SOLUBILITY STUDY OF SILVERHALIDES providing the heat of mixing term in step 1 is assumed 1 o be either negligible or proportional to molecular size
(as defined by cavity surface area). Calculation D e t a h A computer program was written to calculate the area ARW(T)with input information of bond lengths and angles, atomic radii, and the radius of a spherical soivent molecule. The atomic radii, which are essentiaAly the crystal packing radii, were treken from For carbon and hydrogen the aliphatic carbon, 1.7 A; following values were u:ed: ~ ~ r o ~ carbm, a t ~ c 1.77 A, aliphatic hydrogen, 1.2 A; ziromatic hydrogen, 1.0 A. The radius of the water molecule was taken as 1.5 A, The considerations re~,poasiblefor this choice were from scaled particle theory, a = 145 for the wail der Waals water radius
2759 at 298°,23while Bondi gave the maximum crystal packing radius 01 oxygen in ethers as 1.52 The calculated areas are accurate to at least 8.1 A?.
&
Acknowledgments. I would like to thank Slr. Max
14. Marsh and Dr. Lowell G. Tensmeyer for many helpful discussions, and Nr. Donald Saunders for writing a preliminary version of the surface area program. I am also indebted to Dr. Ronald Ropp for some of the solubility measurements. (22) A. Rondi, J. Phys. Chem., 68, 441 (1964). (23) H. Reiss, “Advances in Chemical Physics,” Vol. 10, I. Prigogine, Ed., Interscience, New York, N. Y., 1965. p 1. The value obtained here was found by int,erpolation of values for B number of temperatures in Table XVI.
A Solubility Study of Silver Halides in Molten Calcium Nitrate Tetrahydrate
by Brian Burrows” and Soefjan Noersjamsi School of Chemistry, Macquarie University, North Ryde, New South Wales, 2113,Australia
(Received March 6 , 1978)
The solubility products of AgCI, AgBr, and AgI in molten Ca(N0&.4Ht0 have been determined potentiometrically over the temperature range 40-80’. AGosoln, AHosoln,and AXosoln values were determined for the dissolution equilibria and compared with available data for aqueous solution and anhydrous nitrate melts. Analysis of the partial mole fraction entropies of solution reveals a similarity between the hydrated and the anhydrous nitrate systems in that no significant trend from AgCl to AgI is apparent. This is in contrast to the behavior in aqueous solution.
Introduction An increasing amount of interest has been shown over the past decade in molten hydrate and molten saTt-IlzO systems. ‘This interest stems largely from the fact that these systems form a link between aqueous electrolyte solutions on the one hand and completely ionic melts on the other. Most of the experimental data so far obtained suggest that these very concentrated aqueous solutions more closely resemble ionic xnelts than aqueous solutions. Angel11-3 was the first to propose that hydrate melts euch as Ca(E O& 4Rz0 and I\/IgC12 6H20 could be considered as molten salts with large hydrated cations and unhydrated aniona. This molten salt analogy was based on a comparison of the transport properties of concentrated electrolyte solutions of this type with the transport properties of anhydrous melt systems. The additivity of molar volumes in the Ca(K03)2.4Hz0KNO, ~ y s t e m by , ~ analogy with the fact that molar volumes of binary molten salt mixtures are commonly ~
additive, also suggested the existence of the Ca(H20)2+ ion. Braunstein and coworkers6-s pioneered the application of the quasi-lattice model of molten salts to the study of concentrated electrolyte solutions. This thermodynamic approach is based on studying complex-ion association equilibria in molten salt-HzO and molten hydrate systems. Among the complexes which have been studied are cadmium halide5 and silver (1) C. A. Angeli, J . EZectrochem. Soc., 112, 1224 (1965). (2) C. A. Angell, J. Phys. Chem., 69, 2137 (1965), (3) C. A. Angell, {bid., 70,3988 (1966). (4) J. Braunstein, L. Orr, and W. Macdonald, J . Chem. Eng. Datu, 12, 415 (1967). (5) J. M. C. Ness, J. Braunstein, and H. Braunstein, J . Inorg. Xucl. Chem., 26, 811 (1964). (6) ,J, Braunstein, A. R.Alvarez-Funes, and H. Braunstein, J . Phgs. Chem., 70,2734 (1966). (7) P. C. Lammers and J. Braunstein, J . Phys. Chem., 71, 2626 (1967). (8) J. Braunstein, ihid., 71, 3402 (1967). The Journal
