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

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

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 4 8106-1346

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 # 168564

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

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 8. 41 2. 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, 57 6. 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 73. 9. 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.

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 8 8 8 1. 2 a " * 4 6 6 1.3a " «5 6? l* 4 a * * 1 and 6 6 8 1,5 a * " 2 69 1. 6 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 8 72 1. 2 b " * 4 73 1,3 b * «5 74 1.4b * " 1 and 6 75 1.5b " * 2 76 1.6b " * 7 77 1.7 b " * 3a 78 2. 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. 2.1 0 79 2.2 5 SO 2.3 10 81 8.4 18 82 2.5 80 83 2.6 25 84 2.7 30 85 2. 8 35 8 6 2.9 40 37 2.1 0 48 88 2.1 1 50 89 3. 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. 90 4. 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. 92 5. 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 73. 6. 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 74. 7. 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. 96 8. 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 ).

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

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 0.0 8 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

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 is @0 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 0.0 3 {*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)

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

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 #

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

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

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 : - 2 + + 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

(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

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 *

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 130 0 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 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 0.0 4 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 105 0 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 130 0. 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 0.0 1 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.

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 * 0 0 1 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 * 0 0 1 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

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 0.001 p e r c e n t o f c h lo rid e io n.

*«* 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 1 0 0 gram mass w ere w eighed to IB m illig ra m s; betw een 1 0 0 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 0.008000 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

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 1 0 0 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-

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 * 0.0 2 0. 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 0. 2 0 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 0.3 0 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 0.0 3 m i l l i v o l t s o r l e s s.

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 0 459 (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 0.00002 t o 0.0 0 3 m olal a t 20 0. 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 * 0.0 0 0 8. S hedlovsky and M aciases (43) m easured ^ a c a a t 25 Q from 0.0 0 1 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 0.002 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 0.0 0 1.

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*

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^ +- + 4aA» ) (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)

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

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

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*

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 33 1-1 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 8-------------------- 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

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, 0.0 2 3, 0.0 2 0 and 0.0 1 4 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

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

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* 0.0 8 5 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

28 a s s ig n e d a v a lu e o f 6.0xlO* # lo g p w ill b e -0.1 7 0 6 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 -0.1 6 8 0. 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*85-5.1388 * 0.01355 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 0.0013 p i u n i t s.

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 = 1658,53-6,2364 + 0,01938 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 * 2.3026 1 (4 * 8T t- Of8 ) (78) AH = *T8 d In K» 2.8026 1 ( 1 - GT8 ) (76) dt A 3 * -da f0 - -2.3 0 2 6 B(B + 20T) (77) df A 0 P T J 5 i ^ = -2.3 0 2 6 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,

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

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.

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 1 0.1 0 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 * 0.1 5 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 0.53135 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 * 2.3026 B T /f a t 0 Q a r e 0.83632 and 0.054201 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. 1-1 0.5 3 1 3 3 * 0.0 0 0 1 5-0.23658 ~ T ~ ' ' o s s i i ( ' i - 1 5.4392 * 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 0.00800 m olal a s p o s s ib le, lo g mc i ~= -8.0 9 6 8 * 0.0001 (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 = 5.4392-0.002V - 2.0 9 6 3 * 0.0001 (83)

p^h = 3,3424 1 0.0028 (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 : - -3.3 4 2 4 * 0.0083 P - 10 (83) P = (4.5 4 8-0.0 3 0 ) 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 n @1 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 ± 0.0 0 2 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 quation @4). 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 0.8 7 3 a t io n ie s tr e n g th 0.02006 (F ig u re 8 ). - lo g mh+s 3,3 4 2 4 ± 0,0028 * 21og(0.873 ± 0.0 0 2 ) (89) - lo g mg*-3. 4 4 10.0048 (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 0.007332 (92)

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 * 0 0 6 7 5 5 i O.OO00O7 (93) In t h i s exam ple 4 = 0.0 1 1 3 ft ( f t ) Therefore, 4 + B - 0,018149 ± 0.000007 (95) 4 - B» 0*004539 1 0.000007 (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 0.0071x10-3 (97) (18.149t 0.007)xlQ*3 X - (1.6*19 * 0.0 0 7 6 )1 1 0 * (98) F*U - Bl H+ B) (89) (8.0668 * 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 0 1 0.. 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 * *

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* 0.007 ixlct3 1 ~ (6.755* 0.007)xl0~S E*, (3,1 2 2 * 0.021 )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 4 0.6 6 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 (2.907 0.Q 2 0 )x l0 ~ *. Tbe v a lu e o f pk w ill b e 3.5 3 6 5 t 0,0 0 2 7, 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 0.6 6 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 0.1 6 8 2, i f a* i s assumed to be 6.2 5 x l0 * 8 ; and 0,1 7 0 8, i f a* I s a ssig n e d

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 0.679 and 0.0 7 5 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 0.8 1 1 when a* i s 0.25x10* and 0.8 1 0 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 1 0 7 ;- A B / H = o. 0 1 8 a ) 2 + ( 0. 0 0 6 6 ) + (0,0 0 5 0 )J (1 0 0 ) 4» / B - 0.0150 (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 1.5 0 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 5.1 1 9 4. The mean d e v ia tio n i s ± 0.0065 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^ 5.1194 and pkg= 5.1 1 2 9, i s computed to be 7.596 in th e f i r s t e a s e end 7.7 1 1 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 0.0012 pk u n i t s o r. 0.024x10* "I* u n i t s, a f u r t h e r check can be found

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*

1 IF S R M C 23 1 R. 0. M e k in, Australian Chera Inst J & Proa 4, 867, (1 9 3 7 ). 2. 1* J. ^ n d e rso a, D ie s#, 0. o f C hicago, 1934. 3* "^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, 1947. 4. 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, (1 9 4 8 ). 6* * Cham H er, 42, 1, (1 9 4 8 ).? ** 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, (1 9 4 5 ). 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, (1 9 4 6 ). 1 0. " 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). 1 1. ", 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, (1 9 4 3 ). 1 2. D. B e r th e lo t, Ann ehift a t p h y s, (6 ), 2 3, 1, (1891). 1 3. 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, (1 9 2 4 ). 1 4. 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, (1 9 2 9 ). 1 5. H. T. S. B r itto n, 2 Ohs Soe 1896, (1 9 8 5 ). 1 6. 2m 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. 650. 1 7. N. Dhar and A* I. D a tta, A EleSctroohem 1 9, 407, (1 9 1 3 ). 1 8. p. Debye and 1. B u ck el, P hyaik 2, 24, 135, (1 9 2 3 ). 1 9. M. Buboux and J. F r o n a e lt, J chim phys 24, 245, (1 9 8 7 ). 8 0. 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.

33 22. i. X. Hamer and 3. F. aere, X R esearch H at Bar S ta n d a rd s 1 5, 64?, (1 9 3 9 ). 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, (1 9 3 2 ). 2 6. * " * «jj5 # 652,2179, (1 9 3 3 ). 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 1950. 2. * and 1. A. R obinson, T rans F arad ay Soc 3 6, 975, (1 9 4 0 ). 29. 1. L a rsso n, p r iv a te com m unication quoted by H. B jerrum, Z p h y sik Cheat 106. 219, (1 9 2 4 ). 5 0. *, 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, (1 9 2 4 ). 3 1., Z an o rg Cham 125, 281, (1 9 2 2 ). 22* * " " * 155, 847, (1 9 2 6 ). 3 3. M. M is u ta n i, Z p h y sik Cheat 11. 318, (1 9 2 3 ). 3 4. 0. 0. Maaov, R. 0. B a te s, f. X. Hamer and 3* F. Acre, X Am Cham See 65, 1765, (1 9 4 3 ). 3 5. W. R. Maxwell and X. 1. P a r tin g to n, Tran F arad ay Soo 33, 670, (1 9 3 7 ). 3 6. d. O stw ald, 2 p h y sik Chere, 369, (1889). 3 7. 0. D..Pinching and 1. 0. B a te s, X R esearch Mat Bur S ta n d a rd s, 3 7, 311, (1 9 4 7 ). 3 8. 3. P o p o ff, a..1. H unts and 1. B. Snow, X Phys Cham 32, 1036, (1 9 2 3 ). 3 9. M. R a n d a ll and A. P. Y anselow, X Am Ohea So 4 6, 2418, (1 9 2 4 ). 4 0. * and L. 1. Young, X Am Cheat 3oc 50, 989, (1 9 2 3 ). 4 1. 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, 1946. 4 2. 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 630. 4 3. T. ah ed lo v sk y and P. A. M aclnnes, X Am Chem Soe 5, 1970, (1 9 3 6 ).

40 4 4. u 3. Siam s, J m Chem Soc 48, 1239, (1926). 4 5. #. A. S m ith, 3 p h y sik Ja«m 25, 193, (1898). 4 6. S. 0. Speataaan, J Qhsm Soc 855, (1 940). 4 7. P. Pa id e a, B er. 29, 1699, (1896). 4 3. R. d eg g eh e id er, ^ o n a tsh S3, 599, (1 9 0 2 ).

41 table 1. Buffer ratios and d ilu tion ratios of runs 1 to 8. Dilution ra tio 1 Run Buffer ratio WIO4 ratal 1 0000 I 2 -.4002* <1 3a -.660? I 4 a6303-1 5 : e36?6 1 6 0000 1 7 -.4161 1 8.6695 1 a 3.6527.3893.6617.3352.7432.4183.6617.3751.6587.3417.6545.4122.6448.3643.6654.3372 4 5.2120.09764.2 1 2 8.09314.3076.19815.2 1 1 1 -.2264.09775.2279.08672.2247.0982*7.2152.09442 minus sign was used to designate the ratio KDH/EHKal.

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 xlo4 8 70.41 49.53 29.04 21.43 13.99 4 62.44 44.06 as* 3 0 19*57 *$aat6 *33293,32436.52691 *53093 *32749.32793 *32949 *53135 3.2719 5. 8831 3.3193 5.3577 5.4324 5.3634 5.3765 3.4053 5.4392 3.1749 3.1881 3.2229 3.2 6 0 8 3.3355 3.2720 3.2800 3.3036 3.3424.305.8 2 8.853.869.390.315.833.654.873 2.9397 3.0241 3.0549 3.3189 3.2343 3.0944 3.1213 3.1715 3.2244 10.24 9.46 3.22 7.26 5.83 3.05 7.56 6.74 5.97 8 xlo3 4 2. 6 3 6 23.105 13.900 8.670 3.539 88.010 58.015 3 7. 5 4 2 18.149 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 xlo3 105.046 69.635 34.945 22.101 9.432 82,010 50.015 33.542 13.149 19.774 13.425 7.145 4.761 2.354 19.956 13.4 >9 7.35S 4.639 66.85 64.35 59.86 34.85 46.19 53.45 52.49 49.13 45.46. 4469 4206 3533 3009 2133 2857 2755 2414 2060 271.3 2 6 1.7 2 3 8.1 2 1 5.2 173.3 2 06.6 201.7 137.1 169.2 34.13 81.09 73.32 64.82 53.24 64.79 63.77 58.30 58.31 71.57 50.5S 29.93 2 2.2 1 14.50 6 2.98 4 4.6 2 29.02 20.06 61.15 42.72 28.69 19.29 13.20 62.45 43.64 50.44 20.41 12.72 62.51 34.33 26.27 19.60 13,03 580 26 6.3420 4.3454.315 4.0675.855 5" 074 6.3508 4.2543.824 4.0966.301 5 134 6.3619 4.2653.833 4.1272.746 55 16 6.3770 4. 3805.873 4.1625.638 3-319 6.3960 4.2995. 892 4.2003 631 gy 58026 6.3420 4.2450.815 4.0674 >' 58094 6.3508 4.3543.234 4.1OO0.794 53135 6.3619 4.2651.350 4.1339,732 53211 6.3770 4.2792.871 4.1592.693 59315 6,3960 4. 2904.995 4.3023.623 61330 6.9515 4.9546.314 4.6759.2 1 1-12.137 61435 5.9709 4.5740.332 4.7142.193-8.036 61543 6.990S 4.3939.357 4.7599.174-4.073 51611 7.0334 4.9064.273 4.7334.163-2.594 61785 7.0355 4.9385. 992 4.8393.145-1.143 53.060 53.330 5 ;6 33 33.30 -.0916 3.241 68.44 34.609 34.769 5.569 31.00 -.1288 3.115 47.41 20.614 20.764 5.433 29.47 -.1965 2.968 31.62 11.197 11.337 5. "43 27.49 -.3221 2.733 20.93 5.1 2 6 5.353 5.013 25.10 -.6174 2.580 14.06 54.3-1 54.533 5.6 " 30.33 -.0396 3.346 69.94 35.550 35.720 5*. 520 33.54 -.1335 3.307 40.47 23.366 a". 530 5.431 29.49 -.1825 2.969 33.43 18.339 12!480 5.253 27.64 -.2954 2.796 28.13 4.6 3 9 4.785 5.031 ^5# 31 -.6752 2.599 13.4? I8.1 3 6 4.410 1.398 1.9 5 4-9.354.4569 0?r, > j 11.995 2-8.068 1.337 1.787-8.950. 4181 44.9? 6.051 14.325 1.277 1.630-8.505.3834 M.54 3.847 9.035 1.240 1.539-8.3-05.3614 19.78 1.677 3.9«3 1.1 5 2 1.327-7.554.3137 13.15 5 3.6 0 43,85 23,25 20.50 13.46 61511 6.9349 4.9880,314 4.7093.193 - la. 64? 61533 6.9890 4.3921.833 4.7334.185 S. 161 61705 7,0207 4.923-8.354 4.7867.163-4.616 61730 7.0253 4.9',n4.371 4.80"5.153-2.853 61909 7.0582 4.9613.891 4. -'10.133-1.255 17.699 42.993 1.294 1.675-9.848 4068 64.33 11.407?7.729 1.2-02 1.644-9.172.3995 44.34 6.438 15.670 1.192 1.420-8.545.3437 26 54 3.966 9.67? 1.179 1.391-8.432.3391 20.67 1.727 4.237 1.093 1.195-7.941.2932 13.54 34 61.83 43.01 30.62 3 4.5 6 18.67 53651 7.3793 5.2945.814 5,1 0 5 8.0734-15.319 63767 7.4013 5.3053 5.1416.0723-11.386 63848 7.4161 5.3200.350 5,1788.O663-6.412 63916 7.4887 5.3322.361 5.3023.0620-4.730 63978 7,4401 5.3435.375 3.2275.039? - 3.040 7.050 3 3.4 9 4.5193. 3097-10.127.1321 61.98 5.837 2Q.609. 4948.3449-9.653. 1200 40.12 3.283 16.107.4737.8391-9.348.1184 3 0.6 8 3.413 11.844.4653.2165-9.103. 1063 24.-81 1.553 7.638.4534.2050 -.2, 272. 1011 18.70

