s y s te m , th e p o t e n t i o m e t r i c a l l y m easu red pH o f th e s l u r r y was fo u n d td d i f f e r from th e c o r r e s p o n d in g pH o f th e s u p e r n a ta n t s o l u t i o n by a s much a s 3 .2 6 pH u n i t s . T h is s o - c a l l e d s u s p e n s io n e f f e c t i s commonly a t t r i b u t e d e i t h e r to an a c t u a l d i f f e r e n c e i n Sg+ i n th e s y ste m o r to th e e x i s t e n c e o f a l i q u i d ju n c tio n p o t e n t i a l (E 4) a t th e r e f e r e n c e e l e c t r o d e - r e s i n i n t e r f a c e . J ’ ' In th is in - v e s t i g a t i o n , a c o m p a riso n ,w a s made b etw ee n th e a c t u a l d i s t r i b u t i o n o f C l” i n th e s y s te m , a s d e te rm in e d by C l ^ , and th e a p p a r e n t d i s t r i b u t i o n o f C l” i n th e s y ste m a s d e te rm in e d p o t e n t i o m e t r i c a l l y . The r e s u l t s i n d i ­ c a t e d a n E j w h ich c o u ld b e a s h ig h a s 93 m i l l i v o l t s , d ep e n d in g upon =47" c e r t a i n c h e m ic a l c h a r a c t e r i s t i c s o f th e sy stem . T h is E . c o n s titu te s a p o t e n t i a l s o u r c e o f e r r o r i n p o te n tio m e tr ic d e te r m in a tio n s made i n e x ­ c h a n g e r -w a te r sy stem s w hich may be l a r g e enough to c o m p le te ly i n v a l i d a t e , th e r e s u l t s . D ata o b ta in e d r e l a t i v e to Ej a r e q u a l i t a t i v e l y c o n s i s t e n t w ith t h 6 t h e o r e t i c a l tr e a tm e n t o f O verbeek ( 2 6 ) . B o th c a t i o n and a n io n exchange r e s i n s , e x h i b i t th e s u s p e n s io n e f f e c t : th e fo rm er b e in g p o s i t i v e i n s ig n and th e l a t t e r b e in g n e g a t iv e i n s ig n . The E j was a s e n s i t i v e f u n c tio n o f e l e c t r o l y t e c o n t e n t , a p p ro a c h in g z e ro a p p a r e n tly a s a l i m i t as th e e l e c t r o l y t e c o n te n t ap p ro a c h e d 0 .2 N. SUGGESTION FOR FUTURE RESEARCH I t seems t h a t in f o r m a tio n r e g a r d in g th e fu n d am e n tal c a u s e ( s ) o f ' " ■ / l i q u i d j u n c t i o n p o t e n t i a l s i n c o l l o i d a l - w a t e r sy stem s w ould be d e s i r a b l e . I f th e c a u s e ( s ) w ere known, th e n one w ould p resu m ab ly be a b le to p r e d i c t w h ich sy ste m w ould g iv e r i s e to l i q u i d j u n c t i o n p o t e n t i a l s . S tu d ie s c o u ld be made co m p arin g th e e f f e c t on th e m a g n itu d e o f Ej r e s u l t i n g from r e s i n s a t u r a t e d w ith d i f f e r e n t c a t i o n s . From th e s e s t u d i e s p o s s i b ly c o r r e l a t i o n s c o u ld be made c o n c e rn in g th e m a g n itu d e o f Ej as/, a '.,fu n c tio n '.o f su ^.'^aK to r# '''& A , i o n i e ^ a d i i ^ h y d r a t i o n r a d i i and v a le n c e . -4 8 APPENDIX A I. D e f i n i t i o n s and Sym bolism 1. S u s p e n sio n E f f e c t — th e o b se rv e d d i f f e r e n c e betw een th e d i a l y z a t e pH and th e s u s p e n s io n pH. 2. E j — l i q u i d j u n c t i o n p o t e n t i a l - - t h e p o t e n t i a l c r e a t e d a t th e d i f f u s i o n b o u n d ary o f a r e f e r e n c e e l e c t r o d e . 