w Twrnowmmw imiz&nm omsfmn of *9i«mauo

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1 w Twrnowmmw imiz&nm omsfmn of *9i«mauo by Mur m y Mum T h e sis su b m itted to th e F a e u lty o f th e a ra d u a te School o f th e U n iv e rs ity o f M aryland in p a r t i a l f u l f i l I s o n t o f th e r e tm ir e a e a ts f o r th e d e g re e o f D oetor o f P h ilo so p h y 1051

2 UMI Number: DP70326 All rights reserved INFORMATION TO ALL USERS The quality of this reproduction is dependent upon the quality of the copy submitted. In the unlikely event that the author did not send a complete manuscript and there are missing pages, these will be noted. Also, if material had to be removed, a note will indicate the deletion. Dissertation Publishing UMI DP70326 Published by ProQuest LLC (2015). Copyright in the Dissertation held by the Author. Microform Edition ProQuest LLC. All rights reserved. This work is protected against unauthorized copying under Title 17, United States Code ProQuest LLC. 789 East Eisenhower Parkway P.O. Box 1346 Ann Arbor, Ml

3 i i I w ish t o e x p re s s» y In d e b te d n e ss to Dr# 1 0 f# r 0# B ate* o f th e P h y s ic a l C hem istry S e c tio n of th e g a t io a a l B u rsas s f S ta n d a rd s f o r p e r a is s io a to a s# th e c e l l s, e l e c t r i c a l e q u ip a e n t and o th s r f a s H i t i e s o f th e la b o ra to r y ; f o r h is assists### l a the d e e # lo p * e a t o f th# p ro c e d u re d e s c rib e d l a t h i s t h e s i s s a t l a p a r t i c u l a r, f o r h is a b i l i t y to i l l a f t l a a t e th e stu d y o f e l e s t r o l y t l e s o la tio a s #

4 ill TUBLS OF CGHWE5 IJ3TRGBUCTI0M 1 THEORETICAL DBRIFaTIOH 6 FJCPSRIJOTTAL PROCEDURE 1 1 A* R eagents I - 'o ta s s iu m a c i d m a l a t e 1 1 P o t a s s i u m c h l o r i d e 1 2 P o ta a s iu ib h y d r o x i d e 1 3 P e r c h l o r i c a c i d 1 4 B. P r e p a r e t i o n o f s o l u t i o n s 1 5 C. :,l e c t r o m o t i v e f o re m e a s u r e m e n ts 1 5 SX PllU M SEfA L RESULTS A* ph 1 9 E. I o n i c s t r e n g t h 1 9 C. T he f i r s t i o n i z a t i o n c o n s t a n t, K^# 2 5 P. T h e s e c o n d i o n i z a t i o n c o n s t a n t, K g. 2 6 H:. T h e rm o d y n a m ic c o n s t a n t s 2 8 D I3 CIJSSI0 H OF RtSULTS 3 0 D I3 CUSSI0 H OF ERRORS 3 2 R2 FSREHCKS 3 8 APPENDIX OF TABLES 41 AP'-FJ&DIK O f FIGURES 6 5

5 j& m m ix OF T4BLSS 1. B u ffe r r a t i o s and d i l u t i o n r a t i o s o f ru n s 1 to The e x p erim en tal v a lu e s o f te rm in a l v o lta g e, io n ic s tr e n g th, 42 m o la lity, term s o f e q u a tio n 23 d e riv e d from th e s e q u a n t itie s and a second ap p ro x im atio n o f io n ic s tr e n g th, f o r each te m p e ra tu re in t e r v a l o f 5 d e g re e s in th e range 0 t o 50 C e n tig ra d e, 3* The sta n d a rd e le c tr o d e p o t e n t i a l o f th e s i l v e r - s i l v e r c h lo rid e 53 h a lf c e l l, th e v a lu e o fw2,3028 RT/F and th e p aram eters 4 and B, o f th e Dehye-Huckel e q u a tio n f o r th e taigperatur range 0 to 50 C e n tig ra d e, 4. V alues o f X and Y f o r each e x p e rim e n ta l run in te r p o la te d to 54 eq u al v a lu e s o f io n ic s tr e n g th, 5. S lo p e s f th e p l o t s o f X a g a in s t I o f F ig u re s 2.1 to 2,1 1, V alues o f pdk^ ( - lo g c r K.} a s a fu n c tio n o f te m p eratu re and 8 8 io n ic strength and 4(pcriL/dfl'5 at each temperature. 7. V alues o f - lo g Kg/^ computed fro th e e x p e rim e n ta l d a ta 59 o f ru n s 1, 6, 2, 7 and 3 a, 8. A com parison o f th e e x p e rim e n ta lly determ ined v a lu e s o f pe^ 60 end th e v a lu e s computed on th e b a s is o f e q u a tio n a com parison o f th e e x p e rim e n ta lly d eterm in ed v a lu e s Of pkg 61 and th e v a lu e s computed on th e b a s is o f e q u a tio n 74, 1 0. a com parison o f th e e x p e rim e n ta lly determ ined v a lu e s o f 62 and K w ith th e v a lu e s computed from e q u a tio n s 73 ana 74 r e s p e c tiv e ly, 11. The therm odynamic q u a n t itie s AF#, AH, 6 9 andacp d e riv e d 63 from th e smoothed v a lu e s of th e f i r s t and second io n iz a tio n c o n s ta n ts, 12. T a lu e s o f th e f i r s t and second io n iz a tio n c o n s ta n ts o f 64 d,l- m a ilc a c id a s o b ta in ed fro th e l i t e r a t u r e.

6 V APPMDIX OF FIGURES l a. The computed q u a n tity, X, a s a fu n c tio n o f io n ic s tr e n g th f o r th e te m p e ra tu re reag e 0 to 50 O e n tig ra d e. 1,1 a Run Mo a " * a " «5 6? l* 4 a * * 1 and ,5 a * " a *f " 7 to l.? a " * 3a 71 l b. The computed q u a n tity, Y, a s a fu n c tio n o f io n ic s tr e n g th f o r th e te m p e ra tu re ran g e 0 to 50 C e n tig ra d e. 1.1b RUn Mo b " * ,3 b * « b * " 1 and b " * b " * b " * 3a A s e r i e s o f p l o t s o f X a g a in s t Y a t c o n s ta n t io n ic s tr e n g th f o r each 5 d eg ree i n t e r v a l in th e range 0 to 50 C e n tig ra d e SO p!c^ (-lo g d K ^ ) p lo tte d a g a in s t io n ic s tr e n g th P lo t o f lo g jfg/p -1* lo g p a g a in s t io n ic s tr e n g th A com parison o f: th e e x p e rim e n ta lly d e riv e d value o f pk^ and 94 th e v a lu e s o f pk^ c a lc u la te d by means o f e q u a tio n A com parison o f th e e x p e rim e n ta lly d e riv e d v a lu e s o f pkg and 95 th e v a lu e s o f pkg c a lc u la te d by means o f e q u a tio n Photograph o f th e h y d ro g a ~ e ilv e r~ silv e r c h lo rid e c e l l P lo t o f a g a in s t io n ic s tr e n g th,o b ta in e d from th e d a ta 97 o f Earned and Owen (2 7 ).

7 INTRODUCTION When a weak e l e c t r o l y t e l a d is s o lv e d l a w a te r I t does a o t d is s o c ia te c o m p le te ly. The e x te n t o f th e d ls s o e la tio n depends upon a number o f fa c to rs;-* te m p e ra tu re, c o n c e n tra tio n o f weak e l e c t r o l y t e, c o n c e n tra tio n o f o th e r com ponents in th e e o la tio n and on a p a ra m e te r s p e c if i c to th e weak e l e c t r o l y t e u n d er study* T h is p a ra m e te r, th e Io n iz a tio n cons t a n t ( a ls o r e f e r r e d to a s th e e q u ilib riu m o r d is s o c ia tio n c o n s ta n t) o f th e weak e l e c t r o l y t e and i t s r e l a t i o n to f r e e e n erg y change, i s a v e ry v a lu a b le to o l f o r d e s c rib in g th e b e h a v io r o f an e l e c t r o l y t e in s o lu tio n * i f i r s t a p p ro x im atio n o f th e io n iz a tio n c o n s ta n t may be c a lc u la te d q u ite sim p ly. F or exam ple, th e io n is a tio n c o n s ta n t o f a weak monobasic a c id, HA, which d is s o c ia te s a c c o rd in g to th e e q u a tio n may be approxim ated by th e e x p re ssio n H i ^ H+ + i " (1) K'= -E -JL. (8) i t The q u a n t itie s»%*» and mga r e p r e s e n t th e e q u ilib riu m m o lal concent r a t i o n s o f th e hydrogen io n, an io n and u n d is s o c ia te d a c id r e s p e c tiv e ly. The d a ta re q u ire d f o r an approxim ate c a lc u la tio n a r e th e m o la lity o f one o f th e com ponents and any p ro p e rty o f th e s o lu tio n t h a t depends upon th e e x te n t o f d i s s o c i a t i o n ; - co n d u ctan ce, ph, v ap o r p re s s u re lo w e rin g, s p e c if i c a b s o rp tio n a t a given w a v e -le n g th, e t c. U n fo rtu n a te ly, such f i r s t ap p ro x im atio n s may be g r e a t ly in e r r o r. Some o f th e assu m p tio n s in tro d u c e d in o rd e r to s im p lify th e computati o n a re too d r a s tic * P erh ap s th e m ost q u e s tio n a b le assum ption i s th e use o f c o n c e n tra tio n in th e p la c e o f a c t i v i t y. M o la lity and a c t i v i t y

8 a r t e q u iv a le n t o n ly in id e a l s o lu tio n s. S xoept a t v e ry g re a t d i l u t i o n, no r e a l e l e c t r o l y t e in s o lu tio n behaves i d e a l l y. The a c t i v i t y o f th e c h lo rid e io n f o r exam ple i s l e s s th a n in a 0. 1 m o lal s o lu tio n o f h y d ro c h lo ric a c id. The a c t i v i t y o f a p o ly v a le n t Ion w ill h e l e s s th a n 50 p e r c e n t o f th e m o la lity in a 0. 1 m o lal s o lu tio n. The therm odynamic I o n iz a tio n c o n s ta n t o f th e a c id WL i s c o r r e c t l y d e fin e d by th e e x p re ssio n St V.a&«H4 (3) The ( p a n t i t l e s g t* a ^ - t a H^ r e p r e s e n t th e a c t i v i t i e s o f th e s e v e r a l com ponents. The r e l a t i o n betw een a c t i v i t y and m o la lity i s ex p ressed b y th e e q u a tio n * 1 ' ' V l <*) The new p a ra m e te r, i s c a lle d th e a c t i v i t y c o e f f i c i e n t. E q u atio n 5 may be r e w r itte n i n th e form K - * * ^ (5) I t i s e v id e n t th a t th e f i r s t f r a c t i o n on th e r i g h t hand s id e o f e q u a tio n 5 i s id e n tic a l w ith th e r i g h t s id e o f e q u a tio n 2. T h e re fo re th e r e l a t i o n betw een th e therm odynamic io n iz a tio n c o n s ta n t and th e " a p p a re n t lo n ln - a tio n c o n s ta n t i s sim p ly X * K«r ~ r ± ( 6 ) iiha In o rd e r to O btain some id e a o f th e d if f e r e n c e betw een K* and K, we may c o n s id e r th e c a s e o f th e h y p o th e tic a l m onobasic a c id H I. I t i s n o t u n re a so n a b le to assume t h a t in d i l u t e s o lu tio n th e a c t i v i t i e s o f H* and w ill d i f f e r o n ly s l i g h t l y from th e a c t i v i t y o f o th e r sm all m onovalent

9 3 io n s a t th e same m o la lity * F u rth e r, th e a c t i v i t y o f an u a d 0 la te d m o lecu le i s seldom v e ry d i f f e r e n t from th e m o la lity in d i l u t e s o lu tio n s. I f th e io n ic c o n c e n tra tio n o f the a c id s o lu tio n i s 0.1 m o la l, {This can he accom plished by th e a d d itio n o f an i n e r t e l e c t r o l y t e o r by th e a d d itio n o f th e s o ld s a l t. ) th e n a s u b s t itu t io n o f th e v a lu e o f {*0 1 ~ in a 0, i s o lu tio n ) f o r a^* and a^«in e q u a tio n 3, in d ic a te s t h a t K, ( th e io n iz a tio n c o n s ta n t c a lc u la te d on an a c t i v i t y b a s is ) i s o n ly about tw o * th ird s o f K*, {the io n is a tio n c o n s ta n t c a lc u la te d on a m o la lity b a s i s. ) I t i s t o be a n tic ip a te d th a t a t h ig h e r io n ic ooncent r a t i o n s th e d is c re p a n c y w ill be much g re a te r* A p r e c is e d e te rm in a tio n o f th e io n iz a tio n c o n s ta n t th e re f o r e m ust ta k e in to account th e f a c t t h a t th e r e i s a d if f e r e n c e betw een a c t i v i t i e s and m o la litie s * The e a se o f an e l e c t r o l y t e w ith two d is s o c ia tin g groups in tro d u c e s a n o th e r so u rc e o f u n c e r ta in ty. In such c a s e s th e r e a re two io n iz a tio n c o n s ta n ts to be d eterm in e d. But th e e q u ilib riu m c o n s ta n t f o r one d ie s* o c ia tio n cannot be e v a lu a te d w ith o u t c o r r e c tin g f o r th e e f f e c t o f th e o th e r d is s o c ia tio n ( 5 ). T h at i s, i f th e f i r s t io n iz a tio n c o n s ta n t o f th e a c id H i was b e in g s tu d ie d, i n t e r e s t would c e n te r around th e reac* tlom HgA^ Hf + HA* {?) B ut i t i s to be expected t h a t some o f th e m onovalent a n io n HA* w ill d is s o c ia te f u r th e r a c c o rd in g to th e re a c tio n S H a ^ H ja * A* W T here a r e a few d ib a s ic a c id s t h a t p o s se ss a v e ry h ig h r a t i o o f f i r s t to second io n iz a tio n c o n s ta n t (SO). In such e a se s th e in t e r a c t io n w ill b e n e g lig ib le * But most o f th e common d lo a rb o x y lie a c id s {BO) and a number o f th e s u b s titu te d b en zo ic a c id s t h a t have been s tu d ie d {35)

