thermodynamic properties of chloro-complexes of agcl (aq) (1)

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  • 7/30/2019 Thermodynamic Properties of Chloro-Complexes of AgCl (Aq) (1)

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    Journal of Solution Chemistry, V ol. 14, No. 12, 1985

    T h e r m o d y n a m i c P r o p e r t i e s o f C h l o r o - C o m p l e x e s o fS i lver Ch lo r ide in Aqueous So lu t ionJam es J. Fritz 1Received December 17, 1984; In Final Form October 2, 1 985Available data on the solubility of silver chloride in aqueous solutions of HCI,NaCl, KCI, LiCl, and NH4C I, along with potentiometric measurements o f the ac-tiv iO, o f Ag + in aqueous NaC I-NaC IO 4 mixtures, have been ana/yzed to obtainthe therm odynam ic properties of the (AgC l) ~ AgC l~, A gC I 23 , an d Ag CI ~4 com-plexes. Re sults obtained include the stabili ty constants o f the complexes at 25 ~the virial param eters needed to calculate the activity coefficients of the complexesand the heats of the reactions by which they are formed. These results are usedto calculate tables o f recomm ended values fo r the solubili ty of si lver chloride inthe host solutions as a function o f concentration fr om 0 to 150 ~ an d to ma ke acritical evaluation o f the r eliability o f previous!y published data.K E Y W O R D S : A s C I ; s o l u b i li t y ; c o m p l e x e s ; s t a b il i t y c o n s t a n t s ; h e a t s .

    1 . I N T R O D U C T I O NT h e c o m p l e x e s w h i c h f o r m w h e n s i lv e r c h lo r id e d i s s o lv e s i n

    a q u e o u s s o l u t i o n s o f s o lu b l e c h l o ri d e s h a v e b e e n i n v e s t ig a t e d e x t e n -s i v e ly , b u t t h e p r o p e r t i es o f t h e c o m p l e x e s a r e st il l c l o u d e d i n u n c e r -t a in t y . P r e - 1 9 7 6 v a l u e s (1) f o r t h e s t a b i li ty c o n s t a n t a t 2 5 ~ o f t h ec o m p l e x A g C I ~ v a r y b y a f a ct o r o f 6 , w h i l e t h o s e f o r ( A g C 1 ) ~ A g C I ~ - ,a n d A g C I 43- v a r y e v e n m o r e w i d e l y . S m i t h a n d M a r t e l l 's c r it ic a l c o m -p i l a t io n o f st a b i li ty c o n s t a n t s (2) c o n t a i n s n o v a l u e s f o r a n y o f t h e c o m -p l e x e s . T h e h e a t s o f f o r m a t i o n o f t h e c o m p l e x e s a r e p o o r l y k n o w n . (3)

    M o r e r e c e n t a t t e m p t s t o im p r o v e t h e s i t u a ti o n , u s i n g m e a s u r e -m e n t s a t t e m p e r a t u r es w e l l a b o v e 2 5 ~ h a v e r e s u l te d in o n l y m i n i m a li m p r o v e m e n t . I v a n e n k o a n d P a m f i lo v a ~4) m e a s u r e d s o l u b i li t ie s o fs il v er c h l o r id e i n a q u e o u s s o d i u m c h l o r id e f r o m 6 0 t o 1 6 0 ~ a n dS e w a r d ~5) i n v e s t i g a t e d t h e s a m e s y s t e m i n t h e r a n g e 1 0 0 t o 3 5 3 ~

    1Department o f Chem is try , Th e Pennsylvania State Univers ity , Univers ity Park, PA 16802.8 6 50095-9782/85/1200-0865504.50/0 @ 1985Plen um P ublishing Corporation

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    8 6 6 F r i t z

    Where compar i sons can be made , the i r s t ab i l i ty cons tan t s d i f f e r byf a c to r s f r o m 2 t o m o r e t h a n 1 0, a n d t h e i r h e a t s o f s o l u t i o n b y a s m u c ha s 1 0 0 % . B o t h r e i n t e r p r e t e d t h e s a m e o l d e r d a t a b e t w e e n 1 8 a n d 5 0 ~T he r eason fo r the d i f fi cu lt ie s i s the low so lub il ity o f AgC1 . A tlow co ncen t ra t ions o f ch lo r ides , the so lub il ity o f AgC1 a t 25 %2 i s o f th eo r d e r 1 0 6 M ( m o l e s - l l ) , a n d l e s s th a n 0 . 0 1 M a t c h l o r id e c o n c e n t r a t i o n so f 5M, so tha t p reci s e m ea su rem en ts can be di ff icul t. A t hos t con-c e n t r a t i o n s h i g h e n o u g h t o d i s s o lv e A gC 1 t o m o r e t h a n 0 .0 0 1 M , d e v i a -t ions f rom idea l behav io r a re subs tan t ia l , fu r th e r com pl ica t ing thed e t e r m i n a t i o n .

    T h e p r o b l e m s a r i s i n g f r o m n o n - i d e a l s o l u t i o n b e h a v i o r c a n b eh a n d l e d b y u s e o f a v i r i a l m o d e l(6,7) fo r activ ity co effic ient s. T h ep a r a m e t e r s n e e d e d f o r i o n pa ir s c a n t h e n b e e v a l u a t e d a t t h e s a m e t i m ea s t h e e q u i l ib r i u m c o n st a n t s. T h i s p r o c e d u r e h a s a d v a n t a g e s f o r d a t a o fl es s t h a n o p t i m u m p r ec i si o n . F i r st , i t p r o v i d e s a re l ia b le m e t h o d f o rs m o o t h i n g d a ta . S e c o n d , it m a k e s p o s si b le c o m p a r i s o n o f d a t a f r o mdi f fe ren t sou rces , inc lud ing thos e fo r d i f f e ren t ho s t so lu t ions . F ina lly ,i t p rov ides a s evere t e s t o f the cons i s tency o f a ll o f the da ta .T he p r inc ipal pu rp ose o f th i s paper i s to ana lyze ava i l ab le da ta fo rf iv e a q u e o u s s y s t e m s i n v o l v i n g si lv e r c h lo r i d e t o o b t a i n t h e b e s t v a l u e so f t h e s t a b i l i t y c o n s t a n t s , h e a t s o f f o r m a t i o n a n d t h e r m o d y n a m i cp r o p e r ti e s o f t h e i m p o r t a n t c h l o ri d e c o m p l e x e s f o r m e d a t 2 5 ~ z e r oion ic s t r eng th , toge the r w i th the v i r i a l pa ramete r s neces sa ry to desc r ibet h e i r b e h a v i o r i n f o u r h o s t a q u e o u s c h l o r i d e s a t c o n c e n t r a t i o n s u p t o5 M . C o n c l u d i n g s e c ti o n s g i v e t a b le s o f r e c o m m e n d e d v a l u e s f o r t h eso lub il ity o f s i lve r ch lo r ide in these hos t m ed ia f rom 0 to 150~ an ddiscuss the re l iab i l ity of data available in th e l i tera ture .