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. 41 49.53 29.04 21.43 13.39 4 62.44 44.06 2 8.5 0 19,57 5 fo O 2-43.59 2 6.46 2 0.2 3 13.39 1 61.13 42.7? 23.69 19.29 1 3.2 0 6 62.45 43.64 30.44 20.41 12.72 2 62.51 44.33 26.27 19.60 13.03 7 63.60 43.35 28.25 20.50 13.46 3a 61.33 4.01 30.62 24.56 13.67 q u a n titie s, and a second approxim ation o f io n ic strength. 5 C en tig rad e..53395.52477.53671.52973.5331'".52921.52967.53123.53326.55235.55293.55361.55437,55645.58316. 58369.53423,58511,38621.53316,5333s.58430.5 507.58615.61715.61811.61920.61991.62034.6i o.61902. 62092.62106.6229?.64053.64169.64249.64329.64401 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 5,2 5 2 6 5,2674 5,3026 5,339? 5.4194 5.3479 5.3562 5.3345 5.4212 5.7677 5.7776 5.7899 5.3037 5.8414 5.3253 5,3349 6.3447 5.3607 5.3906 6.3253 5.3390 5.3460 6.3599 5.3795 5.9412 6.9586 6.97?3 6.9911 7.0030 6.9710 6.9750 7.0077 7.0120 7.0457 7.3648 7.3858 7.4003 7.4148 7.4278 3,1556 3.1704 3.2057 3.2423 3.3325 3.2515 3.2597 3.2378 3.3245 3.6709 3.6303 3.6931 3.7069 3.7445 4.2 288 4. 2384 4.2482 4.2641 4.2830 4.2284 4.2411 4.2491 4.2630 4.29 q6 4.3442 4.8616 4.8913 4.3942 4.9111 4.8741 4.9781 4.9107 4.9151 4.9388 5.2695 5.2902 5.3041 5.3183 5.3312.808 -,323,355.370. 390.916.834.856,373.316.333.360. 372.891.816.835.355.873.891.315.335.353.872.394.815.833.860.373.891.?14.835.657.372.891.315.829.351.8 6 3.875 2.9704 3.0064 3,0697 3.1213 3.2213 3,0749 3.1 0 2 0 3.1527 3.2065 3.4943 3.5221 3.5621 3.5379 3.6443 4.0522 4.0313 4,1122 4.1462 4.1323 4.0503 4.0345 4.1109 4.1440 4.1852 4.6665 4.7029 4.7503 4.7762 4.3109 4.694 4.720 4.775 4.795 4.338 5.091 5.1275 5.1640 5.1903 5.215? 10.95 9,85 8.52 7.56 6.0 1 8,4? 7.91 7.04 6, 2? 3.2 0 3.0 1 2.74 O O 07. 88?.828.772.714,656,389.823 775,718 653.216.198.178.167,155. 30?,191.168,160,145.0794.0746.0685.0645.0609 42.565 28.066 13.870 8.640 3.521 33,990 22.253 12.3 6 2 6.730 19.544 12.783 6.514 4.239 1.714-12.138-3.037-4.079-2.595-1.144-12.647-8.16? - 4.616-2.854-1.255-15.319-11.388-6.412-4.716-3.040 104.975 69.596 34.915 22.071 9.414 37.793 57.930 32.61? 18.074 73.575 48.373 24.977 16.470 6.997 53.055 34.606 20.61? 11.196 5.123 54.358 35.791 22.364 12.336 4.657 18.135 11.994 6.051 3.346 1.676 17.699 11.406 6.438 3.965 1.727 7.35s 5. 37 3.233 2.413 1.55? 19.345 13.4C4 7.175 4.791 2.372 19.993 13.464 y QQQ 34.487 23.807 11,949 7.992 3.567 33.233 34.772 20.766 11.338 5.055 54.536 35.555 22.51-13.4Q0 4.787 4?.411 23.069 14. 326 9.036 3.964 4-.993 27.730 15.670 9.674 4.237 33.494 22.609 16.10? 11.844 7.632 69.89 67.55 6 2,2 7 57.24 47.59 56.04 55.00 51.54 47.3 31.33 20.85 80.27 19.64 13.01 5.905 5.776 5.647 5.444 5.212 5.910 5.740 5.636 5.457 3. 1.433 1.375 1.314 1.276 1.227 1.336 1.324 1.289 1,216 1,125.5376.5127. 4965.4305. 4664 4834 4563 3378 ' 3276 2265 3140 3023 2657 0044 455.1 434.9 411.0 385.7 384.3 34.87 33.36 31.89 29.63 27.16 34.93 38.95 31.76 29.73 27 2 2.049 1.398 1.727 1, 62R l! 506 1.725 1.753 1.510 1.473 1.266.2890.?5 op..2465.2308.2176 283.4?7?.4 247.4 224.1 2 78.0 216,5 2 1 1.1 195.4 176.4 58.67 55.11 5?. 7 50.55 44.14 -.09 7 -.1383 -.2116 -.3473 -.6673 -.0967 -.1329 -.1952 -.3175 -.7313-9.531-9.216-3.359-8,606-7,378-9.543-9.473-3.811-8.749-8.131-10.483-10.00? -9.6 9 5-9.392-9.135 92.33 QQ.27 79169 7 1.1 2 57.06 71.36 70.23 64.26 57.92 21.33 2 0.5 0 1 9.6 0 13.72 16.53 3.499 3.359 3.213 3.0 0 1 2.736 3.504 3.310 3.198 3.013 2.793.4792. 4486.4061,5824.3563.4337.4261.3675.3606.3107.1416.128.1209.1133.1070 71.65 5 0.6 2 as. 6 2 2. 24 14 *52 53.00 44.64 89.05 2 0 #OR 63.03 44.38 27.04 20.70 13.63 6?. 49 47.45 31. 55 20.91 14.04 69.96 4:q. 52 33.44 22.11 13.44 63.33 44.90 26.53 19.77 13.15 64.36 44.33 28.53 20.66 13.54 61.79 48.11 30.6? 24.31 l q.7q

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 4 8 70.41.52560 5.3362 3.1392.807 a. 9530 11.14 43.546 49.53.52651 5.2534 3.1554.8 2 7 2.9904 10.22 28.029 29.04.52355 5.2 2 1 7 3.1918. 854 3.0548 7 #: SO J «U. 13.840 21.43.53069 5.3363 3.2299.370 3.1039 7.78 8.618 13.89,.53531 5.4090 3.3131.890 3.2109 6.15 3.507 4 <2.44.5309? 5.3316 3.2353.314 3.0 5 6 6 S.73 33.954 44.06.53146 5.3405 3.2440. 837 3.0842 8.24 22.226 28.50.53315 5.3706 3.2739.855 3.1378 7.23 12.338 19.57.53515 5.4062 3.3094.874 3.1924 6.42 6.710 5 6.03.55454 5.7513 3.6545.814 3.4753 3.27 19.537 43.59.55509 5.7610 3.6642.831 3.5034 3.14 12.770 26.46.55533 5.7742 3.6774.859 3.5454 2.85 6.503 20.23. 55r 63 5.7335 3.6 9 1 6.873 3.5736 2.67 4.230 13.88.55531 5.B773 3.7304. 39? 3.6311 2.34 1.708 1 61.15.56597 6.3107 4. >141. 314 4.0 3 5 4.932 42.72 5 653 6.3 2 0 6 4.2241.833 4.0654.860 qp #59. 5 712 4.3311 4. 3346.8 5 4 4.0975.809 19. >9. 51792 6.3464 4.3499.874 4.1329.736 13.10.53919 6.3680 4. 3712. 9" 4.1719.673 6 65.4 5 cvprqn 6.3 1 1 2 4.2143.814 4.0335.922 43.64 m52^7< 6.3247 4.2278. 33 4.0690.933 30.44! 53784 6.3333 4.7363.351 4.0961.801 >0.41. 58"01 6.3470 4.2500. 372 4.1310.740 1^.7. 5391-6.3<74 4..3704.'94 4.1731.701 2 6?. 51.68077 6.9300 4.8331.313 4.6533.222-12.139 44.33.62185 6.9492 4.8573.331 4.6 9 1 5.204-8.038 2 6. 07.62895 < g683 4.8719.359 4.7399.182-4.079 1 9! 60.62373 619377 4.8858.2 7 4 4 7<Q.q.170-2.595 13.03.6^470 7.0 0 0 0 4.9030 897 4!0037.137-1.145 7 6 3.6 0.62846 6.9601 4.8 6 3 3.313 4.633.807-12.648 43.35 # 5 p 07 q 6.9647 4.3676.333 4.70.196-8.162 30 C V. <C*J OR!62455 6.9973 4.9004.356 4.766.171-4.617 30.50.67484 7.0021 4.9052 373 4.786 164-2.854 13.46.69672 7.0359 4.9390. 392 4.340.145-1.255 3a 61.33.64461 7.3543 5.3591.813 5.0793.0333-15.319 43.01.64570 7.3737 5. 77r1.827 5.H31.0771-11.387 30.60.64660 7.3897 5.3936.850 5.1524.0704-6.412 34.56.'47 4-' 7.4051 5.3036. 367 5.1796.0661-4.716 15.67.64375 7.4191 5.32>5. 376 5.2075.0659-3.040 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 xlo3 104.956 69.559 34.335 22.049 9.400 37.937 57.930 32.533 18.104 73.568 43.360 24.966 16.461 6.939 53.052 34.599 20.503 11.193 5.1 2 2 54.345 35.546 22.357 12.332 4.653 18.134 11.994 6.051 3.346 1.675 17.698 11.406 6.437 3.966 1.727 7.356 5.336 3.283 2.412 1.552 19.884 13.501 7.205 4.813 2.336 20.029 13.497 7.912 4.634 34.494 22.820 1 1.960 8.0 0 1 3.574 53.236 34.779 20.770 11.341 5.256 54.529 35.761 22.517 12.430 4.733 42.412 23.069 14.226 9.035 3.964 42.994 27.730 15.671 9.673 4.2 3 8 33.494 28.610 16.107 11.344 7.633 72.53 69.92 64.30 53.90 48.74 5. I 1 57.03 5 3.2 2 49.05 2 2.16 31.67 2 1.0 2 30.34 18.61 6.108 5.970 5.,c 37 si r* 625 p. *7i-" 6.106 5.913 5.303 5.623 5.364 1.459 1.405 1. 343 1.301 1.250 1.370 1.356 1.253 1.244 1.151.5507.5271. 5036.4913.4759 5288 4389 41.14 3469 2376 3334 3252 2q33 2406 490.0 469.4 441.8 413.8 346.2 37.31 35.64 33.95 31.64 po gp 37.28 35.03 33.68 31.62 23.77 2.157 1.974 1.804 1.692 1.5*3 1.87S 1.238 1.583 1.548 1.324.3033. 2778.2587. 2414.. 2264 294.2 231.7 355.1 230.2 l q1.9 224.6 218.8 201.5 121.8 53.84 57.21 54.75 58,28 45. 46 -.1 0 6 1 -.1424 -.2287 -.3701 -.7033 -.1 0 3 5 -.1 4 2 0-2080 -.3372 -.7737-9.831-9.416-9.056-8.777 - Q.537-9.793-9.702-9.0 2 2-8.954-8.367-10.739-10.284-9.935-9.605-9.321 99.70 94.89 85.39 75.72 60,31 77.08 75.76 63.77 62.25 23.08 22.15 21.17 20.12 17.70 3.744 3.532 3.48? 3.206 2.943 3.740 3.519 3.392 3.200 2.960, 5045.4621. 4242.3976.3700.4561.4469.3353.3776.3250.1486.1362.1269.1185.1114 71.65 50.65 29.99 0 0. 0 g. 14!54 63.04 44.65 29.08 20.10 63.04 44.38 27.04 20.71 13.62 68.51 37.47 31.57 20.93 14.04 69.98 48.54 33.46 22.13 13.44 63.30 44. 66 26.58 19.77 13.15 ^4.35 44.32 28.52 20.66 13.54 61.97 48.10 30.67 24.81 18.70 from the;

