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The thermodynamics of aqueous silver sulphate-lanthanum sulphate solutions
J. inorg, nucl. Chem., 1967, Vol. 29, pp. 1249 to 1253. Pergamon Press Ltd. Printed in Northern Ireland
THE THERMODYNAMICS OF AQUEOUS SILVER SULPHATE-LANTHANUM SULPHATE SOLUTIONS* M. H. LIETZKE and J. O. HALL Chemistry Department, University of Tennessee, Knoxville, Tennessee and Chemistry Division, Oak Ridge National Laboratory,? Oak Ridge, Tennessee (Received 30 November 1966) Abstract--The solubility of AgsSO4 has been measured in 0.001, 0.002, 0.004 and 0-01 M La~(SO4)3
solutions to above 100° to continue the study of the solubility in sulphate solutions of increasing valence type. In addition to presenting new solubility data the present study also includes values of the activity coefficient of AgzSO, at zero concentration in K2SO4, MgSO4, and La~(SO~)3 solutions. IN TWO previous papers the solubility o f AggSO 4 in K2S04 C1)and in M g S 0 4 (~) solutions has been described. In these papers it was shown that an equation o f the D e b y e Hfickel type could be used to describe the solubility data over a wide range o f temperature and ionic strength. The present paper presents the solubility o f AgzSO 4 in La~(S04) a solutions and continues the study in sulphate solutions o f salts o f increasing valence type. In addition to presenting new solubility data the present study also includes values o f the activity coefficient o f Ag2SO 4 at zero concentration in K2SO4, M g S O 4 and La2(SO4) 3 solutions. EXPERIMENTAL The solubility measurements were carried out using the synthetic technique described previously.'3' At each of the four concentrations of La~(SO4)8 used the measurements were extended to as high a temperature as possible. In all cases the upper temperature limit was determined by the combined solubilities of the La~(SO4)3and Ag2SO4. Values of the solubility of Ag2SO4 in H20 were taken from the work of BARRE.~4~ RESULTS AND DISCUSSION In Table 1 are shown the experimentally observed solubilities o f Ag~SO 4 in the four different concentrations o f La~(SO4)z studied. All concentrations are expressed in terms o f molality. I n accordance with previous w o r k tl'2) it was assumed that the solubility p r o d u c t S o f Ag2SO 4 at any ionic strength I could be expressed in terms o f the t h e r m o d y n a m i c (zero ionic strength) value Ks ° by the following equation In S = In Ks ° +
~erx/(I) 1 + AV/(I)
(1)
* Based on a thesis submitted by J. O. Hall in partial fulfillment of the requirements for the degree Master of Science, University of Tennessee. ~"Operated by Union Carbide Corporation for the United States Atomic Energy Commission. tl~ M. H. LIETZKEand R. W. S'rOUOHTON,J. phys. Chem. 63, 1186 (1959). ~2, M. H. LmTZKEand R. W. STOU~HTON,J. phys. Chem. 63, 1984 (1959). t3~ M. H. LIETZKEand R. W. STOUGnTON,J. Am. chem. Soc. 78, 3023 (1956). ~4, M. BARRE,Annl$ Chim. Phys. 24, 202 (1911). .5 1249
1250
M.H.
LmrZKE and J. O. HALL
TABLE 1.---THE SOLUBILITY OF Ag2SO4 nq La~(SO~)8 SOLUTIoNs MLaztS04}s
t
SAgzSO4 robs.)
SAgaS04tcalc.)
