SOLUBILITY OF SILVER SULFATE IN ELECTROLYTIC SOLUTIONS
July, 1959
eter. Let nr be the number of moles removed from the calorimeter of volume V , let n l g and nll be the initial number of moles of gas and liquid, respectively, in the calorimeter; and let n# and n,1 be the corresponding final amounts of gas and liquid. Since the volume of the calorimeter is constant, Le.
+ Vln? = V,nzg + V
Vgnp
d
and the number of moles removed from the calorimeter is given by the expression np n? - nag - nal = n, it can be shown that the total number of moles vaporized nT is given by the relation
+
where VI and Vg are the molar volumes of the liquid and gas,1° respectively, at the temperature and pressure of the vaporization. No experimental data exist for the molar volumes of liquid and gaseous deuterium along the saturation curve. Therefore, V 1 was obtained by extrapolation, to the saturation curve, of the pressure-volume-temperature data of liquid deuterium,ll and V , was obtained in a similar manner from gaseous pressure-volumetemperature data. l 2 Since such extrapolations are not too accurate, particularly in the vicinity of the critical point, the uncertainty in the heat of vaporization a t the highest temperatures can be as much as 5%. The values of Vl/(Vg - V I ) used in the calculations were tabulated for both hydrogen and deuterium (column 5 of Tables I and II), so that the total number of moles can be recalculated in the event that new liquid and gas densities become available. The heats of vaporization of deuterium have been corrected for the presence of the 1% hydrogen deuteride. In making this correction, it was (10) E. Mathias, C. A. Crommelin and H. K. Onnes, Leiden Comm., 154b (1918).
(11) A. 8. Friedman, M. Trzeciak and H. L. Johnston, J . A m . Chem. SOC.,76, 1552 (1954). (12) Unpublished results of this Laboratory.
1183
assumed that a solution of hydrogen deuteride and deuterium behaves ideally. Although the heat of vaporization of hydrogen deuteride between the boiling point and the critical point has not been determined, it was estimated from the results of these experiments (see below). Discussion of Results The large isotope effect obtained in the heat of vaporization is of considerable interest, particularly if the results can be used to predict the properties of all the other hydrogen isotopes. Since the intermolecular forces for all the hydrogen isotopes can be considered to be nearly the same, no correlation can be expected from any classical law of corresponding states. Deviations from such a law, as a result of quantum effects, have already been discussed by DeBoer and Lunbeck. An empirical relationship developed by Friedman, White and Johnston14 states that when a thermodynamic quantity of an isotope series is plotted against the reciprocal of square root of the mass, a straight line is obtained. By. applying this relationship to the heats of vaporization at the boiling point of hydrogen, deuterium and hydrogen deuteride,Is a straight line plot is obtained which, when extrapolated to the mass of tritium, leads to a value of 323 ca./mole. From vapor pressure data, Grillyls has calculated a value of 333 cal./mole for the heat of vaporization of tritium at 25.04"K. Thus the predicted value agrees to within 3% of the experimental value. Assuming that for each value of T / T o (column 8 of Tables I and 11) between the boiling point and critical point, such a linear relationship holds for all the isotopes, the heats of vaporization of hydrogen deuteride and tritium were calculated. The results of these calculations are shown by the dotted lines in Fig. 1; the solid lines represent the experimental results for hydrogen and deuterium. (13) J. DeBoer and R. J. Lunbeok, Physica, 14, 520 (1938). (14) A. S. Friedman, D. White and H. L. Johnston, J . Chem. Phys., 19, 126 (1951). (15) F. Simon and F. Lange, Z . Physik, 16, 312 (1923). (16) E. R. Grilly, J . Am. Chem. SOC.,18, 843 (1951).
