12343
J . Phys. Chem. 1993, 97, 12343-12348
Ion Interaction Model Applied to the CuS04-HzS04-HzO System at 25 O C C. F. Baes, Jr.,*J E. J. Reardon,* and Bruce A. Moyers Chemical and Analytical Sciences Division, Oak Ridge National Laboratory. P.O. Box 2008, Oak Ridge, Tennessee 37831 -61 19, and Department of Earth Sciences, University of Waterloo, Waterloo, Ontario, Canada N2L 3G1 Received: May 25. 1993; In Final Form: September 13, 1993" The modeling of aqueous mixtures of a bivalent metal sulfate and sulfuric acid according to the treatment of Pitzer is complicated by the formation of bisulfate ion and by the need to include the effects of unsymmetrical mixing of ions of like but unequal charge. Because of the economic importance of the recovery of copper by the leaching of its ores with sulfuric acid, it is especially important to improve estimates of Pitzer parameters for the C U S O ~ - H ~ S O ~ - Hsystem. ~O Accordingly, we have applied the Pitzer treatment to available osmotic, solubility, and emf data for this system, with inclusion of unsymmetrical mixing effects. We employed published parameters for the H2SO4-H20 system and evaluated literature data to obtain parameters for the CuS04-H20 system. The best fits to the data for mixtures were given by parameter sets that, in addition to /3(0)[Cu2+HS04-] and /3(l)[Cu2+-HS04-], included at least one other parameter. The best choice of one was $[Cu2+H+-HS04-], and the best choice of two additional parameters was B[Cu2+-H+] and $[Cu2+-H+-HS04-]. The resulting mean activity coefficient (y+) of CuSO4 at trace concentrations shows a dependence on sulfuric acid concentration quite similar to that found previously for FeS04 and for NiS04. For such solutions, predicted values of the quotient ( Y + ~ ) C " S O ~ / ( ~ * ~ ) H ~ Sa Omeasure ~, of the extractability of copper, are in reasonably good agreement with a previous prediction based on the extraction of Cu(I1) by didodecylnaphthalenesulfonic acid in toluene.
TABLE I: Parameters for HzS04 at 25 OC (with
1. Introduction
The Pitzer ion interaction treatmentl has proven to be a very versatile tool for the calculation of activity coefficients, osmotic coefficients, and other thermodynamic properties for a growing number of aqueous electrolyte mixtures. Recently, this treatment has been applied to the systems FeS04-HzS04-H2O2 and NiSO4H~SO~-HZO which , ~ are complicated by the formation of the HS04- ion and by the effects4 of the unsymmetrical mixing of ions of like but unequal charge (Le., H+ with Mz+ and HS04with sod2-). More limited applications of Pitzer's treatment to the analogous system involving C U S O ~have ~ , aided ~ in the development of models for the solvent extraction of Cu(I1) from sulfuric acid. Clearly, however, there is a need for a more reliable set of Pitzer parameters in this system, given the economic significance of the recovery of copper from its ores by sulfuric acid leaching.' Consequently, we have made a more extensive evaluation of available data on the system CuS04-H2S04-H20 than was presented previously. This evaluation has included numerical results of isopiestic and electromotive force (emf) measurements of Majima and Awakuras (kindly supplied by the authors), data on the solubility of CuS04.5H20 in H2SO4 solutions,9 and emf results of Holland and Bonner.lo 2. Computations
and
Included for Unsymmetrical Mixing)' parameter
ref 12
ref 21
ref 2
fl(')[H+S04"] @')[H+S04"] 0[H+S04"] fl(o)[H+-HS04-] fl(I)[H+-HS04-] 0[H+-HS04-] O[S042--HS04-] +[H+S042--HS04-]
0.064 21 0.225 90 0.031 13 0.222 97 0.460 02 -0.002 66 -0.135 34 0.027 81
0.0298
0.0217
0.0438 0.2065 0.5556
0.0411 0.2106 0.5320
The Pitzer parameters 6 and ( Y I are 1.2 and 2.0, respectively; log K for thedissociation ofbisulfateionis taken to be-1.9788. The parameters of Hovey er a1.I2were employed in the calculationssummarized in Tables IV, V, and VI. @
parameters reflecting the interactionof HSO4- ions with the other species present. The previously neglected effect of unsymmetrical mixing, which produces the additional mixing parameter and its derivative with respect to the ionic strength has been included in the present treatment, these terms being calculated as described by Pitzer (eqs 24,25, and 47 in ref 4). As previously, all calculations were carried out with the computer program SXLSQA,Il which has been modified to include the effects of unsymmetrical mixing. The standard error of fit ( u ) was defined in the usual way
Formation of the HSO4- ion
SO:-
+ H + + HSO;
(1)
indeed complicates the estimation of activity coefficients and water activity in acidic sulfate solutions. It necessitates an iterative calculation of the equilibrium concentrations of the species affected by this reaction, including simultaneous evaluation of the activity coefficients of all species, and it introduces additional
* To whom correspondence should be addressed: 102 Berwick Dr., Oak Ridge, TN 37830. t Oak Ridge National Laboratory (retired). t University of Waterloo. Oak Ridge National Laboratory. .Abstract published in Advance ACS Absrracrs, November 1 , 1993.
