93
Solubility of Silver Chloride in Methanal-Water, ater, and Dioxane-Water Mixtures
by K. P. Anderson,* E. A. Butler, and E. M. Woolley Depnrtinent of Chemistry, Brigham Young University, Provo, Utah 84601 (Received August 81, 1970) Publication costs assisted b y Brigham Young University
Results of a study of the solubility of silver chloride at 25’ as a function of chloride ion concentration in 10, 20, 30, 40, a,nd 50% by weight methanol-water, acetone-water, and dioxane-water mixtures and in a 60% by weight, dioxane-water mixture are presented. These results were obtained with a previously established radiot,racer technique that is modified to include specific ion electrode measurements. All observed solubilities! are interpreted in terms of the presence of silver ions, undissociated silver chloride molecules, and dichloroargentate ions. Values of the thermodynamic equilibrium constants relating the activities of these specierr t o the chloride ion activity are obtained by a lenst-squares treatment of tJhesolubility da,ta for each solvent mixture. The observed changes in these equilibrium constants are discussed in terms of electrostat,ics theory, hydration theory, and other specific solvent effects.
Introduction The work reported in this paper is a continuation1 of our study of the solubility of silver chloride as a function of chloride ion concentration in aqueous-nonaqueous solvent mixtures. The solubility of silver chloride and the various equilibria involved has been investigated in 10, 20, 30, 40, and 50% by weight methanol-water, acetone-water, and dioxane-wa ter mixtures and in a GO% clioxane-water )mixture a t chloride ion concentrations betneen ]LO-” and lo-’ M . A radiotracer technique describedl previously1 was used to determine total silver concentrations. The measurement of silver ion concentration with an Orion Model 94-16 sulfide specific ion electrode supplennented the tracer technique. Our purpobe was to determine quantitatively the effects of the composilion of’ the solvent on the concentrations and equilibrium constants of the silver-containing species in solution for different solvent systems and to interpret these effects. The results of a previous investigation OF the solrrbiliity of silver chloridc in water and in eliianol-water mixtures are included in our discussion and arc plotted in all figures.
~ ~ p e r ~ ~~~~~~~~~¶ ~ntal A11 chenzicais used were reagent grade. Solutions were prepared from doubly distilled water which had a specific conduotance 2, even in 0.13 M chloride ion solutions. The second term on the right-hand side of eq lb, K&'yo*, is the B term of Table I and is equal to the molar concentration of the undissociated AgCl species in each solution. If the activity coefficient, yo*, is always unity, then this B term remains essentially constant in all the solvents studied and differences in the experimentally obtained values can be attributed to
~OLU13ILITYOX’hgCl IN
v ARIOUS WATER MIXTURES
6, 3 o
a2
0.4
0.6
( y- 1.273)
0.8
Figure 1. Plots of 6 s = log 5 (water) - log B (solvent), = log Iiz (solvent) -. log Kt (water) +1.20, and 6, = log K , (water) - log K , (solvent) 2.00 according to Born electrostatic motlei (oq 2): e, solvent = water;’ 0, solvent = ethanol-water mixtures ; I A, solvent = methanol-water mixtures; x, solvenl = acetone-water mixtures. The lines correspond to the least-.squares slopes in Table 11. 62
+
(y.-
1.273)
Figure 2. Plots of 6s = log B (water) - log B (solvent), 62 = log IC2 (solvent,) -- log Kz (water) $0.60, and 6, = log K, (water) - log K , (solvent) 1.50 according to Born electrmtatic model (eq 2 ) : e, solvent = water; 0, solvent = dioxane-water mixtures. The lines correspond to the least-squares slopes in Table 11.