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^ xlo3 8 70.41.52721 5.2235 3.1265.807 2.9403 11.47 42.513 49.53.52316 5.2401 4.1431.827 2.9781 10.52 27.999 29.04.53022 5.2763 3.1793.856 3.0443 9.03 13.819 21.43.53262 5.3131 3.9912.870 3.2004 7.94 8.602 13. 89.53727 5.3995 3.3016.890 3.2143 6.30 3.492 4 5 3,4 4 53266 5.3138 3.2225 814 3.0438 9.04 33.928 44.06.53318 5.3279 3.2314.833 3.0727 8.46 22.203 29.50.53492 5.3584 3.2617 0A 3.1266 7.47 12.319 18.57.53703 5.3953 3.2935.3 7 5 3.1825 6.57 6.695 5 62.03.55666 5.7386 3.6413.814 3.4631 3.44 19.520 43.59.55724 5.7487 3.6519.832 3.4921 3.22 12.762 26.46.55802 5.7624 3.6655.859 3.5335 2.93 6.495 20.23.55886 5.7771 3.6302.874 3.5632 2.73 4.226 13.28.56116 5.3173 3.7204.392 3.6 2 1 1 2.39 1.702 1 61.15.58378 6.3003 4.2033.814 4.0251.944 42.78.53937 6.3106 4.2141.834 4.0564. 873 8 8.69.59997 6.3215 4.3249.855 4.0888.815 19.29.59087 6.3 689 4.2403.375 4.2 5 4 3.751 13.20.59215 6!3593 4.2637.892 4.1634.636 6 62.45. 58.390 6.30 24 4.2054.314 4.0274.939 44.39.53964 5.3153 4.2184.834 4.0608.869 30.44.59013 6.3248 4. 2278.052 4.0326.315 20.51.59096 6.3384.4.2415.373 4.1235.753 19.72.59216 6.3594 4.8625.395 4.1651. 634 2 62.51.62449 6.9249 4.8279.313 4.6431.225-12.139 44.33.62563 6.9448 4.S479.832 4.6831.205-8.033 96.07.69675 6.9644 4.3674.859 4.7454.184-4.079 i9."so.62751 6.9777 4.3007.375 4.7647.172-2.595 13.09.62852 6.9954 4.3984.392 4,7991.159-1.144 T 63.60.62613 6.9535 4.8566.813 4.6763.210-12.648 43.85 62648 6.9497 4.3627.831 4.7020.199 S. 162 29.25. 62330 6.9915 4.8946.857 4.7606.174-4.617 20.50.62861 6.9969 4.9000.872 4.7910.162 & 2.854 13.46.63051 7.0302 4.9332.892 4.3340.147 1.257 3a 61.83.64369 7.3431 5.8529.813 5.0731.0845-15.319 48.01.64996 7.3703 5.2747. 828 5.1108.0775-11.387 30.6?. 65079 7.3348 5.2887.851 5.1436.0710-6.412 24.56.65162 7.3994 5!3029.863 5.1749.0663-4.716 19.67.65249 7.4133 5.3163.376 5.2013.0628-3.040 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 104.923 69.529 34.864 22.033 9.3Q5 37.911 57.925 32.569 18.089 73.551 40.351 24.958 16.455 6.934 53.050 34.601 20.507 11.192 5.120 54.343 35.544 22.355 12.331 4.658 13.134 11.994 6.050 3.346 1.675 17.693 11.406 6.437 3.966 1.726 7.0 5 0 5! 036 3.883 2. 412 1.552 19.397 13.531 7,226 4.829 2.401 20,055 13.519 7.931 4.699 34.511 22.820 i i.968 3.0 0 7 3.5 7 9 53.2 3 3 3 4.7 7 7 2 0.7 7 1 11.342 5.258 54.531 35.721 28.520 12.431 4.7q9 48.4X2 23.069 14.280 9.036 3.964 74.73 7XW93 66,72 '60.09 49.93 59.91 58.70 54.74 50.30 22.81 02 00 21.60 20.3 19.04 6.255 6, 10-8 5.957 5.750 5.461 6.231 6.043 5.913 5.735 5.465 1.486 1.490 1.357 1.316 1.964 40.994 1.391 07.730 1.379 15.671 1.275 9.673 1.239 4.239-1.117 31.494 20.610 16.107 11.344 7.632.5586.5313.5144.497q.4892 5535 5174 4379 3611 2493 3589 3445 2996 2530 520.4 496.Q 466.6 436.1 362.5 39.12 37.31 35.49 33.06 29.33 33.83 36.53 35.02 32.69 29.86 2.209 2.015 1.341 1.732 1.597 302.8 239.7 26:2.3 734.6 185.8 231.6 225.0 207.0 186.2 0 0.5 4 5. 03 56.31 5 3.0 0 46.-41 -.11-13 -.1550 -.3356 -.3859 -.7331 -.1077 -.1479 -.3159 -.3500 -.8032-9.940-9-513-9.1 5 0-0.380-0.632 1.935-9.94:8 1.881-9.816 1.625-9.143 I.3 2 5-9.059 1.360-3.493.3121-10.393 # 2772-10.365 *2646-10.040. 2478-9.733.2325-9.446 1 0 5.9 1 100.68 9 0.7 7 79.14 63.79 81.33 80.41 72.96 65.71 24. 42 23.46 92.37 21.22 13.57 3.926 3.750 3.577 3.351 3.063 3.396 3.676 3.523 3.329 3.074..5166.4716.4330.4069.377q.4701.4574.3956.3065.3341.1529.1384.1299.1217.1144 P a xlo3 71.69 50.68 30.01 38.27 14.55 63.06 44.68 29.09 13.63 63.06 44.39 27.04 20.71 13.63 68.47 47.44 31.53 20.93 14.03 69.94 48.51 33.42 22.13 13.43 63.28 44.37 2 6.5 2 19.77 13.15 64.34 44.31 00.53 20.65 13.54 61.96 48.10 30.67 24.01 18.70

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 70.41.52375 5.2 1 2 0 3.I I 5O.806 2.9 2 7 6 11.91 42.479 49.53.53971 5.2 1 2 0 3.1150 # 8 n 2.9765 10.83 29.968 29.04.53136 5,3654 3.1685.353 3.0305 9.32 13.790 21.45.53455 5.3U7 3. 8148. 868 3.0915 S. 10 8.587 13.39.53918 5.3913 3.8944.889 3.1 9 2 2 6.42 3.430 4 fs 0 9 44.53433 5.3079 3.2115.813 3.0315 9.29 33.903 44.06.5343 9 5.3174 3.2208.8 3 2 3.0610 '8.69 22.180 28.50.53666 5.3480 3. 2512.8 5 2 3.1132 7.71 12.295 19.57. 53919 5.3359 3.2892.873 3.1 7 1 2 6.74 6.6 7 8 5 6.2.03.55377 5.7290 3.6313.813 3.4515 3.54 1 9.5 1 0 43.59.55935 5.7330 3.6412.831 3.4S04 3.31 12.753 2 6.46.56015 5.751S 3.6549 857 3.5209 3.0 1 6.487 i o.2 3.5 6 1 0 1 5.7666 3.6697. 872 3.5507 2.81 4.218 13.28.56341 5.8078 3.7109! 890 3.6 0 9 7 2. 46 1.6 9 6 1 61.13»39162 6.2929 4.1964.313 4.0166.9 6 3 42.72.59222 6.3031 4.2065.833 4.0475. 396 28.69.59297 6.3143 4.2177.8 5 2 4.0756. 334 19.29.59376 6.3396 4.2330.373 4.1150.767 13.20.59511 6.3528 4.2 5 6 2.390 4.1550.7 0 0 6 6.45.59174 6. 394.8 4.1978.313 4.0130.959 4 3.64.59249 6.3077 4.2107.832 4.0509.389 30.44.59303 6.3179 4.2209.350 4.0797.832 20.41.59392 6.3323 4.2353.371 4.1153.767 12.72 59516 6.3536 4* ^566.893 4.1584.694 2 6^.51.62511 6.9201 4.8831.312 4. 6422.223-12.140 44.38.62927 6.9400 4.5430.831 4.6823.208-8.039 26.27.63044 6.9601 4.2632.357 4.7893.137-4.080 19 h o.63118 6.9 7 2 8 4.8759.873 4.7579.175-2.595 13.05.63321 6.9905 4. e 936.^90 4.7924.161-1.144 7 63.60.62931 6.9493 4.8584.812 4.6716.213-12.648 43.35. 6302* 9 '9 0 4.3721. 830 4.7103.195-8.162 28.25.'3312 6.9 90 4.2 9 2 1. 854 4.7551.176-4.617 20.50.63243 6.9942 4.8973.870 4.7763.167-2.854 13.46.63432 7.0269 4.9299.890 4.3387.143-1.257 61.33.6528O 7.3445 5.2493.812 5.0684.0854-15.319 48.01.65410 7.3669 5.3549.827 5.1063.0783-11.387 3 0.6 2.65500 7.3823 5.1739. 849 5.1440.071? - 6.412 24.56.65572 7.3947 5.0316.360 5.1673.0630-4.716 13.67 65665 7.4107 5.3494.874 5.1971.0635-3.040 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 4-3 - X Y 2 6 Q xlo3 XlO5 xlo5 xlo10 xlg xlq xlo5 104.390 69.49 34.335 22.01 9.373 87.336 57.902 32.545 18.072 73.541 4.343 24.950 16.447 6.978 53.04c 34.599 20.604 11.190 5.119 54.341 35.542 22.354 12.329 4.551 1.133 11.992 6.050 3.345 1.675 17.698 11.406 6.437 3.966 1.724 7.55* 5.834 3. 2 3 2.412 1.552 1 9.9 3 1 13.5-3 7.355 4.3^5 3.413 20.030 13.452 7.955 4.716 34.521 22.*37 11.976 9,015 3.535 53.242 34.779 20.772 i i. 344 5.2 5 9 5 4,5 3 3 35.720 22.520 12.483 4.790 42.413 ^2.071 14. 22.6 9-036 3.964 42.994 27.730 15.671 9.673 4.239 38.494 28.610 16.10? 11.844 7.632 76.74 73. 33 67.84 60.98 50.77 61.44 60.14 5 6,0 6 51.39 23.37 22.85 22.14 21.40 19.46 6.362 6. 05 5.848 5.544 6.341 6.156 6.015 5. 317 5.533 1.503 1.435 1.370 1.331 1.278 1.405 1.343 1.232 1.267 1.175. 5633.5355.5174.5032. 4852 0 5458 4603 3719 2573 3775 3617 3143 2641 546.3 521.9 490.0 457.3 378.6 40.43 3-. D 5*+ if fj 36.70 34.20 30.73 40.21 37.89 36.18 33.34 30.67 2. 253 2! 060 1.873 1.771 1.632 1.974 1.802 1.644 1.605 1.381.3173 ^0R68. 2677.2532.2354 310.8 297.3 2684.6 237.p 133.5 237.0 230.4 211.8 189.9 62.01 60.2? 57.55 54.87 47.30 -.1141 -.1609 -.8453 -.4011 -.7579 -.1119 -.1540 -.2240 -.3618 -.8267-10.062-9.673-9.241-8.982-3.730-9.889-9.60^ - 9.197-9.119-3.559-10.9 3 4-10.448-10.106-9.33^ - 9.504 111.89 106.50 95.36 31.83 <6.37 86.24 84. 59 7 6. S3 '.91 25.65 34.65 33.53 33.31 19.45 4.063 3.633 3.693 3.467 3.157 4.035 3.608 3.645 3.436 3.159 5233.4333.4416.4163.3963.4794. 43 1.400?.3916.3393. 1555.1406.1313.1243.1158 71.71 50.70 30.03 0 q qq 1 4! 56 5 3.0 9 4 4.7 0 3 9.1 1 30.13 6 3.0 3 4 4.3 0 27.04 20.71 13.64 68.50 47.33 31.50 20.9? 14.03 69.97 43.45 33.39 22.12 13.42 63.27 44.36 3 6.5 1 19.76 13.15 64.33 44.30 28.51 20.65 13.54 61.96 43.10 30.67 24.61 18.70