1
NO - N"
1
wherein Qobs is the observed quantity, QEalc is the corresponding calculated value, Cobs is the estimated uncertainty of the observation, NOis the number of observations, and N, is the number of parameters adjusted. If uncertainties in the data are correctly estimated and the fit is perfect, then the resulting value of u would be unity. 3. The HzSOs-HzO System
In the present study, Pitzer parameters for H2S04 (Table I) were fixed at the values obtained recently by Hovey et a1.12 for solutions up to 6 m. These authors included the effects of
022-3654 /93/2Q91- 12343%04.00/0 0 1993 American Chemical Society
Baes et al.
12344 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE II: Parameters for
cdo4'
parameter
this workb 8") [C U ~ + S O ~ ~ - 0.2 ] 1 34( 27) 2.632( 1 1 5) @(')[CU~+-SO~~-] @(2)[C~2+S04z-] -56.45(2.41) O [ C U ~ + S O ~ ~ - ] 0.01593(159) Eo[cell I]/mV 269.97(22) 1.20 d
at 25 'C
1.5
ref 15 0.21757 2.6260 -56.241 0.013756
ref 14 0.2340 2.527 48.33 0.0044
a Pitzer parameters b = 1.2, 4 1= 1.4, and a2 = 12.0. bNumbers in parentheses indicate uncertainty (lu) in the final digits shown for each value. Standard deviation, in multiples of the uncertainty assigned to each data point (see text).
1
0.5
0
2
4
6
H2SOl / m
Figure2. Solubility of CuS044H20in HzSO4solutionsat 25 OC.Values in acid are from Linke,9 and the value in water is from Miller et 01.;'~ the curve is calculated from parameter set 1 1 in Table VI, along with the parameters of Hovey et 01. in Table I and ours in Table 11.
I - 5 ) ' 0
r
.O
1
3
'
I
I
1
t
'
0.5
I
1
v
'
I
1
1.5
(CUSOq / nl)1'2
Figure 1. Residuals from the fit of the Pitzer parameters in Table I1 to data for CuSO4 solutions at 25 OC. They are the difference between observed and calculated quantities (Q), divided by the estimated uncertainty in the observed quantity (see text). Open triangles, circles, and squaresareosmoticdatafrom BrownandPrue,16Downesand Pitzer,14 and Miller et 0 Z . , I 5 respectively. The filled triangles,circles, squares, and diamonds are emf data from Wetmore and Gordon,I7Getman,18Nielsen and Brown,I9 and Mtiller and Reuther,20respectively.
unsymmetrical mixing in their fit of the data. They employed Debye-Hiickel slopes derived from Archer and Wang,I3giving a value for Ab at 25 OC (0.391 48 kg1lzmol-1/2)identical to that used in the present calculations. 4. The Cd04-H20 System
The parameters used here for CuSO4 (first set in Table 11) were obtained by fitting simultaneously (1) osmotic coefficients at concentrations aboveO.l m from theisopiesticresultsofDownes and Pitzer14and Miller et al.;I5(2) osmotic coefficients below 0.1 m from the measurements of freezing-pointdepression of Brown and Prue,16 corrected to 25 OC by Miller et al.; and (3) emf measurements of Wetmore and Gordon,17Getman,I8Nielsen and Brown,I9 and Miiller and Reuther,2O of the cell
the potential of which is given by the expression
For the potentials o f cell I containing solutions saturated with CuS04.5H20, the solubility found by Miller et aI.I5 (1.4199 m ) was used. Osmotic coefficient (4) values from the freezing-point measurements were assigned an uncertainty of 0.005, largely because of the uncertainty in the correction to 25 OC; 4 values from the isopiestic measurements were assigned an uncertainty of 0.003 at 0.1 m,decreasing to 0.001 at 0.5 m and above. The potentials from cell I were assigned an uncertainty of 0.2 mV. The fit obtained is indicated in Figure 1, where the deviation of each data point is shown as a multiple of the uncertainty assigned to it.
