AR HIV Z A KEM I JU 26 (1954) 191

The Complex and the Composition oi Aqueous Complex Solutions oi Halides and Silver * J. Kratohvil, B. Teiak and V. B. Vouk Applied Chemistry Laboratory, School of Public Health, and Laboratory of Physical Chemistry, Faculty of Science, University of Z agreb, Croatia, Yugoslavia Received June 27, 1954 The' numerous data on complex solubility of silver halides and silver thiocyanate in aqueous solutions have been systematized and the solubility curves constructed. The data are discussed· in relation to the experimental techniques used, to the effect of the ionic str~ngth, and to the influence of the accompanying cations from halide component. The comparison of the solubility curves for various silver halides and silver thiocyanate has been made. In order to evaluate the composition of the complex solu­ tions and to determine the stability constants of the soluble com­ plex ionic species present, use was made of a simple graphical method. By , this method the solubility data from the literature as well iJ,s from the own determinations are interpreted and the results of the interpretation compared with the conclusions of other authors. The reliability of the interpretation of the solubi­ lity data: is discussed.

In the coude of the investigation of the precipitation processes of silver halides and silver thiocyanate the need has arisen for knowing the data of complex solubility of these precipitates in the solutions with excess of the one of the ionic ·constituents of crystall lattice. The data of complex solu­ bility together with the data for the ionic solubility define the solubility curve of a heteropolar precipitate and at the same time the concentration region in which the formation of the solid phase can proceed at all. By inspecting the relevant literature we could not find a systematic, thorough and comparing review of the data, obtained by various techniques and by various authors, of complex solubility of silver halides and silver thiocyanate in aqueous solutions. It seemed worthwhile to make such a review using the data from the literature as well as the results of our determina­ tions.1· 2• 3 We considered also that it would be of interest to investigate the region ·Of the complex solutions of silver halides and silver thiocyanate in order to obtain some insight into the composition ~nd the character of the soluble complex ionic species present. For this reason we elaborated a direct gra-

* This. paper is based on a part of a thesis submitted by J. Kratohvil to the Faculty of Science, University of Zagreb, (April, 1954) in partial fulfillment of the requirements for the degree of Doctor of Chemical Sciences. 192 J. KRATOHVIL, B. TEZAK AND V. B. VOUK phical method for the evaluation of the composition of complex solutions. This method made possible also the determination of the stability constants of the complex ions.

THE SOLUBILITY CURVES OF SILVER HALIDES AND SILVER THIOCYANATE IN AQUEOUS SOLUTIONS As the graphical presentation of data is more convenient for our pur­ poses than the tabulation we are giving them in the diagrams: logarithm of the total concentration of silver ions versus logarithm of the total concen­ tration of halide or thiocyanate ions (Fig. 1., 2., 3., 4., 5., and 6.).

011<1 • GLEDHILL MALAN I :o f"OR&S; CORSESaod COLE . r ENDALl. aod SLOAN p JONTE ond MARTIN o 0 0 q PtNKUS and. HAUGE:N o 0 COMP\.U o d PINKUS ond TlMM(RMANS SOLUBILI T Y o PlNKUS,FREOERlC ond SCHEPMANS .. • U:DEN; BERNE aod LEDEN r /-'l_·.o-5 /_ _ _ +--o------1 - &RNE ond LEDEN /l,.Q2/ zs•c · 2 I I

ION IC. SOLU9JLtT '1 COMPLEX -6 SOLUBILITY

LOG. CNaCI /N/

Fig. 1. S olubility curve of s ilver chloride in a queous solutions a ccording to the data of F o rbes,• Forbes a nd Cole,' Kendall a nd Sloa n ,• P inkus a nd H a u gen ,' Pinkus and Timme rma ns,• Pink u s, F rederic and Schepmans,• J onte a nd M artin,•• L e d en,11 Bern e a nd L e den,12 ·a nd Gle dhill and M alan."