3. Em—membrane p o t e n t i a l - - w o r k r e q u i r e d to b r in g a p o i n t c h a rg e from one s i d e o f th e membrane to th e o t h e r . E = (^ fm - ^ 4 . . yV - - e l e c t r i c a l p o t e n t i a l 5. —c h e m ic a l p o t e n t i a l 6. — th e e l e c t r o c h e m ic a l p o t e n t i a l . e l e c t r i c a l and c h e m ic a l p o t e n t i a l s . -Y i = + RTjn a . ' + ZF v w here R—u n i v e r s a l gas c o n s ta n t ! - - t e m p e r a t u r e a b s o lu te —a c t i v i t y Z—v a le n c e o f io n s p e c ie s F —F a ra d a y s T h is i s th e sum o f th e -4 9 APPENDIX B P hase" P hase" P h a se ' P h a s e '" i s th e d i a l y z a t e . P hase" i s th e i n t e r s t i t i a l e l e c t r o l y t e . P h a s e ' i s th e s o lv e n t o r s o l u t i o n ta k e n up by th e c o l l o i d p a r t i c l e s . F ig u r e 11: T h ree P hase System -5 0 APPENDIX C Membrane P o t e n t i a l and Donnan E q u ilib r iu m S u sp e n sio n (p h a s e " ) D ia ly z a te ( p h a s e " ') S em iperm eable Membrane F ig u r e 12: A t e q u ilib r iu m A /±" = X ^ '" Donnan System f o r a u n iv a le n t c a t io n I . y y 0 + RTlnaJJ+ + ZF Ijt" + R T ln a '^ + Z F ^ '" upon r e a r r a n g i n g 2. RTlna^ = ZF ( " 1 -V ^") and by d e f i n i t i o n E^ = ( ^ - y/") a+ 3. "m * B ln g o in g back now to e q u a tio n I . and w r i t i n g th e e x p r e s s io n f o r an a n io n and r e a r r a n g i n g 4 . y</Q + RT In a" - ZF 5. -RT In ZF 6. RT In ZF In a l " aT~ a-: = am a l" a " _ = =XJq + RT In a I" - Z F ^ " ' ( Y " - Y '" ) or ( f " - y ) Now e q u a tin g 2. and 6 in a V a"' T h is i s th e e x p r e s s io n d e r iv e d by Donnan (14) w hich r e l a t e s th e a c t i v i t i e s o f u n i v a l e n t io n s in th e two p h a s e s . -5 1 APPENDIX D W ater C o n te n t D e te rm in a tio n The m e th o d , o f G reg o r e t a l . c o n t e n t o f th e r e s i n s . firs t, (17) was u s e d to d e te rm in e th e w a te r The r e s i n was e q u i l i b r a t e d w ith e x c e s s w a te r th e n p la c e d i n a s i n t e r e d g l a s s f i l t e r f u n n e l, u n d e r s u c ti o n , f o r l i t t l e more th a n t h r e e m in u te s . As was shown by G reg o r e t a l . , a f t e r t h r e e m in u te s , th e r e s i n m a in ta in e d a r e l a t i v e c o n s ta n t w e ig h t. > ■ T h is i s b e l i e v e d . t o i n d i c a t e t h a t th e i n t e r s t i t i a l w a te r had b een r e ­ . moved, and t h a t any a d d i t i o n a l lo s s o f w e ig h t, a f t e r t h i s tim e , would be due to a i r d r y in g . The r e s i n was p la c e d i n w eig h in g b o t t l e s , w eighed and p la c e d i n a vacuum d e s s i c a t p r . The sam p les w ere w eig h ed p e r i o d i c a l l y u n t i l no f u r t h e r lo s s i n w e ig h t was shown. T h is was ta k e n a s th e d ry w e ig h t o f th e r e s i n . By t r a n s f e r r i n g sam p les to th e w e ig h in g b o t t l e s w ith tim in g and c a r e , good p r e c i s i o n was o b ta in e d . The r e s i n was fou n d to c o n t a in 46%.w a te r , by w e ig h t. A n o th er m ethod, u s e d by G regor e t a l . , was c e n t r i f u g a t i o n . The sam p les w ere p la c e d i n s i n t e r e d g l a s s f u n n e ls w hich