Table I1 includes, for comparison, sets of parameters obtained by Downes and PitzerI4and by Miller et ~ 1Downes . ~ and ~ Pitzer fitted their isopiestic data and the freezing-point results of Brown and Prue,16corrected to 25 OC. Miller et al., in addition to their own isopiestic measurements, included all the data used by Downes and Pitzer, but with what appears to be a more careful correction oftheresultsofBrownandPrueto25 OC. Theosmoticcoefficients calculated from three sets of parameters in Table I1 generally differ by less than 0.002 at concentrations above 0.04 m. Not surprisingly, the values calculated from Miller et al. differ less from the present estimates, while those from Downes and Pitzer show larger deviations, especially below 0.04 m, where they approach 0.008 in 4. 5. The CuS04-HzS04-HzO System
Four sets of literature data were examined for the purpose of assigning Pitzer parameters to mixtures of CuSO4 and HzSO4: The isopiestic measurementsof Majima and Awakura*involved mixtures of 0-1.3 m CuSO4 with 0-2 m H2S04 in 13 isotonic series that covered most of the range of compositions below saturation with CuS04.5H20 (Figure 2). The authors supplied us the numerical results of these measurements, including their estimates of the water activities for each isotonic series (Table III), based on the reference solutions of CuSO4 and/or H2SO4 that were included in each series. Our estimates of the water activities in Table 111, made by applying the Pitzer parameters of Hovey et a1.I2(Table I) and our parameters (Table 11) to the reference solutions, agree well with the estimates of Majima and Awakura but are probably a bit more accurate. The values we found for the two or three reference solutions in each series usually agreed within 0.0001, though in several cases they differed from one another by much larger amounts. The average of our calculated water activities for the reference solutionswas assigned as the "observed* quantity for the mixures within each series. The uncertainties assigned to this average for each series was based on the random scatter judged to be present in the data for mixtures or on the deviations of water activities calculated for the reference solutions, whichever was larger. One of the 103 points for mixtures (0.4223 m CuS04,0.3907 m H2S04) showed a large deviation and was excluded. Majima and AwakuraEmeasured the potentials of two cells PbO,(c), PbS04(c)lCuS04,H,SO,lglass electrode C1- ISE10.01m HCllglass electrode
(11) (111)
The same glass electrode was used alternativelyin cell I1 and cell
The Journal of Physical Chemistry, Vol. 97, NO. 47, 1993 12345
C U S O ~ - H ~ S O ~ - HSystem ~O
TABLE III: Calculated Water Activities for Reference
Solutions at 25 O C from tbe Isopiestic Results of Majima and Awakud solution awO a,(caIc)b uw(mean)f u ( u , ) ~ 0.996 19 0.996 19 0.000 05 0.9963 0.2053 m CuSO4 0.996 21 0.1041 m H2S04 0.996 17 0.1053 m &So4 0.991 67 0.991 68 0.9917 0.000 07 0.4913 m CuSO4 0.991 71 0.2318 m H2S04 0.991 63 0.2340 m H2S04 0.8035 m CuSO4 0.3584 m 0.3592 m 0.4642 m 0.4651 m H2S04 1.1421 m CuS04 0.5406 m 0.5416 m H2S04 1.1891 m CuSO4 0.5624 m H2S04 0.5665 m H2sO4 1.2942 m CuSO4 0.6186 m 0.6193 m &so4 0.8359 m 0.8362 m 1.0360 m H2S04 1.0466 m H2S04 1.1913 m 1.1943 m H2S04 1.4775 m 1.4776 m 1.6000 m H2S04 1.6015 m H2S04 2.0239 m HzS04 2.0243 m
0.9870 0.9832 0.9806 0.9797 0.9778 0.9686 0.9599 0.9532 0.9398 0.9338 0.91 15
0.986 69 0.987 13 0.987 10 0.983 20 0.983 17 0.980 59 0.980 3 1 0.980 27 0.979 65 0.979 47 0.979 31 0.977 47 0.977 29 0.977 27 0.968 59 0.968 58 0.960 14 0.959 69 0.953 29 0.953 15 0.939 91 0.939 90 0.933 87 0.933 80 0.911 52 0.91 1 49
0.986 97
0.000 2e
0.983 19
0.000 1
0.980 39
0.000 14c
0.979 48
0.000 12
0.977 34
0.000 15
0.968 58
0.000 2
0.959 91
0.000 3
0.953 22
0.000 4
0.939 90
0.000 5
0.933 83
0.000 7
0.911 51
0.001
Estimated by Majima and Awakura.8 Calculated from the parameters of Hovey et 01.l~in Table I and our parameters in Table 11. Average ofvalues in column 3, taken to be the water activitywithin each isotonic series. Uncertainties assigned to the water activities in each series. Except where noted, they were based on the random scatter in the data. Uncertainties larger than the scatter in the data. These were based on the discrepancies in the water activities (column 3) calculated for the separate CuSO4 and H2S04 solutions. 111, the latter containing a chloride-responding ion-specific electrode (ISE). The difference of the two cell potentials should be given by