The data presented in Figs. 1. to 6. have been obtained by means of 17 20 various experimental techniques (by observing Tyndall effect1· 2• 3, 4• 5, s, s, • , 18 by analyses of the saturated solutions of solid precipitate6, 1, 11• 14, l 5, l 6, • 20 21 22 10 12 18 19• • • , or by using radioactive tracers • • ). However , we can note the satisfactory agreement between the data of various authors except at the solubility minima (for AgCl and AgBr). But just in these concentration re­ gions the e xperimental difficulties and uncertainties are considerable18. The effect of the ionic strength can be noted also at the solubility minima as well as in the ionic solubility region (provided that the differ ences observed · are not due to the experimental errors). With increasing concentration of the solid phase the influence of ionic strength is considerably diminished or almost completely absent. COMPLEX SOLUBILITY OF SILVER HALIDES 193

It is very interesting to compare the complex solubility curves of silver <:hloride in the solut~ons of various soluble chlorides (Fig. 2. and 3.) . It is evident that complex solubility of increases in the order:

HCl < NaCl < LiCl, KCl < NH4 Cl, and MgCl2 < CaCl2 < SrCl2 < BaCl2 , r especti­ vely. These series correspond (except LiCl) to the increase in size of the accompanying cations from the alkali and alkaline earth m etal groups of -the periodic system of elements. The influence of the accompanying cation irom halide component decreases with the increasing dilution of the solutions. J t may be possibly connected with the sterical factors.

o MgC!, KENDALL and SLOAN

p CoC/2} • SrCl 2 FORBES

o.. BoCl2

+ PRECIPITATION ·

1S'C 1s·c 0 0 LOG. CONC. MeCl /IV LOG. CONC. MeCli /N/

Fig. 1. Fig. 2. :Fig. 2. Complex solubility of silver chloride in aqueous solutions of HCl, LiCl, NaCl,· KC! iind NH,Cl according to the data of Forbes,• Kendall and Sloan,• and Erber and Schiihly." :Fig. 3. Complex solubility of silver chloride in aqueous solutions of Mgci,, CaCh, SrC!, and BaC!, according to the data of Forbes• and Kendall and Sloan.• Fig. 7. represents the solubility curves of all silver halides and silver thiocyanate. For constructing this diagram we have chosen the data obtained with the solutions of uncontrolled ionic strength because these data are more numerous and more complete. From Fig. 7. the following conclusions can be made: 194 J. KRATOHVIL, B. TEZAK AND V. B. VOUK

'<> HELLWI(; /KBr/

•1

-2 z' ' -3 <(."' u z 0 - 4 u 8 L'i 0 _J "t., -5

COMPLEX SOLUBILITY -6

-7

•8 1 0 -z -3 -4 -5 - 6 -7 LOG CONG Br- /N/ Fig. 4. Solubility curve of in aqueous solutions according to the data of Hellwig,'*" Erber," Chafoau and Pouradier,11 Berne and Leden,1s Vouk, Kratohvil and Tezak,' and Gledhill ' ' and Malan."

COMPLEX SOLUBILITY

d HCLLWI(, - Kl COMPL("X p E:R&CR - HI SOLUBILITY .. SCHULZ and Td AK - t

15 •

...L.....~~~-'-~~~~ ...... ~~~--:.,'-'-~~~-:-~~~~~

LO(; Cr /N/ P'lg. 5.. Solubility curve of in aqueous solutions according to the data of Hellwig,'"' Erber," King, Krall and Pandow,20 and Schulz and Tezak.1 COMPLEX SOLUBILITY OF SILVER HALIDES 195

COMPL[X SOLUBILITY 0 .. _,

\ P HELLWIG 'O RANDALL and HALF"ORO -2 +, 0.. o k'R ATO~-NI L /20• / "z • CAVE and HUME /1 • 2 0/ "y3 "' u .. COMPLEX 0-4 o. --' SOLUBILITY " -5

-6 25"C

- 7 0 -2 _,

LOG CKCNS / N / Fig. 6. Solubility curve of silver thiocyanate in aqueous solutions according to the data of Hellwig," Randall and Halford," Cave and Hume" and Kratohvil.'