of
Physical Chemistiy, Vol. 76, N o 10, 1978
2760
BRIANBURROWS AND SOEFJAN NUERSJAMSX
halidee complexes in molten NH4N03.2H20, cadmium one end to give electrolytic contact with the test solubromide eoniplexesG in molten Ca(N0&-41'120, cadtion. No contamination of the best solution due to mium ~ o m p l e x e sin~ ~the ~ LiNO3-KNO3-HzO system. diffusion oeeiared over the course of our experiments and silver chloride eomplexeslO in the NH4N03-H20 (up to 8 hr). A known concentration of AgNO, in Ca(NO&.4H10 served as the electrolyte in the refersystem. Analysis oi" the association constants and their: tempera tun: beha vior in terms of the quasi-lattice eiice half-cell. The silver electrode in f he reference model and ~ i ~ ) ~ ~ ?with was similar to the indicator electrode, Le., it comprised ~ r i corresponding sl~i~ results in a leriglh of 0.05-cm diarnetcr silver v\jre, coiled at one anhydrous melts has further indicated the similarity between very coaocxitrated electrolyte solutions and end to increase the surface area in eout& with the ionic melts. electrolyte. A4 ore direct evidence for the existence of &!I(I120)nm* Cell potentials were measured either wi1 h a millivolt potentiometer (Leeds & Northrop, Type 869I) or with ions came from a spectroscopic study by Angell and Thi:y studied thc coordination states of Gruei~.~ ~ a vacuum t i h e voitiricter (Philips, Model Pi\'l 2446)). In both cases identical measurements were obtained to i(I1,) in aqueous magnesium chloride solutions at ceixiperatures up to 328" and concentrations up to 8 k 0 . l niV within 10 m h and they remaim4 steady Cor d l iir magnesium chloride. 'They successfully preperioda of up to several hours. Thc eifeet of temperdieted2 the cxistence of tetrahedral NiCL2- complexes ature on the solubility of AgC1, A&, arid AgJ was bj7 analogy with N iC&z - in molten CsCl and eoncluded investigated by carrying out a. series oi rum a t 50, 55? that for c o ~ ~ ~ ~corresponding s ~ ~ i ( to ~ Mg(C1)2. ~ s 6Hz0 60, 78, and 88". Procedure. The main compartment of the cell was the speciers Mg(f-5&)$ i- exists as an independent entity. Moynihati and f'ratiello12on the basis of proton magfirst fiPlcd with about 200 g of Ca(NQp3)2.41T20containing a known weight of AgNG. The temperature netic i"esonax3c~studies of calcium nitrate tctrahydrate meli h with anli~,di-c~ti~ KKOa, (Cltd,)&" NOa, and was sei, ad the required level by adjustment of the Haake circulator. The reference electrode rompartMgiNO& further concurred with the fused salt analogy nicnt was filled in situ with the molten hydrate solution for hydra! e m C [ l h . until the liquid level was the same as that in the main This contribution presents results of a potentiometric compartment of the celi. study of the solubility of silver halides in molten CaAs a check on the applicability of the S'ernst equa(N03)1"411,gb,T i l e aim was to analyze and compare tion to the AgIhgSf electrode in the hydrate melt the the t,hermodynarnic data so obtained with similar emf of Iht. concentration cell thermodynamic data for silver halides in aqueous solution and in anhydrous nitrate melts in order to gain AglAgSa'Oa ( N ) , Ca(n'03)2.4H201/ further insigb L nnlo the similarities between molten Ca(N03)2*4Hz0,AgNQ3 ( N ' ) / A g hydrates and amhydrous rriolten salts.