AE = AEo - R T / 2 F 1n(aH2,0,/a, 2)
(3)
wherein AEo contains the standard potentials of the ISE and the PbOz/PbSOd electrodes and the activity of HCl in the 0.01 m solution
They thus obtained activities of H2S04 in aqueous mixtures that covered about the same range of compositions as the isopiestic measurements. The authors supplied us numerical values of these activities as well. The quantity we fitted was the mean activity coefficient of H2SO4 (Figure 3), derived according to the expression
and to which we assigned an uncertainty of &2%,based on the random scatter of thevalues. In fitting thesevalues, an adjustable correction was included to allow for a possible systematic error in hEo. Two of the 3 1 points (one for 0.1 m H2S04 and one for 0.4 m CuSO4 in 2 m H2S04) showed large deviations and were excluded. Solubilities of CuS04.5H20 in solutions ranging from 0 to almost 10 m H2SO4 (Figure 2) are summarized in ref 9. Data up to 6 m, the limit of validity of the parameters given by Hovey et a1.'2 for pure sulfuric acid solutions (Table I), were used here.
0.2 P
P
I
0.1
0
,
i 0
0.5
cum4
1
/ m
Figure 3. Mean activity coefficient of H2S04 at various concentrations vstheconcentrationofCuS04at25 O C . Thenumbersdenotethemolality of H2S04 in the mixtures. The points are from Majima and Awakura;* the curves are calculated from parameter set 11 in Table VI,along with the parameters of Hovey et al. in Table I and ours in Table 11.
The composition range of the saturated solutionswas from about 1.4 m CuSO4 in water to about 0.3 m CuSO4 in 6 m H2S04. An uncertainty of 2% relative error was assigned to the solubilities in acid. The accurately known solubility in water (1.4199 m, from Miller et al.Is) was assigned an uncertainty of 0.002 m. Holland and BonnerIO used cells of the type Cu(c)JCuS04,H2S041glasselectrode (IV) in which the total sulfate concentration was varied from about 0.004 to 0.4 m for fixed ratios mH+/mCu2+in the range 0.36-7.2. They tabulated a sum of potentials
C E= Eo(g1ass) - EO(CU)- E
(6)
that included the measured cell potential E and the standard potentials of the two electrodes. This sum should be given by
(7) Theauthors found that thestandard potential ofthe glass electrode depended on the acid concentration but did not give details of how corrections were applied. When we fitted the sum of potentials with calculated values of the ion concentrations and activity coefficients (YH+ and ycu2+),as indicated on the right above, average deviations of about 10 mV were obtained. This could be reduced to about 2.7 mV when a correction (about 7 mV) was applied to the observed potentials, but systematic deviations remained which increased sharply at sulfate concentrations below 0.01 m within each series for which the ratio mH+/ mC,,z+was constant. The necessary correction and the remaining deviations may well have been caused by residual variations in EO(g1ass). When the results below 0.01 m sulfate were excluded and an adjustable correction was applied to the calculated potentials, it was found possible to fit the remaining data fairly well. An uncertainty of 1 mV was assigned to them. We found (Table IV) that adjustment of j3(O) and j3(') for the Cu2+-HS04- interaction was sufficient to give fairly good fits to the isopiestic data (a1 = 1.44) and the emf data (a2 = 1.87) of Majima and Awakura, but a less satisfactory fit to the solubility data (a3 = 2.66). For the emf data of Holland and Bonner, which was confined to relatively low ionic strengths, it was sufficient to fix j3(O) at any reasonable value and adjust @ ( I ) to obtain a satisfactory fit. The resulting values obtained for j3'0) and j3(') from the first three sets of data were not in good agreement (Table IV), even considering the large uncertainties given by data sets 2 and 3. By refining an additional parameter, C"[Cu2+-HS04-] or one of the various mixture parameters (0 or +) for interaction involving
Baes et al.