COMPUX SOLU01LIT Y

PR(C IPIT AT ION

-3 "~

IJ~ . 4 IONIC SOLOOUTY

~ -5

SOLUBILITY - 6

-7

- 8

0 -2 -3 - 4. - 5 -6 -7 -8 LOG C,- /N/ /X- : a·. Br: Cor CNS- _, Fig. 7. A shematic diagram representing the solubility curves of silver halides and silve thiocyanate iin aqueous solutions according to the data from Figs. 1., 4., 5., and 6. 196 J . KRATOHVIL, B. TEZAK AND V. B. VOUK

a) The complex solubility in the solutions of the corresponding soluble halide or thiocyanate (for amounts of solid phase greater than ~ 10-5 M) in­ creases in the order: AgCNS > AgJ > AgBr > AgCl. b) Increase of the complex solubility in the solutions of silver is in the order: AgI > AgCNS > AgBr > AgCl. c) More silver ions are necessary for dissolving the same amount of solid phase than halide or thiocyanate ions.

THE COMPOSITION OF AQUEOUS COMPLEX SOLUTIONS OF SILVE R HALIDES AND SILV ER THIOCYANATE AND THE STABILITY O F COMPLEX IONS In order to evaluate the composition of the complex solutions and to determine the constitution of the soluble complex species and their stability in the various concentration ranges, we made use of a new, simple, graphical method. To illustrate this method it seemes the best to. use an example. We have chosen the data of our determinations of the solubility of silver bromide 2 in the solutions of potassium bromide and , completed with the results of Hellwig15 and Chateau and Pouradier17• We were interested, namely, in the changes of the concentration ratios of the precipitating components at the boundary of the solubility region and the precipitation region. If the logarithm of the concentration ratios of silver and bromide ions are plotted against the logarithm of the corresponding con­ centrations of bromide ions in excess (Fig. 8.), the solubility curve dissolves

0 HELL\NIC o l

·~di <.) .,,, u<' · or-~~--'

0 -1 -2 LOG C1

- ' 0 HELLWIG I _2 ,___,.~---+---"<-----+----~~C_H_A_T_E_A~U_a_n_d_P_OU_RAD_+l(_R_ __, o KRATO~Vll

.-5

-7

' 8 1"_._._._ _p....._.~_.__ ,~~~-~2,_._~~-~3~~~--.~~~...... _._~_6...... ~~-~,--'-J

LOG Ca,- / N/

Fig. 9. Solubility curve of si[ver bromide in aqueous solutions of potassium bromide and silver .n itrate approximated by ttle secant s having coordinat es determined by Fig. 8 (lower curve) and Fig. 10. (upper curve). b is the slope of a secant.

0 z ..J"' ,-4 1------1\------+----~-1 .;; u " 0 0 _J

LOG. CAg NO,

Flg. 10. P lot of the concentration ratios of bromide and silver ions at the solubility -bound;tJ,'Y,. · versus the corresponding concentrations of silver ions. · · · 198 J. KRATOHV.IL, B. TEZAK AND V. B. VOUK

into several intersecting straight lines. The intersection points are marked with arrows. The corresponding apscissa values (concentrations of bromide ions) were transferred to the solubility curve of Fig. 4. and through the points ·so obtained straight lines were drawn (Fig. 9. , lower part). These lines are the secants of the solubility curve but in the majority of cases they deviate very little from the curve because of small curvature. By each secant of the Fig. 9. the value of its slope is indicated. It is striking that these values are nearly the whole numbers in each case. The same procedure was performed with the solubility data for silver bromide in silver nitrate solutions (Fig. 10. and upper part of Fig. 9.) . From Fig. 11 . it is apparent that the same could be done with other silver halides and silver thiocyanate.

AgCl · No.et• f"ORSES 1 KENOAU. ond SLOAN; JONTt ord MAATIN1 PINKUS" AgBr· K Br ' HELL\JIG; CHATE: AU Gl'ld POU IU.DICR1 KAATOMVIL Agl • Kl : HELL\JlCt SC HULZ

CAVE oncf HUME:

u·~ '~ u

.,u, ~~~~--~-1..~~~.~.~~~7_ ,~~~~----_, LOG C,. / N/ /X'•Cl·. e.; 1; CNS'' Fig. 11. Plot of the concentration ratios of silver and h alide, resp. thiocyan ate ions at the solubility boundaries versus the corresponding concentrations of halide, resp. thiocyanate ions.