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 xlo3 8 70.41.53028 5.2 0 3 1 3.1061.306 2.9193 12.04 42.456 104.866 19.954 7 0.3 3 6135 3 1 7.1 116.73 71.73 49.. 53.53135 5.2 1 9 6 3.1??6.325 2.9556 11.03 27.943 69.473 13.5S7 75.41 5686 3 0 3.3 111.70 50.73 29.04.53346 5.2 5 6 9 3.1600.353 3.0208 9.53 13.769 34.814 7. 376 69.18 4786 873.6 100.03 30.05 21.43.53603 5.3004 3.8033.368 3.0 03 s. 31 3.565 21.996 4, 62.59 3917 843.7 P>6. 66 72.31 15.89.54109 5.3347 3. P874.339 3.1856 6.52 3.470 9.363 51. 55 8657 191.0 6 2.7 7 14.57 4 62.44.53605 5.3007 3.2044.813 3.0246 9.45 33.887 37.870 20.0 9 6 62.46 3902 240.9 89.83 63.10 44.06.53655 5.3092 3.2136.331 3.0518 8.88 22.161 57.383 1 3.5 6 1 61. 29 3736 2 3 4.6 87.99 44.72.28.50.53039 5.3403 3.2436.852 4.1045 7.86 12.280 33.530 7.9 7 0 57.07 3257 215.4 79.79 29.13 19.57.54068 5.3790 X ORpO.373 3.1648 6.85 6.667 13.061 4.727 52. 37 27 87 199.8 71.37 20.15 5-62.03-.56085 5.7199 3.6 2 3 1,.313 3.4433 3.60 19.504 73.535 34.5-7 23.37 5q7.-2 63.17 86.63 63.03 43.59.56142 5-7295 3.6327.330 3.4709 3.38 12.746 4a.336 22.iH4 23.30 54. 61.43 25.65 44.3 26 46.56225 5.7436 3.6467.356 3. 5116 3.08 6.480 24.943 11,933 27.56 508.8 58.-0 24.45 27.05 20.23.56310 5.7579 3.6611.872 3.5421 2.37 4.212 15.441 8.021 21.87 47*. 3 55.91 23.24 20.72 13.23.56564 5.8009 3.7070.391 3.6033 2.49 1.693 6.974 3.5q9 19.77 390.0 47.99 20.18 13.64 1 61.15.59446 6.2887 4.1921.913 4.0133.972 53.045 53.243 6.475 41. 2 ' -.117? 4.143 r-r: #pq 42.72.59509 6.2936 4.2021.331 4.0413.909 34.593 34.730 6, 379 39.43 -.1650 3.964 47.*30 25.60 59553 6.3112 4.2146. 351 4.0744.843 20.605 20.773 6,101 37.22 -.2495 3.733 31.46 19.29.59662 6.3245 4.2280. 974 4.1110.774 11.139 11.345 5.916 35.00 -.4095 3.549 70.91 13.20.59310 6.3500 4.2535. 992 4.1543.701 5.119 5.259 5.579 31.12 -.7640 3.197 14.07 6 52,4 5.59463 6.2909 4.1939.312 4.0131.970 54.350 5 4.5 4 4 6.399 40.95 -.1143 4.110 69.77 43.64.59523 6.3 0 1 0 4. 2040.331 4.0432.905 35. 546 35.728 6. 25 39.0 -.1592 3.928 48.39 30.44.59600 6.3140 4.2170.349 4.0 7 4 3.342 33.357 O'3. 585 6.067 36.51 -.2284 3.709 33.35 20 a4 l 39 6i 8 8 6.3289 4.2319.>371 4.1119.773 12.331 18.485 5.863 34.37 -.3675 3.480 22 11 12.72 ".59313 6.3500 4.2530. 894 4.1556.699 4.652 4.792 5. 5 4 31.18 -.8329 3.212 13.42 62.51.63179 6.9190 4.8230.811 4.6400.229-12.139 18.134 42.412 1.507 3. 270-10.035. 530? 63 26 44.33.63292 6.9381 4.3411.330 4.0793.209-3.038 11.993 23.070 1.442 2.079-9.563.4305 44.35 2 6.2 7.63390 6.9546 4.8577 356 4.7226.189-4.080 6.049 14. 227 1.38 1.926-9.3 :0.4530 20.51 19.60.63497 6.9727 4.3758.373 4.7578.175-2.595 3.045 9.036 1.331 1.772-8.934.4164 15.76 13.00.63603 6.9915 4.8945.891 4.7943.161-1.145 1.675 3.964 1.275 1.625-3.711. 33^7 13.15 63.60.63357 6.9491 4.352?.812 4.6712.213 12 643 17.693 42.994 1.406 1.976-10.046. 4300 64.3? 43.35.63408 6.9577 4.0608. 329 4.6990.200-8.162 11.406 27.730 1.37" 1.899-9.361.4617 44.29 22.25. 03522 6.9 3 2 1 4.8912.353 4.7530.177-4.617 6.437 15.671 1.235 1.651-9.210.4018 28.50 20.50!63020 6.9935 4.3966.870 4.7756.168-2,854 3.966 9.673 1.269 1.610-9.134.3928 20.64 13.46.63814 7.0263 4.9294.091 4.829?.143-1.257 1.726 4.239 1.177 1.334-0.569.3401 13.54 61.33.05694 7.3441 5.2439.811 5.0669.0357-15.319 7.356 33.494.50 38.3179-10.996.1553 61.96 43.01.65a31 7.3672 5.2716.325 5.1045.0786-11.337 5.830 2 0.0 1 0.5350.2003-10.439.1403 48.10 30.62.659?4 7.3330 5.2363. 843 5.1436.0718-6.412 3.233 16.107. 5107.3669-10.091.1310 30.07 24,50.05994 7.3940 5.2933. 60 5.1674.0630-4.716 2.412 11.844.5031.2531-9.336. 1243 24.61 18.67.66030 7.4107 5.3141.375 5.1981.0634-3.040 1.55? 7.63?.4852.2354-9.504. 1153 10.70

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 " 3 70.41.53178 5.1957 3.0937. 805 2.9103 12.29 42,431 49.53.53872 5.3133 3.1153.825 2.9433 1 1.26 29.925 99.04.53502 5.3 5 0 5 3.1536.852 3.0144 9.67 13.755 31.43.53763 5.3 9 3 9 3.1970. 369 3.0750 8.41 S. 555 13.39 *54269 5.3730 3.2311 883 3.1779 6.64 3.458 4 62 44.53753 5.2931 3.1968.812 3.0159 9.6* 33.866 44.06.53314 5.3034 3.2059.831 3.0451 9.01 22.148 28.50. 5400:2 5.3363 3.2370.353 3.0999 7.96 12.270 19.57.54244 j ' 5.3739 3.2771.373 3.1591 6.93 6.659 5 62.03.5 6 3 9 1 5.7142 3.6174.812 3.4333 3.69 19.495 43.59.56344 5.7230 3.6268.830 3.4644 3.43 12.741 26 46.56439 5.7371 3.6403.857 3.5063 3.12 6.476 20.23.56519 5.7521 3.6552.872 3.5362 2.91 4.208 13.23.56733 5.7960 3.6991.890 3.5979 2.52 1.689 1 61.15 42.72 28.69 19.29 13. 20 6 62.45 43.64 30.44 20.41 12.72.59731.59791.59373.59943.60093. 59736.59805.59333.59973.60101 6.3860 6.2960 6.3096 6.3311 6.3470 6.3852 6.2933 6.3111 6.3263 6.3475 4. 1Q95 4.1995 4.2131 4.2246 4.2505 4.1832 4.2013 4.2141 4.2293 4.2505.812.831.852.873.889.812.831.850.871.893 4.0086 4.0373 4.0740 4.1066 4.1483 4.0074 4.0405 4.0729 4.1093 4.1523.980.915.843.732.711.933. 911. 345.773.704 2 62.51.63539 6.9191 4.8221.811 4.6401.229-12.139 44.38.63664 6.9399 4.8429.330 4.6811. 203-8.038 26. 27.63731 6.9593 4.3684.857 5.7284.187-4.080 19.60.63574 6.9748 4.8778.873 4.7598.174-2.595 13.08.63993 6.9946 4.8975.39 0 4.7964 160-1.145 7 63.60.63734 6.9493 4.3529.811 4.6709.213-12.648 43.85.637 *8 6.9 5 7 2 4.8602. 829 4.6962.201-8.162 28.25,63964 6.9 2 9 7 4.8928. 354 4.7553.176-4.617 20.50.64000 6.9957 4»89R8.871 4.7733.166-2.854 13.46.64196 7.0283 4.9314.890 4.8302.143-1.257 3a. 61.83.66108 7.3461 5.2509.311 5.0639.0853-15.319 48.01.66350 7.3693 5.2741.326 5.1031.0730-11.337 30.62.6*345 7.3855 5.2394.849 5.1472.0713-6.412 24.56.66411 7.3965 5.3001.961 5.1701.0676-4.716 18.6?.5*516 7.4140 5.3174.575 5.2014.0629-3.040 30 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 3 104.341 69.455 34.800 21.93* 9.351 37.849 57.870 32.520 13.053 73.526 4".33l 24.939 1*.437 6.971 53.04* 34.597 20.605 11.189 5.113 54.339 35.540 22.352 12.32? 4.6 5 0 19.134 11.993 6.051 3.946 1.675 17.698 11,40* 6.437 3.965 1.725 7.856 5.836 3.293 2.412 1.552 19.979 13.605 7.290 4.876 2.435 20.117 13.574 7.980 4.735 34.536 22.349 11.979 8.025 3.592 53.242 34.791 20.773 11.345 5.260 54.535 35.722 2. 522 1 2.4'4 4.. 791 4>.412 23.070 14.226 9.036 3.964 42.994 27.731 15.671 9.674 4.839 33.494 29.610 16.107 11.844 7.632 79.67 76.68 70.21 63.53 52.35 64.57 6 2.2 5 57.94 59.84 24.13 23.65 22.39 22.12 20.00 6.4*4 6.317 6.129 5.9*3 5.617 6.433 6.290 6.107 5.393 5.617 1.506 1.436 1.373 1.325 1.266 1.403 1.390 1.280 1.262 1.171.5612.5320.5136. 5011.4915 6348 5880 4929 4036 2740 4041 3875 3357 2792 532.4 559.3 524.1 439.3 399.8 41.79 39.91 37.43 35.55 31.55 42.03 39.57 37.30 34.79 31.55 2.269 2.062 I.3 2 3 1.755 1.603 1.969 1.903 1.638 1.594 1.372.3149.2830.2633.2511.2319 322.5 308.3 277.5 247.2 193*6 245.1 238.2 218.6 194.9 63.99 63.55 59.45 56.63 48.46 -.1195 -.1670 -.2506 -.4169 -.7800 -.1173 -.1612 -.2310 -.3720 -.3505-10.083-9.623-9.257-8.941-3.651-10.028-9.371-9.181-9.08? - 8.531-10.943-10.379-10.031-9.797-9.432 120*96 115-19 103.26 89.52 71.35 98.54 90.89 32.33 73*22 27.35 26.44 25*19 23.89 20.60 4.194 4.012 3.779 3.605 3.243 4.213 3.977 3.758 3.523 3.250.5306.4825.4432.4125.3794.4783.4626.3988. 38R8.3370. 1543. 1387.1294. 1233.1140 1 * x lo 3 71.75 50.75 30.07 2 2.3 2 14.53 63.12 44.73 29.14 20.15 63.02 44.37 27.04 20.72 13.64 60.27 47.30 31.50 20.90 14.02 69.76 43.37 33.39 22.10 13.42 63.25 44.85 26.51 19.76 13.15 64.31 44.28 28.50 20.64 13.54 61.96 48.10 30.67 24.61 18.70

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 3 3 70.41 49-53 29.04 21.43 13.89 4 62.44 44.06 28.50 19.57 5 62.03 43.59 26.24 20.23 13.28 1 61.15 42.72 19.39 13.20 6 62.45 43.64 30.44 20.41 12.72 2 62.51 44.38 26.27 19.60 13.0"5 7 63.60 43. 85 23.25 20.50 13.46 3a 61.83 43.01 30.6? 24.56 18.67 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. 35 - 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 3.53313.53420.55651.53902.54433.53915.53972.54164.54418.56492.56549.56639.56729.57000.60018.60075.60224.60339.60000.60030.60165.60259. 603-37.64096.64038.64160.64?54.64374.64096.64124.64349.64333.64598. 66527. 66<75.66770.66327.6695? 5.1912 5.2087 5.2465 5.2975 5.3743 5.2896 5.2 9 9 0 5.3304 5.3719 5.7111 5.7204 5.7351 5.7498 5.7942 6.2877 6.2971 6.3214 6.3484 6.2848 6.2979 6.3118 6.327? 5.3431 6.9547 6.9452 6.9651 6.9305 7.0001 6.9547 6.9609 6.9960 7.0024 7.0351 7.3522 7.3764 7.3920 7.4013 7.4217 3.094? 3.1117 3.1496 3.1916 3.2774 3.1933 3.2024 3.2337 3.2743 3.6143 3.6236 3.6383 3.6530 3.6973 4.1912 4.2005 4.2249 4.2519 4.1878 4.2009 4.2153 4.2302 4.25H 4.8573 4.848? 4.8682 4.8336 4.9032 4 3873 4*. 3640 4.8991 4.9055 4.9381 5.2570 5.2808 5.2958 5.3049 5.3252. 802 822.851 368 83?.809.828.852.870.809.837.855.8 6 9.888.809.829. 370.888.809.828.848.869.891.308 827.355, 870. 838. 308.826. 852.869.839 80 s '.823.847.859.873 2.9026 2.9415 3.0094 3.0666 3.1732 3.009? 3.0385 3.0946 3.1533 3.430? 3.4586 3.5022 3.5310 3.5941 4.0071 4.0376 4.1039 4.1487 4.0036 4.0368 4.0716 4.1082 4.1509 4.6726 4.683? 4.7321 4.7626 4.8000 4.6726 4.6980 4.7599 4.7335 4.8360 5.071? 5.1116 5.1516 5.1729 5. 2072 12.51 11.44 9.79 A, A? 6.71 9.79 9.15 3.05 7.03 3.71 3.48 3.14 2.94 2.54.984.917.787.710.992.919.848.780.707.213.207.185.173.159.213.200.174.165. 146.0348.0766.0722.0672.0611 42.409 27.907 13.744 8.539 3.451 33.353 22.134 12.261 6.653 19.493 12.736 6.474 4.205 1.687-12.139-8.033-4.090-2.595-1.145-12.648-8.162-4.617-2.854-1.257-15.319-11.387-6.412-4.716-3.040 104.319 69.437 34.739 21.970 9.344 87.336 57.856 32.511 18.047 73.524 43.3?6 24.937 16.434 6.969 53.046 34.597 11*188 5.113 54.333 35.539 22.35? To VA? 4! 650 18.134 11.993 6.051 3.846 1.675 17.698 11.406 6.437 3.965 1.725 7.?5* 5.236 3.283 2.41? 1.552 ">0.001 13.623 7.301 4.39? 2.44? 20.130 13.583 7.989 4.741 34.52? 22.854 I I.9 3 9 S. 028 3.594 53.24? 34.7?1 11.346 5. 260 54.536 35.72???. 32? 12.434 4.791 42.412 23.070 14.226 9.036 3.964 42.994 27.731 15.671 9.674 4.239 3?.494 28.610 16.107 11.844 7.63? 80.50 77.3? 70.96 64.33 52.30 64.03 62.74 33.3? 53.17 24.30 23.79 23.00 22.23 20.08 6.439 6.302 5.95? 5.599 6.489 6.297 6.099 5.886 5.609 1.438 1.41? 1.386 1.30.8 1.250 1.388 1.368 1.261 1.243 1.153.5533.5233.5060.4956.4730 64-80 5979 5021 413? 2737 4106 3937 3408 2827 590.7 566.0 529.0 494.4 403.1 41.46 3 9.7 2 3 5.5 0 31.35 42.11 39.65 37.19 34.6 5 31.46 2. 214 2.Oil 1.922 1.710 1. 562 1.925 1.071 1.591 1.545 1.329.3 0 6 2. qy 44! 2561.2456.2 237 3 3 5.7 3 1 0.8 279.9 250.0 195.0 246.9 240.0 330.2 196.0 64.44 6 2.7 0 59.71 56.89 43.61 -.1194 -.1671 -.4192 -.7769 -.1194 -.1628 -.2314 -.372? -.8523-9.960-9.506-9.348-9.923-3.536-9.916-9.739-9.049-3.947-3.395-10.790-10.219-9.884-9.639-9.264 1 2 3.^ 5 117.30 105.30 90.14 70.85 94.09 92.46 33.75 74.28 27.75 26.77 25.43 24.14 20.79 4.161 3.993 3.600 3.2 2 2 4.??6 3.985 3.748 3.509 3.242.5177.4708.4519.4017.3695.4677.4549.3874.3770.3265. 1500.1345.1256.1206.1100 71.77 50.76 30.03 22.34 14.57 63.13 44.74 29.15 20.16 6 3.0 1 44.37 27.04 20.71 13.63 69.19 47.23 20.89 14.01 6 9.6 8 48.30 33.35 22.09 13.41 63.24 44.84 26.50 19.76 13.15 64.30 44.28 28.50 20.64 13.54 61.96 43.10 30.67 24.61 18.70