12346 The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
TABLE VI: Selected Parameter Sets for Mixtures of CuS04 and HB04 at 25 'C (with E8 and W Included for Unsymmetrical Mixing) from Combined Data Sets*
TABLE I V Parameters for Mixtures of CuS04 and H2S04 at 25 OC (with EB and W Included for Unsymmetrical Mixing) from Separate Data Sets' data set 1. u w c 2. (yi)~go,d 3. CuSOd.SH20
no. ab pts fl('J)[Cu2+-HSO4-] @(1)[Cu2+-HS04-] 102 29 14
0.569(6) 0.489(58) 0.517(30)
2.14( 17) 3.64(57) 2.37 (57)
1.43 1.87 2.66
[0.489] [0.5 171 tO.5691
2.88(23) 2.79(23) 2.64(23)
1.05 1.os 1.06
SOP
4. emff
36
Numbers in parentheses indicate uncertainty (1 u) in the final digits shown for each value. Numbers in brackets were not varied during refinement. b Thestandard deviation (defined in the text). It reflects the average deviation of calculated from observed values in multiples of the uncertainty assigned to each data point. Water activities from the isopiesticdata of Majima and Awakura.* The uncertainties assigned are listed in Table 111. Mean activity coefficient of H2S04 from Majima and Awakura.6 The uncertainty in these values was taken to be 1 2 % relative error. In fitting these data, an adjustable factor of 1.033(13) was applied to the calculated activity coefficients (corresponding to an error of 1.26 mV in the standard cell potential assigned by Majima and Awakura). e Solubilities tabulated by Linke? from measurements of all assigned Goodwin and Horsch,*2 Bell and Taber,23 and uncertainties of &2%relativeerror; the solubility in water found by Miller ef u I . , assigned ~~ an uncertainty of 0.002 m. The adjusted solubility = -2.6554( 16), somewhat smaller than the values product was log from the final fits (Table VI). /The emf results of Holland and BonnerlO for cell IV, at sulfate concentrations above 0.01 m and with an adjustable correction of ca. 8.7 mV applied to the calculated values (see text). An uncertainty of 1 mV was assigned to each measurement.