Now the question arises about the .physical significance of these straight lines (secants) and the values of their slopes respectively. If the ions Ag+ and x - (X- = c1-, Br-, r- or CNS-) form complexes with one another, then in the saturated solutions with excess of x- ions the following 11 18 equilibria should exist for the dissolution of the solid AgX •

m AgX (s) + (n--m) x- "" >-- Agmxr;:-n (1) with the equilibria constants (AgmX::'- n] km, n- m = [X-] n-m (2)

If no polynuclear complexes (m > 1) are formed in the solution, but only mononuclear (m = 1), the dissolution equilibria may be represented by COMPLEX SOLUBILITY OF SILVER HALIDES 19<)

AgX (s) + (n-1) x- ~ ~ AgX~- n (3} with the equilibria constants

(AgX~-n) k1 , n- 1 = . (X 1n- l (4)

The stability constants of the complex species (redprocail values of the dissociation constants of the complex) are defined by the following equilibria:

(5 ) A xm- n) ~ . [ gm n . m, n = [Ag+im [X-]n (6) where m and n have the same values as in (1) and (2) . Dividing eq. (2) by eq. (6) we obtain km, n-m --'----- = [Ag+im [X-]m = Lm (7) ~ m . n (L = solubility product), which in the case of mononuclear complexes becomes

k1 , n- 1 --= [Ag+] [X-] = L (8) ~1,n It follows from the eq. (7) or (8) that by knowing the equilibria constants of dissolution and the solubility product it is possible to compute the stability constants. The equations of the straight lines of Fig. 9. (lower part) are:

log [Ag+] =log a+ b log [X-] (9) where log a is the segment on the ordinate and b the slope of the straight line. If only mononuclear complexes are formed in solution, i. e. if the dissolution equilibria may be represented by (3) and (4), then

(10) By taking logarithms of both sides of the eq. (4) and using eq. (10) we obtain

log [Ag+] = log k 1, n- 1 + (n--1) log [X-j (11) By comparing eq .(9) and (11) we see that

a = k i, n- 1 (12)

b = n-l (13)

It means that the values of the s lopes of the straight lines ( secants) by which the solubility curve is approximated represent the number of ligands minus one, bound to the cetral ion in mononuclear complex. This complex predominates in the concentration region of the component in excess defined T;\.BLE: ! l\;) ·o The results· of the interpretation of the soh.ibility data for silver chibride <::? · · in aqueous solutions

Graphical m ethod (Kratohvil ; Tefak, Vouk) Stab. const. ~mn Author Ref. CCI (N) .corn.plex

· · SoluJ;iilit". Potention :. l Sl~peCCI (N) Complex i3m,n ' I I -

' 3- '.'--< BodHi.nder 23 about 4 · . .AgC1 4 5 X 105 and Eberlein ' ~ ~ Forbes (NaCl) 4 AgCl~- 2.2 1-2.5 AgCl~- 5.1 x 1os ~ 0 1-5 Agel;- 3.1 >3 Ag Cl~- 2.0 x 105 ~ { I-< AgCl~- r ~ AgC12- 3.1 x 1os F~rbesand 5 < 0.04 ,' AgCl(aq) 1.1 0.05-0.5 >-3 Cole (NaCl) t::I 0.1-0.5 AgCii- 2 x 1os &:' ~ Forb_es; 4 AgCl(aq) z~ < 0.5 ti

Forbes and 5 AgClj- 0.94 0.01- 0.5 AgCli- 2.2 ~_105 Cole ·(HCl) 1 :0::: ' ~ Agc1;- 1.9 0.6-2 AgCl~- 4.5 Xl05 · I (§ 0.6-6 l\gc1;- 2.98 3-6 Ag Cl!- 1.7 X 10° q { ~ AgCl~-

. 14 Erber and 5-12.5 Ag Cl!- 8 X l05 2.98 6-10 Ag Cl~- 1.7Xl05 Schiihly (HCl)

Pinkus and 8 0.0 0.001-0.01 AgCl(aq) 3.4 X 1Q:J Timmermans (HCl) 0.94 0.01-0 .5 AgCii- 2.2 x 105 1.9 0.5-1 AgCl~- 4.5 X 10s