10 4 do n o t come unde? t h i s categ o ry * #hen th e r a t i o o f f i r s t to second ion* ia a tio n c o n s ta n t i s 500 o r l e s s, th e in t e r a c t io n o f the two e q u i l i b r i a i s to o g r e a t to be ignored* In many in s ta n c e s, th e fo llo w in g g e n e ra l p ro c e d u re has been used to d e te rm in e p r e c i s e ly th e io n is a tio n c o n s ta n ts o f d ib a s ic acid s* x s u it* a b le r e v e r s ib le chem ical c e l l i s chosen* P re fe re n c e has u s u a lly been g iv e n to c e l l s t h a t do n o t r e q u ir e a liq u id Ju n c tio n betw een th e h a lf* c e lls * The e l e c t r o l y t i c c e l l s o lu tio n i s p re p a re d w ith a d e f i n i t e con* c e n t r a t ion o f th e weak e l e c t r o l y t e u n d er study* By v a rio u s m eans, cor* r e s t io n term s f o r th e o v e rla p p in g o f e q u i l i b r i a i* e. h y d ro ly s is o r d is s o c ia tio n, a r e ev a lu a te d * The a c t i v i t y c o e f f i c ie n t term s a re comp* u te d j u s u a lly by some form o f th e D ebye-h uekel equation* Then th e ion* i s a t l o n c o n s ta n ts may be found and used to make a r e c a lc u la tio n o f th e c o r r e c tio n term s* The u ltim a te v a lu e s o f th e io n is a tio n c o n s ta n ts a re a r r iv e d a t a f t e r a s e r ie s o f s u c c e s s iv e ap p ro x im a tio n s. A number o f w orkers have d eterm in ed th e io n iz a tio n c o n s ta n ts o f weak d ib a s ic acid u s in g v a r ia tio n s o f t h i s p ro c e d u re (4, 1 4, 15, 33, 14, 4 4 ) I t i s, a t b e s t, an in v o lv ed and la b o rio u s o o ^ m ta tlo n * B a te s (5) has proposed a s im p le r method f o r th e p r e c is e d eterm in a tio n o f one io n iz a tio n c o n s ta n t o f a d ib a s ic a c id, p ro v id ed th a t th e o th e r io n is a tio n c o n s ta n t i s known. The d a ta o f such a d e te rm in a tio n a r e o b ta in e d from, c e l l s w ith o u t liq u id ju n c tio n * The e l e c t r o l y t i c s o l u tio n i s p re p a re d c o n ta in in g a d e f i n i t e q u a n tity o f th e a c id s a l t o f th e weak d ib a s ic a c id. The p ro d u ct o f th e io n iz a tio n c o n s ta n ts,, i s determ ined g ra p h ic a lly * The v a lu e o f t h i s method l i e s in th e f a c t th a t th e m o la lity term in th e c a lc u la tio n i s in s e n s itiv e to r e l a t i v e l y la r g e e r r o r s in th e h y d ro ly s is c o rre c tio n * S in c e i t has been assumed

11 5 th a t on o f th e io n iz a tio n c o n s ta n ts i s known, th s o th e r may be c a lc u la te d r e a d ily from th e product# j% sim p le r method f o r e v a lu a tin g b o th th e f i r s t and second io n is a tio n c o n s ta n ts o f a weak d ib a s ic a c id from a s in g le s e t o f o b s e rv a tio n s had been su g g ested some y e a rs e a r l i e r by Speakman (4 6 ). In c e r t a i n r e s p e c ts I t i s an alo g o u s to th e method proposed by B ates# The method proposed by Speakman does reduce th e e r r o r s t h a t m ight o th e rw ise be in tro d u c e d when h y d ro ly s is and a c t i v i t y c o e f f i c i e n t c o r r e c tio n s a r e n e g le c te d # In s p i t e o f t h i s re d u c tio n in th e e f f e c t s o f th e u s u a l a p p ro x im a tio n s, a c o rre c tio n f o r th e e r r o r s a r i s i n g from th e two so u rc e s d is c u s s e d above m ust be in tro d u c e d b e fo re Speakm an's method can be used to d eterm in e th e io n iz a tio n c o n s ta n ts o f d ib a s ic a c id s w ith some p re c is io n # The method a p p lie d by apeakman to d a ta o b ta in e d from ph t i t r a t i o n s in c e l l s c o n ta in in g a liq u id ju n c tio n, i s am enable to use w ith any so u rc e o f eraf d ata# F u rth erm o re, i t i s p o s s ib le to m odify th e method o f c a lc u la tio n so a s to in c lu d e th e c o rre c tio n s # The method proposed h e re and a p p lie d to th e d e te rm in a tio n o f th e io n iz a tio n c o n s ta n ts o f d, l - m alio a c id, i s a ro o d ific e tio n o f Speakm an's method th a t w ill p e rm it th e sim u ltan e o u s e v a lu a tio n o f th e io n iz a tio n c o n s ta n ts o f a d ib a s ic a c id u s in g d a ta th a t have been d e riv e d from c e l l s w ith o u t liq u id ju n c tio n # The b a s is o f th e ex p e rim e n ta l method used h e re was f i r s t d e sc rib e d by Earned and E h le rs (2 5, 3 6 ). The p ro ced u re was m odified f u r th e r by Hamer and A eree (30) and l a t e r by B ates and Aoree {?) The a p p a ra tu s and ex p e rim e n ta l p ro c e d u re employed in t h i s work was e s s e n t i a l l y t h a t d e s c rib e d by th e l a t t e r #

12 THSCmmOAL ESH STATION The f i r s t sad second therm odynamic io n is a tio n c o n s ta n ts o f a d ib a s ic a c id a r e d e fin e d by th e e q u a tio n s ( ) and *HA* HA* "f HA' (10) The u s u a l co n v en tio n have been employed a^ - th e a c t i v i t y o f th e io n s p e c ifie d by th e s u b s c r ip t. * th e m o la lity o f th e ion s p e c if ie d by th e s u b s c r ip t. ''Q - th e a c t i v i t y c o e f f i c ie n t on a m o lal b a s is o f th e io n s p e c if ie d by th e s u b s c r ip t. T hree a d d itio n a l te r n s have been d e f in e d :- o( - th e q u a n tity, in m o les, o f th e a c id s a l t added i n i t i a l l y to th e s o lu tio n, jj - th e q u a n tity, in m o les, o f s tro n g a c id added i n i t i a l l y to th e s o lu tio n. ( I f s tro n g b a se i s to be added In s te a d o f a c id, th e sig n o f ^ i s n e g a tiv e.) 1 * (J - ( W C onsider the s o lu tio n o f a m onobasic s a l t o f a weak a c id, MBs,, in a s o lu tio n c o n ta in in g a c o m p lete ly d is s o c ia te d (s tro n g ) a c id, HO. At e q u ilib riu m, th e a c id s a l t w ill have d is s o c ia te d co m p le te ly in to th e c a tio n M* and in to a c e r t a i n amount o f each o f th e th re e p o s s ib le form s th e an io n may ta k e. Some o f th e m onovalent an io n w iu have r e a c te d w ith th e hydrogen io a o f th e s tro n g a c id to produce th e u n d is s o c ia te d a c id, Eg&, and a sm all p o rtio n o f th e m onovalent a n io n w ill have d is s o c ia te d

13 t o produo th e b iv a le n t an io n A* in accord an ce w ith e q u a tio n 8. S in c e the s o lu tio n must be e l e c t r i c a l l y n e u t r a l, th e io n ic e q u i lib rium betw een p o s itiv e and n e g a tiv e c h a rg e s may b e w r itte n =cg-3 +L0!T]*[h«.">f:A*J (12) By d e f i n i t i o n, < e q u a ls th e number o f moles o f a c id s a l t i n i t i a l l y added* At e q u ilib riu m, d w ill e q u a l th e sum o f th e th ro e in te r c o n v e r t ib l e form s o f th e a n io n o f th e a c id s a lt* «+1&T] + I4=] (15) A t th e same tim e < *IK*] (14) E q u atio n 18 may be r e w r itte n in th e form «Iha~ > [&t ] (if?) I f e q u a tio n IS i s re a rra n g e d and th e d e f in i tio n o f B (S q u atio n 11) I s in tro d u c e d, th e n e q u a tio n IS any be w r itte n B * < - [HA*] - [2AS ] (16) o r < - B»pA*3+[2A*J (1?) I f a i s added to b o th s id e s o f e q u a tio n 16 and th e v a lu e o f «a s d e f in ed by eq u atio n 13 i s s u b s titu te d in to th e r ig h t hand s id e o f e q u a tio n 1 6, th e n < B * IA % [SHgAl (18) E quation 18 sa y be used to e lim in a te ^ fro th e e q u a tio n f o r th e f i r s t I o n is a tio n c o n s ta n t (9)#^ % h e u se o f number o f m oles and m o la lity in te rc h a n g e a b ly i s J u s t i f i e d so long a s th e mass o f th e s o lv e n t does n o t f ig u r e in th e d e r i v a tio n * The a c tu a l n u m e rical co m p u tatio n s must be made in term s o f m o la lity

14 8, - a i a Ht, a?u~>- 1 <WtB 0 U-> r R2A ' Id a lik e manner m may be e lim in a te d from e q u a tio n 1 0 by tb e i n t r o - due t io n o f e q u a tio n 17* x = ah*(«- B "BUT^S t r im ) Both e q u a tio n s 19 and SO may be re a rra n g e d to so lv e f o r m ^ -. Y B HA* a ai'+ % T "lg4 {81} _. _ «Hf (* - B) t SUtY + &Ky ^ ^ ri &* m * E q u atin g SI and 8 8 and re a rra n g in g te rm s : B) 's^ga* *^ ^ ( 88) th e e x p e rim e n ta l d e te rm in a tio n o f a ^ t i s made by m easuring th e p o t e n t i a l o f an e l e c t r i e a l c e l l j - Ft,Hg(p=l); S01(^»xi ffiqx**=kbig01t4ig (24) The H e rn st e q u a tio n f o r t h i s c e l l may be w r itte n o r 1 * 1 - ET/F In {ah+ag r.) (m) (E - ]g )A + lo g (Sd) In o rd e r to make th e n o ta tio n l e a s cumbersome s e v e r a l a d d itio n a l q u a n t itie s have been d e f in e d :-. ( E - I + w B, ) ( k s c i,pj F - 10 {87} X -.il ( 8) o<+ B

15 (89) (80)? ^HgA YSi " (31) (38) The new d e f in i tio n s p e rm it a q u a tio n 83 to be w r itte n in th e form p t (33) r = i f i + K iv f (34) To t h i s p o in t th e d e r iv a tio n baa baan c a r r ie d out w ith o u t s a c r i f i c in g therm odynam ic ex a c tn e ss* How wa may c o n s id e r how i t e a a ba used to c a lc u la te d th a two io n iz a tio n c o n s ta n ts in a e t n a l p ra c tic e * The Tar* ia b le e X and Y a r e q u a n t itie s computed from th a e x p e rim e n ta l c e l l v o ltage d e te rm in a tio n s and from th a I n i t i a l m o l a l i t i e s, s in e e *g+ la In* wolted In th a com putation o f th a q u a n tity B and c o n seq u e n tly in th a co m putation o f X and t $ i t m ost ba d eterm ined l a some way. Tha ex p erim e n ta l e o n d itlo n s may be a rra n g e d so th a t <* and jj a r e la r g e whan comp ered w ith mu* so t h a t X and Y a s th e y a r e c a lc u la te d by a q u a tio n s 8 8 and 89 a r e q u ite In sen s i t i r e to r e l a t i v e l y la r g e e r r o r s in mg+* I t can ba seen t h a t a q u a tio n 34 w ill be a l i n e a r e q u a tio n In X and Y i f c e r t a in c o n d itio n s can ba m a t:- i f th e d i f f e r e n t v a lu e s o f th a independent v a r ia b le s found in th a t a q u a tio n do n o t a p p re c ia b ly a f f e c t th a co n stan c y o f l / p and cr S tu d ie s o f s a l t e f f e c t s in d ic a te th a t th e a c t i v i t y c o e f f i c ie n t s o f io n s in s o lu tio n a r e la r g e ly independent o f th a c o n c e n tra tio n o f any s in g le io n ic component b u t depend upon th e io n ic