    2 . D A T A A V A IL A B L ET he pre sen t w ork us ed a ll nu m er ic al re sul ts avai lable (4,5's27) for

    m o n o v a l e n t c h lo r id e s u p t o 6 . 5 M a n d 1 60 ~ T h e m e a s u r e m e n t s h a db e e n m a d e b y n e p h e l o m e t r y a n d b y c h e m i c a l o r r a d i o c h e m i c a l a n a ly s iso f s a t u r a t e d s o lu t io n s . M o s t w e r e c a rr ie d o u t a t th e i o n i c s t r e n g t hp r o d u c e d b y t h e h o s t s o l u ti o n u s e d ; s o m e (2~ w e r e m a i n t a i n e d a tc o n s t a n t io n i c s t r e n g t h b y u s e o f a s u it a b le p e r ch l o r at e . T h e r e w e r e469 da ta po in t s in a ll , abo u t ha l f a t 25 ~ Ov er ha l f o f the m easu re -m e n t s w e r e m a d e i n a q u e o u s N a C I, t h e r e m a i n d e r i n a q u e o u s so l u ti o n so f H C 1, K C 1 , L i C 1, a n d N H 4 C1 . A b o u t o n e t h i rd o f t h e m e a s u r e m e n t sw e r e m a d e a t c o n c e n t r a t i o n s o f h o s t c h l o r id e le s s t h a n 0 . 1 M ( as l o w as5 x 1 0 4 M ) . I n a d d i t io n , t h e r e is a s e t o f 2 8 p o t e n t i o m e t r i c

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    Chloro-Com plexes of Si lver Chloride 867

    m ea su rem en ts (23) o f the ac t iv i ty o f Ag in 5M aqu eou s NaCI-NaC104m i x t u r e s a t 2 5 ~A l l m e a s u r e m e n t s u s e d m o l a r c o n c e n t r a t i o n s , e x c e p t t h em o l a l it ie s g i v e n b y S e w a r d a t 1 0 0 ~ w h i c h w e r e c o n v e r t e d t o m o l a r i ti e sus ing kn ow n dens i t i e s o f aqu eou s NaC 1 so lu t ions . (28) Da ta fo r 150 ~w e r e c o n v e r t e d u s i n g t h e a s s u m p t i o n t h a t t h e f r a c t i o n a l i n c r e a s e s i nv o l u m e o f t h e s o l u t i o n s b e t w e e n 1 0 0 a n d 1 50 ~ w e r e t h e s a m e a s f o rp u r e w a t e r ( a n a s s u m p t i o n w h i c h is n e a rl y e x a c t b e t w e e n 2 5 a n d100 ~3 . P R O C E D U R E3 . 1 . S p e c i e s C o n s i d e r e d

    Prev ious inves t iga to r s have ana lyzed so lub i l i ty da ta o f AgCI con-s ider ing th e species A g +, (AgCI)0, Ag CI~ , AgC1 ]-, a nd AgC1 ~. Bya n a l o g y w i t h s o l u t i o n s o f C uC 1 , w h e r e C u ~ l ~- m a k e s a s ig n i fi c an t c o n -t r ibu t ion to th e so lubi l i ty , (29) th e co m ple x A g ~ l 42- was ad de d to the l is t.3 . 2 . D e t e r m i n a t i o n o f S t a b i l i t y C o n s ta n t s a n d V i r i a l P a ra m e t e r s a t 2 5 ~

    Th e da ta a t 25 ~ we re s epara ted in to two se t s: ( a) tho se w i thc h l o r i d e c o n c e n t r a t i o n s a b o v e 0 . 1 M , w h e r e t h e s o l u b i l i t y i s b r o u g h ta b o u t a l m o s t e x c l u s i v e l y b y t h e f o r m a t i o n o f n e g a t i v e l y c h a r g e d c o m -p lexes , and (b ) th e ( l es s p rec is e ) da ta fo r conce n t ra t ion s be low 0 .1M,w h e r e A g a n d ( A gC 1 )~ m ak e s ign if i can t con t r ibu t ion s ( s ee F ig . 1 ).E a c h s e t w a s su b d i v i d e d i n t o s e p a r at e g r o u p s , o n e f o r e a c h o f t h es o l u b le c h l o ri d e s i n v o l v e d . N o n - l i n e a r le a s t s q u a r e s w e r e t h e n u s e d t oo b t a i n o p t i m u m v a l u e s o f t h e s ta b il it y c o n s t a n t s f o r e a c h o f t h e c o m -p l e x e s a l o n g w i t h t h e v i r i a l p a r a m e t e r s r e q u i r e d t o r e p r e s e n t t h e a c -t iv ity coef f i c ien t s o f ion pa ir s invo lv ing each o f the c om plexes . T hep r o c e d u r e u s e d h a s b e e n d e s c r i b e d i n s o m e d e t a i l p r e v i o u s l y . 29 ,30) T h etwo se t s o f da ta were an a lyzed s ide by s ide , w i th those a t the h ighe rconcen t ra t ions used to op t imize s t ab i l i ty cons tan t s and v i r i a l pa ramete r so f d o u b l y a n d t ri pl y c h a r g e d c o m p l e x e s , t h e s e b e l o w 0 . 1 M f o r t h ep roper t i e s o f (AgC1) ~ and bo th tog e the r fo r the p roper t i e s o f AgCI~.In th i s p roces s a l l pa ramete r s were inc luded in the ca lcu la t ions fo r bo thsets . S o m e i m p o r t a n t d e t a il s o f th e p r o c e ss w e re :