J aques 24 I 2.0 0.6-3 f\gCl~- 3.9 x 1os

3.0 A, 1.2 X 105 4-10.. gCI!- -~ Korenman 25 ? Agc1;- 4.3 X l0 5 n Jonte and 10 AgCI(aq) 2.0 ><103 0.0 0.001-0 .01 AgCl(aq) 3.4 X 103 M artin < 0.1 ~ { 'tl AgCii - 1.8 x 105 0.9 0.02-0 .1 AgC12- 1.6 X 105 t' M :>< Led en; 11 0.0.01-0 .01 J\gCl(aq) 1.2 x 103 0.0 5 1 O.OQQ(i-0.005 AgCl(aq) 5.0 X lo a tll Berne and 0 t-< Led en (I = 5.0) 12 < 1 AgCii - 2.5 x 105 . 1.0 0.01-0 .1 Ag Cii - 4.2X~05 I ~ ......

> 1 AgCii- 1.4 x 106 1.6 x 106 1.9 3 0.2-2 ~gc1j- 2.5 X 106 E:l >'l -- Kl > 1 Age}!- 2.0 X 1os 1.1 X 1os 2.7 3-5 I Agel!- 1.2 x 106 0 t"Ij Berne and 12 0.001...::_o.01 AgCl(aq) 7.0 X 102 Ul Leden (I = 0.2) t1 <: < 0.2 AgCii- 5.3 X l04 1.0 0.02-0 .2 AgCli- 7.4 x 104 trJ ::!J CAg (N) CAg (N) t:I1 \ :i>­ Pinku s, Frederi c I t-< 9 AgCl(aq) 1.13 X 103 -0, 03 0.001-0.01 AgCl(aq) 1.7 X l0 3 ...... and Sch epm ans 0.0~05-0.3{ t1 t, 0.3 2.2 0.8-2 I AgaCI2+ I 2.8 X 105 Bern e and Leden) { Ag 4CI3+ 2.0 X 1os Hellwig 15 ? Ag2CI+ 5.0 X l0 6 (Interpretation: I.\.) Yatsimirskii) .26 I -0 TABLE It tv The results of the interpretation of the solubility data for silver bromide s in aqueous solutions.

Graphical method (Kratohvil, Tefak, Vouk) Stab. const. ~mn Author Ref . CBr (N) Complex Solubility Potentiom. s1gpe l CBr (N) Complex I I ~m.n

L,Iellwig 15 >2 AgBr~- 4.2 >2 AgBr~- 3.0 X'108 ~ ?: ?XJ or Ag2Br!- 3.0XJ020 ~ - 0 AgBr!- ::i: Bodlander 23 ? 8.5X10s <..... and Eberlein _t"'

Erber (HBr). 16 2-9 Ag2Br:- 1.3 x 1010 3.3 2-9 AgBr!- 3.2 X 1os ~

~ N 0.5 AgBr~-· 5.3 X 10s .6 AgBr~- Chateau and 17 < 2.2 0.3-0 7.0X IOS ~ Pour a di er ~ 3.0 O.S-2.5 AgBr:t- 9.6 X 108 z~ t1

>1 AgBr~- 2.0 X 109 3.97 >2.5 AgBr~- 4.0 X IOS ~ ~ .. < orAg2Br!- 4.0 X 1020 0

~ Berne and 18 < 0.5 AgBr2- 1.7 X l07 Leden (I = 5.0)

AgBr~- 1.2 X l09 8.0 X108 1.92 0.05-0 .3 AgBr~- 1.5 x 109 0.5-3 { AgBr:t- 1.6 X 109 1.4X109 2.76 1-5 AgBr!- 3.0X l09

> 3 Ag2Br!- - 1020

· ·

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+ +

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Br

Br3

Br!-

4

3

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AgBr~-

AgBr!

AgBrz

AgBr~

AgBri

Ag

AgBr~-

Ag

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AgBr(aq) AgBr(aq)

AgBr(aq) AgBr(aq)

or or

4 4

1 1

.

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.

