M. H. LIETZKEAND R. W. STOUGHTON
1186
a t least in this case the Debye-Huckel equation holds as well a t elevated temperatures as a t room temperature. Acknowledgment.-The authors wish to express
Vol. 63
their appreciation to G. R. North for performing the experimental solubility measurements and to M. P. Lietzke for programming the equations for the IBM-704 Computer.
THE SOLUBILITY OF SILVER SULFATE I N ELECTROLYTE SOLUTIONS. PART $2. SOLUBILITY I N POTASSIUiM SULFATE SOLUTIOSSl BY M. H. LIETZKEAND R. W. STOUGHTON Contribution f r o m the Chemistry Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. Received JaiLuary 10, 1060
The solubility of AgPSO4 was measured in 0.1, 0.3, 0.5 and 0.8 m KzSO, solutions to about 200'. Based on the values in ure water the solubilities were calculated as a function of KzSO~concentration and temperature on the assumptions that 1) both electrolytes were completely dissociated and ( 2 ) the activity coefficient of AgzS04varied with ionic strength according to an equation of the Debye-Huckel type. The agreement between observed and calculated solubilities was good.
P
A previous paper2 in this series described the solubility of AgzSO4 in KNO3 solutions. It was shown that an equation of the Debye-Huckel type could be used to describe the solubility dat,a in that system over a wide range of temperature and concentration. The present paper describes the solubility of AgzS04in solutions. In contrast to the Ag2S04-RNOs system, which involves a pure solvent medium effect in enhancing the solubility of AgzSO4 over the solubility in pure HzO, the Ag2S04-KzS04 system involves a common ion effect as well as a medium effect. The measurements have been extended over the range 0.1 to 0.8 m &so4 from 25 to 200". Again a high speed digital computer was used to check the applicability of the Debye-Huckel equation to the solubility system. Experimental The solubility measurements were carried out using the same technique described previ0usly.2~~The same observations in regard to hydrolysis of the Ag2S04 made in the case of the Ag,SB,-KNOa system apply to the present sy5tem. Again the measurements were reproducible to =kt2
.
Results and Discussion In Fig. 1 the circled points represent the experimentally observed solubilities of Ag2S04in H 2 0 and in 0.1, 0.3, 0.5 and 0.8 m KzS04 solutions. The points from 25 to 100" in H 2 0 and from 33 to 100" in the KzS04solutions are from the work of Barre.4 On the assumption of complete dissociation of both electrolytes, the stoichiometric ionic strength I of the Ag2S04-K2S04 solutions is given at any molality m of KzS04 by equation l I = 3m
+ 3s
(1)
where s represents the molal solubility of Ag2SO4 in the K2S04 solution. As in the previous paper in this series2 the stoichiometric solubility product of Ag2S04 on a molality basis S a t any molality m of KzS04was assumed to be given in terms of the solu(1) This paper is baaed upon work performed for the United States Atomio Energy Commission a t the Oak Ridge National Laboratory operated by Union Carbide Corporation. (2) M. H. Lietzke and R. W. Stoughton, THISJOVRNAL,63, 1183 (1959). (3) M. H. Lietzke and R. W. Stoughton, J . Am. Chsm. Soc.. 78,3023 (1956). (4) M. Barre, Ann. chim. phys.. [SI24, 202 (1911).
bility product in pure H20 by a Debye-Huckel expression of tnhetype
In this equation So, the molality solubility product of AgzSO4 in pure H20, equals 4s03 a t ionic strength Io = 350; ST is the Debye-Huckel limiting slope a t the given temperature; and A , is either a constant or a term which varies inversely as the square root of the DT product, where D is the dielectric constant, of HzO. The value of D was computed a t each temperature using the equation given by Akerlof and Oshry.6 According to the DebyeHiickel theory the value of ST varies with temperature inversely as the three halves power of the DT product. At any temperature and concentration of KzS04 the solubility product S of the Ag2S04 is given by equation 3 S = 4s*(s m ) (3) Jn starting the calculations a t each concentration of K2SO4 the observed solubility of Ag2S04 a t each temperature was used to compute a value of I. Then using equations 2 and 3 a value of Scalcd (the calculated solubility of Ag2S04) was obtained. This value of Scalcd was used to correct I (equation 1) and the process repeated until successive values of Scalcd agreed to within 0.1%. The calculations were carried out a t 25" intervals from 25 to 200" a t each concentration of KZSO4using three different values of A,, viz., 0.45, 0.65 and 0.85. From a plot of Scaled vs. A, a t each temperature and concentration of KzS04it was possible to find the value of A , which gave closest agreement with the observed solubility. It was found that the value of A s varied little with temperature a t each concentration of K2S04 but did show a small decrease with increasing concentration of KzS04. Table I shows the calculated solubilities of Ag2SO4 corresponding t,o the values of A, averaged a t each concentration of K2S04 and also to an over-all average value of 0.7. Using a single average value of A , is equivalent to assuming that d/(DT)'/*is independent of concentration
+
(5) G. C. Akerlof and H. I. Oshry. J . Am. Chem. Soc., 72, 2844
(1950).