Cu2+ion, the fit to each data set could be improved, but no set of data was extensive enough to indicate clearly the best choice of additional parameters. The four data sets were next combined, with the values of u,h for each observation in a data set i adjusted by a factor
F, = 2.18; F2 = 1.38; F3 = 0.36; F4 = 0.92
@a)
to compensate for different best fits (ut)found previously and for different numbers of points (No,[,which total N0.J in the data sets. The resulting standard error of fit to all the data (Table V) contains about the same contribution from each data set and would have a value near unity for an ideal fit, i.e., if each ui were unity. In fitting the combined data, we found 15 sets of two, three, or four Pitzer parameters (all including @(0)[Cu*+-HS04-]and
setb
parametep j3@)[Cu2+-HS04-] @(1)[C~2+-HS04-] corr factor log K s p AEOlmV 4 fl(O)[C~~+-HS04-1 flB(')[Cu2+-HS04-] $ [Cu2+-H+-HS04-] corr factor log Kap AEOImV 11 @"'[CUZ+-HSO~-] fl(')[C~~+-HS04-] 0 [Cu2+-Ht] $[Cu2+-H+-HS04-] corr factor log K s p AEOlmV 1
valued
01
02
u3
0.5365(78) 1.79 2.34 2.62 2.064( 149) 1.0772( 132) -2.6463 1(5 1) 8.72(35) 0.5190(47) 2.04 1.74 0.86 3.171(109) -0.0 1650( 82) 1.0437(70) -2.64594(27) 8.754( 188) 0.4755(47) 1.51 2.13 0.64 2.428( 137) 0.0835(100) -0.01 932( 1 17) 1.0567(66) -2.64599(24) 8.718( 168)
(74
1715
1.06
1.03
a The standard deviations u1, u2, u3, and u4 (defined as in the text and in Table IV, but with Nv= 0) were produced by the four data sets when the indicatedparameters were applied. From Table V. The adjustable correction factor was applied to the calculated values of ( r t ) ~to~ allow for a possible error in the Eo value assigned to the combination of cells I1 and 111; AEo was applied to the calculated EE values of cell IV for the same reason (see text). dNumbers in parentheses indicate uncertainty (1 u ) in the final digits shown for each value.
,@1)[Cu2+-HS04-]) whose individual values could be refined. The results (Table V) show that the inclusion of one or more of a wide choice of parameters in addition to @(O) and@(')produced a marked improvement in the fit. The covariance among the chosen parameters, however, produced so wide a range of values that many sets could be eliminated because of implausible parameter values (see Discussion below and Table V). The fits to the individual data sets given by selected parameter sets are summarized in Table VI. 6. Discussion The choice of plausible parameter sets in Table V was made by comparing individual parameter values with those tabulated in the recent review of Pitzer.' Values in Table V judged to be improbable are shown in boldface. All values of @(O) and @(l) are in ranges reported for other MX2 electrolytes. Values of CY, however, are below the range (-0.032 to 0.01) of all but one of the many reported values of CY for such electrolytes. Two values of B[CuZ+-H+]are outside the range (0.06-0.1) reported for other
TABLE V Parameters Sets for Mixtures of CuS04 and H2S04 at 25 OC (with E8 and EB' Included for Unsymmetrical Mixing) from Combined DaWb @(O)
parameterset
$1)
Cu2+-HS04-
CuZ+-HS04-
1 2 3
0.5365 0.6004 0.4225
4
0.5190
5 6 7 8 9 10 11 12 13 14 15
0.4055 0.5657 0.6181 0.6601 0.6266 0.4068 0.4755 0.3068 0.6187 0.4263 0.5792
2.064 2.708 3.103 3.171 3.602 2.274 2.642 2.335 2.583 2.760 2.428 3.252 2.900 2.985 2.956
0
e
Cu2+-HS04-
Cu2+-H+
4 C U ~ + - H + - S O ~ ~Cu2+-H+-HS04-
CuZ+-HS0,-S042-
-0.04042
0.106 -0.017
0.086
-0.04075 -0.04434 -0.06984 -0.04542
0.053 -0.006 0.013 -0.012
0.021 0.084 0.095
0.148 -0.019
0.142 -0.050 0.125
-0.034 -0.025
-0.01 1 -0.044
6 2.317 1.131 1.211 1.228 1.323 1.080 1.133 1.110 1.131 1.183 1.095 1.125 1.226 1.211 1.217
a In combining the data sets, the data were weighted as described in the text. b The parameter values in boldface exceed the range of similar values in the compilation of Pitzer.' Only parameter sets 1.4, 1I , and 15, therefore, were retained for consideration (see text and Table VI). CThe standard deviation includes weighting factors defined in the text for each data set.
,
CUSO~-H~SO~-H~O System
The Journal of Physical Chemistry, Vol. 97, No. 47, 1993 12347 I
I
2
I11
*
5:
-
e
m
+I
. ?-
I
*
5:
cu
1
0.01 0.01
I
I
0.1
1
t I
H2S04 / m
-8 -*
N
+I
0.2
1
0.01
I
I
0.1
1
\ c
H2S04 / m
Figure 4. Stoichiometric mean activity coefficient of bivalent metal sulfates at low concentrations in sulfuric acid solution at 25 OC. The curve for CuSO4 was calculated from parameter set 1 1 in Table VI, along with the parameters of Hovey et al. in Table I and ours in Table 11. Those for FeS04 and NiS04 were calculated from parameters given by Reardon and Beckie2 and Reardon,' respectively.