    1 . V i r ia l P a r a m e t e r s . The v i r i a l mode l fo r ac t iv i ty coef f i c ien t s r e -quire s a t leas t th re e pa ram ete rs , (7)/3 (0) /3 (1) an d C, for e ach ion pair in

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    868 F r i t z

    t h e s o l u t i o n . P r e v i o u s ex pe rie nc e(3 ~ h a s s h o w n t h a t s o l u b i li ty d a t a c a nb e r e p r e s e n t e d t o a f e w p e r c e n t t a k i n g / 3 ~1~ a s a s t a n d a r d f u n c t i o n o f13 (o~, a s s u g g es t ed b y P i t ze r an d M ay o r g a . (6~ T h i s p r o c ed u r e w a s f o l -l o w e d f o r A g + - C 1 0 ~ , A g -, a n d all i o n p a i rs i n v o l v i n g c o m p l e x e s ,b e c a u s e o f l ac k o f d a ta . T h e p a r a m e t e r s f o r i o n p a i rs i n v o l v i n g C 1- a n dC 1 0 ; w i t h t h e h o s t c a t i o n s w e r e t a k e n f r o m t h e l it e r a tu r e . (6~ T h e h i g h e ro r d e r p a r a m e t e r s ( ~b , ~ ) o f t h e P i t z e r m o d e l (6~ w e r e n o t i n c l u d e db e c a u s e t h e c o n c e n t r a t io n s o f a ll c o m p l e x e s w e r e s m a l l a n d t h e a m o u n to f d a t a w a s l i m i te d .2. Weighting o f Data. B e c a u s e t h e v a r i o u s d a t a d i d n o t h a v e e q u a lp r e c i s i o n o r re l ia b i li ty ( s e e l a t e r ) , w e i g h t s w e r e a s s i g n e d a s f o l l o w sw i t h i n e a c h d a t a s e t:

    1 . D a t a w h o s e d e v i a t i o n f r o m a d j a c e n t p o i n t s i n t h e s a m ea n d o t h e r s e t s w a s l e s s t h a n t w i c e t h e s t a n d a r d d e v i a t i o no f t h e e n t i r e s e t w e r e g i v e n f u ll w e i g h t .

    2 . D a t a w h i c h d e v i a t e d b y 2 t o 5 s t a n d a r d d e v i a t i o n s w e r er e d u c e d i n w e i g h t p r o p o r t i o n a t e l y .

    3 . D a t a w h i c h d e v i a t e d by m o r e t h a n 5 s t a n d a r d d e v i a t io n sw e r e d e l e t e d .

    3. Possib i l i ty o f a Dinuclear Co mp lex . R e p r e s e n t a t io n o f t h es o l u b i li ty d a t a w a s i n s e n s i t i v e t o p o s s i b l e d i s t r i b u t i o n o f a d o u b l yc h a r g e d c o m p l e x b e t w e e n A g C 1 ]- a n d A g ~ l 42-. T h e c e l l d a t a , ~23~o n t h eo t h e r h a n d , w e r e h ig h l y s e n s i t iv e to s u c h d i s tr i b u ti o n . I n t h e la t te rs t a g e s o f t h e o p t i m i z a t i o n p r o c e d u r e , t h e c e ll d a t a w e r e f i t te d a l o n g s i d eo f t h e s o l u b i l i ty d a t a t o s e l e c t t h e f r a c t i o n ( a c t u a ll y n e g l i g i b le ; s e eb e lo w ) o f d o u b l y c h a r g e d c o m p l e x p r e s e n t a s A g ~ l 4 -.4. Data on Aqueous LiCl. T h e r e w a s n o d i ff ic u l ty i n r e p r e s e n t i n gt h e d a t a f o r s o l u t i o n s i n a q u e o u s H C 1 , N a C 1 , K C 1 , a n d N H 4 C I u s i n g ac o m m o n s e t o f s t a b i l i t y c o n s t a n t s , w i t h s u i t a b l e v i r i a l p a r a m e t e r s f o re a c h m e d i u m . F o r L iC 1, h o w e v e r , t h e r e w a s m a j o r d i s a g r e e m e n tb e t w e e n t h e v a r i o u s s o u r c e s U a A 4 , 2 6 ) a t c h l o r i d e c o n c e n t r a t i o n s a b o v e1 M , s o t h a t n o n e o f th e s e d a t a c o u ld b e u s e d .5. Solubility Product o f AgC l. T h e s o lu b il it y p r o d u c t o f A g C I a n dits t e m p e r a t u r e d e p e n d e n c e h a v e b e e n d e t e r m i n e d a c c u ra te l y f r o m c e llm e a su re m e n ts . ~31"33~T h e v a l u e s u s e d w e r e : K sp ( 25 ~ = 1 . 7 7 x 1 0 1 ~w i t h A H = 1 5 .6 5 0 k c a l- m o l 1 .