0.001
25"0 42"5 55"0 72"5 98"0 105"0
0"0271 0"0301 0"0340 0-0360 0"0420 0"0430
0"0258 0"0307 0"0342 0"0375 0.0409 0.0412
0.002
25-0 56"0 61"0 76.0
0"0273 0.0330 0"0340 0"0366
0"0251 0.0335 0.0344 0"0370
0.004
25"0 45-0 56"0 70"0
0"0274 0"0301 0"0316 0"0348
0"0242 0-0299 0-0323 0"0351
0.01
25.0 45.0 50"0
0.0276 0"0301 0.0315
0"0248 0"0313 0"0327
where ~9'~, is the appropriate Debye-Hfickel slope at temperature T and A is an adjustable parameter. The relationship between the solubility product So of Ag2SO4 in the absence of a supporting electrolyte and the thermodynamic solubility product Ks° was assumed to be given by In So = In Ks° +
~v'(Io) I + A'v/(Io)
(2)
In this equation So = 4SOS; Io = 3so, where s o is the solubility of Ag2SO4 in pure water at the appropriate temperature; and A' is again an adjustable parameter. Substitution of Equation (2) into Equation (1) gives In S = In S O + ~ r
~/(I) 1 + A~/(I)
V'(I°) ] 1 -~ A ~ ( I 0 j J
(3)
In the previous studies il'z~ it was found that the parameter A in Equation (3) was essentially independent of temperature, but did vary with concentration of the supporting electrolyte. In carrying out the calculations it was assumed that only the species Ag +, SOt2-, and La a+ existed in a solution containing Ag~SO4 and Laz(SO4)8 dissolved in water. If s is the molal solubility of AgzSO 4 in a La2(SOl)z solution of molality M, then the molal solubility product of the AglSO 4 is given by S = 4s~(s + 3M)
(4)
while the ionic strength I of the solution is given by I = 3s + 15M
(5)
The overall calculation involved the estimation of the A-parameter in Equation (3)
The thermodynamics of aqueous silver sulphate-lanthanum sulphate solutions
1251
by the method of least squares subject to the criterion that 2~ (Sobs. - - Seale.)i 2 be a minimum. It was assumed that this criterion was met when successive values of the A-parameter did not change by more than 0.1 per cent. For convenience in carrying out this calculation the experimental solubility values were plotted and values of the solubility read from the curves at 5 ° intervals. These values were then used in all subsequent calculations. The calculational procedure was very similar to that reported in the study of the solubility o f Ag2SOa in AgNO 3 solutions. (5) A temperature independent value of A was obtained for Equation (3) at each of the four concentrations of Laz(SO4)z separately. This involved the numerical evaluation of (Os/OA), the partial derivative of the solubility of AgzSO4 with respect to the A-parameter, at each temperature and at each concentration of Laa(SO4)a, so that the original estimates of the value of A could be adjusted to satisfy the least squares criterion. The values of A and their variances obtained at each of the concentrations of Laz(SO4)z with A' set either to 1.0 or 1.5 are shown in Table 2. TABLE 2 . - - T H E VALUES OF A IN EQUATION (3)
A" -- 1.0
MLa2(so4~ 0.001 0.002 0-004 0"01
A
1'31 1"46 1'58 1"26
A' = 1-5 642*
6a 2.
A
0-09 0.21 0.41 0.09
1.87 2"02 2-09 1-55
0.17 0.40 0'76 0.14
* Variance in A. Values of the solubility of Ag2SO 4 calculated with A' set either to 1.0 or 1-5 were essentially the same and are given in Table 1 beside the observed values. As can be seen the agreement between the observed and calculated values is within a few per cent except at 25 °, where differences of 5-10 per cent are to be noted. The reason for the larger differences at 25 ° may be due to the fact that the value of A/(DT) 1/2, where is the A parameter of the Debye-Hfickel theory, and hence of the parameter A, which includes the ii/(DT) 1/2 term, is not entirely temperature independent. In this respect the present system resembles the previous study of the solubility of Ag2SO4 in AgNO~ solutions, (5) where the agreement between the observed and calculated solubilities was poorest at 25°C. In the Ag2SO4-Laz(SO4)3 system the effect may be magnified due to the much larger ionic strength effect. It is interesting to compare values of log Ks° obtained in the present study with values reported previously. (~) This comparison is shown in Table 3. The agreement between the two sets of values is within experimental error. Values of the activity coefficient of AgzSO 4 at zero concentration in K2SO4, MgSO 4, and La~(SO4) ~ solutions have also been computed. These values are given by the Sara/(/)/(1.0 + AV/(/)) term in Equation (1) and are tabulated in Table 4. In order to make comparison between these values easier, they are also plotted in Fig. 1. c5) M. H. LIETZKEand R. W. STOUGHTON, Jr. inorff, nucl. Chem. 28, 1877 (1966). (6) R. W. STOUGI-rroNand M. H. LIETZKE,d. phys. Chem. 64, 133 (1960).