Figure 5. Quotient of mean activity coefficients that reflects the extractability of CuSO4 at low concentrations in sulfuric acid solution at 25 OC. Curve I is given by Tanaka's model;6curves I1 and I11 are given by sets of parameters of Moyer et ~ 1 . and ; ~ curves 1,4, and 1 1 are given by the parameter sets in Table VI, along with the parameters of Hovey et al. in Table I and ours in Table 11.
B[M2+-H+] parameters that have been evaluated with inclusion of the effects of unsymmetrical mixing. All values but one of +[CU~+-H+-SO~~-] are outside the range (-0.055 to -0.015) reported for other +[Mz+-N+-S042-] parameters similarly evaluated. One value of \l.[Cu2+-H+-HS04-] is outside the range (-0.025 to 0.014) reported for other +[M2+-N+-X-] parameters. Finally, two values of +[CU~+-HSO~--SO~~-] are outside the range (4.161 to -0.002) reported for other +[M2+-X--Yz-] parameters. On this basis, we are left with four plausible sets of parameters, nos. 1,4, 1 1 , and 15. Of these, no. 1 1 is considered the best choice, because it gives the best fit to the data (Table VI) and exhibits the lowest covariance among the parameters adjusted. One reviewer of this paper was concerned with the possible influence of the choice of parameters for HzSOd-HzO solutions (Table I) on the parameters obtained for CuS04-HzS04-H20 solutions (Tables V and VI). Of particular concern was the possible covariance of parameters for the H'S04'- interactions with those for the H+-HS04- interactions. Accordingly, we repeated the calculations summarized in Tables V and VI, employing the parameters of Harvie et a1.21instead of those of Hovey et al.lz (Table I). In general, the fits obtained with two and three adjustable parameters were somewhat better than those obtained previously, but the values of @(0)[Cu2+-HS04-] and (?(1)[Cu2+-HS04-] were more widely variable. While a smaller number of parameter sets could be eliminated because of unacceptable values of Q,B, and +, when those exhibiting high covariance among the parameters adjusted were also eliminated, the remaining sets of parameters were the same as sets 4 and 1 1 in Table VI, but with different parameter values. The conclusion is that the choice of parameters to represent binary sulfuric acid solutions has a significant influence on the way ternary mixtures with sulfuric acid can best be represented by the Pitzer treatment. This is probably because HzS04-HzO solutions are being represented as mixtures of H(HS04) and Hz(SO4) in water even though there is insufficient variation in the composition of such mixtures to fix all the parameter values that may be needed. Accordingly, for the present it seems best to adopt as we have done the parameter values of Hovey et al. (Table I), since they are based on data for a wider range of sulfate mixtures (with Na2S04) than is possible to obtain with the acid alone. At trace concentrations of Cu(I1) in aqueous sulfuric acid, the mean activity coefficient of CuSO4 (Figure 4), calculated from parameter set no. 1 1, decreases with increasing acid concentration, reaches a minimum value of about 0.04 at 1.8 m acid, and then
rises. The mean activity coefficients of FeS04 and NiS04, calculated from the parameters of Reardon and Beckie2 and R e a r d ~ nshow , ~ similar behavior, with slightly higher minima at about the same acid concentration. For a given activity of an acidic, cation-exchanging extractant in the organic phase, the extraction coefficient (D)of copper a t low concentrations in sulfuric acid should be proportional to a quotient involving ( Y ~ ) c ~ s o ,(Y&so,, , and the formal acid concentration mH