+
experimental. uncertainty. The values of -log B are plotted vs. the reciprocal of the dielectric constant of the solvent mixture in Figures 1 and 2 . Experimental uncertainty may well account for the deviation of B from its value in pure water in all except the methanol-
95 water solutions. The deviations of B from the pure water value in methanol-water solutions appear to be greater than can be attributed to euperimental error and may indicate deviations in yo* from unity, pussibly reflecting solvent-solvent interactions or partial solvation of species by methanoLg In the calculation of values of KI and K:! we have assumed in all cases that variations m 5 were caused either by experimental error or by variations in yo* so that the product of &IC, is always equal to if,a value in pure water. ‘The tabulated values of K , were also calculated using this assumption. The values of --log K , En Table I for aqueous mcthanol solutions and for the 205x, dioxane -n;ater solution are in good agreement with R, values (obtained by emf measurements of cells with liquid junrt)ions) recently d 1. reported by Feakins, et u,1.l0 KrstLohvll ~ n Tea&] report values of K , and RI for a 50% c4hml-wster mixture and. for a 48.5% acetone -w;&r mixture (obtained by solubility measurememtsl that ave in reasonably good agreemeiit with the values in ‘P’:hle l. wlrich considers clecAn equation derived by trostatic interactions has the gericral form log K’ = MCl/D’ - l / l Y t ~ -i- log ICr’
(2)
where K’ is the equilibrium constaat measured in a solvent of dielectric constant D‘, IC‘’ is the same constant in a solvent of dielectric constant D r t 7and M is a function of the charges and radii of the ion3 Involved. Figures 1 and 2 are plots of log K and log B values us. 1/D with all calculated curves coxistrained to pass through the water points. (The sotual coordinates used are differences between valuers in She solvent mixtures and in pure water.) Table II gives vdues of M , the slope, corresponding to least-squares fit,ting of the best straight lines to these data. It is apparent that the linear relationship predicted by Born is a f:tir approximation of t,he general trends i-hserved, but the different values of M indiealp Ilmt other effectb are also important. The inconstancy of the slopes of log K vs. l,/D plots, though noted often in the literature, is still not adequately explained. It has been attributed to different ion-pair parameters13 and it has been passed off as having no immediate theoretical signilica,nee. Theories of ion pair and triple ion Eormation as developed by BjerrumIs and by Fuocia anti K r t ~ u s s prol~ (9) K. P. Anderson, E. A. Butler, and E. hf. Woolley, J . Phys.
Chem., 71, 4584 (1967). (10) D. Fealcins, K. G. Lawrence, P. J. Voice, and A . R. Willmott, J. Chem. Xoc. A , 837 (1970). (11) S. Kratohvil and B. Tezak, Arh. Kem., 26, 243 (1954). (12) M. Born, Z . Phys., 1, 45 (1920). (13) “Solute-Solvent Interactions,” J. F. Coetzee and C.D. Ritchie, Ed., Marcel Dekker, New York, N. Y., 1969, Chapter 5 : “The Selective Solvation of Ions in Mixed Solvents,” by 13. Schneider. (14) J. E. Prue, “Ionic Equilibrium,” Pergamon Press, Ehsford, N. Y., 1966, p 111.
The Journal of Physical Chemistry, Vol. 76,N o . 1 , 1971
96
E(. P. ANDERSON, E. A.
Table I1 : Slopes of Plots of Log K vs. 1/D (Equation 2 and Figures 1, 2 )
--Log K , and log k Log Kz
MeOH
EtOH
A’cetone
Dioxane
266a
184b
278”
128a
78”
9Sf
170
908
a 30% point omitted from calculations. 10% point omitted from calculations. 0 40% point omitted from calculations. d 60% point omitted from calculations. e 10% and 20% point omitted from calculations ; however, inclusion of the 20% changes the value to 16 and inchding a11 points changes it to 74. 10% and 20% points omitted from calculations; the value changes to 94 if the,y are included. 507, and 60% points omitted from calculations. The break in the line shown occurs at about 0.13 dioxane mole fraction; a 1:6 dioxane water complex has been reported. J. R. Goates and R. J. Sullivan, J . Phys. Chem., 62, 188 (1958).