16 10 s tr e n g th o f th e so lu tio n * (9, 27) T h e re fo re, I t should he p o s s ib le to m a in ta in ^ and 0 * c o n s ta n t w ith in th e e r r o r o f th e d e te rm in a tio n, by com paring v a lu e s o f X and I d e riv e d from e x p e rim e n ta l m easurem ents o f s o lu tio n s c o n ta in in g d i f f e r e n t r a t i o s o f a c id s a l t to s tro n g a c id { o r s tro n g h ese) a t c o n s ta n t io n ic s tre n g th * I f t h i s i s done, i t i s poss i b l e to o b ta in a fa m ily o f s t r a i g h t l i n e s c o rre sp o n d in g to d i f f e r e n t v a lu e s o f th e io n ic s tre n g th * The s lo p e s o f th e se l i n e s a re th e n p lo tte d a g a in s t io n ic s tr e n g th and th e r e s u l t a n t cu rv e i s e x tra p o la te d to a e ro io n ic s tre n g th * S in c e d*approaches u n ity a t i n f i n i t e d i l u t i o n, th e v a lu e a t th e in te r * c e p t i s c o n sid e re d to be X^* The o p e ra tio n may be re v e rs e d, and w ith th e a id o f th e new ly e v a l u a te d K p v a lu e s o f 0 * may be computed f o r d i f f e r e n t v a lu e s o f io n ic stre n g th * The q u a n tity Kg/p can th e n be computed from e q u a tio n 34* The q u a n tity Xg/p may now b e p lo tte d a g a in s t io n ic s tre n g th s a tre a tm e n t analogous t o th e com putation o f X^* In t h i s c a s e th e i n t e r c e p t a t a e ro io n ic s tr e n g th should be K s in c e 1/a ap p ro aches u n ity a t i n f i n i t e d ilu tio n *

17 M pm m m fal mog&wmn 4 * B a g e n ts 1* P otassium soldi m a la te * E qulm olar q u a n t itie s o f re a g e n t g rad e d, l - m a lic a c id and p o ta ssiu m hydrogen c a rb o n a te were d is s o lv e d in e a t e r. The s o lu tio n was m a in tain ed a t $0 0 f o r s e v e ra l m in u te s, a c tiv a te d c h a rc o a l was added and th e s o lu tio n was f i l t e r e d * The f i l t r a t e was cooled in an lc e -w a te r h a th and e th y l a lc o h o l (95 p e r c e n t) was poured in to th e s o lu tio n u n t i l th e volume had heen doubled* The p r e c i p i t a t e o f cru d e p o ta ssiu m a c id m e la te was s e p a ra te d by f i l t r a t i o n * T h is p re c i p i t a t e was r e c r y s t a l l i z e d f iv e tim es by f i r s t d is s o lv in g th e s a l t in h o t w a te r and r e p r e o i p lta tin g i t by th e a d d itio n o f e th y l alco h o l* The s a l t c o lle c te d a f t e r th e f i f t h r e c r y s t a l l i s a t i o n was d rie d o v e rn ig h t a t and was k e p t in a d e s ic c a to r* The p o ta ssiu m a c id m alate was assayed by a c id im e tric t i t r a t i o n a g a in s t a s ta n d a rd s o lu tio n o f p o ta ssiu m hydroxide* The s ta n d a rd base had p re v io u s ly been s ta n d a rd ise d a g a in s t p o ta ssiu m a c id p h th a la te (MBS S tan d ard Sample 8 4 b ) A fte r th e f i r s t r e e r y s t a l l 1za t io n, th e d rie d s a l t was c a lc u la te d to be 99*69 p e r c e n t p o ta ssiu m a c id m alate* A fte r th e th i r d r e e r y s t a l l i z a t i o n th e a s s a y had r i s e n to 99*98 p e r cent* A f te r th e f i f t h r e c r y s t a l l i z e! i o n i t was 99*99 p e r cen t* T e s ts were made to d eterm in e w hether th e d rie d p o ta ssiu m a c id mala t e was h y g ro sco p ic, f o u r sam p les, each w eighing fo u r gram s, w ere p la c e d in w eighing b o ttle s * The sam ples w ere d rie d f o r f o r t y h ours a t 105 C and im m ediately p la c e d in a d e s ic c a to r* The sam ples were allow ed to co o l to room te m p e ra tu re and th e n weighed* A fte r th e w eights had been ta k e n, th e b o t t l e s w ere l e f t open f o r 48 h o u rs in a room a t 82 0, 45 p e r c e n t

18 18 r e l a t i v e h u m id ity. The sam ples in c re a se d in w eight by an av era g e o f 1.5 m illig ra m s o r sh o u t p e r c e n t. A fte r th e sam ples had been l e f t open f o r two w eeks, th e av erage in c re a s e in w eight o f sam ple was 2. 4 m illig ra m s o r 0,07 p e r c e n t. A p p a re n tly p o ta ssiu m a c id m a la te i s n o t a p p re c ia b ly h y g ro sco p ic u n d er norm al la b o ra to r y c o n d itio n s. However, a s s p r e c a u tio n, th e s a l t was d rie d f o r an h o u r a t b e fo re th e p re p a ra tio n o f each s e t o f s o lu tio n s. 2. P otassium c h lo r id e. P o tassiu m c h lo r id e, th e so u rce o f c h lo rid e io n i s th e e l e c t r o l y t i c c e l l, was p rep ared a c c o rd in g to th e p ro ced u re su g g ested by P in ch in g and B ates (3 7 ) C h lo rin e gas was bubbled in to a s a tu r a te d s o lu tio n o f p o ta ssiu m c h lo rid e f o r an h o u r, fh e s o lu tio n was b o ile d to remove th e gaseous c h lo rin e and brom ine and th e n cooled t o 2S C. Hydrogen c h lo rid e g a s, g e n e ra te d by th e a d d itio n o f sodium c h lo rid e to c o n c e n tra te d s u l f u r i c a c id, was bubbled in to th e potassiu m c h lo rid e s o lu tio n u n t i l no more appeared to be a b so rb e d. The s o lu tio n was f i l t e r e d ; th e p r e c i p i t a t e was weshed w ith co ld a b s o lu te e th y l a lc o h o l and d rie d in an oven a t The d rie d s a l t was fused under d ry n itro g e n in a p la tin u m c r u c ib le and was allow ed to s o l i d i f y. The fused p o ta ssiu m c h lo rid e was te s te d f o r th e p re sen c e o f f r e e a l k a li* S e v e ra l fiv e-g ra m sam ples w ere t i t r a t e d w ith m olal h y d ro c h lo ric a c id, u s in g bronthym ol b lo e as th e in d i c a to r. The end* p o in t was e stim a te d by com paring th e t e s t s o lu tio n w ith a c o lo r s ta n d a rd p rep ared from th e in d ic a to r and a p h o sp h ate b u f f e r o f ph 7 ( 8 ). The p o ta ssiu m c h lo rid e was a ls o te s te d f o r brom ide im p u rity u sin g th e p ro ced u re o f R, a. A iek in (1) a s m odified by P in c h in g and B a te s ( 3 7 ) # In t h i s t e s t, brom ine i s d e te c te d by o c ld iz in g brom ide ion to f r e e brom ine and a d so rb in g th e brom ine on p ap er s a tu r a te d w ith f lu o r e s c e in.

19 13 The Ermine d is p la c e s hydrogen from th e flu o re e o e ln to form e o sin ( te t r a b r o a f lu o r e s e e ln ) k p o s itiv e t e s t f o r brom ine i s in d ic a te d by a p in k sp o t o f eosin* th e t e s t i s e x tre m e ly s e n s itiv e and w ill d e te a t 0 * p e r e e n t brom ide* I f t e r th e p u r if i c a tio n p ro c e d u re, th e p o ta ssiu m c h lo rid e c o n ta in e d ab o u t 0 * p e r c e n t p o ta ssiu m h y d ro x id e and 0*008 p e r c e n t p o tassiu m brom ide as in d ic a te d by th e t e s t s d e s c rib e d above* 3* P o tassiu m h y d ro x id e * The sta n d a rd s o lu tio n o f p o ta ssiu m hydrox id e was p re p a re d from? T. B aker *A03 S tan d ard * p o ta ssiu m hydrox id e p e lle ts * Two hundred grams o f p o ta ssiu m hydroxide were d is s o lv e d in d i s t i l l e d w a te r o f " c o n d u c tiv ity * g rad e to sak e a s o lu tio n o f about 400 m l. a s o lu tio n o f b arium hydroxide was p re p a re d by b o ilin g an exc e s s o f barium hydro x id e in D i s t i l l e d w ater* The m ix tu re was cooled to room te m p e ra tu re, c e n trifu g e d f o r te n m inutes and th e s u p e rn a ta n t l i q u id was decanted* The amount o f p o ta ssiu m carb o n a te co n tam in ant was in d ic a te d on th e la b e l to be 1 *S p e r cent* m amount o f barium hydrox id e s o lu tio n c a lc u la te d to be s u f f i c i e n t to p r e c i p i t a t e th e c a rb o n a te im p u rity was added to th e p o ta ssiu m hydro x id e so lu tio n * A d d itio n a l b a r ium h y droxide s o lu tio n was in tro d u c e d dropw lse u n t i l no f u r th e r p re c i p i t a t i o n was observed* A pproach to th e e n d -p o in t was e stim a te d by th e fo llo w in g p ro c e d u re. One ml o f th e s u p e rn a ta n t liq u id was w ithdraw n and p la c e d in a te s t- tu b e * I t was th e n d ilu te d w ith th r e e ml of w ater and one ml o f the barium h y d ro x id e s o lu tio n was added. The e n d -p o in t was c o n sid e re d to have been reached when o n ly v e ry s l i g h t t u r b i d i t y was o b serv ed. a s im ila r t e s t u s in g 0.3 a l o f 1 norm al s u l f u r i c a c id was made in o rd e r to d eterm in e w h eth er barium io n had been added in excess* In t h i s

20 ease th e re a ls o was a s l i g h t t u r b i d i t y a t th e e n d -p o in t. The c o n c e n tra te d p o ta ssiu m hydroxide s o lu tio n was c e n trifu g e d f o r f i f t e e n m in u tes and th e s u p e rn a ta n t liq u id p ip e tte d in to a p a r a f f in lin e d oarboy c o n ta in in g ab o u t sev en te en l i t e r s of *c o n d u c tiv ity * w a te r. The w a te r in th e carboy had been scrubbed p re v io u s ly by b u b b lin g p u r i f ie d n itro g e n th ro u g h i t o v ern ig h t* The c o n c e n tra te d p o ta ssiu m hydrox id e was added to th e w a te r a l i t t l e a t a tim e w ith o u t sto p p in g th e stre a m o f n itr o g e n, a sam ple o f th e d i l u t e s o lu tio n was removed and t i tr a t e d r a p id l y so th a t th e m o la lity co u ld be more c lo s e ly a d ju s te d to 0. 1 m o la l. The d i l u t e p o ta ssiu m hydro x id e s o lu tio n (0.1 m o lal) was s ta n d a rd is e d by a s e r i e s o f w eight t i t r a t i o n s a g a in s t p o tassiu m a c id p h th a l- a t e ( IIS S tan d ard Sample 34b) in a carbon d io x id e - f r e e atm o sp h ere. Three d ro p s o f p h e n o lp h th a le ln s o lu tio n were added a s i n d i c a to r. The t i t r a t i o n was c a r r ie d to a p a le pink c o lo r com parable w ith a c o lo r sta n d a rd p re p a re d from a b o ra te b u f f e r ( ph 3.6 ) and th e p h en o lp h th a le in in d ic a to r. 4. P e r c h lo r ic i c i d H eagent grade p e r c h lo r ic a c id (TO p e r c e n t) was d ilu te d w ith ^ c o n d u c tiv ity * w ater to make a s o lu tio n ab o u t 0. 1 mola l. The a c id s o lu tio n was s ta n d a rd iz e d by a s e r i e s o f g ra v im e tric t i t r a tio n s a g a in s t th e p o ta ssiu m hydro x id e s o lu tio n d e s c rib e d ab o v e. A t e s t was made f o r c h lo rid e io n im p u rity in th e p e r c h lo r ic a c id u sin g s i l v e r n i t r a t e s o lu tio n a c c o rd in g to th e p ro ced u re d e s c rib e d by B asin (4 1 ). The p e r c h lo r ic a c id was found to c o n ta in l e s s th a n p e r c e n t o f c h lo rid e io n.