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 XlO3 8 70.41 49.53 29.04 21.43 13.39 4 62.44 44.06 27.50 19.57 5 62.03 43.59 26.46 20.23 13.23 1 61.16 42.79 19.29 13.20 6 6 2. 4 5 43.64 30.44 20.41 12.72 53459 535'? 53803 54040 54601 54070 54126 5 4 5 3 5 5 6 * 9 1 56747 56341 56933 57712 60305 60365 60517 60690 60361 60453 60550 60676 5.1393 5.2066 5. 3 4 4 6 5. 8328 5.3730 5.2376 5.2965 5.3286 5.3706 5.7086 5.7176 5.7387 5.7475 5.7924 6.8910 6.3007 6.3851 6.3530 6.2879 6.3000 6.3143 6.3304 6.3507 3.0923 3.1096 3.1477 3.1359 3.2761 3.1913 3.2001 3.2320 3.2730 3.6118 3.6208 3.5359 3.6507 3.6955 4.1945 4.2041 4.2236 4.2564 4.1909 4. 2 0 3 0 4.2178 4.2334 4.2537 301 2.8993 12.60 42.400 321 2.9339 11.51 27.900 350 3.OO65 9.35 13.737 863 3.0599 3.73 8.524 336 3.1709 6.75 3.447 803 3.0061 9.36 33.346 327 3.0351 9.82 22.127 851 3.0919 8.09 12.257 869 3.1518 7.05 6.651 808 3.4:266 3.74 19.490 827 3.4553 3.50 12.734 354 3.4933 3.16 6.472 868 3.5277 2.97 4.202 88 7 3.5913 a. 56 1.686 308 4.0093.979 323 4.0402.912 869 4.1066.732 337 4.1522.704 303 4.0057.937 ft 97 4.0330.916 846 4.0726.846 367 4.1094.777 891 4.1535.702 104.310 69.430 34.732 21.955 9.340 87.329 57.849 33.507 19.045 73.521 48.324 24.935 16.431 6.967 53.046 34.598 11.239 5.119 54.338 35.539 22.353 12.328 4.650 20.010 13.630 7.303 4.90? 3.446 20,137 13.595 7.993 4.743 34.541 29.856 11.991 8.031 3.596 53.242 34.780 11.345 5.239 54.535 35.722 22.522 12.434 4.791 60.85 77.70 71.17 65.18 52.95 64.38 6 3.0 8 58.62 53.23 24.44 23.95 23.13 2. 35 20.16 6.391 6.250 5.907 5.541 6.444 6.266 6,056 5.842 5.576 6537 6037 5065 4248 2804 4144 3930 3438 2833 597.5 573.4 534.9 499.7 406.4 40.84 39.0? 34.90 30.70 41,53 39.26 36.67 34.13 31.09 327.1 312.2 221.1 253.1 197.4 248.1 241.3 221.3 196.2 64.80 63.09 60.03 57.17 48.77 -.1179 -.1647 -.4130 -.7625 -.1170 -.1615 -.2892 -.3633 -.8419 124.31 118.51 106.43 94.95 73.43 95.02 93.52 84.43 74.47 23.07 27.12 35.72 24.42 20.98 4.099 3.937 3.538 3.154 4.163 3.946 4.695 3.456 3.303 71.78 50.77 30.09 22.35 14.59 63.13 44.74 29.15 20.1? 62.99 44.37 27.04 20.72 13.64 68.09 4?. 22 20.87 14.01 69.58 48.29 33.33 22.07 13.41 2 68.51 44.33 26.27 19.60 13.03 7 63.60 43.35 2 2. 2 5 20.50 13.46 64285 64415 54543 64640 a 64476 64513 64737 64778 64979 6.9315 6.9524 6.9730 6.9386 7.0076 6. f. 7.0043 7.0109 7.0432 4.3346 4.8555 4.8761 4. 3917 4.9107 4.8653 4.3721 4.9073 4.9139 4.9463 807 4.6433.225-12.139 826 4.6895.204-8.038 354 4.7390.132-4.079 868 4.7637.170-2.595 887 4.3065.156-1.144 306 4.6779.210-12.648 824 4.7039.198-8.162 851 4.7'c;71.171-4.617 868 4.7909. 162-2.354 887 4.3420.144-1.256 13.134 11.994 6.050 3.846 1.676 17.698 11.406 6.437 3.966 1.726 4'% 412 28.070 14.226 9.035 3.964 4^.994 27.730 15.671 9.673 4.238 1.464 1.395 1.330 1.3 2 3 1.223 1.364 1.343 1.238 1.919 1.132 2.142 1.946 1.769 1.64? 1.509 1.859 1.803 1.532 1,486 1.281-9.797-9.349-3.969-8.653 - g.387-9.774-9.607-8.877-8 ".774-8.238.5010.4553.4161.3869.3569.4516.438. 3730.3626.3145 63.23 44.84 26.50 19.76 13.15 64.29 44.28 28.50 20.64 13.54 3a 61.33 48.01 30.62 24.56 18.67 7.3604 67105 7.3353 67199 7.4005 67 260 7.4103 67383 7.4309 5.2652 5.2897 5.3043 5.3139 5.3343 80? 5.0739.0834-15.319 21 5.1134.0761-11.337 24 f) 5.1590.0693-6.412 553 5.1809.0559-4.716 372 5.2153.0609-3.040 7.856 5.336 3.293 2.412 1.552 38.494 22.610 16.107 11.844 7.832.5430.5139.4962.4355.4631 2949.2634.2463.2357.2145-10.590-10.012-9.692-9.490-9.070.1445.1391. 1208.1157.1055 61.96 48.10 3 0. 6? 94.61 18.70

51 Table 2.10. The experim ental values of term inal voltage, ionic strength, m olality, terms of equation 23 derived from these Hun xlo3,q 70.41 49.53 79.04 21.43 13 0 9 4 6 2.4 4 44.06 23.50 19.57 5 52.03 43.59 26 46 20.23 13.28 1 6 1.1 5 48.72 19.29 13.20 6 62*45 43.64 30.44 20.41 13.72 2 62.51 44.38 19 'J o 13.03 7 6 3.6 0 43.85 28.25 20.50 13.46 3a 61.33 43.01 30.62 24.56 18.57 q u a n titie s and the second approximation of ionic strengt 4$ Centigrade v o l t s.53600.53708.53953.54137. 54?64 542 20.54279.54477.54739.56328.56936.57041.57133.57419.60587.60654.60 04.60989.60568.50638.60740.60339.60971.64660.64793.64924.65028.65143..54.354.64399.65124.65169.65375.67374.67530.67629.67690, 679,82 tjj <:; «*.O' PWH -log 3 K+ B * - B Jp i r X Y r 2 uv X lc 4 3 5 -.1 0 9 3 xlo xlo xlo3 xlo3 xlo xlo xlo6 xlo xlo 3.1910 5.2051 5. 2468 5.2339 5.3753 5.2392 5.2985 5.3299 5.3714 5.7113 5.7194 5.7360 5.7506 5.7959 6.2977 6.3093 6.3321 6.3514 6.2947 6.3058 6.3219 6.3376 6.3585 6.9429 6.9639 6,9847 7.0002 7.0194 6.9736 6.9806 7.0164 7.0235 7.0561 7.3728 7.3975 7.413? 7.422.8 7!4437 3.0 9 4 0 3.1 1 1 1 3.1499 3.1870 3.2734 3.1928 3.2020 3.2332 3.2746 3.6150 3.6 6 2 6 3.6392 3.6537 3.6990 4.2012 4.2118 4.2355 4.2648 4.1977 4. 2083 4.2249 4. 2406 4.2595 4.3459 4.8670 4.8377 4.9033 4.9224 4.8767 4.8337 4.9195-4, 9266 4.9592 5* 2773 5.3019 5.3170 5.3 2 6 4 5.3 4 7 2.793 2 1R 346.863.8 8 4.804. 824 850.8 6 7.804.A 03.851.86*.886.806.825. 86?. 88$. 804.824. 844 ST!890.803.8 2 3.8 5 1. 86* 1836. 803. 823.848.86$. 886. 803.819.843 O : c* t j.569 2.5930 2.9367 3.0047 3.0590 3.1714 3.0033 3.0339 3.0920 3.1306 3.4255 3.4534 3.4991 3.5257 3.5949 4.0139 4.0447 4.1115 4.1587 4.0083 4.0406 4.0775 4.1146 4.1533 4.6553 4.6878 4.7476 4.7783 4.3173 4.6361 4.7135 4.7763 4.8006 4.3540 5.0369 5.1285 5.1*87 5.1903 5.225? 12.65 11.57 9.89 8.73 6.74 9.9? 9.25 3.09 7.07 3.75 3.52 3.17 2.96 2.54.969.902.774.694.931.911.836.768.695. 221.201.179.167.15?.206.193.167.158.140.0891.0744.0678.0645.0595 42.395 27.794 13.733 S. 523 3.448 33.840 22.124 12.257 6.649 19.489 12.732 6.471 4.203 1.688-12.138-8.037-4.079-2.594-1.143-12.648-8.162-4.616-2.594-1.256-15.319-11.386-6.412-4.716-3.040 104.305 69.424 34.778 21.954 9.341 37.823 57.846 32.507 18.043 73.520 48.322 24.934 16.432 6.969 53.047 34.599 11.190 5.120 54.339 35.540 22.353 12.329 4.651 16.134 11.994 6.050 3.846 1.676 17.693 11.406 6.433 3.B4B 1.726 7.856 5.337 3.233 2,413 1.552 20.015 13.636 7.313 4.903 2.445 20.143 13.598 7.998 4.745 34.542 22.358 11.992 8.030 3.594 53.241 34.779 11.344 5.253 54.535 35.7? 2 2!521 12.483 4.790 42.411 28.069 14.225 9.035 3.9*3 42.994 27.730 15.670 9.673 4.233 33.494 50.609 16.107 11.844 7.632 80.54 77.41 70.31 65.01 5 2.6 7 64*1$ 6 2.3 1 5 3.4 5 53 *14 24,2? 23*35, 22.95 22.20 20.00 6.293 6.141 5. Q14 5*435 6.343 6.123 5*950 5.7 4 6 5.5 0 1 1.426 1.333 1.225 1. 250 1.195 1.323 1.30? 1.204 1.194 1.099.5273.4990.4319.4716.4496 6485 5992 5014 2775 4115 394$ 3415 2924 588,8 $ 6 3.7 5 2 6.8 492.7 400.0 39.60 37.71 33.30 29.54 40.24 3. 23 35.49 33.02 30.2^ 2.033 1.845 1.677 1.561 1.430 1.7*5 1.709 1,449 1.402 1.20? " J 6>^.2490.2323 2224.2021 325.3 3 U.0 279.4 252.4 194.4 247.2 240.2 220.4 195.5 64.32 62.83 59.57 56.77 48.43 -.1149 -.1601 -.4020 -.7365 -.1145 -.1585 -.2229 -.3560.0214-9.5 4 4-9 103-5.730-5.4 >5-5.138-9.493-9.355-8.6 3 2-8.520-7.992-10.292-9.735-9.412-9.219-8.806 123.87 117.70 105.67 94.49 72.63 94.37 92.73 84.00 74.26 27.66 26.90 25.34 24.08 20.63 3.975 3.791 3.427 3.033 4.044 3.843 3.576 3.343 3.117.4755.431''.3943.5351. 4237.4155.3527 *3420.2962.1221.1140.1092.09941 71.79 50.78 30.09 22.35 14.59 63.13 44.75 29.15 20.17 62.97 44.37 27.04 20.72 13.63 63.00 47.13 20.35 14.01 69.54 48.21 33.3? 22.06 13.41 03.23 44.84 26.50 19.76 13.15 64. 29 44. 28 28.50 20.64 13.54 61.96 48.10 30.67 24.61 18.70