s a t i n s p e c i a l c e n t r i ­ fu g e f l a s k s . They w ere c e n t r if u g e d f o r t h i r t y m in u te s a t 1500 g ' s . T h is was found to be a d e q u a te to e x t r a c t n e a r l y a l l o f th e i n t e r s t i t i a l w a te r . The E f f e c t o f P e r c e n t R e s in in S u sp e n sio n upon th e A p p a re n t pH o f th e S u sp e n sio n A s e r i e s o f sa m p le s, c o n ta in in g tw e n ty m i l l i l i t e r s o f d i s t i l l e d w a te r and v a r y in g am ounts o f r e s i n from 1 .5 gms. to 5 .5 gms. d ry w e ig h t, w ere m easured f o r s u s p e n s io n pH. The pH o f th e r e s i n was p l o t t e d v e rs u s -5 2 - th e am ount o f d ry w e ig h t o f r e s i n . (S ee f i g u r e 1 3 .) I t was fou n d t h a t th e pH v a r ie d b u t v e r y l i t t l e , g o in g from 3 .6 to 2 .9 . The r e l a t i v e l y h ig h pH v a l u e s , o b s e rv e d h e r e , a r e due to th e f a c t t h a t , w h ile m e a su rin g th e pH, th e r e s i n was s t i r r e d c o n s t a n t l y . s e ttlin g , Upon th e pH o f th e r e s i n sam p les was a l l 1+0.1 pH. D e te r m in a tio n o f th e Volume O ccupied by Wet R e sin A colum n o f r e s i n was p r e p a r e d i n a 50 m i l l i l i t e r b u r e t . The c o l ­ umn was th o ro u g h ly w e tte d w ith w a te r and th e w a te r l e v e l was above th e r e s in le v e l. Some o f th e w a te r was a llo w e d to d r a i n down, w e ll below th e r e s i n l e v e l . , and th e n so m e.o f th e r e s i n was sco o p ed o u t and p la c e d i n a w eighing, b o t t l e . The am ount o f r e s i n t h a t was ta k e n o u t was alw ays a p p ro x im a te ly a h a l f in c h l a y e r . th e e x t r a c t i o n . r e s i n volum e. The b u r e t was r e f i l l e d w ith w a te r a f t e r The d i f f e r e n c e in r e s i n l e v e l s was ta k e n , a s th e w et T h is m ethod was r e p e a te d f o r s e v e r a l s a m p le s. The r e s i n sam p les w ere w eighed r e p e a t e d l y , u n t i l no f u r t h e r lo s s o f w ie g h t was ’ d e t e c te d w ith a d d i t i o n a l d r y in g ' Method- o f S e p a r a tio n o f P h a s e m , P hase" and Phase* Two m ethods w ere u s e d f o r s e p a r a t i o n o f p h a s e 1" . re s u lts . B o th gave s i m i l a r P h a s e "1 may b e e f f e c t i v e l y s e p a r a t e d e i t h e r by d e c a n tin g th e d i a l y z a t e o r by f o r c in g th e d i a l y z a t e o u t th ro u g h a s i n t e r e d g la s s f u n n e l. The r e s i n , p h a s e " , and ,.,phase1 a r e l e f t b e h in d . C o n s id e rin g p h a s e 1 an d th e w a te r c o n t e n t o f th e w et r e s i n to be id e n ­ t i c a l , th e s e p a r a t i o n o f p h a s e " was s i m i l a r to th e e x p e rim e n ts f o r d e t e r ­ m in in g th e w a te r c o n t e n t. The s i n t e r e d g l a s s f u n n e l was c e n t r if u g e d f o r t h i r t y m in u te s a t 1500 g 's to remove p h a s e " . C h lo r id e s i n p h a s e ’ was pH o f R e sin -5 3 - Amount o f R e sin g ram s/20 m i l l i t e r s o f d i s t i l l e d w a te r F ig u r e 13. The E f f e c t o f 7» R esin on S u sp e n sio n E f f e c t -5 4 - w ashed o u t o f th e r e s i n sam ple w