THE SOLUBILITY OF SILVER SULFATE I N ELECTROLYTE SOLUTIONS. PART 1. SOLUBILITY I N POTASSIUM NITRATE SOLUTIONS1 BY M. €1. LIETZKE AND R. W. STOUGHTON Contributionfrom the Chemistru Division, Oak Ridge National Laboratory, Oak Ridge, Tenn. Received January 30, 1969
The solubility of Ag?S04has been measured in water to 230') in 0.1 and 0.6 m KNOJ to 200", and in 1 m KNOa to 150'. Rased on the soluhilities in pure water and a Dehye-Huckel expression for the variation in the activity coefficient of Ag,SO, with ionic strength at any temperature, solubilities were calculated a t various temperatures and KNOa concentrations. The agreement between observed and calculated values was good. It is concluded that in this case the Debye-Huckel equation holds as well at elevated temperatures as at room temperature and that it is not necessary to assume any complexing in these solutions to explain the data.
In a previous paper2 it was shown that at 25' a plot of the log of the stoichiometric solubility product s of Ag2SO4 (on a molality basis) W r m the square root of the ionic strength I was essentially medium* This was independent Of the true on the basis of assumed complete dissociation (1957).
(1) T h i paper ie based 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, J . A m . Chem. SOC.,79,2067
1 184
M. H. LIETZKE AND R. W. STOUGHTON
VOl. 63
other media. In all cases the measurements have been extended over a wide range of ionic strength and from 25" to at least 200'. Since the calculations involved in testing the above assumptions would be extremely tedious on a desk calculator a high speed computer has been used in all cases.
Experimental The solubility measurements were carried out using the same technique described previously.4 The determinations could be made only on a heating cycle since the solutions supersaturated upon cooling. I n the present work AgtSOI crystals and aliquot8 of previously analyzed KNOa solutions were weighed into the fused silica tubes. Since the AgzSOc molality could be calculated directly, subsequent analysis of the contents of every tube was unnecessar I n contrast to systems containing Agz'E?Od dissolved in acid,4 where the tubes could be heated many times to check a given point,, the tubes containing Ag2SO4 crystals and KNOa solution could usually be heated only once. Even after one heating it was evident that a very small amount of Ag,O had formed by hydrolysis. As long as a tube was heated only once and the work was conducted relatively rapidly consistent and reproducible results were obtained. A second heating of the same tube showed a slightly different solubility and a darkening of the appearance of the reci itate, clearly indicating the formation of AgZO. $he sol)ubilities reported therefore do not strictly represent equilibrium conditions. However the authors are convinced that the reported data are those which obtain in the absence of hydrolysia and that the hydrolysis reaction is significantly slower than the dissolution of AgzS04 to produce a metastable condition. Slow hydrolysis also was observed even when a small amount of HNOa had been added. This situation is as should be expected in view of the calculated decrease of the acid quotients for HSOr- and "03 with temperature;b in order t o increase appreciably the H * concentration, enough HNOa would have to be added to change markedly tne various concentrations of species assumed t o exist. Hence it was necessary to use several tubes to determine each point on the solubility diagram. The solubility points were reproducible to 1 2 ' in 0.1 and 0.6 m KNOt and to about 1 5 " in 1.0 m KNOs.
.
0
0.02
0.04
0.06
0.08
0.10
0.12
rnAgzSO4.
Fig. 1.-The solubility of Ag2S04 in KNOs solutions: 0, obsd. solubility; --, calcd. solubility assuming A. is constant at each KNO3 concn.; - - - -, calcd. solubility assuming A . varies as (DT)-'/z,
whether or not the supporting electrolyte contained a common ion and regardless of valence type. Moreover, the curves, which showed a monotonic increase with d , all fell below the limiting (Debye-Hkkel) slope, i.e., they showed a smaller dependence on ionic strength. These facts suggested that (1) no sulfate complexing need be postulated in these systems and that (2) a DebyeHiickel expression of the type c
Results and Discussion could be used to describe the data. In this equation SO and SOrepresent the molal sohbility and the molal solubility product of AgzS04,respectively, in pure water at temperature T; ST is the DebyeHuckel limiting slope for a 1-2 electrolyte (AgzSO3 a t that temperature; 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 water. The value of D is assumed to vary with temperature in accordance with the equation given by Akerlof and O ~ h r y . ~In the case of Ag2S04solubility in pure water So = 4so8a t ionic strength 10= 380, while the expression for I depends upon the supporting electrolyte. In order to test the validity of the two assumptions a study of the solubility of AgzS04 in a variety of electrolyte media was initiated as a function of temperature and ionic strength. AgzS04 was chosen because the solubility range in water and in a variety of electrolyte media is sufficiently high so the measurements can be made visually. Furthermore, the compound is sufficiently stable over the temperature range used that one does not encounter insurmountable difficulties with side reactions. The present paper describes the solubility of AgzSO4 in KNOa solutions; subsequent papers in. the series will describe the solubility of Ag2S04in (3) 0. C. Akerlof and H. I. Oshry, ibid., 7a, 2844 (1950).