5a Table 2.1 1. 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. 41.53732 5-1921 3.0951.797 2.3931 12.65 42.395 104.905 20.015 80.19 6430 324.4 122.79 71.79 49-53.53345 5.209? 3.U 2 7.'317 2.9371 1 1.5 6 27.395 69.425 13.535 77.14 5951 3 1 0.0 116.3? 50.73 29.04.54083 5-2468 3.1499.345 3.0037 9.91 13.731 34.776 7.314 7 0.8 1 5014 279.6 105.42 30.09 21.43.54331 5-2855 3.1886.8 6 2 3.0596 8.72 8.524 21.955 4.907 64.77 4196 251.5 93.78 22.35 13.39.54921 5-3TT5 3.2 8 0 6.833 3.1736 6.7 2 3.450 3.343 2.443 52.41 2747 193.5 71.32 14.59 4 62.44.54367 5-2911 3.1959.804 3.0053 9.398 33.844 97.927 20.139 63.36 4073 346.1 93.52 63.13 44.06.54427 5-3004 3.2039.923 3.0347 9 I23 22.1 2 6 57!348 13.596 62.53 3910 239.2 91.89 44,74 2 8.5 0.54629 5-3319 3.2353.846 3.0900 8.13 12.253 32.503 7.997 5. 17 3384 219.4 83.25 29.15 19.57.54339 5-3725 3.2757. 866 3.1507 7.07 6.649 19.043 4.745 53.00 2809 195.3 73.33 20.17 5 62.03.57073 5-T139 3.6171.804 3.4276 3.74 19.490 73.521 34.541 24.15 5-33.2 64.02 27.40 62.95 43.59.57123 5-7209 3.6241.323 3.4549 3.51 12.733 49.333 22.857 23.77 564.8 6 2.6 2 26.71 44.37 2 6.46.57243 5.7396 3.6428.8 5 0 3.5 0 1 6 3.15 6.473 24.936 11.990 22.76 5 1 8.2 59.09 24.92 27.04 20.23.57330 5-7332 3.6563.867 3.5323 2.93 4.206 16.435 3.027 22.07 486.9 56.47 23.78 20.71 1 3.2 8.57626 5-7993 3.7024.335 3.5963 2.53 1.6 8 8 6.970 3.593 19.34 393.7 43.06 20.79 13.64 1 61.15,60372 6.3055 4.2090.304 4.0195.956 53.043 53.240 6.180 32.20 -.1114 3.333 63.00 48.72.60941 6.3163 4.2193. 8 84 4.0517.888 34.600 34.778 6.029 36.35 -.1547 3.654 47.13 19.29.61094 6.3402 4.2436 * 866 4.1186.761 11.191 11.343 5.707 32.57 -.3 8 8 1 3.301 20.35 1 3.2 0.61301 6.3724 4.2759.2-85 4.1699.676 5.1 2 1 5.297 5.293 28.07 -.6998 2.831 14.01 6 6 2.4 5.60853 6.3026 4.205-6.804 4.0162.963 54.341 54.533 6.2 2 9 38.00 -.1104 3.394 69.49 43.64.60923 6.3135 4.2166.884 4.0434.895 35.542 35.720 6.073 36.83 -.1539 3.707 48.20 30.44.61030 6.3302 4.2339.842 4.0359.821 22.355 22.519 5.863 34.37 -.2153 3.462 33.30 20.41.61128 -.3455 4.2485.864 4.1225.754 12.331 12.431 5.643 31.35 -.3452 3.223 22.05 12.72.61266 6.3670 4.2700.8 8 9 4.1673.6-30 4.653 4.739 5.370 28.34 -.7344 2.963 13.41 2 6 2.5 1. 6503s 6.9552 4.8583.803 4.6677.215-19.138 19.134 42.411 1.386 1.921-9.276.4496 63.23 44.33.65177 6.9769 4.8800.832 4.7097.195-8.037 11.994 28.069 1.318 1.733 Q#R35.4063 44.84 26.27.65303 6.9966 4.3996.850 4.7534.174-4.079 6.050 14.225 1.260 1.563-3 ; 494.3733 26.50 19.60.65399 7.0115 4.9146.866 4.7396.162-2.594 3. 846 9.035 1.217 1.482 *8.2 1 0.3481 19.76 13.08.65539 7.0334 4.9364. 885 4.3303.148-1.143 1.6 7 6 3.963 1.158 1.340-7.896.3169 13.15 7 63.60.65235 6.9844 4.3875.803 4.6969.201-12.647 17.699 42.993 1.296 1.679-9.259.4073 64.29 43.85.65232 6.9933 4.8964.321 4.7250.188-8.161 11.407 27.729 1.270 1.612-9.033.3913 Ait OP 28.25.65508 7.0285 4.9316.847 4.7374.163-4.616 6.438 15.670 1.171 1.370-3.392.3335 2 3.5 0 20.50.65552 7.0354 4.9335 864 4.8115.154-2.853 3.966 9.672 I.I 52 1.327-8.288.3238 20.64 13.46.65764 7.0635 4.9715.885 4.8653.136-1.256 1.727 4.238 1.068 1.140-7.764.2796 13.54 3a 61.33.67801 7.3861 5.?909.803 5.1003.0794-15.319 7.85-6 38.494.5113.2619-9.930. 12340 61.96 48.01.67958 7.4106 5.3150.818 5.1405.0724-11.386 5.937 28.609.4342.2344-9.445.11491 43.10 30.6?.63056 7.4259 5.3297.841 5.1793.0662-6.412 3.983 16.107.4630.2190-9.140.10745 30.67 24.5s.63136 7.4369 5.3404.853 5.2023.0629-4.716 2.413 11.844.4567. 2086-3.926.10739 24.61 13.67.68258 7.4574 5.3608. 962 5.2373.0573-3.040 1.552 7.632.4357.1393-3.532.09333 18.70

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 2.3026 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 X2.3036 xlo ' 0 0.33652 0.054201 0.4883 0.3241 5.33404.055194 '.4921.3349 10.33140.056186.4960.3358 15.22854.057178.5000.3266 30.2255?.058170.5043.3273 35.22345.059163.5085.3281 30.21918.060154.5130.3290 35.21571.061146.5170.3297 40. 21214.062138.5221.3305 45.20829.063131.5270.3314 50.20439.064123.5319.3521

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 0.06 0,05 0.04 0,03 0.025 0.0 0 0 0.014 0.06 0.03 0.04 0.03 0.025 0. 020 0,i314 0 2 6 6.8 261 *5' 253.1 238.4 225.2 305.2 170.0 30,,65 81,,00 7 0,,65 73.,35 6 8, 45 61.55 51.35 5 278.1 271.9 062 6? * 247.5 234.0 213 0 Lf O 173 0 90,*45 S3,.15 35.,00 79.;bo 74, 75 67.60 53.95 10 2^8.0 881.3 27 i.3 255*0 240*9 219.5 176.0 97 <,40 «94, 75 91.,40 85.,40 79.,80 7.1.70 59 15 296.5 289 *2 379.1 262*2 246.3 223.0 181.0 :103.;ao 1100.,70 97.140 90, 70 33. 75 74.80 6 2,.0 0.6 5 20 3 0 3. a 296.7 286.2 26. 4 251.1 025,0 104.4 109. 15 106. 30 100.,65 95. ]Q qr,5; 90 79.0 0 65'.20 25 310*5 302 *7 291.9 273.4 2 5 6.6 230.4 1*6.0 113. 85 110. 95 107.,00 99.95. 92! 55 81,60 67, 30 30 3 1 6.0 308 *8 ; 296 *3 277.2 2 6 0.1 233 *6 189. 6 118. 05 115.,00 111.,00 103,,15-95. 10 84.35 69, 70 35 316*4 310.1 398.6 279.6 262.7 237,0 190.0 100 *,30 117,,00 118. 60 105.,30 97. 50 86. 85 71, 50 40 320*1 311 *7 300 0 280*8 264.8 240.3 190.6 101. 60 118,, 20 113.,'65 106,,30 99. 75 89.50 71,.80 45 319*0 310 *4 299.8 *279.2 264.1 040.5 190.0 100 *.65 117 i 40 118.,35 105., 60 99.,20 89.0 0 70,.80 50 317*5 309 *3 299 *6 279.2 8 6 3.6 239 *0. 18.0 119*70 1 1 6..65 112, 40 105. 30 98. 75 8^.2 0 70,.00 0 206.3 204.0 198 8 18-.4 130,0 169.1 64. 82 64. 32' 6 2..85 58, 80 55. 95 52.75 5 2 1 6.0 813.4 XT 0 197.0 137,6 176. 4-71. 33' 70. 90 69. 08 64.,82 61. 33 57.84 10 224.0 280.4 214.1 207.8 194.0 m.6 77. 0 0 76. 50 T44 60 69.,42 6 5. 85 62.12 15 231*0 OOJ 0 :-J O 231.6 208.8 199.1 1 5- q 81. 78' 81. 33 7 S. 06 73. 63 69. 80 ' 63.60 20 238.2 233.0 227.1 213." 203.0 189.4-86. 17 85. 43 83* 11 77. 50 73. 33 6B.78 23 243.1 237.0 231*3 217. B' 205.5 192.2-89. 10 8 0. 57 X, Q.<.? 52' 80. 50 76. 12 71.20 30 244.4 241 234.6 220,6 203.9 194.7 92. 40 91.*68 89. 48- S3. 15 78. 48 73.0,6 35 246.4 243 0 236 *3 228*0 210*0 195.4 94. 00' 93. 40 90. 96 84. 52 79. 65 74.10 40 247.5 244.9 237.5 223* 2 211.0 195.9 94. 98 94. 38 91. 8 5 ' 85. 30 80. 18 74,.30 45 246.6 243.2 336 2 228. 8 010.6 195.4 94. 30 93. 80 91. 00' 84. 30 79. 80 74.10 50 245.5 242 *2 233.1 201.2 210.0 194.8 93. 40' 92. 80 90. 40 84. 0 0 79. 23 73..75 0 5 56,41 55. 60 54. 70 53.23 52.25 30. 15 44. 50 01, 00' 20. 77 20. 33 19. 30 19. 37 IB, 58 16. 70 10 5 '\5 q 57* 72 56. 72 55.37 54.10 31. 92 43. 95 29. 30 02. 43 21. 96 21. 40 80, 91 19..96 17. 82 15 60*30 59*.41 58* 35 36*90 33.57 33. 20 47. 13 24. 2? 03. 76 23. 25 22. 64 00 l.. 1:0 20,.98 IB. 72 20 61.73 60. q5- *59. 79 5B.2B 5 6,8 8 54. 40 43. 00 83. 50 24. 98 04, 4* 23. 80 03. 84 20.,08 09. 63 25 62.93 62.;0 2 60. 95 59*38 57.93 53. 45 43. 90 06. 48' 25. 97 05. 41 04. 73 24, 15 23, 03 20. 38 30 64.75 6 2. 91 61. 85 60.23 5-8 78 56. Q8 49. 35 27. 21 of. rv vo 0 6. 28 85. 52 84. 91 03-56. 37 fn 20. 94 33 64,33 63. 38 62, 18 60.50 59*. 02 49. 35 0 7. 60 27, 10 06. 51 25. 75 23* 13 23..90 21. 07 40 64.58 63. 70 6 2. 55 60.85 59.32 56. 65 49. 73 07. 94 27. 44 0 6]86 of 05 25. 42 04, Ip 21.,24 45 64.16 6 3. 35 62. 30 60.37 58.80 56. 25 49. 05 07. 56 07. 17 06. 64 25. 73 25. 01 03.*86 01. 00 50 63.80 63. 21 6.0.03 59.97 53*33 56. 00 48. 70 87. 30 pf» ' 096 26. 42 85. 36 04, 61 83. 57 20. 83