ith d i s t i l l e d w a te r . D e te r m in a tio n o f th e Volume o f P h a s e '" , P h ase" and P h a s e ' . The r e s i n was e q u i l i b r a t e d w ith 11 m l. o f d i s t i l l e d w a te r . was d e c a n te d and p la c e d i n a w eig h in g b o t t l e and w eig h ed . P hase"' From th e d e n s it y o f w a te r a t 2 7 ° C ., th e volum e o f p h a s e '" was c a l c u l a t e d . The volum e o f p h a s e ' was c a l c u l a t e d from th e w a te r c o n te n t and th e d e n s ity v a lu e . The volum e o f p h a s e " was c o n s id e r e d t o be th e d i f f e r e n c e o f th e t o t a l volum e and th e sum o f p h a s e '" and p h a s e '. TABLE V I I I Volumes o f th e S e p a r a te P h ases P hase I g . Sam ples 2 g . Sam ples 9 .2 3 c c . 7 .5 7 c c . . " 0 .9 0 c c . 1 .7 0 c c . i 0 .8 7 c c . 1 .7 3 c c . m D e te r m in a tio n o f C h lo r id e D i s t r i b u t i o n by R a d io lo g ic a l M ethods F o r d e te r m in a tio n o f th e C l ^ d i s t r i b u t i o n , a r e s i n sam p le was e q u i l i b r a t e d w ith one m i l l i l i t e r o f 0 .0 0 7 6 9 N H C l^ and te n m i l l i l i t e r s o f d i s t i l l e d w a te r . The sam ple was s t i r r e d o c c a s i o n a ll y and th e n a l ­ lowed to e q u i l i b r a t e o v e r n i g h t . l e a s t 24 h o u r s . The t o t a l e q u i l i b r a t i o n p e r io d was a t The pH o f th e s u p e r n a ta n t d id n o t change s i g n i f i c a n t l y a f t e r t h i s tim e . The t h r e e p h a s e s w ere s e p a r a te d a s d e s c r ib e d on p ag e 5 2 . The s e p a r ­ a t e p o r t i o n s w ere n e u t r a l i z e d w ith e x c e s s HaOH and th e n e v a p o r a te d to d ry n e s s i n s t a i n l e s s s t e e l p la n c h e ts , The sam p les w ere c o u n te d i n a G e ig e r-M u e lle r c o u n te r . Each sam ple was c o u n te d f o r a- f i v e m in u te p e r io d . C l36 S e lf - A b s o r p tio n A number o f NaCl3 ^ s o l u t i o n s w ere e v a p o ra te d to d ry n e s s i n s t a i n l e s s s t e e l p la n c h e ts i n o r d e r to a s c e r t a i n w h e th e r o r n o t any s e l f a b s o r p tio n was ta k in g p la c e i n th e sam p les u se d i n th e s tu d y o f C l” d i s t r i b u t i o n . The am ount o f s a l t was v a r i e d from 0 .2 mg. t o 90 mg. and th e c o u n t r a t e was d e te rm in e d . f i g u r e 14. From th e s e d a ta a p l o t was..made; th e r e s u l t s a p p e a r i n From th e g ra p h i t i s e a s i l y s e e n t h a t s e l f a b s o r p ti o n would b e o f no c o n c e rn f o r th e sam p les u se d i n t h i s i n v e s t i g a t i o n . The sam ples u s e d i n th e i n v e s t i g a t i o n w eig h a p p ro x im a te ly 0 .2 m illig r a m . A cco rd in g to f i g u r e 14 no a p p r e c ia b le a b s o r p tio n ta k e s p la c e f o r sam p les o f t h i s w e ig h t. D e te r m in a tio n o f C h lo r id e by P o te n io m e tr ic M easurem ent F o r d e te r m in in g th e c h l o r i d e a c t i v i t y , a Beckman s i l v e r b i l l e t comb i n a t i q n e l e c t r o d e #39187 was u se d a s a A g,AgCl e l e c t r o d e . T h is e l e c ­ tr o d e i s d e s ig n e d to be u se d w ith th e . Beckman Model G pH m e te