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    Chloro-Complexes of Si lver Chlor ide 869

    3 .3 . Heats o f So lu t ionThe hea t s o f so lu t ion ( ze ro ion ic s t r eng th ) a s soc ia ted w i th fo r -m a t i o n o f t h e c o m p l e x w a s e v a l u a t e d b y a s e c o n d o p t i m i z a t i o n p r o c e -d u r e , u s i n g t h e d a t a a t t e m p e r a t u r e s o t h e r t h a n 2 5 ~ a f te r t h e b e s tva lues o f the s t ab i li ty con s tan t s a t 25 ~ had be en s e lec ted . T he q uan-t it y a n d q u a li ty o f a va il ab le d a t a d i d n o t p e r m i t e v a l u a t i o n o f t h e t e m -p e r a t u r e d e p e n d e n c e o f t h e v i r i a l p a r a m e t e r s a n d g a v e o n l y r o u g h i n -d i ca ti o ns o f t h e t e m p e r a t u r e d e p e n d e n c e o f th e h e a t s o f s o lu t io n . T h ed a t a o n s o l u t i o n s w i t h l e ss t h a n 0 . 1 M c h l o r i d e w e r e g i v e n p r i m a r yw e i g h t i n o p t i m i z i n g t h e h e a t o f s o l u t i o n f o r ( A g C I) ~ t h o s e a b o v e

    0 . 1 M f o r A g C 1~- a n d A g C I ~ , w i t h b o t h u s e d f o r A g C 1 2.T a b l e I . S t ab il it y C o n s t a n t s , F o r m a t i o n C o n s t a n t s , a n d H e a t s

    o f R e a c t i o n t o F o r m C o m p l e x Sp e c ie s a t 2 5 ~ Z e r o I o n i c S t r e n g t h aF o r m a t i o n C o n s t a n t S t ab i li ty C o n s t a n t

    hH~ Ac~ ~ l n hH~p e c i e s K l n p

    (Ag CI) ~ 3.1 x 10 7 (-*-25%) 9.1--- 1.0 8 l 9 103 -6.6Ag CI~ 2 .5 x 10 "5 (---25%) 10.5---0.3 5 1. 4x 105 -5.1A gC I~- 2 .0 x 10 -5 (-!--10%) 5.6---0.5 -4 1.1 105 -10.0AgC143- 7 ,8 -7 (-----2 5% ) -1.0---1.0 -30 4 .4 x 103 -16.7

    a Equ i l ib r ium cons tan t s bas ed o n 1M s tandard s ta te 9 Un cer ta in t ies in s tabil ity con s tantsa n d t h e i r h e a t s o f r e a c t i o n s a m e a s f o r t h e c o r r e s p o n d in g f o r m a t i o n c o n s ta n t s , b U n i t s :k c a l - m o l1 . CValue fo r A Vp a re thos e wh ich gave the bes t f i t to expe r imen ta l da ta .9 , . -1 -1T h e i r u n c e r t a i n ty i s o f t h e o r d e r o f 1 0 c a l - m o l - d e g .

    4 . RESULTST h e o p t i m i z a t i o n p r o c e d u r e u s e d a t 2 5 ~ f i tt e d t h e w e i g h t e ds o lu b i li ty d a t a t o a n a v e r a g e ( r .m . s .) d e v i a t i o n o f 5 % a b o v e 0 A M a n d15% be low 0 .1M . T he to ta l s i lver co nc en tra t io ns of th e ce l l da ta ~23)we re f i t t ed to 1%, co r resp ond ing to 0.6 m v in po ten t i a l. T he d a ta usedt o o b t a i n t h e h e a t s o f so l u t i o n w e r e f i t t e d t o 1 3% o v e r b o t h r a n g e s o fc o n c e n t r a t i o n .Tab le I g ives the r esu l t s ob ta ined a t 25 ~ ze ro ion ic s t r eng th , fo rt h e s t a b i l i t y c o n s t a n t s o f t h e s e v e r a l c o m p l e x e s a n d f o r t h e formationconstants K~n fo r r eac t ions such as Eq . (1 ) , a long wi th the co r re spon d ing

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    8 7 0 F r i t z

    T a b l e I I . V i r ia l P a r a m e t e r s f o r I o n P a ir s a

    Io n Pa ir /3 (o) /3 (1) C

    H + - A g C I 2 0 .2 2 2 3 0 . 3 6 8 0 -0 .0 1 0 11H + -A gC I ~- 0 .3563 1 .6425 -0 .00016H +-AgC 143- 0.6228 5.1600 0.00069N a + - A g C I ~ 0 . 1 48 0 0 . 2 9 3 0 - 0 .0 1 5 2 0N a + -AgC132- 0.1288 1.2000 -0.01076N a + -AgC143- 0 .3436 4 .0000 -0 .01951K + - A g C I2 0 .2165 0 .3620 -0 .01200K + -AgC1 ] - 0 .0200 0 .8410 -0 .02435K + - A g C I ~ 0 .2 2 41 3 .5 1 30 - 0 .4 3 8 0N H + -A g C I2 -0 .0 9 4 2 -0 . 1 2 0 0 -0 . 0 1 6 7 9NH~'-AgC132- -0.0284 0.60 00 -0.00055N H +- A gC I 43- -0.0394 2.4133 -0.01073A g + -CV 0 .0599 0 .1800 0 .03283A g + -C1 0 ~ 0 . 1 3 7 4 0 . 2 8 2 0 0 .0 0 9 18

    F o r ( A g C I ) ~ l n y = A I, w i t h A a s fo l l o w s :H C1 s o l u t i o n s A = 0 . 1 5 6 ; N aC1 s o l u t i o n s , A = 0 . 2 4 4

    K C 1 s o l u t i o n s A = 0 . 2 6 8 ; N H 4 C I s o l u t i o n s , A = 0 . 20 4a U n c e r t a i n t i e s i n / 3 - - - 0 . 0 0 6 f o r p a i r s i n v o l v i n g A g C I2 a n d f o r a l l o t h e r s ; f o r C t h r o u g h o u t .s t a n d a r d h e a t s a n d A C p f o r t h e s e r e a c ti o n s .