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 0.0 6 0.0 5 0.0 4 0.0 3 0.0 2 5 0.0 2 0 0.0 1 4 0.06 0.05 0.0* 0.03 0.005 0.0*0 0.014 Hun t 0,<*iV* 1 0 *101.1 2 1.1 5 2 5 *111.1 3 1.1 6 4 & 10.1 1 9.1 4 1.1 7 6 15 *123.146.1 8 1 6 20.1 3 0.1 3 0.. 189 25 *134.1 5 5.1 9 3 30. 136.1 5 9. 196 35 *134.1 5 9.1 9 4 40 130 4138.1 9 1 45.1 2 5.1 5 2.1 8 4 50 * 126.1 4?. 181.2 0 3.258. 344.6 2 5. 221 272.3 6 9 '.6 7 3.2 3 8.292.3 94.710.2 4 2.298.4 0 0.7 3 7.2 5 5.3 1 1.4 2 7.7 6 7.2 5 7.314.4 3 9.7 7 4.2 6 0.316.4 4 4.7 3 0.2 6 5.3'20.4 4 1.777. 253.3 2 2.4 3 8.763-.25i.313.4 2 8.7 3 7.2 4 1.297.4 1 2.700 3.134 3.435 3* *^5 3 X 9 2 4.114 4.010 4.370 4.3«3 4.060 3.9 2 S 3.784 3.115 3.355 3.577 3.330 3.965 4.05'? 4.175 4.1X0 3.966 3.334 3.702 3.037 3.270 3.485' 3.6 4 0 3.748 3.843 3.895 3.895 3.853 3.718 3.593 2.938 3.162 3.363 3.502 3.613 3.693 3.738 3.736 3.638 3.570 3.435 2.953 3.081 3.376 3.396 3.318 3.590 3.636 3.632 3.372 3.463 3.342 2.753 2.973 3.157 3.260 3.390 3.454 3.300 3.490 3.4aa 3.3 3 3 3.2 0 3 2.600 2.790 2.960 3.070 3.170 3.315 3.2 5 3 3.250 3.190 3.090 3.935 2 0-9.2 1 6-9.0 8 0-8.9 2 0 5 9.4 6 2 9.3 3 6 9.1 7 2 10 9.6 7 6 9.5 3 3 9.3 1 6 15 9.736 9.6 4 4 9.4 6 6 20 9.9 3 7 9.7 6 0 9.5 5 2 25 9.9 7 0 9.7 7 6 9.5 6 0 30 9*948 9.7 5 5 9.5 4 3 35 9.7 9 8 9.630. 9.4 4 7 40 9.6 5 2 9.4 8 5. 9.3 0 0 45 9.4 1 2 9.2 1 7 9.0 8 2 50 9.0 3 8 8.9 3 0 3,7 9 0 7 0-9.2 4 5-9.2 1-9.1 0 5 9.5 4 0 9.4 9 9.3 8 10 9.7 8 5 9.7 1 9.5 2 15 99925 9.8 5 9.66 20 10*010 9.9 1 9.7 3 25 1 0.0 1 0 9.9 1 9.7 3 30 10.000 9.9 2 9.7 7 35 9.9X 0 9.8 4 9.6 8 40 9.7 6 0 9.6 8 9.5 1 45 9.4 9 0 9.4 2 9.2 4 50 9.2 4 0 9.1 5 3.96 >8*710-8.5 6 8-8. 370': -7,9 5 0 3.9 5 2 8.8 2 0 8,6 4 7 S. 418 9.1 4 2 9.0 0 0 8.8 3 0 8.5 9 4 9.2 4 0 9.0 9 8 8.9 3 0 8.6-7 9.3 0 4 9.1 5 8 8.9 9 0 8,7 5 9 9.3X 3 9.1 6 9 9,0 0 5 8,7 < 5 9.3 1 0 9.15S 8.9 7 0 a. 700 9.1 9 0 9.0 3 0 8,5 8 0 9.0 7 8 8.9 2 2 8,7 20 8,4 3 0 8,8 32 8.6 6 2 8,4 6 4 8,1 3 3 8.5 9 0 8.4 3 6 3,2 4 0 7.9 5 5 >8.85-8.6 6-8..40-7,9 6 9.1 3 9.9 2 8.6 4 8,2 1 9.2 1 9.0 5 3.7 7 3.4 0 9.3 5 9.1 5 8.9 0 8.5 3 9.4 4 9.2 3 3.9 8 8.6 0 9.4 4 9.2 3 3.9 3 a. 60 9.4 9 9.2 9 9.02 8.58 9.3 8 9.1 6 8.8 7 8,4 0 9.2 1 8.9 9 3,7 2 8.2 9 8.9 3 8.7 1 8.4 5 8,0 4 8.6 6 8,4 5 8.1 9 7.7 7.04435.04675.04930.05040.05133.05175.05190.05025.04060.04575.04330.0403.0433.0452.0470.0473..0479.047"'. 0 4 '7.0453.0439.0407.04330.04535.04740.04860.04940.05000.04980.04343.0 4 * 9 5.04434.04200.0406.0431.0449.04*4.0470.047?.0471.04*2.0447.0474, -3403.04163.04570.04550.04660.04750.04830.04760.04643.04505.0 4 7 6 5.04043.0 3 9?.0416.0 4 3 3.0447.045?.0453.045?.0 4 4 3.0437.0405.0382.03955.04170.04325.04430.04515.04530.04500.04385.04270.04056.03830.03**.03,,r.040?.0 414.0470.0 4 7 1.0416.0406.0391.037?.0351.03815.04035.04190.04570.04360.04423,04335, 042.25,04110,03995,33675.0344.3366.0382.0393.0399.0400.0395. 0384.0370.0351.0332.03625.03375.04010.04105.041.3-0.04230.0 4 1 4 5.04045.33930.0371?.03500.0334.0343.0359.0370.0376.3377.0.571.3361. 034?.0329.0310.03390.03643.03765.03860.03925,0 2 9 6 0.03835.03800,03650.03460.03255.0295.0313.0323.0337.0342.0 3 4 4.0339.0329.0317.0293.0282

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.0 5 0.04 0.03 0.025 0.020 Sun t 0 0-9.99-9.82-9.60-9.30-9.11-8. 9 5 10.34 10.17 9.96 9.64 9.43 9.19 10 10.60 10.40 10.15 9.82 9-61 9.37 15 10.75 10.54 10.30 9.96 9.75 9.51 20 10.83 10.65 10.40 10.0? 9.85 9.59 25 10.79 10.65 10.40 10.07 9.85 9.59 30 10.65 10.57 10.32 9.99 9.76 9.49 35 10.43 10.43 10.18 9.85 9.63 9.34 40 10.33 10.23 10.00 9.6? 9.45 9.16 45 10.16 9.97 9*72 9.38 9.21 9.89 50 9.840 9.65 9.43 9.10 8.89 8.60 X xlo 0.0176.0174.0169.0162.0156.0152 5.0186.0132.0173.0171.0165.0159 10.0195.0189.0183.3175.0170.0163 15.0199.0193.0137.0178.0173 -..0166 20.0201.0196.0109 0130.0175.0168 25.0200.0196.0190.0181.0175.0163 30.0198.0194.0188.0180.0174.0166 35.0193.0188.0183.0176.0170.0162 40.0137.0183.0173.0171.0165.0158 45.0190.0176.0171.0165.0159.0152 50.0172.0169.0164.0158.0153,0146

57 fabl 5 Slopes of th e plots of X against 1Cobtained fro Figures 2.1 to 2.11. Io n ia S tren g th 0.0 6 0.0 5 0.0 4 0.0 3 0.0 2 5 0.0 2 0 0.0 1 4 T em perature 0 0 2.9 9 0 2.9 9 5 3.0 1 4 2.9 7 0 2.9 5 7 2.9 0 7 2.9 2 3 5 3.1 3 9 3.1 2 4 3.1 2 3 3.1 0 0 3.0 5 9 3.0 3 2 3.0 5 8 10 3.2 7 3 3.2 6 1 3.2 7 0 3.2 3 1 3.2 1 5 3.2 3 3 3.2 2 6 15 3.3 5 7 3.3 8 6 3.3 8 2 3.3 4 9 3.3 2 8 3.3 2 5 3.2 9 7 20 3.4 8 0 3.4 7 6 3.4 7 5 3.4 4 5 3.4 5 0 3.4 2 5 3.3 7 0 25 3.5 4 0 3.5 3 5 3.5 3 0 3.5 3 0 3.5 1 9 3.5 1 3 3^480 30 3.6 1 2 3.6 2 0 3.6 3 0 3.5 9 4 3.5 8 6 3.5 6 1 3.5 3 5 35 3.6 4 3 3.6 4 0 3.6 4 3 3.6 3 3 3.6 1 0 3.6 0 1 3.5 7 6 40 3.6 7 0 3.6 6 3 3.6 7 2 3.6 5 6 3.6 3 5 3.6 1 9 3.6 0 4 45 3.6 6 5 3.6 6 5 3.6 6 0 3.6 5 3 3.6 2 0 3.5 9 8 3.5 8 0 50 3.6 3 5 3.6 3 5 3.6 5 5 3.6 3 2 3.6 1 5 3.6 0 5 3.5 9 0

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 50 0. Ionic strength Ofl 0.0 6 0.0 5 0.0 4 0.0 3 0.0 2 5 0.0 2 0 0.0 1 4 0 3-5 2 4 3 3.5 2 3 6 3.5 2 0 9 3.5 2 7 2 3.5 2 9 1 3.5 3 6 5 3.5 3 4 2 5 3.5 0 3 2 3.5 0 5 3 3.5 0 5 4 3.5 0 7 2 3.5 1 4 4 3.5 1 8 3 3.5 1 4 6 10 3.4 9 5 1 3.4 3 6 6 3.4 8 5 5 3.4 9 0 7 3.4 9 2 8 3.4 9 0 4 3.4 9 1 3 15 3.4 7 4 0 3.4 7 0 3 3.4 7 0 8 3.4 7 5 1 3.4 7 7 8 3.4 7 8 2 3.4 3 1 9 20 3.4 5 3 4 3.4 5 8 9 3.4 5 9 0 3.4 6 2 3 3.4 6 2 2 3.4 6 5 3 3.4 7 2 4 95 3.4 5 1 0 3.4 5 1 6 3.4 5 2 2 3.4 5 3 5 3.4 5 3 6 3.4 5 4 3 3.4 5 8 4 30 3.4 4 2 3 3.4 4 1 3 3.4 4 1 3 ' 3.4 4 4 4 3.4 4 5 4 3.4 4 8 4 3.4 5 1 6 35 3.4 3 8 5 3.4 3 8 9 3.4 3 3 5 3.4 3 9 7 3.4 4 2 5 3.4 4 3 6 3.4 4 6 6 40 3.4 3 5 3 3.4 3 6 2 3.4 3 5 1 3.4 3 7 0 3.4 3 9 5 3.4 4 1 4 3.4 4 3 2 45 3.4 3 5 9 3.4 3 5 9 3.4 3 6 5 3.4 3 7 3 3.4 4 1 3 3.4 4 3 9 3.4 4 6 1 50 3.4 3 9 5 3.4 3 9 5 3.4 3 7 1 3.4 3 9 9 3.4 4 1 9 3.4 4 3 1 3.4 4 4 9 S x t r a p s la t e d V alua a(p<r%) 0.0 0 0 3.5 3 7 7 -.2 8 5 5 3.5 2 0 2 -.1 8 5 10 3.4 9 4 5 -.2 5 1 15 3.4 3 2 5 -.2 4 9 20 3.4 7 2 5 -.1 9 3 25 3.4 5 8 6 -.1 6 4 30 3.4 5 2 0 -.2 0 4 35 3.4 4 6 9 -.1 7 0 40 3.4 4 4 0 -.1 7 9 45 3.4 4 6 3 -.1 3 8 50 3.4 4 5 2 -.1 3 6

