Densities and viscosities of CuSO4-H2SO4-H2O solutions

Hydrometallurgy, 21 (1988) 1-7 Elsevier Science Publishers B.V,, A m s t e r d a m - - P r i n t e d in T h e Netherlands

D e n s i t i e s and Viscosities of Solutions

1

CuS04-H2SO4-H20

J. H O T L O S a n d M. J A S K U L A

Department of Physical Chemistry and Electrochemistry, Jagellonian University, 30 060 Cracow (Poland) (Received April 30, 1987; accepted in revised form October 26, 1987 )

ABSTRACT Hotlos, J. and Jaskula, M., 1988. Densities a n d viscosities of CuSO4-H~SO4-H~O solutions. HydrometaUurgy, 21: 1-7. Density and kinematic viscosity data for the ternary system CuSO4-H2SO4-H~O were determined over wide ranges of concentrations (0.2M < c(:,,so, < 1.15M, 0.25M < c.~so4 < 2.5M) and temperature (25 ° C < T < 60 ° C ). T h e results are described using empirical functions.

INTRODUCTION

Solutions containing copper sulfate and sulfuric acid are interesting principally because they have been used in industrial copper electrorefining for over 100 years and also in electroplating baths. To describe the processes occurring in these solutions it is necessary to know a number of physico-chemical parameters, of which density and viscosity are of basic importance. When investigating transport phenomena and thermodynamic equilibria in CuSO4-H2S04 solutions, it became apparent that there was a lack of reliable pertinent data valid over a wide range of component concentrations and temperatures. The available literature data are dissipated and incoherent, and systematic determination of density p and kinematic viscosity u was required. EXPERIMENTAL

Densities and viscosities were determined for 38 solutions containing CuSO4 and H2SOa at four temperatures, 25, 35, 45 and 60 ° C. Copper sulfate pentahydrate p.a. (POCh Gliwice) additionally twice recrystallized, sulfuric acid p.a. (Merck) and double distilled water were used. The concentration of copper sulfate was varied between 0.2 and 1.15 M, and that of sulfuric acid between 0.25 and 2.5M. The solutions were prepared in such a

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way that their molar concentrations at 25 ° C were at the points of the planned concentration matrix. The concentrations of the components were determined independently by potentiometric titration with E D T A or N a O H , respectively. Densities of the solutions were measured using 25 ml pycnometers equipped with their own thermometers (at 25 and 35 °C) and 10 ml pycnometers (at 45 and 60 ° C ). The pycnometers were calibrated with four times distilled water at various temperatures. The temperature was maintained within + 0.5 ° C. The experimental deviation was + 1 k g / m 3. Kinematic viscosities were determined with a capillary viscometer with suspended level (Seidert-Deckert viscometer), calibrated with water. The efflux time varied within the range 124.26 + 0.07 s at 25 + 0.1 °C to 66.02 _+0.05 s at 60 + 0.1 ° C. The viscometer was supported in a thermostatic water bath, the temperature of which was maintained within 0.1°C. For each solution, two independent sets of experiments have been made and in each 5-10 efflux times were measured. The reproducibility of the measurements was perfect (0.1% ), but taking into account errors which come from the temperature control inaccuracy and from using the simplified formula (with no corrections) for viscosity calculations, the error of viscosity determination was estimated to be about 1%. RESULTS AND DISCUSSION

Density There are many papers devoted to determination of the density of either CuSO4 or H2SO4 aqueous solutions. Very useful data and empirical functions p(c,T) can be found in SShnel's paper [1]. Fewer data on densities are available for the ternary system CuSO4-H2SO4H20 [2-6], and only a few solutions have been examined. Recently, Price and Davenport [7 ] have published an extensive paper devoted to determination of density in two ranges of concentration and temperature, corresponding to solutions used in electrorefining (large amounts of copper and acid, t > 50°C), and to those used in electrowinning (a small amount of copper sulfate, t < 40 ° C ). Important ranges of concentration and temperature still remain for which the density has not yet been measured. In the present work, the densities of CuSO4-H2SO4 solutions in a wide range of concentrations and temperatures were determined systematically. The results (Table 1 ) show that the density depends on CuSO4 concentration much more than on H2SO4 concentration, and that the dependence on temperature is relatively small. All the density results were described as a function of three variables: p (X, Y,T) = ( K + L × X + M × Y) × exp (Ep/T)