r . T his e l e c t r o d e i s two e l e c t r o d e s i n one u n i t , c o n t a in in g an A g,AgCI e l e c tr o d e and an A g,AgCI r e f e r e n c e . e l e c t r o d e i n a s o l u t i o n t h a t i s s a t u r a t e d w ith r e s p e c t to b o th KCl and AgCI . Betw een th e r e f e r e n c e e l e c t r o d e and th e sam ple s o l u t i o n , t h e r e . i s . a r e s e r v o i r c o n t a in in g a 10% s o l u t i o n o f c o n n e c ts th e sam ple w ith th e r e f e r e n c e e l e c t r o d e . T h is b r id g e s o l u t i o n T h is p r e v e n ts c h l o r i d e io n s from th e r e f e r e n c e e l e c t r o d e from c o n ta m in a tin g th e sam p le. A l i n e n f i b e r c o n n e c ts th e r e f e r e n c e e l e c t r o d e to th e b r id g e s o lu ti o n .a n d -5 6 - C o u n ts/m in u te Back S c a t t e r i n g E f f e c t from S t a i n l e s s S t e e l . M illig ra m s o f S o lid F ig u r e 14: C l"^ S e l f A b so rp tio n / -5 7 - th e b r id g e s o l u t i o n to the, sam p le. Some e l e c t r o d e s , p r e p a r e d by th e m ethod o f Brown ( 1 1 ) , w ere a l s o used. T hese e l e c t r o d e s w ere u s e d i n c o n ju n c tio n w ith a S .C .E . An A tte m p t to D eterm in e a„*. by R a te s o f E s te r H y d ro ly s is The am ount o f r e s i n to be u se d f o r e a c h sam ple was w eighed i n a 50 m i l l i l i t e r E rlen m ey e r f l a s k . Enough w a te r was added to th e sy stem to occupy a l l o f p h a s e 1 and p h a s e ” . i n volum e. The am ount o f a c id was co m p arab le The a c i d s o l u t i o n s v a r ie d from .0 .0 to 2 .1 2 i n pH. o f th e r e s i n was m easu red a t a te m p e r a tu r e o f 35°C. The pH The r e s i n and a c id sam p les w ere p la c e d i n a c o n s t a n t te m p e r a tu r e b a t h , sh ak en and allo w ed t o r e a c h 35° C. sam p le. One m i l l i l i t e r o f p u re m e th y ! a c e ta te was added to each The z e ro tim e was ta k e n a t t h i s p o i n t . The r e a c t i o n was s to p p e d by a d d in g j u s t enough NaOH to t i t r a t e th e t o t a l e q u i v a le n t s o f H+ i i n th e sy ste m . The sam p les w ere im m e d ia te ly b ack t i t r a t e d w ith a s ta n d a r d HGl s o l u t i o n and p h e n o lp h th a le in . -5 8 - LITERATURE CITED P e rio d ic a ls I. A n d e rso n 3 D. M. and Low3 P. F . 3 S o i l S c i . S oc, Amer. 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I n c . 5 0 -6 5 :1 0 3 (1931) 17:218 (1953) 8 :5 9 3 (1953) T e x ts 29. M acIn n es, D. A ., THE PRINCIPLES OF ELECTROCHEMISTRY P u b lis h in g C o r p ., New Y ork p . 221 (1939) 30. K u n in , K, ION EXCHANGE RESIN 2nd E d i t i o n (1950) 31 . N achod, F . C. ION EXCHANGE R e in h o ld W iley & Sons I n c . , New Y ork A cadem ic P r e s s , New Y ork p . 45 (1949) T heses 32 . D a v is , L. E . , U n iv e r s it y o f C a l i f o r n i a (1941) Ph.D . t h e s i s 33. Du R e i t z , C ., Tekn H ogskola n , S to ck h o lm (1938) Ph.D . t h e s i s 34 . Moreno Camacho, E d g a r d ,. U n iv e r s ity o f C a l i f o r p i a (1957) 35 . O ls e n , R. A ., C o r n e ll U n iv e r s it y (1953) Ph.D . t h e s i s 150873 I _______ ,T .-rr HUtVFB^rrY LIBRARIES 3 1762 10015372 3 /C _ 150873 H