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 0 5 10 15 20 25 30 35 40 45 50 3 a.2 6 1 5. a m.1777.1 449.1 1 8 7, 2645 2202,1826.1 487. 1158.2 5 1 7,2 1 1 9, 1628.1 4 0 7.1 1 4 9 *253 8.2 105.1588,1 4 2 2,1 1 6 2 *2491,2 193.1 7 5 2,1 575.1 366 4.9 4 7 9 4.9 6 3 4 4.9 3 1 4 5.0 0 3 2 5.0 2 1 2 4.9 4 7 4 4.9 7 0 4 4.9 3 1 9 5.0 0 2 5 5.0 1 5 5 4.9 3 5 9 4.9 7 2 1 5.0 0 6 4 5.0 1 2 2 5.0 4 5 5 4.9 5 6 7 4.9 9 1 7 5.0 0 4 4 5.0 1 0 5 5.0 4 4 7 4.9 5 8 4 4.9 8 3 9 5.0 0 3 4 5.0 1 6 8 5.0 2 9 9 4.9 3 6 1 4.9 5 3 1 4.9 6 3 3 5.0 0 1 4 5.0 0 8 2 4.9 3 5 6 4.9 5 8 7 4.9 7 0 9 5.0 0 1 1 5.0 0 3 6 4.9 4 2 6 4.9 6 4 7 4.9 3 7 5 5.0 0 2 9 5.0 1 3 1 4.9 4 9 4 4.9 5 4 0 4.9 9 4 6 4.9 9 9 6 5.0 3 4 0 4.9 4 9 6 4.9 7 3 4 4.9 9 0 4 5.0 0 6 1 5.0 1 9 6 4.9 2 4 1 4.9 4 2 6 4.9 5 4 9 4.9 3 0 7 5.0 0 1 6 4.9 2 5 6 4.9 5 0 4 4.9 6 3 5 4.9 3 2 8 5.0 0 6 3 4.9 2 8 3 4.9 5 4 0 4.9 7 7 5 4.9 9 4 4 5.0 1 0 3 4.9 3 5 7 4.9 4 4 5 4.9 8 3 7 4.9 8 9 3 5.0 2 4 4 4.9 3 5 7 4.9 5 3 6 4.9 7 8 2 4.9 9 4 9 5.0 1 0 0 4.9 1 9 3 4.9 3 7 9 4.9 5 2 9 4.9 7 6 3 4.9 9 8 6 4.9 2 3 2 4.9 3 6 7 4.9 6 1 6 4.9 3 0 6 4.9 9 4 2 4.9 2 4 9 4.9 5 1 0 4.9 7 4 6 4.9 9 6 1 5.0 0 6 8 4.9 3 0 3 4.9 4 0 9 4.9 7 9 9 4.9 8 5 4 5.0 1 3 9 4.9 3 9 5 4.9 5 5 6 4.9 7 3 3 4.9 3 9 6 5.0 0 5 1 4.9 1 7 6 4.9 3 5 3 4.9 5 6 2 4.9 7 3 9 4,9 9 7 3 4.9 2 0 7 4.9 4 4 0 4.9 6 0 2 4.9 3 0 5 4.9 9 4 9 4.9 2 4 3 4.9 4 9 3 4.9 7 2 6 4.9 3 7 7 5.0 0 3 6 4.9 3 6 0 4.9 5 4 2 4.9 7 9 1 4.9 8 4 6 5.0 1 7 3 4.9 3 0 0 4.9 5 5 2 4.9 7 3 4 4.9 8 6 8 5.0 0 3 3 4.9 1 9 0 4.9 3 6 2 4.9 6 0 6 4.9 7 3 3 5.0 0 1 0 4.9 2 2 3 4.9 4 0 3 4.9 6 2 1 4.9 3 3 2 4.9 9 6 2 4.9 2 5 9 4.9 4 9 5 4.9 6 3 3.4.9 3 9 3 5.0 0 6 9 4..9323 4.9 4 4 7 4.9 7 9 8 4. 9R55 5.0 1 3 1 4.9 3 1 5 4.9 5 7 3 4.9 7 5 3 4.9 8 7 8 5.0 0 4 0 4.9 2 0 9 4.9 3 8 3 4.9 7 3 6 5.0 0 1 4 4.9 1 S 6 4.9 4 2 3 4.9 6 3 7 4.9 8 1 1 4.9 9 7 6 4.9 3 4 8 4.9 5 1 1 4.9 7 3 6 4.9 9 1 7 5.0 0 9 8 4.9 3 1 2 4.9 4 3 5 4.9 8 1 5 4.9 3 8 2 5.0 2 0 5 4.9 3 1 8 4.9 5 8 3 4.9 7 7 0 4.9 3 3 9 5.0 0 7 1 4.9 2 9 2 4.9 4 5 1 4.9 7 8 9 5.0 0 8 7 4.9 2 2 6 4.9 4 6 a 4.9 6 9 6 4.9 9 1 5 5.0 0 3 0 4.9 9 3 4 4.9 5 8 9 4.9 7 0 2 4.9 9 9 2 5.0 1 7 1 4.9 4 0 2 4.9 4 9 5 4.9 9 0 1 4.9 9 6 7 5.0 2 9 1 4.9 4 0 3 4.9 6 7 1 4.9 8 4 8 4.9 9 4 8 5.0 1 5 9 4.9 3 3 5 4.9 5 5 1 4.9 3 9 9 5.0 3 0 5 4.9 3 1 3 4.9 5 3 1 4.9 7 3 4 5.0 0 0 6 5.0 1 0 8 4.9 4 1 1 4.9 6 7 1 4.9 9 0 3 5.0 0 3 5 5.0 2 5 8 4.9 3 6 3 4.9 5 0 6 4.9 9 9 2 5.0 0 6 3 5.0 3 3 1 4.9 4 8 1 4.9 7 5 9 4.9 9 3 4 5.0 0 3 9 5.0 3 5 5 4,9 5 2 2 4.9 7 0 8 5.0 0 3 2 5.0 3 7 7 4.9 4 4 0 4.9 6 4 9 4.9 9 3 0 5.0 1 5 3 5.0,228 4.9 5 6 1 4.9 3 1 5 5.0 0 4 3 5.0 2 2 2 5.0 3 0 5 4.9 6 3 3 4.9 7 3 1 5.0 1 3 6 5.0 2 1 1 5.0 5 3 0 4.9 6 3 5 4,9 9 0 2 5.0 0 8 0 5.0 1 7 9 5.0 2 9 3 4.9 6 6 3 4.9 8 5 1 5.017S 5.0 5 8 5 4.9 5 9 6 4.9 7 9 0 5.0 0 5 5 5.0 2 9 7 5.0 4 2 6 4.9 6 9 9 4.9 9 5 9 5.0 1 7 6 5.0 3 4 8 5.0 5 4 8 4.9 7 5 8 4.9 3 7 1 5.0 2 7 0 5.0 3 4 1 5.0 6 6 6 4.9 7 7 5 5.0 0 4 0 5.0 2 1 1 5.0 3 2 3 5.0 5 3 6

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*-4 8 88888 ** 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

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 74 0 25 5.1 1 9 4.0065 5 25 5.1 0 8 5.0064 10 25 5.0 9 8 8.0 053 15 25 5.0 9 6 0.0 059 20 25 5.0 9 6 3.0 053 25 25 5.0 9 7 4.0 052 30 25 5.0 9 9 5.0 055 35 24 5.1 0 4 6.0 064 40 24 5.1 1 7 9.0058 45 24 5.1 3 3 0.0070 50 24 5.1 4 9 4.0 0 5 9 Average mean d e v ia t io n.0059 5.1 2 1 0.0016 5.1 0 8 3.0003 5.1 0 0 2.0014 5-0954 -.0006 5.0 9 3 9 -.0 0 2 3 5.0 9 6 0 -.0 0 1 4 5.1 0 0 8.0 0 1 3 5.1 0 2 7 -.0 0 1 9 5.1 1 9 6.001? 5-1332.0002 5.1 4 9 4.0000 A verage A P & o

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 0 2.9 0 0 2.9 0 0.0 0 0 A 5 10 3.0 1 9 3.2 0 3 3.0 4 7 3.1 8 1.0 2 6 -.0 2 2 13 20 3.2 9 2 3.3 6 9 3.2 9 3 3.3 9 4.-003'.0 2 5 25 3.4 7 9 3.4 7 1 -.0 0 8 30 3.3 3 2 3.5 3 3.0 0 1 35 3.5 7 4 3.5 7 3 -.0 0 1 40 45 3.3 9 7 3.5 7 9 3.5 9 5 3.5 9 3 -.0 0 2.0 1 9 50 3.5 6 8 3.5 8 5 -* 0 0 3 Average difference.010 % xlo6 xlo6 xlo6 0 7.5 9 6 7.5 6 8 -.0 9 8 5 10 7.7 8 9 7.9 6 5 7.7 8 4 7.9 4 0 -.0 0 5 -.0 2 5 15 20 8.0 1 7 8.0 1 3 8.0 3 8 8.0 5 6.0 1 1. 043 25 7.9 9 1 8.0 1 7.0 2 6 30 35 7.9 5 2 7.3 6 0 7.9 2 9 7.8 9 4 -.0 2 3.0 3 4 40 7.6 2 2 7.5 9 3 -.0 2 9 45 7.3 6 2 7.3 5 9 -.0 0 3 50 7.0 8 9 7.0 8 9.000 Average d if f e r e n c e *021

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. 0 4.421 1391.7-10.36-33.37 5 4.4?5 1420.6-10.93-34.49 10 4.531 1246.8-11.60-3 5.U 13 4.591 1369.7-12.2? -35.73 30 4.654 809.4-12..84-36.35 as 4.719 706.0-13.46-36.97 30 4.738 519.8-14.08-37.39 33 4.860 339.9-14.70-38.31 40 4.935 137.7-15.32-30.33 43 5.013-5 1.1-15.94-39.45 50 5.095-257.1-16.56-40.07 0 6.399 932.3-19.30-48.37 5 6.5 0 1 738.0-20.69-49.26 10 6.607 419.6-21.57-50.14 15 6.717 236.5-22.46-51.03 m 6.831-65.9-23.35-51.91 as 6.951-282.2-24.33-52.80 30 7.074-548.6-25.12-53.63 35 7.197 -'..819.0-26.00-54.57 40 7.330-1094 -26.89-55.45 45 7.467-1374 -37.77-56.34 SO 7.608-1653 28.66-57.22

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 23 3.9 5 36 «n a!* «* 3.9 9 B erthe l o t 1891 IT 3. S3 12. Malden 1896 * 25' 4.0 4? Smith 1898 Inversion of 100 3.9 9 s 8.3 45 sucrose W egschelder 1902 Conductivity IT 4.0 s 7.5 48 D har-d atta 1913 Solubility «9. 1? Lars son 1922 Clectroisetrlo 18 4.0 s 7.8 31 A uerheeh-dm olesyk H 1924 ao 3.8 6 1 3.9 4 B jerrus" 1924 ft 15 4.0 13 Coops 1924 Conductivity; 25 3.7 6 16 larsson 1924 «n» 15 3.3 2 29 18. 4.0 * 6.9 30 Roth-Mllms 1926 «25 3.9 3 42 Ml sutanl 1925 Elea trosie trio IS :! 4. 7. 1 3.5 33 Larsson ' 1926 - S o lu b i11 ty 25'' 4.0 * 7.3 32 jdubo.ux- Kroatae-1 n % 1927 23 ' 3.9 5 s 7.4 19 Hamer 1943 Elaetrametric 25 3.6 3 7.5 9 21 Men 1 95 1 25 3.4 8 7.9 9 20 3.3 7 8.0 1 15 3.2 9 8.0 2 fhs values f E{ have been 'obtained from th e original determination by Ostwald (3 ) and u @& by th e bo authors In order to ca l culate Kg.

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 1. 0.02 0.04 0.06 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,

JUa Fig. 1.2.0 8» ' O 30 2 5 2 0 1.25 1 5 1 0 :.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. 0.02 0.04 0.06

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

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. 2 0.04 0.06

69 \ Fig.1.5. Run 2 XxlO6 vs u - 8 _ c -9 0 3 5 0 30 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 0.02 0.04 0.06

-7_ Fig. L6.a Run 7 Xxl06vs p - 8_ -0 50* 0 40-9 0 30-1 0 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* 0.02 0.04 0.06

n Fig. I.7.a Run 3a XxlO6 vs j 035' 0 3 0 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 5 0.02 0.04 0.06

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- 0.02 0.04 0.06 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.

22. Run 4 O 40 35 O 3 0 ' O 20 YxlOu vs jf n tit;, v, at 5 and >eer. m e ".sod by.4x10 ' u n its, 0.02 0.04 0.06

74 0 6 2 2.8 2.4 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. 0.02 0.04 0.06 IONIC STRENGTH

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

7 6 Fig. I.5.b so Run 2 YxlO1vs i 0.02 0.04 0.06

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 <?

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

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 0.1 2 6 u n its to tbs right for saob auaosaa iv«mm of tbs faaily of ourrss 0.0 1.0 2.0

Fig. 2.2 YxlO vs XxlO /* 75 I.b. Th» ordinafca *xla has baen fcranapoaad 0.116 unit# tofcb# ri^ht fq wh, SUOMMlT# MBflMNPOf jutt'/ T family of curraa. ^ f t 0 0 0 ^ 0.0 2.0

0 Fig. 2.3 V.b. The ordinate axis haa been trenapoaed 0.120 unita to the rifht for eeoh auooeaaire earber of the fasllx of currea. 2.0

88 15 Fig. 2.4 YxlO8 vs XxlO4 0, k---- 5 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

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 0.125 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.

84 2.5 Fig. 2.6 YxlO8 vs XxlO4 0 5 0 N*b. The o rd in a te a x is has been transposed 0.1 2 5 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. 2.0 3.0

8 5 3 0 Fl«2.7 5 * 0 0 0 0 1.0 3.0

86 35 Fig. 2.8 0 5.0.5 2.0

8T 40 Fig. 2.9 5

86 Fig. 2.10 45 b / 5.0 g 1 0 i.o

Fig. 2.11.0

Fig. 3.1 - log 1^ p 5 49 85 10 o ' o' 5 - o 48 47 / - o o o 20 0.02 M 0.04 0.06 5

91 1-5 -25 o ------- Fig. 3.2 ~ s o-. - o 14-4 30 O 0 35 0 O ------- o o -------- _ G 4 ------------ 40 0 o ' 0 1-4 /to r G ---------- G --------------- 50 1 G 1. o 0.02 0.04 0.06

5.13 * A 5.11 % w V 9 9 5.12 * 9 w 9 5.10 5.11 - K 5.09 nr r V 9 9 w o O 5 i a 10 A V w * * 1 --- - ---- 5.11 9 m i. A * A. 5J09 99 "9 5.09 9 i^ a a - 5.09 99 9 9 5.11... a 5.09 w 9 9 9... 9 15 I o «: 20 9..A, ------ 9 --- 2 5 * % I" * * e1 0.0 2 0.0 4 0.0 6 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.

5.11 * % - 5.0SL _ / ^ w «w Fig. 4.2 30 * _ 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 50.... %- 0.0 2 0.0 4 0.0 6 P

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 73. 3 0 0 4 7 5 2 5

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 74. 5.12 2 5 o T - C

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