and Matheson20used the activity of mater in equilibrium equations to explain the results of thermodynamic investigations of ionic reactions in mixed solvents. Using this approach the equations for our studies are AgCl(HzO),
266 $
C
JJ AgCl(s) + mHzO
Ka = aAgCl(s) x
’
vide tests to determine whether or not a particular species forms through purely electrostatic bonding. These tests indicste that bonding in the various silver chloride species is polar covalent rather than purely ionic in character. The structure-breaking effects of small amounts of orgartic solvent added to water are a possible explanation of the noticeable deviations from the “straight” lines in Figures 1 and 2 a t low organic component concentrations. l7 The slopes for the log KI (-log K,) curves appear to be inversely proportional to the molar volume of the organic component and directly proportional to its dipole moment. I n the solutions containing dioxane the ions apparently “see” only one of the dioxane oxygens a t a time, ie., dioxane acts as if this “half-molecule” has a dipole moment of about 1.7. Equations 3, 4, and 5 illustrate this relationship when the slope of the log KI line in methanol (molar volume 40.5 and dipole moment 1.70) is taken as the reference slope. The approprinte vstlues of molar volume and dipole moment for ethanol are 58.3 and 1.69, for acetone 73.5 and 2 89, and lor dioxane 85.2 and “1.7.”
BUTLER, AND E. M. WOOLLEY
(15) J. Bjerrum, Kgl. Danske Videnskab, Selskab, Mat. Fys. Medd., 7, No. 9 (1926). (16) R. M. Fuoss and C. A. Kraus, J. Amer. Chem. Soc., 5 5 , 1019 (1933). (17) F. Franks, “Physioo-Chemical Processes in Mixed Solvents,” F. Franks, Ed., Smerican Elsevier, New York, N. Y., 1967, pp 50-75. (18) E. S. Amis, Inorg. Chim. Acta Rev., 3, 7 (1969). (19) W. L. Marshall, J . Phys. Chem., 74, 346 (1970). (20) R. A. Matheson, ibid., 73, 3635 (1969).
97
SOLURIL~YY OF AgCI. IN VARIOUS WATERMIXTURES Log A -- (n!,
log c = ( 4
+ p) log
+ log K,’
(17)
+ log KI’K2’Ka’
(19)
a820
p ) log aH20
It should be noted that A , €3, and C are empirical constants whose values are not dependent upon theoretical assurnpltions regarding which species are present. The negative logs of A , B, and the log of C are plotted us. the negative log of the activity of water for all four solvent mixtures in Figure 3. We have chosen to define the activity of water as19 aH.,o = [HzO]J55.36
(20)
The sta.ucture-ba.ealiing effects of small amounts of organjc compounds are notable as discussed earlier. When these effech are ignored, one obtains nearly straight lines as indicated in eq 17-19. The slopes of these lines are tabulated in Table 111.
I
A
A
Figure 3. Plots of 6~ = log B (water) - log B (solvent), 6, = log C (solvent) - log C (water) +1.10, and 6~ = log A (water) - log A (solvent) 1.90 according to solvation model (eq 17, 18, and 19): 0, solvent = water; ‘3, solvent = ethanol-water mixtures;’ A, solvent = methanol-water mixtures; X, solvent = acetone-water mixtures; El, solvent = dioxane-water mixtures. The lines correspond to the least-squares slopes in Table 111.
+
Table I[II: Slopes of Plots of log K us. -log (Equat,ions 17-1!3 and Figure 3)
(%a
+ pq ))
(P m
UHZO
I’deOH
Et013
Acetone
Dioxane
4 1 1
4 2 0
6 4 0
6 4 0
A reasonable interpretation of these results in terms of hyd.rated species i,sgiven in Table IV. These results indicate two water molecules strongly
Table IV : Possible Hydration of Species Present in Solvent Mixtures
bonded to silver ion as with the diammine silver(1) ion. Chloride ion has been reportedz1to have a primary solvent shell of 4 in water. (However, many different values for coordination number of solvated cations and anions have been reported and the number appears to be a function of the method of measurement.21-2a) Apparently the primary solvent layer of chloride ion is not breached by dioxane or acetone, a t least up to the concentrations indicated. The fewer numbers of water for chloride ions in methanol and ethanol may be due to penetration of the primary hydration shell by these protic water-like molecules. (21) K. D. Mischchenko, Zh. Fie. Khirn., 26, 1736 (1952). (22) I. N. Maksimova and N. N. Zatsepina, ibid., 43(4), 1023 (1969). (23) Yu. P. Aleshko-Ozhevskii, Zh. Strukt. Khim., 10(6), 1107 (1969).
The JournaZ of Physical Chewcistry, Vol. 7.5, N o . 1 I 1971