    A g C l ( s) + ( n - 1 ) C l - ( a q ) = A g C l ~~, Kin---- a ( A g C l ~ " ) / a ( C 1 - ) ~ (1 )N o r e s u l t s f o r A g :C 14 2- a r e g i v e n i n T a b l e I , s i n c e t h e b e s t f i t t o t h e c e lld a t a w a s o b t a i n e d w i th no c o n t r i b u t i o n f r o m t h i s s p e c ie s . T h i s i n d ic a t e st h a t t h e f o r m a t i o n c o n s t a n t f o r t h is s p e c ie s c a n b e n o m o r e t h a n 1 t o2 % as l a r g e a s t h a t f o r A g C 1 ]-, viz., K24 ~ 4 x 1 0 -7 a t 2 5 ~T a b l e I I g i v e s t h e v i r i a l p a r a m e t e r s f o r i o n p a i r s i n v o l v i n gc o m p l e x s p e c ie s a l o n g w i th t h o s e ( p r e v io u s l y u n k n o w n ) f o r A g + - C 1 -a n d A g + - C I O L F o r c o m p u t a t i o n a l c o n v e n i e n c e t h e a c ti vi ty c o e f fi c ie n t so f ( Ag C1 )0 w e r e e x p r e s s e d i n t e r m s o f a si m i la r s e t o f p a r a m e t e r s , t h e nr e - e x p r e s s e d b y e q u a t i o n s o f t h e f o r m l n y AgCl = A I , w h i c h a r e g i v e n a tt h e b o t t o m o f T a b l e I I.

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    Chloro-Com plexes of Si lver Chloride

    Table I I I . S t a n d a r d T h e r m o d y n a m i c P r o p e r t ie s a t 2 5 ~

    871

    Species (AHf 298 (AGf~ $2~ Cp(AgC1) ~ -21.3- --1 .0 -17.30 23 2 0AgC12 : -59 .9 - 51 .30 50 1 - 15 10AgCI ~ - - 104 .8 0 .5 - 8 2 .50 47 2 - 52 10AgC I 43- -151.5--- 1.0 -11 2.0 0 31_+ 3 -1 08 10

    oa Un i ts : A H f and A G f , k c a l - m o l 'l ; S a n d C p , c a l - m o l l - K 1 .T a b l e I I I g iv e s t h e s t a n d a r d t h e r m o d y n a m i c p r o p e rt ie s o f t h ev a r i o u s c o m p l e x e s a t 2 5 ~ z e r o i o n ic s t r e n g t h , t a k i n g th e p r o p e r t ie s o fA gC l ( s ) an d C 1- (aq ) f ro m t he NB S C i rcu l a r 500. (34)

    5 . D I S C U S S I O N

    5 .1 . Re l i ab i l i t y o f Resul t sT h e u n c e r t a i n t i e s g i v e n i n T a b l e s I - I l l w e r e o b t a i n e d a s f o l l o w s .F o r t h e e q u i l i b r i u m c o n s t a n t s t h e y a r e t h e c h a n g e r e q u i r e d t o d o u b l e

    t h e s t a n d a r d d e v i a t i o n o f t h e o v e r a l l fit. F o r t h e v i ri al p a r a m e t e r s a n dt h e h e a t s o f r e ac t io n , t h e y a r e t h e a m o u n t s r e q u i r e d t o p r o d u c e ac h a n g e o f o n e s t a n d a r d d e v i a t i o n i n r e g i o n s w h e r e t h e s o l u b i l i t y w a ss e n s it iv e to t h e c o n c e n t r a t i o n o f t h e c o m p l e x in v o l ve d . T h e u n c e r -t a in t ie s i n t h e r m o d y n a m i c p r o p e rt ie s i n T a b l e I I I w e r e d e r i v e d f r o mt h o s e o f T a b l e s I a n d I I. ( N o t e t h a t t h e u n c e r t a i n t i e s i n t h e e n t r o p i e sa r e d o m i n a t e d b y t h o s e i n th e h e a t s o f r e a c ti o n .) T h e h e a t o f r e a c ti o nt o f o r m ( A g C I) 0 is u n c e r t a i n b e c a u s e o f th e f e w m e a s u r e m e n t s a va il-a b l e w h e r e i t i s t h e m a j o r c o n s t i t u e n t o f t h e s o l u t i o n .T h e r e a r e h i d d e n u n c e r t a in t ie s in t h e h e a t s o f r e a c t io n d u e t o t h ef a c t t h a t t h e a v a i l ab l e d a t a d i d n o t p e r m i t e v a l u a t i o n o f t h e t e m p e r a t u r ed e p e n d e n c e o f t h e v i r ia l p a r a m e t e r s . T h e o v e r a l l r e s u l t is th a t t h e A C pg i v e n f o r t h e h i g h e r c o m p l e x e s c o n t a i n t h e e f f e c t o f v ir ia l p a r a m e t e rv a r i a ti o n s i n a d d i t i o n t o t h e t r u e t h e r m o d y n a m i c A Cp.

    5 . 2 . C o m p a r is o n w i t h P r e v io u s R e s u lt sT a b l e I V A c o m p a r e s p a s t v a l u e s o f e q u i l i b r iu m c o n s t a n t s w i t ht hos e ob t a i ne d i n t he p re sen t work . (R ef s . 36 - 39 g i ve equ i l i b r i um

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    8 7 2 F r i t z

    T a b l e I V A . C o m p a r a t i v e V a l u e s o f S ta b il it y C o n s t a n t s ~

    oCI o n i c (A g C1 ) ~ A g CI2 AgC12 - AgC14 -

    St ren g th B in /32n f l3n f l 4 n R e f .25 0 798 1.6 x 1050 3250 2.5 x 105H C1b 1.7 x 105

    0 7.3 x 105H C1b 3 . 9x 105 1 .2 x 1060 4 . 5 x 1 050 2040 1.76 1050 1100 1.1 x 105 1.1 x 105 2 .0 x 1050 2579 1 .9 x 105 1 .Tx 1050 1 . 4 x 1 050 1 7 4 0 l a x 1 05 1 . 1 x 1 05 4 . 4 x 1 03 T h i sK C Id 5 . 0 x 1 05