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6-4 6-4

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Kratohvil Kratohvil

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Kratohvil Kratohvil

T

T

, ,

rpretation imirskii) imirskii)

s

e

nd nd

ouk, ouk,

and and

a

Leden Leden

Yat

Hellwig Hellwig

(Int

Y

Berne Berne

Vouk , , TABLE ill l>-.) The results of the interpretation o'f the solubiiity data for silver ioQ,ide ~ in aqueous solutions

St b t (3 Graphical method (Kratohvil, Tefak, Vouk) a . cons. m n I Author I Ref. I C1 (N) Complex ISolubility Potentiom. Sl~peI cl .f,N) I Complex (3m,n

Hellwig 15 I AgI2- 3.0 0.3-0.8 AgI!- 1.0X1014 .::-< .:;;: 0.3-2 :;e •:i>.., Ag I~- 3.83 0.8-2 Ag I~- 1.5Xl014 1 0 :I: 7.0.~ 1.Q29 or Ag2I!- ~ ~ Bodliinder 23 ? Ag I!- 5.5 X 1015 r Eberlein and I I I ~ ,.,, ? Ag2I:- M N< ;i. ~ ? Ag2I!- ;i. I I z t1

? Ag2I:- I I ~- p:i <· Ag2I~- ~ 1030 0 ? I I I I q ~

Korenman 25 I ? Ag I!- I 2.5 x 1014

King, Krall 20 < 1 Ag I~- 1.94 0.1--,0.25 AgI;- 4.0 X 1013 and Pandow I I

>1 po~ynuc~~ar 2.93 Q.4-2 Ag I!- I l.4 X l()14 complexes •

1 '

;

~ () 0

,, t:-< t:-< tzj Oi

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.

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15

26

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and

(HI)

Tefak

Erber

Schulz

Hellwig Yatsimirskii) (Interpretation TABLE IV N The results of the interpretation of the solubility data for silver thiocyanate ~ in aqueous solutions .

Grap hical method (Kratohvil, Tefak, Vouk) Stab. ccinst. ~mn Author Ref . CONS (N) Complex Solubility Pot entiom . s1gpe I Complex CONS (N) I I ~m.n Hellwig 15 0.6-1.2 AgCNSi - I 2.82 0.6-1.2 AgCNS~- 5.0 X 1010 :-< I ::>:: l::d

Randall and 21 2.87 0.3-1 AfCNS!- 5.0 X 1010 ~ Halford 0 <::i:: Bodliinder 23 ? AgCNS2- 6.0 X 109 ..... and Eberlein r ~ 1.4X 1011 1.5 X l011 AgCNS!- t-3 l'J N< ;i. Ferrel, 27 AgCNSi - 4.0 X 1010 ::>:: j ;i. Ridgion and 0.6-0 .9 l Riley ~ l AgCNS~- 6.0 X 1010 t1 :<:

Cave and 22 < 0.2 AgCNSi 1.5 x 108 ~· Hume < 0 2.0 x 1010 c::: < 0.2 AgCNS~ 2.0 X 109 2.1 ' 0.04-0.13 AgCNsi - ::>::

> 0.2 AgCNS!- 1.0 X lOlo 2.8 0.2-2 AgCNS~- 6.0 X 1010

Kratohvil 3 2.1 0.08-0 .15 AgCNS~- 2.0 x 1010

I 2.8 0.15-1 AgCNS~- 6.0X l010 I I COMPLEX SOLUBILITY OF. SILVER HALIDES 207 by .the corresponding apscissa values of the points through which the secants are laid. Thus the possibility is given for determining the composition of the com­ plex species present from the solubility curve of silver halides and silver thiocyanate. According to the eq. (12) the segment on the ordinate represents the equili­ brium constant of dissolution of AgX and the formation constant of the cor­ responding complex respectively. By means of the. relation (8) it is possible to compute the stability co.nstants of the mononuclear complex ions of silver halides and silver thiocyanate. Naturally, quite analogous considerations and relations are valid for the solubility of silver halides and silver thipcyanate in solutions with excess of silver ions . Lt is necessary to point out that in each concentration region of the com­ ponent in excess, defined by the limiting points of the secant, besides the dominant complex the presence of other complexes is also possible; That may be the reason for the difference of the values of slopes from whole numbers. Between rthe regions determined by each line (secant) there may be very often small ,transition regions without any dominant complex species. The slope of the steepest line on the Fig. 9. is b = 4.2, meaning that in the <;orresponding concentration region of bromide ions the complex AgBr §- predominates. As the probability for the existence of such a complex is small we have to assume the formation of polynuclear complexes at high · concen­ trations of the component in excess, e. g. according to the following equilibrium:18 2 Agxi- ~ >- Ag2x:- + 2 x- For the formation constants of polynuclear complexes eq. (2) is valid. If we suppose that