1252
M.H.
LIETZKE and J. O. HALL
TABLE 3.--VALUES OF LOG Kao FOR AgsSOt vs. aXMPERATtr~ t
--log/(8 ° (Ref. 6)
--log Ks° (present study)
25 50 75
4.84 4.62 4.54 4.53
4.81 4.67 4.58 4"54
100
As can be seen all the values lie above the Debye-Hfickel limiting slope. Since good agreement between calculated and observed solubilities of Ag~SO4 was obtained in all three systems with the assumption of complete dissociation of all electrolytes involved, it appears that any ion association in these solutions is probably of a low order. Hence the Ag2SO4-La2(SO4)3 system is similar to the Ag2SO4-K2SO 4 and the AgzSO4-MgSO4 systems in that the molal solubility product of Ag2SO4 in all three systems may be described using a single parameter Debye-Hfickel expression. In all three systems this parameter seems to be ionic strength dependent and at least in the K2SO4 and MgSO4 systems temperature independent. Although the calculations in the 1.0
' I fDeby'eSlope
' I H[ickel
' I Limiting
'
I
'
I
'
at 25 °
.9
.8
7Ag2so4Ot zero cone.
vs
~"MgSO 4
yAQ2SO46t zero cone.
vs
~"LQ2(S04}3
.7 t00 o
.6+
~ o .4-
.¶
-
,
0
I
.4
,
I
.8
,
I
1.2
,
I
t.6
,
I
,
2.0
YT
F[o. 1.--The activity coefficient of AgzSO4 at zero concentration in K=SO4, MgSO4 and Las(SO~)8 solutions.
The thermodynamics of aqueous silver sulphate--lanthanum sulphate solutions TABLE 4.--THE
1253
AgzSO4AT ZERO CONMgSO, ANDLa~(SO4)3SOLUTIONS
ACTIVITY COEFFICIENT OF
CENTRATION IN K 2 S O 4 ,
MKzS04
t 25
0"1 --
0"5 --
0'186 0"168 0'151
0"8 --
50 75 100
0"375 0"354 0'332
0-141 0"126 0"110
t
0.1
0.5
1.0
25 50 75 100
0'382 0'364 0'343 0"321
0"213 0"197 0"179 0"161
0'154 0'140 0'125 0"109
t
0"001
0'002
0"004
0"01
25 50 75 100
0.770 0.760 0.748 0.735
0.701 0.688 0.673 0.657
0.619 0.604 0.587 0.568
0-501 0.483 0.464 0.441
MMgso~
MLa2IS04) 3
La2(SO4)3 system were carried out on the assumption that the A-parameter in this case also was temperature independent, the relatively poorer agreement between the observed and calculated solubilities at 25 ° may indicate a slight temperature dependence. In both the KzSO, and MgSO4 solutions the ionic strength effect, which tends to increase the solubility of Ag2SO4, overbalanced the c o m m o n ion effect, which tends to decrease the solubility, except at temperatures below about 80 ° and at the lowest concentration of supporting electrolyte studied, namely 0.1M. F r o m the trend in the solubility of Ag2SO4 as a function of concentration in both K2SO4 and MgSO4 solutions it appears that at concentrations of the supporting electrolyte somewhat below 0-1M the c o m m o n ion effect will at all temperatures overbalance the ionic strength effect and decrease the solubility of Ag2SO 4 below that observed in pure water. In the case of La2(SO4)3 the limited solubility in water prevented studies of the solubility of Ag2SO a in solutions of La~(SO4)3 much above 0.01M. In this system at the concentrations of La2(SO4)3 studied the solubility of the Ag~SO a was everywhere lower than in pure water. As can be seen in Fig. 1, however, values of the activity coefficient of the Ag2(SO4) 3 solutions follow the same trend and are consistent with those computed in the KeSO4 and MgSO, solutions.