In Fig. 1 the circled points represent the experimentally observed solubilities of AgzSOl in HzO and in 0.1,0.6and 1.0 m KNOI solutions. The points at 25" are lower than those observed by H a r k i d and are in better agreement with the calculated values. The results in HzO up to 100" were obtained from the work of Barre.' The curves in Fig. 1 represent the calculated values using the best A , a t each concentration. The stoichiometric ionic strength I of the AgzS04-KNOa solutions is given at any molality m of KNOa by m plus three times the molal solubility of AgzS04,s, in the same medium, i.e. I=m+38
(2)
Under the same conditions the solubility product of the AgzSOeon a molality basis is given by B = 488
(3)
I n starting the calculations at each concentration of KNOs the observed solubility of AgzS04 at a given temperature was used to compute a value of I . Then using equations 1 and 3 a value of Saalcd (the calculated solubility of Ag2SO4)was obtained. This (4) M.H.Lietake and R. W.Stoughton, ibid., 78, 8023 (1956). (5) See M. H. Lietzke and R. W. Stoughton, THISJOURNAL, 68 1190 (1959). (6) W. D.Harkins, J . Am. Chem. Soc., 88, 1807 (1911). (7) M.Barre, Ann. china. phys., [SI24, 211 (1911).
July, 1959
SOLUBILITY OF SILVER SULFATE IN ELECTROLYTE SOLUTIONS
value of Scaled was used to correct I and the process repeated until successive values of Scaled agreed to within 0.1%. The calculations were carried out at 25" intervals from 25 to 200" a t each concentration of KN03 using three different values of As, viz., 0.9, 1.1and 1.3. A plot of Scalcd us. A , was then made a t each temperature in order to determine the value of A, which gave best agreement with the observed value. It was found that a t each concentration of KNOBthe value of A , was practically temperature independent; this implies that &/ (DT)'/qis temperature independent, where 8. is the (z parameter of the Debye-Hiickel theory.8 Hence the values were averaged a t each concentration of 4iN03 and the Soalod value corresponding to the average value was read from each graph. In addition an over-all average A, was calculated and the corresponding values of Scaled also were obtained from the graphs. Both sets of Soalcd values are given in Table I. TABLE I THESOLUBILITY O F Ag3SOcIX KNOa SOLUTIONS Saalod
A B = 1.33
KNO3, m
0.1
t,
Soalod
"C.
8obsd
25 50 75 100 125 150 175 200
0.0329 .0404 ,0463 ,0505 ,0530 ,0538 .0529 .0461
Soalod
As = 1.33 As = 1.11
0.0320 ,0407 ,0471 ,0514 ,0536 .0538 ,0518 .0479
0.0327 ,0416 ,0482 .0528 .0552 .0556 .0539 .0501
(E) DT
'/la
0.0320 ,0406 ,0469 ,0509 .0528 .0527 .0516
...
(S) A s = 1.07 '/?