    NaC IO4 e 1.1 x 106 2.1 x 1051 . 6 x 1 06 1 . 1 x 1 05N aCIO 4 e 1 2 0 0 2 . 5 x 1 05 l a x 1 06 2 x 1 05N aCIO 4 e 5 3 2 0 1 . 0 x 1 05 8 . 3 x 1 05 1 . 0 x 1 05 T h i s

    15 0 2290 2 .1 6x 1051 5 0 2 4 0 0 1 . 8 x 1 05 6 . 4 x 1 04 1 . 3 x 1 04 T h i s18 0 1 .7 x 105 1 .4 x 10620 HCIO4 aNaC 104 2810 4.7 x 105 1 106 1.1 x i0635 0 1690 1 .3 9x 10535 0 1330 1 .1 x 105 6 . 4x 104 1658 T hi s60 0 776 6,31 x 1046 0 0 4 8 5 5 . 6 5 x 1 04 1 . 8 9 x 1 04 2 0 9 T h i s1 0 0 0 5 1 3 1 . 7 4 x 1 04 7 . 4 1 x 1 04

    1 0 0 0 7 5 9 2 . 8 8 x 1 04 7 . 0 8 1 03 8 71 0 0 0 1 8 0 2 . 5 7 x 1 04 3 . 8 3 x 1 03 1 1 T h i s1 5 0 0 7 5 9 2 . 8 2 x 1 04 5 . 3 7 x 1 03150 0 72 1.23 x 104 6.78 x 102 0.5 T hi s160 0 324 1.55 x 104160 0 61 1 .0 3x 104 5 .0 7x 102 0 .3 Th i s

    16171920213622243738w o r k3922 c24w o r k22w o r k182522w o r k4w o r k45w o r k5w o r k4w o r k

    a / 3 1 n r e f e r s t o t h e e q u i l i b r i u m c o n s t a n t f o r f o r m a t i o nv a r i o u s l o w c o n c e n t r a t i o n s . CR e f . 2 2 p r e s e n t s t w op e r i m e n t a l p r o c e d u r e s , d 4M. e 5M.

    o f A g C 1n f r o m A g + a n d C I - . b A ts e t s o f v a l u e s f r o m d i f f e r e n t e x -

    c o n s t a n t s b u t d id n o t c o n t a i n u s a b l e n u m e r i c a l d at a.) F o r c o n v e n i e n c e ,a l l c o n s t a n t s w e r e c o n v e r t e d t o s t a b i l i t y c o n s t a n t s , u s i n g t h e k n o w ns o l u b i l it y p r o d u c t C3~) w h e r e n e e d e d . F o r / 3 ~ , / 3 2 , a n d / 3 3 , p r e v i o u s v a l u e ss c a t te r a r o u n d t h e p r e s e n t s e t . F o r / 3 4 , e a r li er v a l u e s q u o t e d f o r z e r o

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    Chloro -Com plexes o f S i lver Ch lor ide 8 7 3

    T a b l e I V B . S o l ub i li ty P r o d u c t s o f S i lv e r C h l o r i d e a tH i g h er T e m p e r a t u r e s

    ~ R e f . 4 R e f . 5 T h i s w o r k

    100 2 .9 5x 10 8 2 .24 10 -8 3 .6 x 10 -8150 - 1 .5 5x 10 -7 4 .3 10 7160 4 .4 7 10 -7 6 . 7x 10 -7

    T a b l e V . H e a t s o f R e a c t i o n a n d S t a n d a rd E n t r o p i e s o f C o m p l e x e sat 25 0(2 , Ze ro Ionic S tren gth

    A H ~ S ~S pe c i e s c a l -mo l 1 c a l -mo l -d e g "1 R e f .

    (AgC1) 0 -2700 37 20- 6 6 0 0 2 3 T h i s w o r k

    AgC I~ -3900 56 20- 5 0 0 0 5 0 T h i s w o r kAgC143- -14 ,00 0 19

    - 1 7 , 8 0 0 3 1 T h i s w o r k

    i o n i c s t r e n g t h a r e m u c h t o o h i g h , a p p a r e n t l y b e c a u s e o f f a i l u r e t oaccoun t fo r the l a rge nega t ive dev ia t ions in the ac t iv i ty coef f i c ien t s o ft h e t r i p l y c h a r g e d c o m p l e x a t i o n i c s t r e n g t h s w h e r e i t c o n t r i b u t e s s u b -s tant ia l ly to the so lubi l i ty .T h e p r e s e n t i n t e r p r e t a t i o n o f t h e r e s u l t s a t l o w c o n c e n t r a t i o n s

    a n d h i g h e r t e m p e r a t u r e s r e q u i r e s v a l u e s o f t h e s o lu b il it y p r o d u c t o fAgC1 hig her tha n tho se ob ta in ed by Iv an en ko (41 or Seward . (5~ R epre -s e n t a t i v e v a l u e s a re c o m p a r e d in T a b l e IV B . T h e h i g h e r v a l u e s o b -ta ined h e re r e f l ec t a s s ig nm en t o f a la rge r pa r t o f the so lub il ity a t lowc o n c e n t r a t i o n s t o A g a n d a s m a l le r p a r t t o n e u t r a l A g C 1 .T a b l e V c o m p a r e s p r e v i o u s v a l u e s f or h e a t s o f f o r m a t i o n a t 25 ~o f t h e c o m p l e x e s ( f r o m A g a n d C 1 - ) a n d t h e i r s t a n d a r d e n t r o p i e s w i tht h o s e o f t h e p r e s e n t w o r k . T h e t w o p r e v i o u s s e t s o f i n v e s ti g a t o rsd e r i v e d t h e i r r e s u l t s f r o m m u c h s m a l l e r d a t a s e t s t h a n t h o s e u s e d h e r e .Excep t fo r (AgC1)0 , p rev ious r esu l t s ag ree w i th the p resen t s e t to abou tthe co m bin ed uncer ta in t i e s . In add i t ion , Iva ne nk o (4~ and Sew ard (5~p r e s e n t h e a t s o f c o m p l e x f o r m a t i o n a b o v e 6 0 ~ w h i c h d i sa g r e e s u b -