21 *«* B. P re p a ra tio n o f s o lu tio n s The s o lu tio n s w ars p re p a re d by w eighing o u t sam ples o f b o th th e s o l id s a l t s and th e d i s t i l l e d w a te r. S a l t s were weighed w ith a p r e c is io n o f - 0 * 1 m illig ram * 'e l u t i o n s o f l e s s th a n gram mass w ere w eighed to IB m illig ra m s; betw een and 500 grams th e y were weighed t o t 1 0 m illig ra m s ; s o lu tio n s w ith g r e a t e r mass th a n 500 grams were w eighed to 150 m illig ra m s. P o tassiu m c h lo rid e was added to aafce each s o lu tio n m olal w ith re a p e d t to th e c h lo rid e ion* Min s e t s o f s o lu tio n s, f i r e d ilu tio n s p e r s e t, w ere p re p a re d. The e x p e rim e n ta l r e s u l t s o f one o f th e s e ts w ere d iscard e d b ecause o f exce p t io n a lly la r g e d r i f t s l a th e c e l l v o lta g e s* In s e v e ra l o th e r c a s e s, one o f th e f iv e d ilu tio n s had to be d is c a rd e d f o r s im ila r reasons* The v a lu e s o f th e b u f f e r r a t i o s and th e d i l u t i o n r a t i o s employed in each ru n a re p re s e n te d in T able 1* 0* E le c tro m o tiv e fo rc e M easurem ents The g la s s v e s s e l which se rv e d a s th e body o f each c e l l and th e method o f male la g th e d ilu tio n s and f i l l i n g th e c e l l s in a hydrogen atm osphere w ere o r i g i n a l l y d e s c rib e d by B ates and A cres ( 7 ). a p h o to graph o f th e c e l l i s reproduced in F ig u re 7* A stream o f p u r if i e d hydrogen, p rep ared by p a s s in g th e gas th ro u g h co p p er tu r n in g s m ain tain ed a t about 400 0, was s a tu r a te d w ith w ater v ap o r by b u b b lin g th e gas th ro u g h a r e s e r v o ir o f th e s o lu tio n "B% in th e p a r t i c u l a r c e l l b e in g f i l l e d * The hydrogen was th e n p assed u nder th e p la tin iz e d e le c tr o d e s, *0 % and o u t th ro u g h a s id e -a rm and bubble t r a p, "X** The s i l v e r - s i l v e r c h lo rid e e le c tr o d e s were in s e r te d in th e

22 16 sea and v e r t i c a l member o f th e cell," * * A f te r th e s o lu tio n had been in tro d u c e d, th e s o lu tio n f la s k l i n e was removed and th e hydrogen l i n e a f f ix e d to th e same sta n d a rd ta p e r *A*. By s u ita b le m a n ip u la tio n, th e s o lu tio n earn b e used to wash o u t, f i l l th e c e l l and th e s id e tubes* The p la tin i z e d "hydrogen* e le c tr o d e s were p re p a re d by a m o d ific a tio n o f th e method o f P o p o ff, Kuntz and Snow (38)* B rig h t p la tin u m f o i l e le c tr o d e s w ere p la tin i z e d in a s o lu tio n o f c h lo ro p la tin io a c id conta in in g 80 m illig ra m s o f le a d a c e ta te p e r ml o f so lu tio n * a c u r r e n t o f 500 m illia m p e re s a p p lie d f o r about a m in u te and a h a l f seemed to p roduce th e optimum c o a t o f p la tin u m black* The s i l v e r - s i l v e r c h lo rid e e le c tr o d e s were p re p a re d by c o v e rin g a t i g h t l y wound h e lix o f p la tin u m w ire w ith a p a s te o f s i l v e r oxide* The o s i l v e r oxide was reduced to s i l v e r in a fu rn a c e m ain tain ed a t 540 0* la o h e le c tro d e was removed from th e oven, cooled and th e n c h lo rld lz e d l a 0.5 norm al h y d ro c h lo ric a c id by a p p ly in g a c u r r e n t o f 8 t o 7 m i l l i am peres f o r f o r t y f iv e m in u tes (7). The c h lo rld lz e d e le c tr o d e s were w ashed, s e t in a 0 * 1 norm al s o lu tio n o f h y d ro c h lo ric a c id and i n t e r compared in th e h y d ro c h lo ric a c id s o lu tio n a f t e r th e e le c tr o d e s had been s ta n d in g fo r 34 hours* E le c tro d e s t h a t v a rie d more than 0*05 m i l l i v o l t s from th e mean w ere d iscard e d * a p a i r o f s i l v e r - s i l v e r c h lo rid e e le c tr o d e s and a p a i r o f "hydrogen* e le c tr o d e s were used in each c e ll* Each p a ir was mounted in a tw o- h o le d neoprene s to p p e r and was Jamsed t i g h t l y I n to th e p ro p e r arm o f th e g la s s c e ll* F iv e c e l l s, one f o r each d i l u t i o n o f a g iv e n b u f f e r r a t i o, were ru n c o n c u rre n tly * M easurem ents o f te rm in a l v o lta g e betw een th e s i l v e r - s i l v e r c h lo rid e e le c tr o d e s and th e "hydrogen* e le c tr o d e s w ere made in dup-

23 1? lic a fc e, The e l e c t r i c a l a p o o ra tu s employed in th e m easurem ent c o n s is te d o f e Leeds end H ortbrup Type M l p o te n tio m e te r end a Type m galvane* m e te r. le a d in g s o f p o t e n t i a l were made to tq ^ O l m i l l i v o l t. The te m p e ra tu re o f th e h a th c o n ta in in g th e c e l l s was m a in tain ed to b e t t e r th a n * The te m p e ra tu re sch ed u le u sed, w ith some m inor e x c e p tio n s, was 25,15, 0, 10, 8 0, 3 0, 40, 5 0, 45, 3 5, 8 8. In d iv id u a l p o in ts were d is c a rd e d i f the c e l l p o t e n t i a l m easurement v a rie d b y more th an m i l l i v o l t s from th e curve o b ta in e d by p l o t t i n g e a f a g a in s t te m p e ra tu re. A ll p o in ts o f a g iv e n d ilu tio n were d is c a rd e d i f th e f i n a l v a lu e a t 28 C d if f e r e d from th e i n i t i a l v a lu e by more th a n m i l l i v o l t s. n o rm a lly th e c e l l s reaohed e q u ilib riu m in a b o u t t h i r t y m in u te s. E q u ilib riu m was judged to have been a ch iev ed when re a d in g s o f th e same s e t o f e le c tr o d e s ta k e n te n m inutes a p a r t, d if f e r e d by m i l l i v o l t s o r l e s s.

24 axpsrimaital BSSULT3 The p o te a tio m e tric m easurem ents f o r a l l e ig h t s u c c e s s fu l r m e a r e assem bled l a th e second column o f T able 2* The v a lu e s o f 1 and w ere c o rre c te d l a accord an ce w ith th e changes la th e fundam ental e l e c t r i c a l u n i t s d ecid ed upon a t th e l t d? co n fe re n c e o f th e I n te r n a tio n a l Union o f C hem istry (1 0 ) The v a lu e s o f 2*3026 R f /f used in th e c o m p u ta tio n s, m o d ified in accord an ce w ith th e se chan g es, were o b ta in e d from KBS C ir c u la r (3) (T able 3 ). A* ph V alu es o f ph w ere computed by th e u se o f th e e q u a tio n ph= (B - S )A + 10S *gi-n Shqi (SB) A p lo t o f the mean a c t i v i t y c o e f f i c ie n t o f h y d ro c h lo ric a c id a g a in s t io n ic s tr e n g th was p re p a re d from d a ta p u b lish e d by Harned and Owen(8 7 ). T h is p lo t has been rep ro d u ced a s F ig u re 8. The v a lu e s o f th e mean a c t i v i t y c o e f f i c ie n t o f h y d ro c h lo ric a c id were c a lc u la te d by H em ad and I h l e r s (26) from th e p o te n tio m e tric d a ta o f c e l l s w ith o u t liq u id Ju n c tio n. D e te rm in a tio n s o f th e a c t i v i t y o f h y d ro c h lo ric a c id u s in g s im ila r c e l l s have been made by N. 1. A nderson ( 8 ) f o r th e range o f m o ls lity t o m olal a t Their v a lu e s o f V - 2 i accord w ith th o se f H arned and I h l e r s to * S hedlovsky and M aciases (43) m easured ^ a c a a t 25 Q from to 0,1 m o lal u s in g c e l l s c o n ta in in g a liq u id ju n c tio n. The l a r g e s t d e v ia tio n s in th e v a lu e s o f ^ g x betw een t h e i r r e s u l t s and th e r e s u l t s o f Sarned and I h l e r s i s a t a s in g le eo -» p a ra b le p o i n t A ll th e o th e r c a lc u la te d p o in ts a g re e t o

25 Thor a r e no c o rro b o ra tiv e s tu d ie s f o r te m p e ra tu re s above 85 c, b u t B an d all and Young (40) e o m p u te d 'f* ^ from th e f r e e z in g p o in t m easurem ents o f B an d all and Vanselow (3 9 ). T h e ir d a ta a r e in e x c e lle n t a g re e m ent w ith th e d a ta o f Harmed and I h l e r s and 0 C. The l a r g e s t d i f f e r ence in th e v a lu e o f i s 0 *0 S a t 0.3 m olal b u t in th e ran g e from d i l u t e s o lu tio n to 0 * 1 m o la l, th e l a r g e s t d if f e r e n c e betw een th e two s e t s o f d a ta la 0*0004* B. Io n ic s tr e n g th Io n ic s tr e n g th l a d e fin e d by th e e q u a tio n (A- Bi (36) - th e v a le n c e o f th e ion s p e c if ie d by th e s u b s c rip t* The c a lc u la tio n of io n ic s tr e n g th o f s o lu tio n s p re p a re d w ith o u t th e a d d itio n o f s tro n g a c id o r s tro n g b a s e, i s somewhat d i f f e r e n t from th e c a lc u la tio n s t h a t a r e re q u ire d when e i t h e r s tro n g a c id o r s tr o n g b a se have been added to th e s o lu tio n o f p o tassiu m a c id m alate* a s o lu tio n p re p a re d s o le l y w ith th e a c id s a l t w ill be a m ix tu re o f th e io n s M+, H+, H i", A* * 1 The io n ic s tr e n g th o f such a s o lu tio n w i l l be ex p ressed by K * i f IV + h*+ *!2ir + 4aiA«) (3?) The q u a n tity was d e fin e d e a r l i e r by th e e q u a tio n s * = A* +mfia-+ Hjj& <1S> H ere and l a th e eu b eeau eat tre a tm e n t th e e o c tr lb u tio n o f th e h y d ro x y l ion i s n e g le c te d s in c e th e r a t i o o f added b a se to a c id s a l t i s n e v e r so h ig h th a t m^g- i s g r e a t e r th an 1 0 " m olal*

26 20 «s V B? th e use o f th e s e d e f i n i t i o n s o f <*, e q u a tio n 37 may he r e w r itte n :* K - * < ««- V * * * + * ) (88) fh e u n d is s o e ia te d s o ld p re s e n t s t e q u ilib riu m must h e re been produeed s s a r e s u l t o f th e r e a e tlo n zmr ^ s u + as (a) ah lla 4* a rise s in p a rt fro a tea above reaotlon and la p a rt fro* the r e a c tio n Ha* H* + 4* (39) The number o f m oles o f A* produeed by th e r e a e tlo n 3 I s e q u a l t o th e number o f m oles o f HgA produeed by th e same re a e tlo n * G oassqm entlyi* [Hi+fHgA] - Ct"J (40) T h is may b e re a rra n g e d :* [^4]= L A m]. l H +] (41) 1 n e e fo rm u la tio n f o r lo n lo s tr e n g th may be o b ta in e d by s u b s t i t u t i n g e q u a tio n 41 In e q u a tio n 38. f -i< r< + ib gt+ a^ a) (48) ^ - << *»g* + *A» (48) A f i r s t appro x im atio n o f io n ie s tr e n g th may be made by n e g le o tln g th e second and th i r d te rm s on th e r i g h t o f th e e q u a lity * When s tro n g b a s e, EOS, i s added to th e a e ld s a l t s o lu tio n, th e io n s in s o lu tio n w i l l be 1 *, K+, H+, Eh* and A* «th e io n ie s tr e n g th o f soeh a s o lu tio n may b e eomputed by means o f th e e q u a tio n ts^ aA» ) (44) U sing th e to o d e f i n i t i o n s o f <x, (e q u a tio n s 13 and 1 4 ), a s b e fo re ^ = (g o (.* + * g * - 3m^s) (48)

27 2 1 a s b e f o r e, th e o n ly so u rc e o f f r e e s o ld I s tb s r e a c tio n m r ^ a* +BgA is ) But tb s added h y d ro x y l io n r e a c t s w ith tb s m onoralen t a n io n a c c o rd in g to tb s e q u a tio n OfT + HA* ^ A% HgO (46) S in c e tb s. c o n d itio n s b a rs b een so cbossn t h a t m0h- s i l l be n e g lig ib le a t e q u ilib riu m, tb s A* produced by t h i s l a s t r e a c tio n w ill be eq u a l to tb s q u a n tity o f s tro n g b a s s (ICOH) added i n i t i a l l y * A sm all amount o f A* i s a ls o produced by tb s r e a c tio n BA* ^ S % A* (39) T h e re fo re in t h i s c a s e, tb s number o f m oles o f a* e x i s t in g a t e q u i l i brium must be th e same a s th e sum o f th e m oles o f s tro n g b ase added, f r e e a c id produced and hydrogen ion produced* A* = + if* + BgA (4?) Io n ic s tr e n g th o f such a s o lu tio n may now be fo rm u lated a s \l - ju^-v» H+ - 3 ^ ^ + S m ^ } (48) Y - + «- * +» v ) ( «j )«* - <* -f+a8r +«^ga (so) As b e f o r e, a f i r s t ap p ro x im atio n o f io n ic s tr e n g th may be made by negl e c t i n g th e t h i r d and f o u r th term s on th e r i g h t s id e o f th e e q u a lity * When a s tro n g a c id, B3, i s added to th e a c id s a l t, io n ic s tr e n g th i s d e fin e d by th e e q u a tio n P *< V + V T v + * w + 4V > (sl) I f u se i s made o f e q u a tio n 13 and th e d e f i n i t i o n o f p, e q u a tio n 51 may be r e w r itte n = + + 4»A») W

28 zz In t h i s e a s e, th e f r e e s e id, HgA, i s produced by th e two r e a c tio n s H+ H4." 5=5 HgA (7 ) SHt* r=» H g i + A (8) In t h i s e a s e, HgA = a ^ fflg+ + m4 * (S 3 ) - (3 - (54) p. «(3 * + p * a ^. - B g ^ -f SmA«) (55) pl= J(g<* + 2 ^ + 2aA*) (56) -A = * ag* a^a (5?) H ere to o, a f i r s t ap p ro x im atio n o f io n ic s tr e n g th may be made by negl e c t i n g th e second and t h i r d term s to th e r i g h t o f th e e q u a lity. The c o r r e c tio n term s in th e v a rio u s io n ie s tr e n g th e q u a tio n s may be e v a lu a te d b y th e fo llo w in g p ro c e d u re. F i r s t, th e v a lu e s o fy * c o rre sp o n d in g to th e ap p ro x im ate io n ic s tr e n g th a t each e x p e rim e n ta l p o in t may be I n te r p o la te d from th e d a ta o f B am ed and I h l e r s (36) p lo t te d in F ig u re 8. A pproxim ate v a lu e s o f and ap p ro x im ate v a lu e s o f may be computed from th e d a ta o f ru n s 1 and 8 b y p l o t t i n g 1 a g a in s t Y in th e m anner d e so rlb e d on pages 9 and 1 0. These approxim ate c o n s ta n ts may th e n be used to oosgm te th e two a d d itio n a l term s in each o f th e io n ie s tr e n g th e q u a tio n s 4 3, 50 and? A d e s c r ip tio n o f th e method f o r c a lc u la tin g ph h as a lre a d y been p re se n te d on page 1*. I f th e assum ption i s made th 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 hydrogen io n i s eq u a l t o th e mean a c t i v i t y c o e f f i c ie n t o f h y d ro c h lo ric a c id, e q u a tio n 35 may be used t o c a lc u la te ph * - lo g aig* - l e g i g * ^! ) /k i- le g B fcx ^H C l (58) - lo g» {E - l ) / k - v l o g «0 i- X q x - W