As = 1.07 As = 1.11
0.6
25 50 75 100 125 150 175 200
0.0488 ,0605 .0699 .0771 ,0821 .0849 .0855 .0838
0.0463 ,0590 .0691 .0770 ,0831 .0870 .0889 .0888
0.0455 ,0579 .0678 .0755 .ON3 .OS49
0,0463 .0584 .0678 ,0746 ,0792 ,0812
.0865 .0860
,0808 .0776
Q
($ )y* 3 a
A B = 0.88 As = 1.11
1.0
25 50 75 100 125 150
0.0628 .0760 .0880 ,0990 .lo7 .113
0.0580 .0746 ,0884 .IO0 .111 .119
0.0512 .0653 .0769 .0862 .0936 .0992
DT
0.0580 .0739 .0864 .0964 .lo4 .lo9
aD'T' is the DT product a t 25'.
Solubility values calculated on the assumption that at each m, A, = A,' (D' T' / D T ) ' / 2 ie., , that the (z parameter is temperature independent, also are shown in Table I. Here il,' is independent of D and T , and DIT' is the DT moduct a t 25". On this assumption -4, increases *by about 16% in going from 25 to 200". ( 8 ) NOTEADDED I N ~aoo~.--hctually the Debye-Huckel equation was derived in terms of molar concentrations c rather than molal concentrations m,and c is approximately equal t o the product of m times the solvent density do. Further, the quotient (do/DT)'/2 is nearly independent of temperature. Hence a nearly temperature independent A , is consistent with a temperature independent d.
1185
As can be seen in Fig. 1 the calculated and observed plots are all concave to the left even at 1.0 m KN03. It will be shown in subsequent papers that this is not true when Ag2S04is dissolved in solutions involving more than a pure ionic strength effect. It is evident from Table I that the AgzSOl solubilities based on a value of A, which decreases with increasing concentration of KN03 show close agreement with the experimentally observed values, while those based on an over-all average A , are not as good at. 1 m KNOB. The greatest difference between the observed and calculated solubilities in the latter case was 18%) and the average a t all concentrations was about 4%. The d parameters corresponding to the values of A , a t 25" are as follows: 0.1mKN03,As= 1.33,d = 4 . 0 b . ; 0.6m KN03, A , = 1.07, 8. = 3.3 b.; and 1.0 m KNOp, A , = 0.88, d = 2.7 b. The decrease in the value of d is consistent with an hypothesis involving smaller hydration spheres for the ions as the concentration of KN03 increases. Since temperature independent values of A, give calculated solubilities which agree more closely with the observed solubilities than do values of A, which vary as (DT)-'/a (Table I) it appears that the (DT)-'/2 variation may be just about offset by a decrease in the d values (or the solvent density) with increasing temperature. The attainment of solubility equilibrium in the 1.0 m KNOS solution a t the higher temperatures was slow. Yet it mas necessary to heat the tubes sufficiently rapidly so that the Ag2S04 did not hydrolyze to any large extent. Since no single A, value fits the data as well in 1 m KN03 over the entire temperature range as in the 0.1 and 0.6 m KN03 solutions, and since the 25" value was easy to check within 1%, it appears that the solubilities observed in 1 m KN03 solution a t the elevated temperatures are too high. However, they represent the best measurements that could be made under the restricting condition of competitive hydrolysis. The data obtained above 150" in the 1.0 m KN03 solution were meaningless and hence the values are reported only to 150". Any tendency of the sulfate ion to hydrolyze should be maximized a t the highest temperatures and the lowest ionic strengths, i.e., where the bisulfate acid quotient is lowest. The conditions of lowest ionic strengths obtain in pure water. At 200" in pure water the ionic strength is about 0.1; using the appropriate value S and an estimated value for the concentration productg for water dissociation under these conditions, the ratio of HSO,-/ Sod-- is only about 0.002, on the assumption of no hydrolysis of silver ion. Any hydrolysis of the latter ion would of course tend to enhance bisulfate formation. It is evident that with the assumption of complete dissociation of both the AgzS04and KxO3 a Debye-Huckel t)ype of expression for the solubility product of Ag2S04in KK03 solutions can be used to fit the solubility data over a wide range of concentration and temperature. It is further evident that (9) H. 5. Harned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," Reinhold Publ. Corp., New York, N. Y., Third Edition, 1958, pp. 643-649.
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 H20 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).