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    8 74 F r i t z

    I 0 0 , t , ~ ~ _ .~ . .. .. _ .~ ~

    p e r I)~c e n t 4 0

    2 0 . ,. / I0 - 5 . 0 - 4 . 0 - 3 . 0 - 2 . 0 - I . 0 1 .0 2 . 0 3 .0 4 . 0 5 , 0l o g M N a c l M N o c t

    Fig . l . D is t r ibu t ion (pe rcen t ) o f d i s s o lved AgC I be tw een s pec ies as a func t ion o f mo la r i tyo f NaCI s o lu t ions a t 25 ~

    s tan t ia l ly w here ver th ey can be com pared . T he r esu l t s o f Sew ard (5)imply l a rge pos i t ive va lues o f ACp fo r fo rmat ion o f a l l complexes ;p res en t r e su l t s g ive smal l pos i t ive A Cp fo r the neu t r a l and s ing lycharged c om plexes , a nd a sm al l nega t ive ACp fo r A gCI ]-.5.3 . Com parison wi th Com plexes Formed by CuC I

    T he solubi l ity prod uc t o f AgC 1 31) is ab ou t 1000 t im es sm al lert h a n t h a t o f C u C I , a s a r e t h e f o r m a t i o n c o n s t a n t s K~n o f i tsm o n o n u c l e a r c o m p l e x e s . A s a r e s u lt , t h e s t ab il it y c o n s t a n t s o f t h e s ec o m p l e x e s ( T a b le I ) a r e n e a r ly t h e s a m e a s th o s e f o r m e d f r o mCUC1,(29) on the ave rage lower by a fac tor o f two, em pha s iz ing th es t r o n g s im i l ar it y b e t w e e n t h e p r o p e r ti e s o f A g + a n d C u + . I f t h ed imer iza t ion cons tan t fo r AgCl i i s abou t the s ame as fo r CuCI~ (0 .2 ) ,i ts fo rm at ion con s tan t K24 wo u ld be abo u t 1 x 10 ~~ (p resen t va lue ~ /3Na+ > /3K+ > /3NH~ A s w i t h

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    Chloro-Complexes of Si lver Chlor ide 875

    CuCI, no general trends are apparent with C. Comparing the two sub-stances, /3 for AgC1 are larger and C smaller (negative rather thanpositive). These differences imply slower buildup of complex con-centrations for AgC1 at low chloride concentrations, tending towardmore rapid increase at high concentrations.5.4 . Composi t ion o f So lu t ions

    Figure 1 shows the calculated distribution of dissolved AgCIamong the various species in aqueous NaC1 at 25 ~ Concentrations ofNaC1 below 0.1M are given on a logarithmic scale for clarity. Similarsorts of distributions could be derived from the results of Tables I andII for other temperatures or other aqueous media.6 . C A L C U L A T E D S O L U B IL IT IE S O F S IL V E R C H L O R I D E

    The information above makes it possible to calculate thesolubility of silver chloride at chloride concentrations and temperatureswhere good experimental data are not available, to at least the same ac-curacy as the better experimental data. Table VI gives the results ofsuch calculations. The solubility differences from one chloride toanother become apparent only at the high concentrations. The cal-culated values in Table VI agree with reliable experimental data to anaverage of about 5%, where direct comparison can be made. Valuesquoted for 0 ~ represent a small extrapolation in temperature and aresomewhat less reliable.The minimum solubility of silver chloride at low chloride con-centrations is of special interest. Figure 2 is a plot of the solubility ofAgC1 in aqueous NaC1 at 25~ between 4x10 4 and 0.012M. Theminimum solubility of about 4.0x 10TM occurs in 0.0027M NaCI, atabout the point where (AgC1)~ becomes the major contributor to thesolubility. These results are in the range given by Berne and Leden (24)from earlier results, but are distinctly higher than those given byBarney e t a 1 . ( 3 6 ) for KC1 solutions at 25 ~ However, the latter resultsare too low to agree with the known solubility product of AgC1, in aconcentration region where interionic attraction affects are quite small.

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    8 7 6 F r i t z

    T a b l e V I . S o l u b i li ty o f S i lv e r C h l o r i d e f r o m 0 to 1 5 0 ~ aM(salt) 0 ~ 15 ~ 25 ~ 35 ~ 50 ~ 70 ~ 90 ~ 120 ~ 150 ~

    HC1 Solutions0.10 0.00068 0.00169 0.00299 0.00516 0.0111 0.0284 0,0988 0. 20 0 0.5570.50 0.0069 0.0141 0.0224 0.0354 0.6691 0. 16 1 0.515 1.04 2.721.00 0.02 7 0.0495 0.0737 0.1 09 0. 1 96 0 .4 19 1.228 2.36 5.891.50 0.06 8 0.1 17 0. 16 7 0. 23 9 0. 4 0 9 0.821 2,23 4.16 9.972.00 0 . 1 4 0 . 22 7 0. 31 6 0. 44 5 0.735 1.42 3.65 6.63 15.43.00 0 . 4 2 0 .641 0.865 1.17 1.86 3.41 8.22 14.4 31.84.00 0.97 1.44 1.89 2.52 3.88 6.91 16.0 27.5 59.15.00 2.01 2.81 3.65 4.77 7.22 12.6 28.6 48.3 102

    NaC1 Solutions0.10 0.00068 0.00170 0.00300 0.00517 0.0111 0.0284 0.0987 0. 20 6 0.5560.50 0 .0077 0.0153 0.0240 0.0375 0.0718 0. 16 4 0.578 1.04 2.700.80 0.0 21 0.0372 0.0554 0.0824 0.1481.00 0.0 34 0.0594 0.8644 0.1 26 0.2191.50 0.092 0.150 0.210 0.293 0.4852.00 0. 20 0.3 09 0.420 0.57 3 0.9153.00 0 . 6 3 0.942 1.24 1,64 2.514.00 1.59 2.26 2.91 3.77 5.635,00 3.5 4.79 6.05 7.73 11.3