(9) Values of the above quotient of activity coefficients calculated by various sets of Pitzer parameters are compared as a function of acid concentration in Figure 5. The curves labeled I, 11, and I11 were calculated from sets of Pitzer parameters described previously by Moyer et ales;curves labeled 1, 4, and 1 1 were calculated from the parameter sets in Table VI. Curve I1 depends primarily on values of @(o)[Cu2+-HS04-] and j3(1)[Cu2+-HS04-]estimated from Majima and Awakuras alone. Curve I is based on Tanaka's model6 of the extraction of Cu(I1) by a @-hydroxyoxime in xylene and includes the association of aqueous Cu2+and S042-ions. Curve I11 is based on our model of the extraction of Cu(I1) by didodecylnaphthalenesulfonicacid (HDDNS) in t o l ~ e n ewithout ,~ association of Cuz+ and S042-. Curves 1, 4, and 1 1 reflect the differences produced in the present treatment by use of two, three, and four Pitzer parameters, respectively, to describe the additional interactions in mixtures of CuSO4 and HzS04. The extent of agreement of curves 4 and 1 1 , which are based on the best fits to the data considered here, indicates that the quotient of activity coefficients, and therefore the extractability of Cu(II), can be predicted with an uncertainty of about f10% over most of the range of acid concentration shown. That these curves are in reasonably good agreement with curve I11 derived from the extraction of Cu(I1) by HDDNS supports the model developed by Moyer et aL5 to describe the chemistry of the organic phase in this system. Acknowledgment. This research was funded in part by the Division of Chemical Sciences, Office of Basic Energy Sciences, US. Department of Energy, under Contract DE-ACOS840R21400 with Martin Marietta Energy Systems, Inc. The authors express their thanks to H. Majima and Y. Awakura for supplying us supplementary numerical results from their investigations.*
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The Journal of Physical Chemistry, Vol. 97, No. 47, 1993
References and Notes (1) Pitzer, K.S . Activity Coefficients in Electrolyte Solutions, 2nd ed., Pitzer, K.S., Ed.; CRC Prcss: Boca Raton, FL, 1991; pp 75-153. (2) Reardon, E. J.; Beckie, R. D. Gemhim. Cosmochim. Acta 1987,51,
2355. (3) Reardon, E. J. J . Phys. Chem. 1989. 93, 4630. (4) Pitzer, K. S . J . Solution Chem. 1975,4, 249. ( 5 ) Moyer, B. A.; Baes. C. F., Jr.; Case, G. N.; Lumetta, G. J.; Wilson, N. M. Sep. Sci. Technol. 1993, 28, 81. (6) Tanaka, M. Materials Trans. JIM 1990, 31, 409. (7) Ritcey, G. M.; Ashbrook, A. W. Solvent Extraction Principles and Applications to Process Metallurgy; Elsevier: New York, 1980. (8) Majima, H.; Awakura, Y. Metall. Trans. 1988, 198, 347. (9) Linke, W. F. Solubilities, 4th ed.; D. Van Nostrand Co.: New York, 1958; Vol. 1, p 970. (10) Holland, V. F.; Bonner, 0. D. J . Am. Chem. SOC.1955, 77, 5833. (11) Baes, C. F., Jr.; Moyer, B. A.; Case, G. N.; Case, F. I. Sep. Sci. Technol. 1990, 25, 1675.
B a a et al. (12) Hovey, J. K.;Pitzer, K.S.; Rard, J. A. J . Chem. Thermodyn. 1993, 25, 173. (13) Archer, D. A,; Wang, P. J. Phys. Chem. Ref.Data 1990, 19, 371. (14) Downes, C. J.; Pitzer, K.S . J . Solution Chem. 1976, 5, 389. (15) Miller, D. G.; Rard, J. A.; Eppstein, L. B.; Robinson, R.A. J.Solution Chem. 1980, 9, 467. (16) Brown, P. G. M.; Prue, J. E. Proc. R. SOC.London 1955, A232,320. (17) Wetmore, F.E. W.; Gordon, A. R. J . Chem. Phys. 1937, 5, 60. (18) Getman, F. H. J. Phys. Chem. 1930,34, 1454. (19) Nielsen, R. F.; Brown, D. J. J . Am. Chem. Soc. 1927,49, 2423. (20) Miiller, V. F.; Reuther, H. 2.Elecktrochem. Angew. Phys. Chem. 1941,47,640. (21) Harvie, C. E.; Msller, N.; Weare. J. H. Ceochim. Cosmochim. Acta 1984,48,723. (22) Goodwin, H. M.; Horsch, W. G.Chem. Metall. Eng. 1919,21, 181. (23) Bell, J. M.; Taber. W. C. J . Phys. Chem. 1908, 12, 174. (24) Footc, H. W. J . Am. Chem. Soc. 1915,37, 290, 1200. (25) Footc, H. W. I d . Eng. Chem. 1919, 11,629.