Acknowledgement--The authors wish to express their sincere appreciation to Dr. R. W. STOUGHTON for helpful discussions concerning this work.
THE THERMODYNAMICS OF AQUEOUS SILVER SULPHATE-LANTHANUM SULPHATE SOLUTIONS* M. H. LIETZKE and J. O. HALL Chemistry Department, University of Tennessee, Knoxville, Tennessee and Chemistry Division, Oak Ridge National Laboratory,? Oak Ridge, Tennessee (Received 30 November 1966) Abstract--The solubility of AgsSO4 has been measured in 0.001, 0.002, 0.004 and 0-01 M La~(SO4)3
solutions to above 100° to continue the study of the solubility in sulphate solutions of increasing valence type. In addition to presenting new solubility data the present study also includes values of the activity coefficient of AgzSO, at zero concentration in K2SO4, MgSO4, and La~(SO~)3 solutions. IN TWO previous papers the solubility o f AggSO 4 in K2S04 C1)and in M g S 0 4 (~) solutions has been described. In these papers it was shown that an equation o f the D e b y e Hfickel type could be used to describe the solubility data over a wide range o f temperature and ionic strength. The present paper presents the solubility o f AgzSO 4 in La~(S04) a solutions and continues the study in sulphate solutions o f salts o f increasing valence type. In addition to presenting new solubility data the present study also includes values o f the activity coefficient o f Ag2SO 4 at zero concentration in K2SO4, M g S O 4 and La2(SO4) 3 solutions. EXPERIMENTAL The solubility measurements were carried out using the synthetic technique described previously.'3' At each of the four concentrations of La~(SO4)8 used the measurements were extended to as high a temperature as possible. In all cases the upper temperature limit was determined by the combined solubilities of the La~(SO4)3and Ag2SO4. Values of the solubility of Ag2SO4 in H20 were taken from the work of BARRE.~4~ RESULTS AND DISCUSSION In Table 1 are shown the experimentally observed solubilities o f Ag~SO 4 in the four different concentrations o f La~(SO4)z studied. All concentrations are expressed in terms o f molality. I n accordance with previous w o r k tl'2) it was assumed that the solubility p r o d u c t S o f Ag2SO 4 at any ionic strength I could be expressed in terms o f the t h e r m o d y n a m i c (zero ionic strength) value Ks ° by the following equation In S = In Ks ° +
~erx/(I) 1 + AV/(I)
(1)
* Based on a thesis submitted by J. O. Hall in partial fulfillment of the requirements for the degree Master of Science, University of Tennessee. ~"Operated by Union Carbide Corporation for the United States Atomic Energy Commission. tl~ M. H. LIETZKEand R. W. S'rOUOHTON,J. phys. Chem. 63, 1186 (1959). ~2, M. H. LmTZKEand R. W. STOU~HTON,J. phys. Chem. 63, 1984 (1959). t3~ M. H. LIETZKEand R. W. STOUGnTON,J. Am. chem. Soc. 78, 3023 (1956). ~4, M. BARRE,Annl$ Chim. Phys. 24, 202 (1911). .5 1249
1250
M.H.
LmrZKE and J. O. HALL
TABLE 1.---THE SOLUBILITY OF Ag2SO4 nq La~(SO~)8 SOLUTIoNs MLaztS04}s
t
SAgzSO4 robs.)
SAgaS04tcalc.)