29 2 3 The m o la lity o f m alete ion p r e c a s t In s o lu tio n s p re p a re d w ith added s tro n g a Id, may m ost r e a d i ly be e stim a te d b y means o f th e ap p ro x im ate T alu es o f KJSI* The "ap p a re n t" io n iz a tio n c o n s ta n ts K and K a r e de~ fin e d by th e e q u a tio n s ( 80) The p ro d u c t o f th e two i s i - K* = V,mA» A. (#1) 2 fu r K1 K! («> T h is can be re a rra n g e d to g le e? l v a* 5 r e (8 3 ) V On s u b s t i t u t i n g th e v a lu e o f th e m o la lity o f th e u n d is s o c ia te d a c id g ir e n by e q u a tio n 54 in to e q u a tio n 65 one o b ta in s j - K,'K g ((i- «+ *»,«) a^8 s Zm ft. l i.gwff.,,,1 (64) V S in c e ^ i s much l a r g e r th a n m^ and m^*, a e u f f i c i e n t l y a c c u ra te e s t i m ate o f m * may be made w ith th e a id o f th e e q u a tio n A V ==~i (65) V A d i f f e r e n t e q u a tio n was found to be more s a t i s f a c t o r y f o r e r a l u s t in g th e c o r r e c tio n term in th e case o f added s tro n g b ase o r in th e c a se o f th e p o ta ssiu m a c id m a ia te ta k en by i t s e l f. An ap p ro x im atio n o f th e therm odynam ic io n is a tio n c o n s ta n t, X^, r a th e r th a n th e "ap p aren t*

30 4 d is s o c ia tio n c o n s ta n t &*, was o b ta in e d by e x tr a p o la tin g to i n f i n i t e d i l u t i o n, t h e ap proxim ate d a ta o b ta in e d fro run 8, Use was made o f th e e q u a tio n d e s c rib in g th e f i r s t d is s o c ia tio n o f a d ib a s ic a c id ;* ki ~ v x 7 (9) S in ce an approxim ate v a lu e o f i s a l l th a t i s r e q u ir e d, s e v e r a l a s s u c t i o n s may be made to s im p lify th e c a lc u la tio n s * I t was assumed th a t t h 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 n d is s o e ia te d a e ld JY l, i s n o t s i g n i f i c a n t l y le s s th a n 1 and a l s o t h a t Y ^ - i* n o t s i g n i f i c a n t l y d i f f e r e n t f r o m * I t i s im p o ssib le to e v a l u a t e t h e a c t i v i t y c o e f f i c ie n t H i f o r a s in g le io n b u t th e re a re some d a ta th a t m y b e c i te d a s j u s t i f i c a tio n fo r t h i s l a s t assum ption* For exam ple, th e mean a c t i v i t y c o e f f i c i e n t s o f e l e c t r o l y t e s have been ta b u la te d by Earned and Oven (?} In a fe v in s ta n c e s th e v a lu e o f th e mean a c t i v i t y c o e f f i c i e n t a t 8 0, 0.1 m o la l, i s d i f f e r e n t from th e mean o f th e s e e l e c t r o l y t e s by p e rh a p s 5 p e r cent* In th e m a jo rity o f th e s a l t s th e d if f e r e n c e from th e mean i s l e s s th a n 3 p e r cent* B ates,d iam ond,m en and A cres {9) have found t h a t th e r e a re no s p e c if i c e f f e c t s in a stu d y o f th e e f f e c t s s tro n g e l e c t r o l y t e s on th e a c t i v i t y c o e f f i c ie n t s o f p-p h e n o Is u lfo n a te b u ffe rs * E q u atio n 9 may be r e w r itte n on th e b a s is o f th e s e a s s u m p tio n sjv " V 1 (M ) I f e q u a tio n 13 i s in tro d u c e d in p la c e o f m ^ - in e q u a tio n 6 6, th e n. < * + B - v > - v * * i v E f l67) The q u a n tity m g^* a p p e a rin g on th e r i g h t s id e o f e q u a tio n 67, may

31 2o be n e g le c te d in t h i s c a lc u la tio n o f th e m o la lity o f th e f r e e acid* 0* The F i r s t I o n iz a tio n C o n sta n t, The f i r s t ap p ro x im atio n o f io n ic s tr e n g th has been ta b u la te d in th e f i r s t column o f T ab le X* The f i n a l t a l u s o f io n ic s tr e n g th has been ta b u la te d in th e l a s t column o f T ab le X* V alues o f I and T h a re been c a lc u la te d by means o f e q u a tio n s 28 and 29 and th e r e s u l t s a ls o tab-* u la te d in T able 2. These v a lu e s o f X and Y w ere p lo t te d a g a in s t io n ic s tr e n g th (F ig u re s 1.1 a to 1.7 b ) k fa m ily o f c u rv e s was draw n, each cu rv e b e in g made up o f v a lu e s o f X o r o f Y c a lc u la te d f o r s o lu tio n s o f th e same b u f f e r r a t i o and te m p e ra tu re. The v a lu e s o f X and Y c o rre s p o nding to v a lu e s o f io n ic s tr e n g th 0.0 6, 0.0 5, 0.0 4, 0.0 3, , and were in te r p o la te d from t h i s fa m ily o f c u rv e s. The v a lu e s o f X and Y o b ta in e d by t h i s in te r p o la tio n a re p re s e n te d in T ab le 4. a second s e r i e s o f g rap h s (F ig u re s 2.1 to 2.11) was p re p a re d by em ploying th e v a lu e s assem bled in T able 4«^X was p lo tte d a g a in s t Y and a fa m ily o f s t r a i g h t lin e s was drawn by Jo in in g th e p o in ts c o r r esponding to c o n s ta n t io n ic s tr e n g th and te m p e ra tu re b u t v a ry in g b u f f e r r a t i o. The s lo p e s o f th e s e l i n e s w ere computed and assem bled in T able 3. The lo g a rith m s o f th esev alu es w ere p lo tte d a g a in s t io n ie s tr e n g th a t each te m p e ra tu re (F ig u re s 3.1,3.2 ) I t has been assumed t h a t l o g X g ^ ^ i s, t o a f i r s t ap p ro x im atio n, a l i n e a r fu n c tio n o f io n ic s tr e n g th a t th e se d i l u t i o n s. A c c o rd in g ly, th e b e s t s t r a i g h t l i n e was drawn th ro u g h th e p o in ts and th e l i n e e x tra p o la te d to s e ro io n ic s tr e n g t h. The v a lu e s o f p(fi^ ( - lo g (fk^) a t d i f f e r e n t v a lu e s o f th e

32 io n ie s tr e n g th, th e e x tra p o la te d v a lu e s o f pg^ a t a e ro io n ie s tr e n g th and th e slo p e* o f th e s t r a i g h t l i n e s a r e g iv en in f a b le. D. The second I o n iz a tio n C o n sta n t, K Z 0 se may once a g a in be made o f e q u a tio n 34* fh e second io n iz a tio n c o n s ta n t, K, may be computed from th e v a lu e s o f th e in t e r c e p t o f th e IS p l o t o f 1 a g a in s t T (E ^hg/p} I f th e ex p e rim e n ta l e r r o r s f o r a l l th e m easured p o in ts a re ab o u t e q u a l in m agnitude, i t i s to be expected th a t th e b e s t v a lu e s of th e in t e r c e p t may be o b ta in e d by th e s h o r te s t e x tra p o la tio n s. f o r t h i s re a s o n, o n ly th e d a te d e riv e d from th e f iv e ru n s made w ith th e more b a s ic s o lu tio n s ( and w ith the s m a lle s t v a lu e s o f X and Y) were used in th e com p u tatio n o f One. Kx Bd(TK1 b ee. been evaluated, th e o n ly re g a in in g t e w in e q u a tio n 34 i s %?/(> Values o f - lo g Kg/f> a c re computed f o r each expe rim e n ta l v a lu e o f x and I o b ta in e d in thee f iv e ru n s. The r e s u l t s o f th e com p u tatio n a re assem bled in f a b le 7* In t h i s case how ever, lo g p I s n o t e x p re s s ib le a s a li n e a r fu n c tio n o f io n ie stre n g th * The m ost s u c c e s s fu l d e s c r ip tio n f o r th e a c t i v i t y c o e f f i c ie n t s o f Ions in d i l u t e s o lu tio n i s th e f a m ilia r Debye*au ek e l e q u a tio n T his form o f th e D ebye-iluokel e q u a tio n h as been used to com pute th e a c t i v i t y c o e f f i c ie n t te rm, p, In e q u a tio n 34* The q u a n tity p (e q u a tio n 34) i s th e p ro d u c t f s e v e ra l a c t i v i t y c o e f f i c ie n t s o f io n s in th e s o lu tio n. In such a c a se an e m p iric a l m o d ific a tio n has been used so can be ex p ressed sim ply* I t h a s been assumed t h a t a, an "average* v a lu e o f th e " io n ic d ia m e te r", may be s u b s titu te d f o r a^ in

33 2? e q u a tio n 68, I f t h i s i s done, th e e q u atio n becomes 1 0 «P * «- ~8 ->i;' I (M ) I 1 + B«Y I t i s e v id e n t t h a t i f a p ro p e r v a lu e o f a* i s found and lo g ^ l a com puted, t h i s q u a n tity may h e added to th e e x p e rim e n ta l!y d e riv e d q u a n tity lo g t h i s sum should h e a o o n a ta n t, lo g Kg, a t any s p e c if ie d tem p eratu re* fh e constan cy o f t h i s sum c o n s titu te s a e r i t e r - io n f o r d e te rm in in g th e c o r r e c tn e s s o f th e v a lu e s o f lo g p computed hy means o f th e Ocbye^Haekel e q u atio n * A c c o rd in g ly, a p l o t o f lo g K$/^> (e x p e rim e n ta lly d e riv e d ) and lo g ^ {computed from th e Bebye»Huc.k#l e q u a tio n ) a g a in s t ^ was made a t each te m p e ra tu re ( f ig u r e s 4*1 and 4*2) I f th e p ro p e r v a lu e o f logj> h as heen u s e d, such a p l o t w ill he a s t r a i g h t lin e p a r a l l e l to th e a b s c is s a. fh e computed v a lu e s o f lo g K2^ a t 85 0 were p lo tte d a g a in s t io n ic s tr e n g th and a smooth cu rv e was drawn th ro u g h th e p o in ts* fh e v a lu e o f th e o rd in a te f o r each o f two a r b i t r a r i l y ohoaen v a lu e s o f th e a b s c is s a ( A* and j i - 0*06) w ere re a d from t h i s c u rv e. The d if f e r e n c e betw een th e o r d in a te v a lu e s o f th e s e two p o in ts i s K la g - lo g r» * lo g f l r % f l liq u a tio n 69 m y be s u b s titu te d in to e q u a tio n 70 and th e r e s u ltin g e x p re s s io n re a rra n g e d to s o lv e f o r a *. a *8 v - 0 I D The v a lu e o f a* o b ta in e d by th e s o lu tio n o f e q u a tio n 71 i s 6*85x10. Ho s ig n if ic a n c e i s a tta c h e d to th e t h i r d f ig u r e. The te rm, lo g ^, I s q u ite in s e n s itiv e to changes in *. For exam ple, i f a* i s B8

34 28 a s s ig n e d a v a lu e o f 6.0xlO* # lo g p w ill b e a t ^ i O.Sb. The v a lu e o b ta in e d f o r lo g ^ (a *? 6.85x10* ) a t th e e a se io n ic s tr e n g th i s The e f f e c t o f d i f f e r e n t v a lu e s o f a* on lo g p w ill b e even l e s s e t lo w er v a lu e s o f Io n ie s tr e n g th. f h e sane v a lu e o f a* was used a t a l l te m p e ra tu re s. Ifce v a lu e s o f tb s * p a ra m e te rs A and 1 in tb s Debye-Huoleel e q u a tio n ( f a b le 8} w ere taken from th e re e a m p u ta tio n o f th e s e q u a n t itie s by M anov.b ates, Busier and A cres (3 4 ) i n av era g e was ta k e n o f th e v a lu e s o f - lo g ( f ig u r e s 4.1 and 4.3 ) o b ta in e d bp th e was a ssig n e d to p ro ced u re d e s c rib e d above, m a r b i t r a r y m i g h t o f two th o s e v a lu e s computed from ru n s 1 and 6, s ln o e th e s e ru n s w ere p rep ared w ith no added s tro n g a c id o r b ase and c o n seq u e n tly fu rn is h e d v a lu e s o f Y and X c l o s e s t to th e o r ig i n. 1. therm odynam ic C o n sta n ts Harried and to b in s o n (88) have su g g ested th e use o f th e e m p iric a l e q u a tio n - lo g K a pk «A/T + B + Of (72) to d e s c rib e th e b e h a v io r o f th e I o n iz a tio n c o n s ta n t a s a f u s e tio n o f te m p e ra tu re, fh e p a ra m e te rs o f such an e q u a tio n have been c a lc u la te d f o r b o th io n iz a tio n c o n s ta n ts o f u n ite acid * f o r th e f i r s t io n iz a tio n c o n s ta n t o f d t l - a a l i e a c id pk,, 1338* * T (73) f f h e p&i v a lu e s d e riv e d from th e e x p e rim e n ta l d a ta and th e p l^ v a lu e s c a lc u la te d from th e e q u a tio n above a r e assem bled in T ab le 3 and rep re s e n te d g r a p h ic a lly in f ig u r e 3. The m m d e v ia tio n betw een th e comp u te d p o in ts and th e smoothed curve i s p i u n i t s.