(1)

TABLE 1 Densities p and kinematic viscosities u of solutions in the system CuSO4-H2SO4-H20 mcuso~

(mol/kg)

mH~s04 (mol/kg)

Densities (kg/m :~) and viscosities (m2/s) 25°C

1.158 1.004 0.854 0.698 0.550 0.401 0.199 1.179 1.015 0.863 0.709 0.557 0.408 0.202 1.024 0.873 0.721 0.563 0.409 0.204 0.815 0.901 0.732 0.576 0.421 0.208 0.908 0.741 0.593 0.427 0.212 0.764 0.596 0.442 0.217 0.613 0.441 0.219

0.256 0.256 0.255 0.256 0.255 0.254 0.255 0.515 0.512 0.508 0.511 0.511 0.514 0.511 0.826 0.831 0.830 0.826 0.823 0.832 1.061 1.324 1.320 1.328 1.316 1.330 1.828 1.836 1.860 1.820 1.839 2.383 2.362 2.396 2.370 2.813 2.793 2.792

35°C

45°C

60°C

p

uXIO 6

fl

PX10 6

p

uXIO 6

p

uXIO ~

1187 1166 1143 1121 1099 1075 1044 1199 1177 1156 1133 1111 1089 1059 1194 1173 1149 1128 1107 1078 1175 1198 1175 1153 1132 1105 1223 1200 1179 1158 1131 1227 1205 1184 1157 1225 1203 1178

1.52 1.42 1.33 1.24 1.17 1.10 1.00 1.56 1.46 1.38 1.28 1.21 1.11 1.03 1.52 1.43 1.31 1.24 1.16 1.07 1.38 1.50 1.38 1.30 1.22 1.13 1.55 1.46 1.38 1.30 1.19 1.58 1.48 1.38 1.28 1.56 1.44 1.34

1181 1159 1137 1116 1094 1071 1039 1194 1172 1150 1130 1107 1084 1054 1189 1168 1145 1123 1100 1072 1169 1194 1172 1150 1126 1099 1217 1194 1176 1153 1125 1221 1201 1178 1152 1218 1197 1171

1.25 1.16 1.08 1.00 0.935 0.884 0.827 1.30 1.17 1.10 1.02 0.974 0.893 0.831 1.20 1.12 1.05 0.997 0.93(I 0.871 1.12 1.20 1.11 1.04 0.978 0.913 1.26 1.18 1.11 1.04 0.971 1.25 1.18 1.11 1.04 1.25 1.16 1.09

1175 1155 1133 1110 1087 1064 1036 1188 1166 1143 1124 1099 1080 1052 1184 1163 1139 1116 1095 1070 1168 1191 1168 1146 1123 1094 1210 1192 1169 1147 1120 1219 1192 1175 1144 1212 1191 1161

1.03 0.938 0.891 0.825 0.779 0.730 0.674 1.04 0.972 0.908 0.843 0.793 0.737 0.688 0.978 0.923 0.866 0.819 0.770 0.724 0.913 0.983 0.906 0.854 0.808 0.758 1.02 0.961 0.906 0.860 0.815 1.04 0.963 0.914 0.859 1.02 0.956 0.902

1166 1142 1122 1098 1080 1057 1028 1177 1153 1133 1117 1095 1068 1042 1172 1152 1130 1108 1089 1061 1155 1174 1153 1133 1111 1084 1196 1177 1160 1134 1108 1200 1181 1159 1131 1199 1178 1156

0.778 0.727 0.669 0.640 0.604 0.569 0.527 0.798 0.732 0.695 0.657 0.615 0.580 0.541 0.754 0.707 0.674 0.640 0.606 0.564 0713 0.764 0.704 0.665 0.632 0.580 0.794 0.746 0.708 0.673 0.615 0.796 0.744 0.716 0.656 0.794 0.743 0.709