    KC1 Solutions

    0.317 0.927 1.80 4.510.452 1.278 2.41 5.890.936 2.41 4.39 10,21.70 4.13 7.28 16.24.42 10.16 17.1 36.19.63 21.2 35.1 72.018.9 40.7 66.5 134

    0.10 0.00067 0.00166 0.00293 0.00504 0.0108 0.0276 0.0956 0,0200 0.5370.50 0.0083 0.0159 0.0248 0.0374 0.0698 0.1 55 0. 47 4 0. 93 9 2.401.00 0.04 1 0.0699 0.0994 0.14 1 0.2371.50 0. 12 0.1 98 0.271 0.371 0.5922.00 0. 2 9 0. 45 1 0.6 05 0.811 1.263.00 1.20 1.70 2.22 2.89 4,334.00 3.8 5.24 6.64 8.50 12.45.00 11.0 14.8 18.4 23.0 32.7

    NH4CI Solutions

    0.463 1.21 2.22 5.181.08 2.57 4.43 9.632.22 4.99 8.31 17.27,36 15.7 25.4 49.920.8 42.6 67.5 12952,7 106 164 300

    0,10 0.00071 0.00176 0.00313 0.00539 0.0116 0.0297 0.1430.50 0.0085 0.0169 0.0268 0.0424 0.0827 0 .1 93 0.6221.00 0.039 0.0677 0.0989 0.14 6 0. 26 1 0.5618 1.661.50 0 .1 2 0. 18 0 0.2 49 0. 34 8 0.586 1.18 3.302.00 0 , 2 8 0. 401 0. 527 0.708 1.13 2.17 5,753.00 1.2 1.51 1.85 2.32 3.39 5.95 14.54.00 3,9 4.73 5.51 6.56 8.91 14.4 32.35.00 12 13.8 15.2 17.4 22.3 33.5 69.4

    0,216 0.5381,26 3.303.25 8.206.28 15.410.7 25.626.0 64.056.3 126117 257

    g Units: mmol-1 1.

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    Chloro - Comple x e s o f S i lv er Ch lo r ide 8 7 7

    1.0

    S o l yx I0 e

    0 .5 J

    I0 ( 0 . 0 0 5 0 . 0 I OMNaClFig . 2 . Ca lcu la ted s o lub i l i ty o f AgC I (mola r i ty ) in a que ous NaC1 a t 25 aC fo r hos t

    conce n t r a t ions be tw een 4 x 10"4M and 0 .012M.

    7. CR ITIQUE OF PU BLISHED SOLUBILITY DA TAE x a m i n a t i o n o f th e d a t a u s e d i n d i ca t es t h a t m o s t p i e ce s o f e x -p e r i m e n t a l w o r k w e r e c o n s i s t e n t i n t e r n a l l y a n d w i t h o t h e r s w i t h i n t h e

    u n c e r t a i n t y o f t h e w e i g h t e d r e p r e s e n t a t i o n , vizSh 5% (r .m.s . ) form e a s u r e m e n t s a t o r n e a r 2 5 ~ a n d a t c h l o ri d e c o n c e n t r a t io n s o f a t le a s t0 .1 M , a n d 1 3-1 5% f o r m e a s u r e m e n t s at lo w C1- a n d / o r t e m p e r a t u r e sw e l l a b o v e 2 5 ~F o r c h l o ri d e c o n c e n t r a t i o n s a t o r a b o v e 0 . 1 M a n d t e m p e r a t u r e sbe tw ee n 15 and 35 ~ t he r esu l t s o f F o rbes , (11) P ink us an d H au ge n , (16)(17) (18)P i n k u s a n d T i m m e r m a n s , L i e s er , B e r n e a n d L e d e n , (24) a n dK e n d a l l a n d S l o a n (13) a p p e a r t o b e t h e m o s t re l ia b le . T h e r e s u l t s o fP i n k u s a n d B e r k e l a i k o (is) ( r e p e a t e d l a te r b y P i n k u s et aL ) , G a r r e t t e t cL

    (20) Shierholz, (9) Barlow,(14) an d Ja qu es (21) app ear un rel ia ble , diffe ringf r o m t h e o t h e r s b y m o r e t h a n 10% a n d b e i n g e i t h e r u n i f o r m l y h i g h o re r ra t ic . T h e r e m a i n i n g r e s u lt s a r e m a r g i n a l , e x c e p t f o r t h e w o r k o fM i r o n o v w h o s e m e a s u r e m e n t s (25) i n a q u e o u s N a C1 a t 1 8 ~ a p p e a r r e li -ab l e up t o 2 M NaC1, bu t a re d is t inc t l y l ow a t 3 an d 4M. Hi sm ea su re m en t s (~6) a t 25 ~ a re subs t an t i a l ly l ow.F o r t h e h i g h e r c h l o r i d e c o n c e n t r a t i o n s a n d t e m p e r a t u r e s a b o v e35 ~ t he r esu l t s o f D ed e and W alther ,(14 ) Ivanenko , (4 ) an d S ew ard (is)

    appear r e li ab l e wi th in t he 15% l imi t . S ew ard ' s r e su l t s fo r t he h igh erc o n c e n t r a t i o n s a t 1 00 ~ a r e i n e x p li c a bl y l o w c o m p a r e d w i t h t h o s e o fI v a n e n k o a n d t h e g e n e r a l t re n d s o f o t h e r d a ta .F o r c h l o r i d e c o n c e n t r a t i o n s b e l o w 0 .1 M , t h e r e s u l t s o f L i e s e r (18)a n d M i r o n o v (23) a r e i n g o o d a g r e e m e n t w i th e a c h o t h e r a n d w i t h t h e

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    pre sen t work . Th ose o f Jon t e and M ar t i n ~22) i n aqu eou s NaCI a t 15 and25 ~C appear re l i ab le bu t t ho se a t 35 ~ a re marg ina l l y h igh . T ho se o fBe rne and L ed en

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