35 2 9 In th e case o f th e second io n is a tio n c o n s ta n t, pkg = 1658,53-6, ,01938 f (74) T was th e e q u a tio n o b ta in e d. The e x p e rim e n ta lly computed and th e smoothed v a lu e s o f p&2 a r e compared in T able 9 and in F ig u re 6, Xn t h i s c a s e, th e mean d e v ia tio n betw een th e computed and th e smoothed p o in ts was c a lc u la te d to h e *0,0011 pk u n i t s, The e x p e rim e n ta lly d e riv e d and th e smoothed v a lu e s o f Kx and Ks have been assem bled In T able 11. The therm odynamic q u a n t itie s a s s o c ia te d w ith th e e q u ilib riu m eon* s t e n t s may h e computed a f t e r p erfo rm in g sim ple o p e ra tio n s on e q u a tio n 7 2. A f = - IT In K * (4 * 8T t- Of8 ) (78) AH = *T8 d In K» ( 1 - GT8 ) (76) dt A 3 * -da f B(B + 20T) (77) df A 0 P T J 5 i ^ = B(BOT) (78) dt V alues o f th e s e q u a n t itie s f o r th e two d is s o c ia tio n c o n s ta n ts have h e m asaesfeled in T able 1 1,

36 DISGtSaiuN 4 c o n s id e ra b le number o f d e te rm in a tio n s o f th e io n iz a tio n c o n s ta n ts o f m a lic a c id h a re bean made in th e l a s t s i x t y y e a rs and a number o f d i f f e r e n t m ethods b a re been u sed, fh e v a lu e s o f th e io n iz a tio n c o n s ta n ts o b ta in e d by th e se e a r l i e r w orkers h are been assem bled in T ab le 12* The columns d e sig n a te d and KJ l i s t th e v a lu e s t h a t h a re n o t been c o rre c te d f o r a c tiv ity * In most of th e d e te rm in a tio n s to be found in th e l i t e r a t u r e, th e a u th o r has made no m ention o f a c a lc u la tio n u s in g a c t i v i t i e s r a t h e r th a n c o n c e n tra tio n s. U nless th e a u th o r made a d e f i n i t e s ta te m e n t th a t a c t i v i t y c o e f f i c ie n t s had been used to c o r r e c t th e e q u ilib riu m e q u a tio n s, i t was assumed t h a t th e io n iz a tio n cons t a n t s had been c a lc u la te d on a c o n c e n tra tio n b a sis* The v a lu e s o f th e ' apparent** io n iz a tio n c o n s ta n ts l i s t e d in T able 12 a r e u n ifo rm ly h ig h e r t h a t th e thermodynamic io n iz a tio n c o n sta n ts* T his i s to be a n tic ip a te d s in c e th e a c t i v i t y c o e f f i c ie n t c o r r e c tio n would d e c re a se th e v a lu e o f th e io n iz a tio n co n stan t* The f i r s t therm odynamic io n iz a tio n c o n s ta n t o f d,l- m a lie a c id has been d eterm ined by L arsson (89) and by Hamer (2 1 ). The v a lu e fo r computed in t h i s p a p e r is in q u ite good agreem ent w ith t h a t o f L arsso n ( a t 15 0) b u t i s about 4 p e r c e n t low er then the v a lu e o f com* p u te d by Hamer ( a t 25 G ). I t i s c l e a r from T ab le IS t h a t agreem ent betw een th e v a rio u s w orkers i s b e t t e r fo r d e te rm in a tio n s o f th e f i r s t io n iz a tio n c o n s ta n t th an f o r th e second io n iz e tio n co n sta n t* Three p re v io u s w orkers have d eterm in ed th e therm odyaaaic io n iz a tio n c o n sta n t &2. L arsso n in p a r t i c u l a r, has d eterm in ed Kg by th re e d i f f e r e n t e x p e rim e n ta l m ethods*(3 0,3 1,3 8 ) &11

37 31 th e s e p re v io u s d e te rm in a tio n s e r e somewhat lo w er th e n th e v a lu e s g iv e n here# fh e v a lu e s o f Duboux ana Frommelt (19) and L arsson (38) o b ta in e d fro s o l u b i l i t y m easurem ents a g re e f a i r l y w ell w ith th e v alu e o f Cg o b ta in e d by Easier (81) on th e b a s is o f ph t i t r a t i o n s. But th e s e v a lu e s a r e ab o u t 0.5xl< T 6 lo w er th an th e v a lu e o b ta in e d h e re. On th e o th e r hand o th e e le c tr o m e tr ie d e te rm in a tio n o f L arsso n (31) a t 18 0 i s in f a i r agreem ent w ith th e v a lu e o f o b ta in e d in t h i s p a p e r, m s ta te m e n t a a y be made about th e r e l a t i v e a e e u ra e y o f th e s e d e te rm in a tio n s o f f h e r a t h e r la r g e d lf f e r e n e e s do s e rv e to em phasize th e f a c t t h a t th e d e te rm in a tio n o f th e second io n is e tio n c o n s ta n t I s n o t a s s a t i s f a c t o r y a s th e d e te rm in a tio n o f th e f i r s t io n iz a tio n c o n s ta n t.

38 msqmmon of mens A rig o ro u s d e te rm in a tio n o f itte e r r o r s in v o lv ed in th e co m putation o f io n is a tio n c o n s ta n ts i s d i f f i c u l t b ecause o f th e d ev io u s n a tu re o f th e c o m p u tatio n. However, a re a so n a b le id e a o f th e o v e r s e ll e r r o r can be o b ta in e d by c a r r y in g th ro u g h a sam ple c a l c u la tio n. Even though th e s e n s i t i v i t y o f th e p o te n tio m e tric c i r c u i t i s about t O. 01 m i l l i v o l t, th e agreem ent betw een i d e n t i c a l c e l l s o r even betw een s e t s o f e le c tr o d e s in th e same c e l l a r e no b e t t e r th an m i l l i v o l t. I t h as been assumed f o r th e p u rp o se o f t h i s d is c u s s io n t h a t th e e r r o r in th e m easurem ent o f emf i s about * m i l l i v o l t. The c e l l p re p a re d w ith th e low est c o n c e n tra tio n o f b u f f e r s o lu tio n o f Bun 4 developed a p o t e n t i a l o f v a t 0 0. The v a lu e s o f th e s ta n d a rd e le c tr o d e p o t e n t i a l, E, and th e v a lu e o f k * B T /f a t 0 Q a r e and r e s p e c tiv e ly (T able 3} I t may be s a f e l y assumed th a t th e e r r o r s in 1 and k a r e n e g lig ib le compared to th e e r r o r in th e e x p e rim e n ta lly d eterm ined v a lu e o f S * ~ T ~ ' ' o s s i i ( ' i * 0.008V (80) k The q u a n tity p^h has been d e fin e d by B a te s ( 6 ) : - P_H = S - B + log *c l- (81) k S in c e th e m o la lity o f th e c h lo rid e ion was m a in tain ed a s c lo s e to m olal a s p o s s ib le, lo g mc i ~= * (82) I f t h i s v a lu e i s s u b s titu te d in to e q u a tio n 81 j - p^b = V * (83)

39 p^h = 3, (84) The q u a n tity, F, h a s been d e fin e d e a r l i e r (E q u atio n 2 7 ). I t earn b e seen by ia e p e o tio n th a t P i s th e a n t ilo g of-p^h. In t h i s sam ple c a lc u l a t i o n : * P - 10 (83) P = ( ) JClO"* (88) The e r r o r s in tb e m o lal q u a n t i t i e s * and ^, lik e th e e r r o r s in a a ^ -, a r e n e g lig ib le in com parison w ith tb e e r r o r in I. But a ^ + i s involved in tb e c a lc u la tio n o f B (E q u atio n 1 1 ). Tbe v a lu e s o f Sgg-f were computed by means o f tb e fo llo w in g e q u a tio n :- - lo g s ^ * ( I - l ) / k + lo g jbqx-* 2 l o g ^ x (?) I f e q u a tio i s s u b s titu te d in to tb e above e q u a tio n, i t becomes - lo g + 2 leg^nox (88) Tbe mean a c t i v i t y c o e f f i c i e n t of h y d ro c h lo ric a c id has a lre a d y been d is c u s s e d on page 1 8. In tb e l i g h t of t h i s d is c u s s io n, an e r r o r o f ± h as been a s s ig n e d t o e ach v a lu e o f ^ g ^. Tbe q u a n tity p^h f o r t h i s exam ple has a lre a d y been computed (E The se e n a c t i v i t y c o e f f i c ie n t o f h y d ro c h lo ric a c id i s a t io n ie s tr e n g th (F ig u re 8 ). - lo g mh+s 3, ± 0,0028 * 21og(0.873 ± ) (89) - lo g mg* (90) r = (8.9? ± 0.0? )x l0 (91) I t can b e seen th a t th e e r r o r in»g+ i s over one p e r c e n t. T his i s l a r g e r th a n th e e r r o r s in any of th e q u a n t itie s c o n sid e re d so f a r. B ut in most o f th e c a l c u la tio n s, tb e q u a n tity B i s so la r g e th a t i t i s q u ite i n s e n s itiv e to e r r o r s in I n th e exam ple u n d er d is c u s s io n :- s (92)

40 a s w a s n o t e c b e f o r e m ) S u b s titu tin g I n to e q u a tio n 11 tb e p ro p e r n u m e rical v a lu e s * - 0 * i O.OO00O7 (93) In t h i s exam ple 4 = ft ( f t ) Therefore, 4 + B - 0, ± (95) 4 - B» 0* (96) Tbe q u a n t itie s 1 and X may now be computed b y tb e u se o f e q u a tio n s 28 and 29 re s p e c tiv e ly * ( w ) X = I*-8*8 ±0.030)xlQ~4x(6.7SS x10-3 (97) (18.149t 0.007)xlQ*3 X - (1.6*19 * )1 1 0 * (98) F*U - Bl H+ B) (89) ( * tf086)xlo*tx l*.e 8 9* 0.007)xlO~a j99) (18.1*9* 0.007)xl0 3 I - (5.28± 0.071)xl0 The e v a lu a tio n o f depends upon tb e s lo p e o f tb e p l o t o f X a g a in s t T. Tbe s lo p e nay b e e x p re sse d by th e e q u a tio n *1- y 2 Ki = <101> S i x., t h i. P lo t P U. H T.r y to t h. o r l g l a. Xg a t T, o«n 9. oboeen to be n e g l ig ib l e when compared to and Y^. Hi s lo p e s a y b e approxim ated b y tb e eq u atio n * *

41 35 * i * r t ^ h <i0 s s > I f th e equation S3 sad 29 * r t s u b s titu te d in to t h i s approxim ate e x p r e s s io n :- u a»>. a o 3 ) 1 55 («+ BP PB uu*' *i * IlS L ij l (104) 3 Tike n u m e ric a l T a lu e s may be s u b s titu te d in t o e q u a tio n 104* K# ^ (44346 * Q.OaQjxlO^xU.eSt* ixlct3 1 ~ (6.755* 0.007)xl0~S E*, (3,1 2 2 * )xlq "4 (106) t h i s co rresp o n d s to a r e l a t i v e e r r o r in tb e d e te r a in a tio n o f K* o f p e r e e a t. Tbe p r e c is e v a lu e o f K* d eterm in ed g r a p h ic a lly a t t h i s v a lu e o f tb e io n ie s tr e n g th i s ( Q 2 0 )x l0 ~ *. Tbe v a lu e o f pk w ill b e t 0, , The p ro ced u re employed in th e com putetion o f K as depends upon th e e x p e rim e n ta lly d e riv e d q u a n tity K^Kg/ja, th e in te r e e p t o f th e p l o t o f X a g a in s t Y. I t is to b e e x p ected th a t t h i s q u a n tity w ill be in e r r o r to th e same e x te n t a s any d e te rm in a tio n o f Y. The e r r o r in Y h as been e v a lu a te d in e q u a tio n 100. The r e l a t i v e e r r o r in Y i s about i. $ p e r s e n t. The r e l a t i v e e r r o r in E^ a s e v a lu a te d above i s p e r e e n t. f i n a l l y, th e e r r o r in v o lv ed in th e d e te rm in a tio n o f ^ m ust be cons id e re d P o s s ib le e r r o r s a r i s i n g from th e use o f s l i g h t l y d i f f e r e n t v a lu e s o f th e p aram eter a 4* o f th e D ebye-huekel e q u a tio n, h as a lre a d y been touched upon on page 27. i r r o r s a r i s i n g from t h i s so u rc e w ill be l a r g e s t in th e most c o n c e n tra te d s o lu tio n s. For exam ple, - lo g ^ c a lc u la te d f o r th e most c o n c e n tra te d s o lu tio n o f Hun 1 a t 0 0 w ill b e , i f a* i s assumed to be x l0 * 8 ; and 0, , i f a* I s a ssig n e d