SOLUBILITY OF SILVERSULFATEIN POTASSIUM SULFATE
July, 1959
TABLE I THESOLUBILITY OF Ag&304IN K&O, SOLUTIONS Sosled
Kg01
4 OC.
8ob.d
Aa = 0.766 Aa = 0.7
0.1
50 75 100 125 150 175 200
0.0343 0.0326 0.0338 .0412 .0402 .0410 ,0461 .0403 .0476 .0491 .0504 .0519 ,0500 ,0531 .0544 .0509 ,0541 ,0556 .0501 .0530 .0550
0.3
50 75
0.0372 0.0385 0.0373 .0404 .0497 .0470 .0565 .0595 .0572 .0675 .OG91 .0603 .0795 .0781 .0752 .0925 .0875 .0843 .lo7 .099 .0941
240
1187
r - 4
Aa = 0.60
(%a’za 0.0352 ,0432 .0489 .0533 .0554 .0550 .0544
An = 0.665
100
0.041 .052 .0018
0
0.02
0.04
0.06
0.08
0.10 f?Aqp*
0.12
0.14
0.46
048
0.20
8
Fig. 1.-The solubility of Ag2S04in K&04 solutions.
ture-independent values of A , averaged at each concentration of KzS04 give calculated solubilities 175 agreeing most closely with the observed. In all 200 cases above 0.1 m KZSO4the value of A, which varA. 0.643 ies as ( D T )-‘/e gives calculated solubilities which 0.5 50 0.0431 0.0438 0.0402 are too low a t the highest temperatures. These 0.0464 same observations also were made in the Ag2SO475 .0541 .0575 .0523 .0594 KN03 solubility system.2 However, in contrast to 100 ,0668 .0704 .0644 ,0715 the Ag&O4--KNO3 system the direction of curva125 .Os14 ,085 ,0766 .083 ture of both the observed curves and the calculated 150 .0977 .0990 .0895 .0945 curves changes a t higher concentrations of IizS04. .119 ,104 175 .11G .lo4 The d parameteis corresponding to the A s values a t 200 ,138 .121 .135 .117 25” areasfollows: for0.1mKzS04,A, = 0.766, d = Aa = 0.648 2.3 A,; for the higher concentrations of &So4 the 0.8 50 0.0515 0.0478 0.0433 0.0400 values of A , decrease slightly with d = 2.0 A. As 75 .0652 .0040 .0576 .0681 in the Ag2SO4-KNOs system, the decrease in the 100 .ON9 .OS05 .0724 .0805 value of d is consistent with an hypothesis involving 125 .lo1 .0995 .OS83 ,101 smaller hydration spheres for the ions as the con150 .122 .122 .lo6 .113 centration of KzS04 increases. Also, the tempern175 .I47 .127 .144 .I27 ture-independent values of A , give calculated solu200 .167 .182 .153 .14G bilities which agree more closely with the observed a D’1”is the 02’product at 2 5’. solubilities than do values of A , which vary as and temperatures; here 12 is the “distance of closest (DT)-’/g (Table I); this fact may be interpreted approach” parameter of the Debye-Huckel theory. 011 the basis of the Debye-Hiickel equation by conShown also are the calculated solubilities of Ag2SO4 cluding that the (DT)-’/a variation tends to be corresponding to an over-all average value of A , offset by a decrease in the d value (or the solvent which varies with temperature as (DT)+a; in density) with increasing temperature. It is evident that with the assuinption of complete these calculations it is assumed that d is independent of concentration and temperature. The solu- dissociation of both the Ag2S04and &SO4 a Debyebilities calculated with the values of A , averaged a t Huckel type of expression for the variation in the cach concentration of K2S04are also plotted in Fig. molality solubility product of Ag2S04 with ionic strength in K2SOI solutions can be used to fit the 1. A comparison of the observed and calculated solubility data over a wide range of concentration solubilities in Table I indicates that the tempera- and temperature. Acknowledgment.-The authors wish to express (6) Using a constant value of A S is more ncarly equivalent to astheir appreciation to L. N. Cain for performing the uming that d(do/DT)’/z is independent of ooncentration and temperexperimental solubility measurements. ature; here do is the density of the solvent. 125 150
,071 .079 .0843 .092