(14) we can write [Ag+] a km, n-m = _m_ [_X___ ] _"_ _m _ = m (15) where a is the segment on the ordinate. If the values of m are assumed or if they are known from other ·sourcesg, e. . fr.om potentiometric measurements, then the slope of the straight line (n-m) in eq. (15) will represent the tot.al number of ligands (n) minus the number of silver ions (m) bounding these ligands. The value of aim gives the possibility of computing the stability constants ~ m . n by means orf eq. (7). By using the procedure described previously w e have interpreted the data of our own determinations of complex solubility and the data of other authors whose r esults were r epresented in Fig. 1. to 6. Tables I, II, III, and IV give the r esults of the interpretation of the solubility data of the various authors as well 208 J . KiiATOHVIL, B. ·TE2AK AND v: B. VOUK

as the results .of the potentiometric measurements in the complex solutions of silver halides and silver thiocyanate. In each table the author's name, the reference, the concentration .range of the component in excess in which the measurements were performed and the corresponding stabiJity constants ~m . u are indicated. On the right side of each table the results of the interpretation of the solubility data using the gr:aphical method described above are also given, It ·is evident from these tables that the interpretation of the comple:X: solubility data by ·various methods led to essentially the same results and that the agreemerit between the values of the stability constants computed by our method and the values determined by other authors is quite satisfactory. : · With regard to our graphical interi:)retation of the experimental results: it is necessary to remark that we are riot able to · establish with certainty. the presence of the polynuclear complex ions. The same holds also for other· methods of interpretation of the solubility dat a. Thus,' the conclusionS obtained fr.om tlie experiments at high concentrations' of the component in exceS.S, where the formation of polynuclear complexes is most ·probable,. are not necessarily always the correct ones and the only possible (e. g. the data of E.rbei; 'especially for silver iodide). But if we take into account tha:t maximal coordination number of silver is four, and that at high concentrations w~ approa~h the ratio [Ag] : "[X] ~ m ·: n, where rn and n are numbers ~ven smaller. than 5, .'and if we make use of the resuits from other experiments, e. g. · potentiometri~ measure­ ments, · then· -the ·conclusions obtained from the interpretation of the solubility data at hiigli concentrations can be accepted with confidence.