42 3 0 3 th e rain 6 00x10 fit# v a lu e s o f ^, f o r th o s e v a lu e s o f a *, #1X1 ho and r e s p e c tiv e ly. I f th e seme s o r t o f c a lc u la tio n i s node f o r th e most d i l a t e s o lu tio n o f Hub 2 (fit =0.114 ), th e n when a* i s 0.25x10* and when a* 1# 6.00x10*. A c co rd in g ly, th e av era g e r e l a t i v e e r r o r l a th e a c t i v i t y c o e f f i c ie n t ter,^>, h a s been assumed to be 0.5 p e r c e n t. The form ula f o r th e " p ro p a g a tio n o f e r r o r " h as a sim p le e x p re ssio n f o r th e p ro d u c t o f a number o f v a r ia b le s A R /r- A * /x ) + (A y/y)2 + (107) + «. - " U.». -..». >»» * in to e q u a tio n ;- A B / H = o a ) 2 + ( ) + (0, )J (1 0 0 ) 4» / B (109) The a v e ra g e v a lu e o f &g a t 0 C has been d eterm ined to be 7.593x10* I f th e r e l a t i v e e r r o r i s p e r c e n t, th e a b s o lu te e r r o r w ill be i 0 i 0.119x10 An In d ep en d ent check o f th e In d e te rm in a te e r r o r s may be had by u s in g th e d a ta o f T ab le 9. I t ha been found th a t th e mean o f 25 d e te rm in a tio n s o f p&g a t 0 C i s The mean d e v ia tio n i s ± pk u n i t s. I f th e a n t ilo g o f p ig I s d eterm in ed f o r pjc^ and pkg= , i s computed to be in th e f i r s t e a s e end in th e second c a s e. The d if f e r e n c e i s 0.115x10* ; a v a lu e alm ost I d e n tic a l w ith th e e r r o r te rm 0.119x10** c a lc u la te d ab o v e. In a c t u a l i t y, th e p r e c is io n o f th e av era g e v a lu e o f K should b e somewhat b e t t e r th a n th e e r r o r c a lc u la te d above, s in c e th e av erage v a lu e s o f a r e b ased on 35 d e te rm in a tio n s a t each te m p e ra tu re. The sta n d a rd d e v ia tio n o f th e m m w ill c o n se q u e n tly be ap p ro x im ate ly pk u n i t s o r x10* "I* u n i t s, a f u r t h e r check can be found

43 3 7 i s T ab les 9 sad 10 b y com pering tb e e x p e rim e n ta l e r e ra g e s o f pk sad s Kg w ith tb e v a lu e s reed from tb e smoothed curve* l o r e I t ssm b e s e e s t h a t th e o v erag e d if f e r e n c e betw een tb e e x p e rim e n ta l sad smoothed v a lu e s f o r tb e te m p e ra tu re ran g e 0 t o 60 0 I s 0*9011 p u n i t s o r 0*0 1 "K* s a lts * T h is rem ark ab le agreem ent i s f o r tu i to u s b u t i t in d l* s a te s tb e c o n s is te n c y o f tb e e s tim a tio n o f e rro r*

44 1 IF S R M C 23 1 R. 0. M e k in, Australian Chera Inst J & Proa 4, 867, ( ). 2. 1* J. ^ n d e rso a, D ie s#, 0. o f C hicago, * "^jmouncement o f changes l a e l e c t r i c a l and p h o to m etric u n its * N at Bur S ta n d a rd s C ir c u la r 3459, May IB, F. Auerbach and S. Sm olczyk, L p h y sik Cham, 110, 65, (1924)* 5. R. G. B a te s, 2 m Cham 3o s, 70, 1579, ( ). 6* * Cham H er, 42, 1, ( ).? ** and 8. F. A oree, 2 R esearch N at Bur S ta n d a rd s, 30, 129, (1943). 8* * and 3.?. A oraa, 2 R esearch N at Bur S ta n d a rd s, 3 4, 373, ( ). 9. ",J?.?* Diamond, M. Id e a and s. F. Acres, J R esearch N at Bur S ta n d a rd s, 3 7, 851, ( ) " and 0.. P in c h in g, J R esearch N at Bur S ta n d a rd s, 4 2, 419, (1949) ", G* L. S ie g e l and S. 7* A oree, 2 R esearch N at Bur S ta n d a rd s, 3 1, 208, ( ) D. B e r th e lo t, Ann ehift a t p h y s, (6 ), 2 3, 1, (1891) N. B jerrum, p r i r a t e com m unication quoted by 7. K. B ro n sted and E. P e d e rso n, Z phys Ohcm, 108, 188, ( ) N. B je rn sa and a. Unaack, Kgl Danske V idonskab S e lsk a b a,m a t-fy a Madd, 9, Bo 1, ( ) H. T. S. B r itto n, 2 Ohs Soe 1896, ( ) m C oops, M s s., D e lf t, a s quoted by la n d o lt~ B o ra s te la 3 th I d. 1 s t Supp p N. Dhar and A* I. D a tta, A EleSctroohem 1 9, 407, ( ) p. Debye and 1. B u ck el, P hyaik 2, 24, 135, ( ) M. Buboux and J. F r o n a e lt, J chim phys 24, 245, ( ) R. dene and 0. K# In g o ld, 2 Ghm 3oc 8153, (1931). 21. i. J. Hamer u n p u b lish ed com m unication.

45 i. X. Hamer and 3. F. aere, X R esearch H at Bar S ta n d a rd s 1 5, 64?, ( ). S3* " and 8* F. Acre, X R esearch Hat Bur S ta n d a rd s 35, 381, (1945) 24. ", 3. B. P in c h in g and s. P. & ree, X R esearch N at Bur S ta n d a rd s, 3 5, 539, (1945)* 25* H. S. Earned and R. 1* E h le r s, X m Ghem Soc 54, 530, ( ) * " * «jj5 # 652,2179, ( ). 27. * and B. B. Owen, "The P h y s ic a l C hem istry o f E le c tro * l y t i c S o lu tio n s " 2nd I d. R einhold P u b lis h in g Co Hew York * and 1. A. R obinson, T rans F arad ay Soc 3 6, 975, ( ) L a rsso n, p r iv a te com m unication quoted by H. B jerrum, Z p h y sik Cheat , ( ) *, p r iv a te com m unication quoted by X, N. ir o n s te d and K. P ed erso n, Z p h y sik Cheat 109, 185, ( ). 3 1., Z an o rg Cham 125, 281, ( ). 22* * " " * 155, 847, ( ) M. M is u ta n i, Z p h y sik Cheat , ( ) Maaov, R. 0. B a te s, f. X. Hamer and 3* F. Acre, X Am Cham See 65, 1765, ( ) W. R. Maxwell and X. 1. P a r tin g to n, Tran F arad ay Soo 33, 670, ( ) d. O stw ald, 2 p h y sik Chere, 369, (1889) D..Pinching and B a te s, X R esearch Mat Bur S ta n d a rd s, 3 7, 311, ( ) P o p o ff, a..1. H unts and 1. B. Snow, X Phys Cham 32, 1036, ( ) M. R a n d a ll and A. P. Y anselow, X Am Ohea So 4 6, 2418, ( ) * and L. 1. Young, X Am Cheat 3oc 50, 989, ( ) X. R o sin, "R eagent C hem icals and s ta n d a rd s " 2nd I d. I. Yen N o stran d Hew Y ork, i. a. R oth and f ilm s, u n p u b lish e d d a ta quoted by Landolt*B orn* s t e i n 5 th E d., 1 s t Supp. p T. ah ed lo v sk y and P. A. M aclnnes, X Am Chem Soe 5, 1970, ( ).

46 u 3. Siam s, J m Chem Soc 48, 1239, (1926) #. A. S m ith, 3 p h y sik Ja«m 25, 193, (1898) S. 0. Speataaan, J Qhsm Soc 855, (1 940) P. Pa id e a, B er. 29, 1699, (1896) R. d eg g eh e id er, ^ o n a tsh S3, 599, ( ).

47 41 table 1. Buffer ratios and d ilu tion ratios of runs 1 to 8. Dilution ra tio 1 Run Buffer ratio WIO4 ratal I * <1 3a -.660? I 4 a : e36? a * minus sign was used to designate the ratio KDH/EHKal.

48 42 ta b le 2.1, th # e x p e r im e n ta l v a lu e s o f te r m in a l v o lt a g e,le n t o s tr e n g th,m o la lity ; term s of eq u atio n 23 d e riv e d from th ese q u a n t it ie s and the aeeend approxim ation o f io n ie Hun J*i - E? jyfi 'HSl -log, V K+ JC xlo3 volte xlo as* *57 *$aat6 *33293, *53093 * *32949 * xlo stre n g th # 0 C e n t i g r a d e * <XV B <* - B e p2 X y h xlo3 XlO3 xlo5 xlo, 1 0 xlo6 xlo9 xlo , >9 7.35S S , " gy >' OO , , S ; " " * a" ! ^5# ? I ?r, > j ? M « ,85 23, , la. 64? S , ',n " ' ? ? , ,1788.O , ? Q ,

49 43 Table 2,2. The e x p e r im e n ta l values of term inal voltage, ionic stren g th, m olality; term s In equation 23 derived, from these Hun h f i i. E xlo3 volts R TO ,57 5 fo O ? a q u a n titie s, and a second approxim ation o f io n ic strength. 5 C en tig rad e '" , ,58511, ,5333s i o ? i.0* (" I IT S'O Y*hci -10s H+ B 8 d - B P p2 X Y ^ 2 k w xlo* xlo3 xlo3 xlo3 xlo5 xlo10 xlo6 xlq^ xlo3 5, ,2674 5,3026 5,339? , ? , q ,323, , ? , , , ? , ,4? , 2? O O ? ,656, , , ?, ,160, , ? ? ? s ? C y QQQ , Q ? ? , ,216 1, ' , 62R l! ?5 op ?7? , ? ,606-7, ? QQ , as * #OR ? :q ? l q.7q

50 44 fa b le 2.3. Hun i E xlqfhe e x p erim e n tal v a lu e s o f te rm in a l v o lta g e, io n ic q u a n titie s and th e second approxim ation o f io n ic v o lts r 'O p H w Yt HGl -log mg+ xlo a #: SO J «U , < ? S r B ? > qp # > " cvprqn m52^7< ! > " ^ < ' ? < g ! <Q.q ^ ! # 5 p 07 q C V. <C*J OR! a r H '47 4-' > xlo' s tre n g th, m o la lity ; term s of e q u a tio n 23 d e riv e d stre n g th ou B o( - B 2 10 Centl.grade.,..p X X I1 2 xlo3 xlo-" xlo5 xlo10 xlo" xlo9 xlo I ,c 37 si r* 625 p. *7i-" q po gp *3 1.87S l q , Q , ? , g. 14! ^ from the;

51 4 5 Table 2.4. The experim ental values of term inal voltage, lonio q u a n titie s and a second approximation of Ionic strength. Hun h. E - S PwH T hoi IE xlo3 volts -log 0g+ {i+ B xlo^ xlo , A ! S i9."so , T S & a ? ! strength, m olality; the terms of equation 23 derived from these 15 Centigrade. of + 8 A - B $ p2 X t xlo3 xlo5 xlo5' xlo xlo6 9 xicr Q ! , , i i q9 48.4X XW93 66,72 ' , q Q : : I # * q P a xlo

52 46 fable 2.5. Run & h i IS - li it X lo 3 volts fa experim ental values of term inal voltage, ionic q u a n titie s and a second approxim ation of io n ic s tre n g th. pwh ^HCl -log fflh+ rah+ xlq^ B 3 x lo B I I 5O # 8 n , U S fs ' S S i o ! » * ^ ^ h o e 936.^ * 9 ' ' O ? s tre n g th, m o la lity, term s of e q u a tio n 23 d eriv ed from th ese 20 C en tig rad e. + B X Y 2 6 Q xlo3 XlO5 xlo5 xlo10 xlg xlq xlo c * ^ * , i i , ^ ? , D 5*+ if fj ! ^0R p ? ^ ^ < S3 ' ? q qq 1 4! ?

53 47 table 2.6. The experim ental values of term inal voltage, ionic strength, m o lality, terms of equation 23 derived from these quantities ana & second approximation of ionic strength 05 Centigrade*. Run C2» 4J 0 PWH ' h (ihgl -la g B 0( + 3 i - B P 3 & xlo VOIts x lo 4 x lo 3 x lo 3 x lo 3 X lo 5 _ p k X 1 P* 2 in xlo * XlO6 x 10 9 xlo ?? S s , P> P X ORpO , q a iH , * q ' -.117? r-r: #pq , * , , O' a4 l 39 6i > " ? : ^ ? ? " ! , ? a ? , ? 7.63?

54 Table 2*7. The experim ental values of term inal voltage, ionic strength, m olality, terms of equation 23 derived from, these Run i h x lo 3 Jj# q u a n t i t i e s and a seco n d a p p ro x im a tio n o f io n ic stre a m volts ii - s k PWH '{+ '-H O I - l o g Bjj+ «ii+ x lo 4 B * x lo " , S * * : j ' Q * , »89R a * ?.5* C e n tig ra d e + B <h - 3 P P 2 X X 5 ID 6 x lo x lo xlo - x lq 9 X lo 3 x lo * ".33l * * ? ,40* ' > * * I * ? * * * R * x lo

55 49 Table 2.8. The experim ental values of term inal voltage, ionic stren g th, m olality, terms of equation 23 derived from these R un x lo " a ? q u a n t i t i e s and a second a p p ro x im a tio n o f io n ic s tr e n g th J e n t i g r a d e. 0 4 «,<u> PWH YV - l o g '-H O I H+ B <* + B A - B i>~ X Y H 2 k 6 v o l t s x lo 4 X lo 3 x lo 3 x lq x lo 5 x lo 10 XlO xlo9 x lo ? < ? ? ? H ? * ? , s ' ? ? ? ? A, A? ? * ? To VA? 4! ?5* ? "> ? 2.44? ? I I S ? 34.7? ???. 32? ? ? ? ? ? ? ? Oil qy 44! ? ^ ??