0.001
25"0 42"5 55"0 72"5 98"0 105"0
0"0271 0"0301 0"0340 0-0360 0"0420 0"0430
0"0258 0"0307 0"0342 0"0375 0.0409 0.0412
0.002
25-0 56"0 61"0 76.0
0"0273 0.0330 0"0340 0"0366
0"0251 0.0335 0.0344 0"0370
0.004
25"0 45-0 56"0 70"0
0"0274 0"0301 0"0316 0"0348
0"0242 0-0299 0-0323 0"0351
0.01
25.0 45.0 50"0
0.0276 0"0301 0.0315
0"0248 0"0313 0"0327
where ~9'~, is the appropriate Debye-Hfickel slope at temperature T and A is an adjustable parameter. The relationship between the solubility product So of Ag2SO4 in the absence of a supporting electrolyte and the thermodynamic solubility product Ks° was assumed to be given by In So = In Ks° +
~v'(Io) I + A'v/(Io)
(2)
In this equation So = 4SOS; Io = 3so, where s o is the solubility of Ag2SO4 in pure water at the appropriate temperature; and A' is again an adjustable parameter. Substitution of Equation (2) into Equation (1) gives In S = In S O + ~ r
~/(I) 1 + A~/(I)
V'(I°) ] 1 -~ A ~ ( I 0 j J
(3)
In the previous studies il'z~ it was found that the parameter A in Equation (3) was essentially independent of temperature, but did vary with concentration of the supporting electrolyte. In carrying out the calculations it was assumed that only the species Ag +, SOt2-, and La a+ existed in a solution containing Ag~SO4 and Laz(SO4)8 dissolved in water. If s is the molal solubility of AgzSO 4 in a La2(SOl)z solution of molality M, then the molal solubility product of the AglSO 4 is given by S = 4s~(s + 3M)
(4)
while the ionic strength I of the solution is given by I = 3s + 15M
(5)
The overall calculation involved the estimation of the A-parameter in Equation (3)
The thermodynamics of aqueous silver sulphate-lanthanum sulphate solutions
1251
by the method of least squares subject to the criterion that 2~ (Sobs. - - Seale.)i 2 be a minimum. It was assumed that this criterion was met when successive values of the A-parameter did not change by more than 0.1 per cent. For convenience in carrying out this calculation the experimental solubility values were plotted and values of the solubility read from the curves at 5 ° intervals. These values were then used in all subsequent calculations. The calculational procedure was very similar to that reported in the study of the solubility o f Ag2SOa in AgNO 3 solutions. (5) A temperature independent value of A was obtained for Equation (3) at each of the four concentrations of Laz(SO4)z separately. This involved the numerical evaluation of (Os/OA), the partial derivative of the solubility of AgzSO4 with respect to the A-parameter, at each temperature and at each concentration of Laa(SO4)a, so that the original estimates of the value of A could be adjusted to satisfy the least squares criterion. The values of A and their variances obtained at each of the concentrations of Laz(SO4)z with A' set either to 1.0 or 1.5 are shown in Table 2. TABLE 2 . - - T H E VALUES OF A IN EQUATION (3)
A" -- 1.0
MLa2(so4~ 0.001 0.002 0-004 0"01
A
1'31 1"46 1'58 1"26
A' = 1-5 642*
6a 2.
A
0-09 0.21 0.41 0.09
1.87 2"02 2-09 1-55
0.17 0.40 0'76 0.14
* Variance in A. Values of the solubility of Ag2SO 4 calculated with A' set either to 1.0 or 1-5 were essentially the same and are given in Table 1 beside the observed values. As can be seen the agreement between the observed and calculated values is within a few per cent except at 25 °, where differences of 5-10 per cent are to be noted. The reason for the larger differences at 25 ° may be due to the fact that the value of A/(DT) 1/2, where is the A parameter of the Debye-Hfickel theory, and hence of the parameter A, which includes the ii/(DT) 1/2 term, is not entirely temperature independent. In this respect the present system resembles the previous study of the solubility of Ag2SO4 in AgNO~ solutions, (5) where the agreement between the observed and calculated solubilities was poorest at 25°C. In the Ag2SO4-Laz(SO4)3 system the effect may be magnified due to the much larger ionic strength effect. It is interesting to compare values of log Ks° obtained in the present study with values reported previously. (~) This comparison is shown in Table 3. The agreement between the two sets of values is within experimental error. Values of the activity coefficient of AgzSO 4 at zero concentration in K2SO4, MgSO 4, and La~(SO4) ~ solutions have also been computed. These values are given by the Sara/(/)/(1.0 + AV/(/)) term in Equation (1) and are tabulated in Table 4. In order to make comparison between these values easier, they are also plotted in Fig. 1. c5) M. H. LIETZKEand R. W. STOUGHTON, Jr. inorff, nucl. Chem. 28, 1877 (1966). (6) R. W. STOUGI-rroNand M. H. LIETZKE,d. phys. Chem. 64, 133 (1960).