REFERENCES 1. K. Sc h u 1 z and B. Te z,a k, Arhiv kem. 23 (1.951) _200. 2. v. B. Vouk, J. Kratohvil and B. Tezak, Arhiv kem. 25 (1953) 219. 3. J. K rat oh. v i), Thesis,. University of Zagreb (1954). 4. G. S. Forbes, J. Am. Chem. · Soc. 33 <(1911) 1937; cit. from A. Seide 11, Solu­ bilities of Inorganic and Metal Organic Compounds, 31.'d Edit., Vol. 1., · New: York 1940. 5. G. S. F o r bes and H. I. Co 1 e, J . Am. Chem. Soc. 43 (1921) 2492. 6. J. Kenda 11 and C. H. Sloan, J ._ Am. Ch~m. Soa. 47 (1925) 2306. 7. A. PI n k us and M. Haugen, Bull. soc. chim. Belges 45 (1936) 693. 8. A. Pink us and A. Timmermans. Bun. soc. chim. Belges 46 .(1937) 46. 9. A. Pinkus, S. Frederic and R. Schepmans, Bull. soc. chim. B elges 41' (1938) 304. 10. J . H . Jonte and D.S. Martin, J. Am. Chem. Soc. -74 (1952) 2052. 11. I. Led en, Svensk Kem. · Tidskr. 64 (1952) 249. 12. E. B er n e and I. Led en, · Svensk Kem. Tidskr. 65 (1953) 88. 13. J. A. Gledh.ill and G. McP. Malan, Trans. Faraday Soc. 50 .(1954) 126. 14: W. Erber and A. Schiihly, J . prakt. Chem. 158 (1941) 176; cit from C. A . 35 (1941) 7801. 15. K. He lJ. wig, z.: anorg. Chem. 25 (1900) 157; cit. from Chem. Zentr. 1900, II, 715, and A. S e ·i de 11, of Inorganic and Metal Organic Compounds, 3rd Edit., Vol. l., New York 1940. 16. W. Erber, Z. anorg. ang. Chem. 248 (1941) 32. 17. H . Chat ea u and J. Pour ad i er, Science et inds. phot . ~ 24 (1953) 129. 18. E. Berne and I. Leden, Z. Nat'urforsch. Sa (1953) 719. 19. W. Erber, Z. anorg. allg. Chem 248 (1941) 36. . . 20. E. L. King, H. J. K r a 11 and M. L. P and ow, J . Am. Chem. Soc. 7

o23. d G. B 1 a n d er and W. Eber 1 e in, Z. anorg. Chem. 39 (1904) 197 ; cit. from Chem. Zentr. 1904, I, 1243. 24. S. Jaques, Helv. Chim. Acta 29 (1946) 1041. 251• I. M._ Koren man, J. Gen. Chem. (U.S.S.R.) 16 (1946) 157. 26. K. B. Ya t s i mi r ski i, Doklady Akad. Nauk S.S.S.R. 77 (1951) 819 . .27. E. Ferrell, J.M. Ridgion and H . L. Ril ey, J. Chem. Soc. 1936, 1121.

IZVOD Kompleksna topljivost i sastav kompleksnih vodenih otopina argentum halogenida i argentum rodanida J. Kratohvil, B. Te2ak i V. B. Vouk Sredili smo mnogobrojne podatke iz literature za kompleksnu topljivost argen­ tum halogenida i argentum rodanida i nacinili krivulje topljivosti (apscisa: log. ukupne koncentracije halogenid, odnosno rodanid iona; ordinata: log. ukupne kon­ -centracije argentum iona) (SL 1. do 6.). Diskutirali smo podatke topljivosti s obzirom na upotrebljene eksperimentalne m etode, utjecaj ionske jakosti i utjeca j popntnih kationa iz halogenidne komponente. Usporedili smo krivulje topljivosti za ra.zlicite argen tum halogenide i argentum rodanid (SL 7.). Da bismo odredili sastav kompleksnih otopina i izracunali konstante stabiliteta prisutnih kompleksnih iona, razradili smo jednu jednostavnu, graficku metodu. Obradom eksperimentalnih podataka konstatirali smo, naime, da se krivulje toplji­ ·vosti argentum halogenida i rodanida mogu aproksimirati nizom sekanti, cije se vrijednosti nagiba malo razlikuju od cijelih brojeva (Sl. 8. do 11.), a predstavljaju broj ligan,ada manje jedan vezanih u mononuklearni kompleksni ion. Taj kompleks domiriira u koncentracijskom podrucju komponente u suviSku, definiranom koordi­ natama tocaka na krivulji topljivosti, kroz koje je povucena sekanta. Na taj smo n acin obradili podatke iz literature i rezultate interpretacije usporedili sa zakljuccima ·drugih autora (Tabl. I. do IV.). Konstatirali smo, da ·Se rezultati podudaraju kako s obzirom na sastav prisutnih kompleksa, tako i s obzirom na vrijednosti odgovara­ jucih konstanti stabiliteta.

LABORATORIJ ZA PRIMIJENJENU KE).VIIJU SKOLA NARODNOG ZDRAVLJA MEDICINSKI FAKULTET, ZAGREB • Primljeno 23 . jula 1954 . FIZICKO-KEMIJSKI INSTITUT, :PRIRODOSLOVNO-MATEMATICKI FAKULTET, ZAGREB