56 50 Table 2.9. The experim ental values of term inal voltage, ionic stren g th, m olality, terms of equation 25 derived from these quantities and the second approximation of ionic strength 40' Centigrade Run xlo3 v olts.0 p H Y *H dl " l o s h* mh+ XlO xlo 5( + B <K - 8 F F^ X X H 2 xlo3 XlO3 xlo5 10 xlo xlo* xlo9 XlO '? * OO : a ft ? , , ? , ? ? a f 'c; '% ^ ? , g " a ? f) ?

57 51 Table The experim ental values of term inal voltage, ionic strength, m olality, terms of equation 23 derived from these Hun xlo3,q * 'J o a q u a n titie s and the second approximation of ionic strengt 4$ Centigrade v o l t s ? , 679,82 tjj <:; «*.O' PWH -log 3 K+ B * - B Jp i r X Y r 2 uv X lc xlo xlo xlo3 xlo3 xlo xlo xlo6 xlo xlo , ? ! , * R A * ?. 88$ ST! * $ O : c* t j * ? ? ? S B4B , ? 2 2! * *1$ *14 24,2? 23*35, Q14 5* * ? $ ,8 $ ^ * , ? " J 6>^ U > '' * ?

58 5a Table The experim ental values of term inal voltage, ionic strength, m olality, terms of equation 23 derived from these quantities and the second approximation of ionic s tr e n g t f c 50 C e n t i g r a d e. Run E Jud X*i* -O h i PwH ' *HC1 -log Bjjr Bljj* B 0( + 3 <k - B p2 X Y ^ 2 3 f xlo3 vo It a XlO4 xl03 xlo3 xlo xlo5 xlo10 x lo xlo9 xlo^ Q TO ? 3.U 2 7.' ? TT I ! , T , * s Q#R ; * Ait OP I.I a ? ? s

59 53 fable 3. fhe standard eleetrod p otential of the liver- silv er chloride h a lf-c e ll, the value of the i» parameters A and B of the Debye-Haekel equation and th e p aram eter H f/f f o r th e tem perat u r e ran g e 0 to 5 0 ' Centigrade. 1 E k * Rt/F 4 B 0 abs v X xlo ' ' ?

60 54 Table 4.1. '/aluas of X and t for each experim ental run Interpolated a t equal values of Ionic stren g th. X xlo'* Y xlo9 Zonlo Sir igth Run t OQ , , ,i *5' ,,65 81,,00 7 0,,65 73.,35 6 8, ? * Lf O ,*45 S3, ,00 79.;bo 74, ^ i.3 255*0 240* <,40 «94, ,40 85.,40 79., * * :103.;ao 1100., , , a , , ]Q qr,5; ' *5 302 * * , ! 55 81,60 67, *8 ; 296 * * , ,00 103,, , * , *,30 117,, , , *1 311 * * ,, ,'65 106,, , *0 310 * * * i , , , , *5 309 *3 299 * * * , ^ , , ' , XT , ' , m T , *0 OOJ 0 :-J O q ' S ' " * B * B' X, Q.<.? 52' , * S , *3 228*0 210* ' * ' , ' * ' , , 00' IB, '\5 q 57* , *30 59*.41 58* 35 36* ? l.. 1:0 20,.98 IB q5- * B.2B 5 6, , 4* , ; * ' , 15 23, Q of. rv vo fn , , * , * ]86 of , Ip 21., * * pf» ' ,

61 Table 4.2. Values of X and 1 for each experimental run Interpolated a t equal -v a lu es of Ionic stren g th. X xlo ' xlo9 I o n ic Strength * * Hun t 0,<*iV* 1 0 * * & * * * * ? ' ' i * *^5 3 X « S '? X ' aa * , * X >8* ': -7, ,6 4 7 S , X , ,7 < S a , ,7 20 8, , , , , > , , a , , , , "'. 0 4 ' * * ? * , ? ? ? **.03,,r.040? ? ,04335, ,04110,03995, ? ? , ,

62 56 fable 4.3* Values of X and t to r aoh experim ental run Interpolated a t equal values of lonlo strength X xlo6 lonlo Strength 0.06 Q Sun t ? ? * X xlo ,0146

63 57 fabl 5 Slopes of th e plots of X against 1Cobtained fro Figures 2.1 to Io n ia S tren g th T em perature ^

64 58 tab le 6* Values o f (-lo g crl^) as a function of temperature and Ionic strength and dcpa^^/^^ t each 5 d e g r e e interval in the range 0 to Ionic strength Ofl ' S x t r a p s la t e d V alua a(p<r%)

65 59 Tabl 7. 7,lues of -log % /p computed from the experimental of runs 1, 6, 2, 7 end 3*» H un l o n i o Temperature Strength OQ a a m , , , , * , , *2491, , , R S a , , , S

66 u t 4* m eo m m M o y i o u io u i ou* o u i o $ H > Xt J * 14- V»l M \jt M Vj* V*t Vrt M KM \tf \M * * * * * * # «+ 4* ^*Ui U* 4* #- X* COM3 so V* m Gf\^c5\Qg oo rg m &0~4 i o m O c r \ g i m u i eo-*4 W yview MW VjIMMW M * «4*-i* 4 a - u * o\oo' i~*^ VJi 04 ^-* 4 M 'O 'O to '-4 Ov-4 Ull&Oi * 0*04 HU1 H* ** OS t i o i a o o o o y W 4 ^ y H H V O fo ^ exparis&ant&x caloul& ted by aquation 73

67 Table 9. A comparison o f the experim entally determined valu es o f pk0 and the values computed on the b a sis o f equation 7^* t Number p l 0 4Z o f Oq G et#ns e x p e rim en ta l average Mean d e v ia t io n P*2 AP*c2 c a lc u la te d by e q u a tio n Average mean d e v ia t io n ? A verage A P & o

68 62 f a b le 10. A com parison o f th e e x p e r im e n ta lly determ ined v a lu e s o f and w ith th e v a lu e s computed from e q u a tio n s 73 and 74 r e s p e c t iv e ly * Ionisation t A Constant C experimental calculated by. e q u a tio n 73 A x lo * xlc '4 x lo 4 IL A ' * Average difference.010 % xlo6 xlo6 xlo Average d if f e r e n c e *021

69 63 *v%, F*V j*% la b lc * IX. Tn& ta a r& o d y n a tn io q u a n t i t i e s ^ F fi H * andaop d s r lv s d from U r n stcom i o n i s a t i o n constants. m o o l h m d valu aa o f tha f i r s t & M fonatani t A f AH? AO 0 keal. oal. oal. oal ? U ? as m as ' SO

70 e Table IS. '/slu ss c f the f ir s t- and second la n ia a tlo h - constants o f m ails acid obtained from the 11teratare. i^uthor fe a r Kethod t n *1 ^3. 2 *2 00' xlo4 XlO4 xlo 6 xlo 6 H eferen ee Os tv a ld 1889 C o n d u ctiv ity «n a!* «* B erthe l o t 1891 IT 3. S3 12. Malden 1896 * 25' 4.0 4? Smith 1898 Inversion of s sucrose W egschelder 1902 Conductivity IT 4.0 s D har-d atta 1913 Solubility «9. 1? Lars son 1922 Clectroisetrlo s A uerheeh-dm olesyk H 1924 ao B jerrus" 1924 ft Coops 1924 Conductivity; larsson 1924 «n» * Roth-Mllms 1926 « Ml sutanl 1925 Elea trosie trio IS :! Larsson ' S o lu b i11 ty 25'' 4.0 * jdubo.ux- Kroatae-1 n % ' s Hamer 1943 Elaetrametric Men fhs values f E{ have been 'obtained from th e original determination by Ostwald (3 ) and by th e bo authors In order to ca l culate Kg.

71 Fig 1.1.a O 5 N*b. Ordinate values for the curves at 45 and^50 C have been Increased by 0.1x10 unite. Figure The computed quantity, X, as a fu n ctio n o f io n ic stre n g th for the tenqpereture ranre 0 to 50 C entigrade,

72 JUa Fig » ' O :.oc. Run XxlO V S U 7K I N. b. Values of the q u a n tity, X, a t 45 and 50 Je n t.^ ra ^ e have been in creased by ).lx lo u n its

73 Fig. I.3.a Run 5 XxlO5 vs p N. b. Values o f the q u a n tity, a t 45 and 50 C nave been increased b; 0.8x10 * u n its. TJJJZ O O T u r n

74 r Runs I&6 XxlO7 vs n N. b. Yelugs o f the q u a n tity, X, a t 3 5,4 0, 45 and 50 j hare bef»n decreased by 1x10 u n its

75 69 \ Fig.1.5. Run 2 XxlO6 vs u - 8 _ c N. b. Yaluea o f the q u a n tity, X, a t 3 0,3 5,4 0,4 5 and_ 0 J have been increased by l x i o u n its. i O

76 -7_ Fig. L6.a Run 7 Xxl06vs p - 8_ -0 50* N.b. Ye luga of thg q u a n tity, I, a t 30,35,40,45,and 0 been increased by 1x10* u nits# C have O 1 0 * 25*

77 n Fig. I.7.a Run 3a XxlO6 vs j 035' b o ( n.b. Values of tbe q u a n tity, a t 30, 35, 40, 45 and 30 C hare been increased by 1x10 u n its* O

78 72 Run 8 YxlO vs p N.b. V alues o f the.qu? r t i t y, Y, e t _ U L'*.nr 5 0 C have been increased by 1x 13 '"' u n it F igu re lb. fhe con^ut^d q u an tity, Y, as a fu n ction o f io n i? stren g th *or the tem perature ran^e 3 to 5 0 C entigrade.

79 22. Run 4 O O 3 0 ' O 20 YxlOu vs jf n tit;, v, at 5 and >eer. m e ".sod by.4x10 ' u n its,

80 Run 5 Fig. I.3.b YxlO vs u N.b. Values of the quantity Y, at 45 and 50 G have been increased by 0.2x10 9 u n its IONIC STRENGTH

81 iv. 5oo * o r ^u, y j$ 6 Y*/n9 *64 *?U«,

82 7 6 Fig. I.5.b so Run 2 YxlO1vs i

83 5/ >9. <h ^ b Soo^^e9 tf A ^ R Y\ xio'i 6*e«^ ' < / -. «t 6*, J 0 ^ lo 'J p S O %, /, < J *a. ' < 5 0 Qd <?

84 Run 3 o yxio II VS F i Q l'?.b

85 Fig. 2.1 YxlO vs XxlO fig u r e s 2.1 to.1 1. A s e r ie s of ; l o t s o f a g a in st Y at con stan t io n ic stre n g th at each tem perature in the range 0 to 50 Centigrt.de. P o U / / / P Mo ba Ths ordioats azla ha a basn trsnspossd u n its to tbs right for saob auaosaa iv«mm of tbs faaily of ourrss

86 Fig. 2.2 YxlO vs XxlO /* 75 I.b. Th» ordinafca *xla has baen fcranapoaad unit# tofcb# ri^ht fq wh, SUOMMlT# MBflMNPOf jutt'/ T family of curraa. ^ f t ^

87 0 Fig. 2.3 V.b. The ordinate axis haa been trenapoaed unita to the rifht for eeoh auooeaaire earber of the fasllx of currea. 2.0

88 88 15 Fig. 2.4 YxlO8 vs XxlO4 0, k N.b.?vs<» ""' ir, *p» r, b '< -.i.in t ra n? -sf»d 0.1 r u- : t? t t ->.e fo r su' -'ogpiv0 rr ~ Dr t 1' f6 m ll\ of 'u rves, 00,00

89 09 20 Fig. 2.5 YxlO8 vs XxlO4 N.b, The o rd in a te fcxis has been 3 tra n sp o se d u n its to th e risrh t fo r each s u c c e ssiv e member o f th e fam ily of c u rv e s.

90 Fig. 2.6 YxlO8 vs XxlO N*b. The o rd in a te a x is has been transposed u n its to the r ig h t fo r each su c c e s s iv e member of the fam ily of cu rves

91 Fl«2.7 5 *

92 86 35 Fig

93 8T 40 Fig

94 86 Fig b / 5.0 g 1 0 i.o

95 Fig

96 Fig log 1^ p o ' o' 5 - o / - o o o M

97 o Fig. 3.2 ~ s o-. - o O O o o _ G o ' /to r G G G 1. o

98 5.13 * A 5.11 % w V * 9 w K 5.09 nr r V 9 9 w o O 5 i a 10 A V w * * m i. A * A. 5J09 99 " i^ a a a 5.09 w I o «: A, * % I" * * e Fig. 4.1 Figure 4. i lo t of -lo g in s t ion;? s tre n g th fo r the tem perature ren*e 3C t-jv»0 Jen t i^-ede.

99 5.11 * % - 5.0SL _ / ^ w «w Fig * _ i.l? C %» v, %r-..10 * - r~"\ V..y' >.13 + * % A A.11. w # ' - ^ m >.15 f - : m * A. Ll O ~W W c% m.16 T F.... 9>... i - >.14 i ro n 0 0 o 0 l O % P

100 5,4 Fifl. 5 X F igure 5. 1 comparison of the ex p erim en tally derived valu es of pk. and the values of pk 1 c a lc u la te d by means Of equation

101 95 Fig. 6 F ig u re 5. A comparison of the ex p erim en tally derived value of pk r 5 and the values o f pko c a lc u la te d by meens^of equation o T - C

102 F ig u re 7. P h o to g ra p h o f th e h y d ro g e n s i l v e r - s i l v e r e h lo r ia c e l l