1252
M.H.
LIETZKE and J. O. HALL
TABLE 3.--VALUES OF LOG Kao FOR AgsSOt vs. aXMPERATtr~ t
--log/(8 ° (Ref. 6)
--log Ks° (present study)
25 50 75
4.84 4.62 4.54 4.53
4.81 4.67 4.58 4"54
100
As can be seen all the values lie above the Debye-Hfickel limiting slope. Since good agreement between calculated and observed solubilities of Ag~SO4 was obtained in all three systems with the assumption of complete dissociation of all electrolytes involved, it appears that any ion association in these solutions is probably of a low order. Hence the Ag2SO4-La2(SO4)3 system is similar to the Ag2SO4-K2SO 4 and the AgzSO4-MgSO4 systems in that the molal solubility product of Ag2SO4 in all three systems may be described using a single parameter Debye-Hfickel expression. In all three systems this parameter seems to be ionic strength dependent and at least in the K2SO4 and MgSO4 systems temperature independent. Although the calculations in the 1.0
' I fDeby'eSlope
' I H[ickel
' I Limiting
'
I
'
I
'
at 25 °
.9
.8
7Ag2so4Ot zero cone.
vs
~"MgSO 4
yAQ2SO46t zero cone.
vs
~"LQ2(S04}3
.7 t00 o
.6+
~ o .4-
.¶
-
,
0
I
.4
,
I
.8
,
I
1.2
,
I
t.6
,
I
,
2.0
YT
F[o. 1.--The activity coefficient of AgzSO4 at zero concentration in K=SO4, MgSO4 and Las(SO~)8 solutions.
The thermodynamics of aqueous silver sulphate--lanthanum sulphate solutions TABLE 4.--THE
1253
AgzSO4AT ZERO CONMgSO, ANDLa~(SO4)3SOLUTIONS
ACTIVITY COEFFICIENT OF
CENTRATION IN K 2 S O 4 ,
MKzS04
t 25
0"1 --
0"5 --
0'186 0"168 0'151
0"8 --
50 75 100
0"375 0"354 0'332
0-141 0"126 0"110
t
0.1
0.5
1.0
25 50 75 100
0'382 0'364 0'343 0"321
0"213 0"197 0"179 0"161
0'154 0'140 0'125 0"109
t
0"001
0'002
0"004
0"01
25 50 75 100
0.770 0.760 0.748 0.735
0.701 0.688 0.673 0.657
0.619 0.604 0.587 0.568
0-501 0.483 0.464 0.441
MMgso~
MLa2IS04) 3
La2(SO4)3 system were carried out on the assumption that the A-parameter in this case also was temperature independent, the relatively poorer agreement between the observed and calculated solubilities at 25 ° may indicate a slight temperature dependence. In both the KzSO, and MgSO4 solutions the ionic strength effect, which tends to increase the solubility of Ag2SO4, overbalanced the c o m m o n ion effect, which tends to decrease the solubility, except at temperatures below about 80 ° and at the lowest concentration of supporting electrolyte studied, namely 0.1M. F r o m the trend in the solubility of Ag2SO4 as a function of concentration in both K2SO4 and MgSO4 solutions it appears that at concentrations of the supporting electrolyte somewhat below 0-1M the c o m m o n ion effect will at all temperatures overbalance the ionic strength effect and decrease the solubility of Ag2SO 4 below that observed in pure water. In the case of La2(SO4)3 the limited solubility in water prevented studies of the solubility of Ag2SO a in solutions of La~(SO4)3 much above 0.01M. In this system at the concentrations of La2(SO4)3 studied the solubility of the Ag~SO a was everywhere lower than in pure water. As can be seen in Fig. 1, however, values of the activity coefficient of the Ag2(SO4) 3 solutions follow the same trend and are consistent with those computed in the KeSO4 and MgSO, solutions.
Acknowledgement--The authors wish to express their sincere appreciation to Dr. R. W. STOUGHTON for helpful discussions concerning this work.