4 TABLE 2 Polynomial (1) coefficients, percent average (av. err.) and percent maximal (max. err.) deviation of densities obtained experimentally and calculated using polynomial (1)

L

M

Kind of concentration used

K

X - C u +÷ (g/l) at 25°C Y-H.~S04 (g/l) at 25°C

841

X - C u S O 4 (mol/l) at 25°C Y - H2S04 (mol/l) at 25°C

841

124

X - C u S Q ( mol/kg H20 ) Y - H2S04 (mol/kg H20 )

846

118

1.95

av. err. (%)

max. err. (%)

0.14

0.50

47

0.14

0.44

39

0.19

0.62

0.48

where: p = density (kg/m 3 ), K,L,M= fitted coefficients; their values depend on the way of expressing solution concentration (Table 2), X , Y = C u S Q and H~SO4 concentrations (g/l) or (mol/1) or (mol/kg), T=absolute temperature, E/, = temperature coefficient; its value, Ep = 53, was found by using the same procedure as for determining E in function (2). Those investigating physico-chemical properties of CuSO4-H2SO4 solutions have used different ways to express the solution concentrations. Thus comparison of values obtained by various authors is difficult or even impossible. For this reason, the polynomial (1) was fitted three times to the experimental data, concentrations being expressed in: mole/dm3, mole/kg of water, and g of copper (or sulfuric acid) per dm 3. The resulting polynomial coefficients and the average and maximal matching errors are shown in Table 2. The results calculated by polynomial ( 1 ) agree very well with the data obtained by Claessens et al. [4], Buzhinskaya et al. [5] and Price and Davenport [7], but they differ a little from the values reported by Eisenberg et al. [3 ].

Viscosity The papers quoted above, during the discussion of density of C u S O 4 - H 2 S O 4 solutions, are devoted also to determining viscosity. Additional data (for dilute solutions) were presented by Asmus [8] and Brasher and Jones [9]. The results obtained by various authors show considerable discrepancies, especially those of Buzhinskaya et al. [6 ] differ strongly from other results, some by more than 10%. In their comprehensive paper, Price an Davenport [7] presented a large number of experimentally determined viscosities and proposed an empirical function V(Ccuso4, CM2so4,T) to describe them. Though this function enables one to calculate the viscosity of a solution for various concentrations

and temperatures, the accuracy with which it describes experimental data (within O.lcP at 20-40 ° C and 0.04cP above 50 ° C ) is unsatisfactory. Moreover, the cited function must contain some error since it does not reproduce the experimental data. Beside the solutions investigated in the above-mentioned papers, there are ranges of concentration and temperature in which the viscosities of CuSO4H2SO4-H20 solutions have not been measured. The present work attempted the systematic determination of viscosity in this system. The influence of the components concentrations on the viscosity (Table 1) is analogous to that on the density, increase in CuSO4 concentration causing a 3-4 times larger change in v than the corresponding increase in H2SO4 concentration. Contrary to the density, the influence of temperature is considerable. Claessens [4] and Price [7] attempted to describe the dependence of viscosity on concentration using "total ionic concentration", F, defined as F--- ~cizi, assuming that CuS04 is fully dissociated and the H S O j ion is completely undissociated. The proper description of the behaviour of viscosity in the investigated solutions in terms of ionic strength is much more complicated than those proposed in [4] and [7], because in reality the H S O j ion dissociates to a certain degree, whereas copper sulfate is not completely dissociated [10]. Undissociated species must also be taken into account. The influence of temperature on viscosity was examined by plotting In v vs. 1/T, and it was found that in each case this relation was perfectly linear (correlation coefficients > 0.999 ). This allowed the determination of values of "activation energy" Ea; these lay within the range 15.02-16.53 k J / m o l and the average value was 15.74 _+0.36 kJ/mol. The E a values depend on solution composition, but considering the relatively large error in their determination (average error estimated at 0.34 kJ/mol) it is possible only to state that the "activation energy" tends to increase when CuSO4 concentration increases. This agrees with the observation of Alamelu and Suryanarayana [11] for solutions containing CuS04 and with those of Claessens et al. [4] and Eisenberg et al. [3] for CuSO4-H2SO4 solutions. To describe the present experimental data the following function is proposed:

v(x,y,T) /m2s-l= lO-11X (AO+AI x x + A 2 x y +A3xx2+A4XxXy+A5xy2)Xexp(E/RT)