All chemicals used were analytical reagent grade and were used directly without further purification. All except the Ca('03)2.4'20 were dried at 126)". The caXcium nitrate tetrahydrate was found to have a melting point of 42.7" which agrees with the iiterature vnlue." The silver wire used was of 99.99% purity from Johnson, Mathey & Co. The cell used was a jacketed reaction vessel of 250-ml cnprwity, A rubber stopper formed the enclosure at the top. Through this stopper wcre supported a thermometer, indwxkur electrode, and reference electrode compartment. k!itirring was achieved magnetically via a small Teflon-cavered magnetic bar. The temperature of t h ? cell was coiitrolled to within 3t0.02" by a constant tcrnperature circulator (Haake ED Unitherm). The e-vaporation of water was minimized by having a very small dead space above the solution. The absence of drift in the cnnf values indicated that any water loss w m negligible. The reference dectrode was immersed in the solution to be tested. It was made from a I-cm diameter Pyrex tube with a fine-porosity sintered-glass disk sealed into The Journal of PhwicUl Chemistry, Val. 76, No. 19,1972
was measured at 42 and 60". In the above cell N and N' indicate mole fractions in the reference half-cell and the indicator half-cell, respectively. The mole fractions are based on Ca(N08j2.4R20as one component. Weighed increments of AgNO3 u,epe added to the indicator half-cell through a small funnel. After each addition the emf was monitored until it was stable to within 1 8 . 2 mV for at least 15 mirr. The solubility experiments were carried out in the follou~kngcell. Ag/Agn'Oa ( N ) , Ca(NO&.4H,O// G,z(N0&.41-120, AgSO3 ( N ' ) , KX (AT") /Ag The emf was measured after each weighed addition of KC1, KBr, or liI as appropriate. The potential of the silver indicator electrode responded immediately after each addition. (9) I. J. Gal, Inorg. Chem., 7, 1611 (1968). (10) M. Peleg, b. Phgs. Chenz., 75, 2060 (1971). (11) 6. A . Angell and D. M.Gruen, J. Amer. Chem. Soc., 88, 5192 (1966). (12) C. T. Moynihan and A. Fratiello, ibid., 89, 5546 (1967).
SOLUBILITY STUDY. OF SILVER HALIDES
2761
_ l _ _ _ l _ l l _ l l _ _ _ l _ _ * - - - - ~
Table a:
Solubility Products,
K s n , a . b of
Silver Halides in Molten Ca(N0&.4Hz0
,------------AgCI----------. l', O
323.2 328.1 333.2 343.1 353.3 a
c--------AgEr-----------. T , "K K~~
ICsp X 10"
K
2.20 i 0.23 3.05 rt 0,19 5.80 f 0.27 ll.50 1 0 . 1 3
323. 1 333.2 338.3 343.1 353.2
21.16+0.22
Mole fraction scale.
-
7----A4gx T,OK
XSPx 1017
323.1 338.1 343.1 348.2 353. I
0 , 4 1 * 0.005 2.78 f 0.0% 6.22 i 0.82 7.63 & 0.04 14.75 P 0.06
Average values from a t least four determinations.
The Ag/Ag+ electrode was well behaved in molten GajNOa)z.4Hz0since, when checked at 42 and 60", the average difference between the experimental and theoretical (calculated from the Nernst equation) emf's was found to be AO.1 mV over the concentration range 6 X IOw4 to 4 X ion fraction of Ag+. The emf data appear as supplementary material in the microfilm edition.13 This good agreement of experiment with theory indicates that junction potentials were insignificant and deviations from ideal behavior were negligible; Le., the activity coefficient of AgN08 was unity. In calculating the solubility product of the silver halide it wap assumed that complex formation would have no significant effect OR the value of the solubility product, KSp. Thus the equilibrium silver ion concentration, [&+], at, any time after the melt had been saturated with AgX, was calculated from the measured enif vzu the Nernsl equation. The equilibrium concentration of free halide ion [X-] was determined from the relationship =
1014
2.72 f 0.09 6.20 rt 0.02 10.76ztO.04 17.39 rS: 0.44 36.56A0.08
~e$u~~s
[X-1
x
+
4 7 ~ -- C A ~ [As+] ~
(1)
where Cx- represents the concentration of K X which has been added a t any instant and CA,+ is the initial concentration of Ag'Kc'e),. The solubility product was then given by [Ag+][X- 1. The results are summarized in Table I . More data appear as supplementary material in the microfilm edLition.la Tien and Rarringtor~'~ have pointed out that ion pair formation such as AgX would not affect the value of K,, as determined by this potentiometric method. They also assumed that one could consider complexes such as AgX2- to be absent provided K,, was constant over a wide range of kg+ ion and Cl- ion concentrations. This latter assumption has been criticized by Fiomni, el aZ.,L5who pointed out that when the simple complexes AgX2-, AgX, and Ag2X+ are taken into account an expression of the following form, involving K,,, is obtained
-~
where and 0 1 , ~ are the stability constants for the species Ag&- arid Ag2X*, respectively. If only the complex AgX2- is present then eq 2 reduces to
ie., the solubility product term becomes KSp(1
+
P2,IKSP).
Thus one is only justified in neglecting complexes such as AgX2- provided & , I is not too large or in other words the product P2,1Ksp