(2)

where x is CuS04 molality (mol/kg H20), y is the H 2 S O 4 molality, and T is absolute temperature. The values of the coefficients AO-A5 and the value of E (which has the physical meaning of activation energy) were determined in the following way: ( 1 ) the value of E, was assumed, and for all experimental data the value of the expression v/exp (E/RT) was calculated,

(2) using the multiple regression method, the coefficients AO-A5 in eqn. (2) were evaluated, (3) the average error of approximation was computed, (4) changing the assumed value of E, operations 1-3 were repeated in cycles and the value of average error of approximation was examined. The dependence of average error of approximation on the assumed value E had a distinct minimum, which afforded the optimum value of "activation energy" in C u S Q and H2SO4 solutions in the investigated range of concentration and temperature. This value, 16.28 kJ/mol, agrees with the value obtained by averaging E a for all 38 solutions. Using the optimum value of E = 16.28 kJ/mol, the AO-A5 coefficients were computed and had the following values: A0--164 A 3 = 3 2 A I = 48 A 4 = 2 A 2 = 13 A 5 = 3 where the kinematic viscosity v is expressed in m2/s. The experimental values and those calculated from the polynomial differed by less than 2.5%, whereas the average matching error was 0.86%0. Using the polynomial (2), the viscosity values for the compositions and temperatures investigated by the other cited authors were calculated. Good agreement was obtained with the results reported by Claessens et al. [4] and Arvia et al. [6]; Price's and Davenport's data [7] were somewhat lower at lower temperatures and somewhat higher at higher temperatures. Greater discrepancies were observed for the data of Eisenberg et al. [3] (which were questioned by Price and Davenport) and for those of Buzhinskaya et al. [5] which, as was previously mentioned, differed considerably from all the other reported values. ACKNOWLEDGEMENTS

The study was supported by a grant within a research programme 03.08 coordinated by the Institute of Inorganic Chemistry and Metallurgy of Rare Elements in Wroc|aw.

REFERENCES 1 SShnel, O. and Novotny, P., 1985. Density of Aqueous Solutions of Inorganic Substances. Academia, Prague, pp. 102, 296-298. 2 Holler, H.D. and Peffer, E.L., J. Amer. Chem. Soc., 38 (1916) 1021-1029. 3 Eisenberg, M., Tobias, C.W. and Wilke, C.R., J. Electrochem. Soc., 103{7) (1956) 413-416. 4 Claessens, P. Feneau, Cl. and Breckpot, R., Bull. Soc. Chim. Belges, 77 (1968) 213-236.

5 Buzhinskaya, A.V., Kandyba, L.L., Kondrashova, P.S. and Migina, A.I., Zh. Prikl. Khim (Leningrad), 47(7) (1974) 1486-1490. 6 Arvia, A.J., Bazan, J.C. and Carozza, J.S.W., Electrochem. Acta, 11 (1966) 881-889. 7 Price, D.C. and Davenport, W.G., Metall. Trans. B, 11B (1) (1980) 159-163. 8 Asmus, E., Ann. Physik, 36 (1939) 166-182. 9 Brasher, D.M. and Jones, F.R., Trans. Faraday Soc., 42 (1946) 773-779. 10 Freeman, R.W. and Tavlarides, L.L., J. Inorg. Nucl. Chem., 43 (10) (1981) 2467-2469. 11 Alamelu,S. and Suryanarayana, C.V., Acta Chim. Acad. Sci. Hung., 21 (1959) 333-341.