Complex Formation in Lead Sulfate Solutions G. Gardner and G. H. Nancollasl Chemistry Department, State University of New York at Buffalo, Buffalo, N. Y. 14214 CHARACTERIZATION of the complex species in lead sulfate solutions is difficult because of the small solubility of the salt (1.35 X 10-4M at 25 "C) (I). In a recent study of the kinetics of crystallization and dissolution of the salt (2), it was found that stable supersaturated solutions could be prepared with a lead sulfate concentration of at least 1.78 X 1O-W. By careful control of concentrations and experimental technique, such solutions are sufficiently stable to enable measurements to be made for the determination of the thermodynamic association constant, K,of the reaction:
Pb2+
+ Sob2- $ PbSO4
Under the very dilute conditions necessary for this study, the conductivity method was chosen for the determination of the extent of ion association. Because there is a considerable amount of interest in the use of the new lead ion-selective electrodes, a parallel potentiometric study of the lead sulfate system was made also. The concentrations were near the limit of useful application of these electrodes, and it was necessary to obtain very precise emf's in order to yield meaningful thermodynamic association constants. In such dilute systems, it is very desirable to use as many different experimental approaches as possible in order to determine the extent of ion-pairing. EXPERIMENTAL
Potassium sulfate and lead nitrate (Fisher Certified Reagents) were recrystallized from conductivity water before use. Potassium chloride, used for cell constant determination, was recrystallized twice, heated to redness in a platinum crucible, and cooled in a desiccator. Conductivity Measurements. The screened Jones and Joseph ac bridge (3) was similar to that described previously ( 4 ) but with the addition of a tuned null-detector (General Radio Co., Type 1232-A) which served in the balancing of the bridge. The conductivity cell, of the Hartley-Barrett type with greyed platinum electrodes, contained a vibratory stirrer (Vibromix Model E, Chemapec Inc.) and measure0.005 "C ments were made in an oil thermostat at 25 contained in a room thermostated at 25 f 2 "C. Conductivity water was prepared by passing double distilled water through a mixed-bed ion exchange column directly into the cell; its specific conductivity was usually about 2 X lo-' ohm-'. The cell was calibrated using dilute solutions of potassium chloride and the extended Onsager equation (5).
*
=
149.92 - 93.85~'"
+50~
In a typical experiment, weight buret additions of solutions either of potassium sulfate or lead nitrate were made into a 1 To whom all correspondence regarding this paper should be addressed.
(1) B. van't Riet and I. M. Kolthoff, J. Amer. Chem. SOC.,64, 1045 (1960). (2) D. M. S. Little, Ph.D. Thesis, University of Glasgow, Scotland, 1964. (3) G. Jones and R. C . Joseph, J . Amer. Chem. SOC.,50, 1049 (1928). (4) G. H. Nancollas and N. Purdie, Trans. Faraday SOC.,57, 2272 (1961). (5) C. W. Davies, J. Chem. SOC.,1937,432. 794
ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, J U N E 1970
weighed amount of conductivity water in the cell. The other reagent was then added in small weighed amounts and the steady resistance readings were recorded. All experiments were made with a stream of presaturated nitrogen gas passing over the solution in order to exclude carbon dioxide. Potentiometric Measurements. Emf measurements were made at 25 f 0.05 "C using the cell Lead electrode/solution understudy/ KCl(sat)/calomel electrode together with a Beckman Research pH meter (Model 1019). The cell consisted of a double-walled borosilicate glass vessel of 250-ml capacity. Water, thermostated at 25 =!= 0.05 "C was circulated in the space between the walls, and the experiments were made in a nitrogen atmosphere. The calomel electrodes incorporated a fiber type junction (Corning Type 476001) which was found to have the smallest rate of diffusion of potassium chloride into the cell solution. The latter was measured using a potassium ion selective electrode and was always less than 10-5 gram ion of potassium per hour. The Orion Solid State lead electrode (Model 94-82) was calibrated before and after each experiment in solutions 0.2 of lead nitrate. The electrode response was 30.50 mV/log apbZf and the drift in E" with time varied from 0.1 mV to 1.0 mV per day. Normally the latter was constant at approximately 0.3 mV/day and it was possible to correct the measured emf values for the small drift in E". Activity coefficients of z-valent ions, f,, were calculated using the Davies extended form of the Debye-Huckel equation (6)
*
[
-log fz = A z 2 1 ~
- 0.311
In a typical experiment, standardization in situ was first carried out by adding lead nitrate to a solution of approximately 10F3Msodium perchlorate in the cell and then, without removing the electrodes, additions of potassium sulfate solution were made. Emf's were reproducible to *0.15 mV. RESULTS AND DISCUSSION
Under the conditions of the experiments, the concentrations of the ion pairs PbN03+ and KS04+ amounted to only 0.1 to 0.15% of the total lead sulfate and could be neglected. The measured specific conductivity K , of solutions containing mixtures of lead nitrate (ml molar) and potassium sulfate (mz molar) can be written 1 0 3(obsd) ~
=
2A,t(mz)
+ 2As0,~-(m, - [PbSOd) +
- [PbSOrl) -k ~ A N o (~ m- ~=) 2 m d ~ ~ 8f 0 , ~ ~ ~ A P ~ ( N- O~ ~[ )P Z~ S ~ ~ ] A (2) P~SO+
2Apbz+(mi
If no complex were formed, the calculated specific conductance 103K (calcd)
=
2111d~~s0, f 2miA~b(~O~)t
(3)
and it follows from Equations 2 and 3 [PbSOr] =
IO3{ ~(calcd)- K(obsd)] ~AP~so,
(4)
(6) C . W. Davies, "Ion Association," Butterworth, London, 1962.
Table I. Conductivity of Lead Sulfate Solutions at 25 “C rnl
X 105M
rn2
X 105M
8.9015 5.0966 8.8652 8.2433 8.8464 9.8835 8.8230 11.912 8.7742 16.147 8.7156 21.240 7.1010 10.454 10.900 10.412 14.501 10.373 16.669 10.349 7.8301 8.4331 11.621 8.3997 14.693 8.3726 Mean K = 561 f- 21 (std dev).
Pb2+ X 105M
8.7086 8.5624 8.4694 8.3874 8.2028 7.9813 6.8100 10.445 13.879 15.978 7.5615 11.218 14.185
m2x105~ 4.9037 7.9405 9.5065 11.476 15.576 20.506 10.163 9.9574 9.7514 9.6581 8.1645 7.9968 7.8646
Table 11. Lead Electrode Measurements at 25 “C s04’- x 1 0 5 ~ Pba+ X 1O6M m2 X 105M ml X 106M 17.91 8.777 18.47 9.342 17.54 10.82 18.27 11.55 15.12 9.003 15.57 9.447 14.72 11.12 15.28 11.68 14.78 8.780 15.22 9.219 13.80 8.904 14.16 9.274 12.77 11.28 13.26 11.77 12.25 9.210 12.60 9.554 11.25 11.43 11.66 11.84 9.275 9.191 9.595 9.511 8.433 9.224 8.764 9.554 Mean K = 500 f 50 (std dev).
Equivalent conductivity values were calculated using the appropriate Onsager equations at 25 “C (7). Apb(Nol)l = 140.96149.03Z”2 AK2soc
= 153.52-155.22Z”2
ApbSo,
= 149.52-257. 56Z”2
Values of [PbS04] were calculated using Equation 4, by an iterative procedure involving the ionic strength
Z = 3ml
+ 3m2 - 4[PbS04]
(5)
Activity coefficients were calculated from Equation 1 and the results of the conductance measurements are given in Table I. The results of the potentiometric experiments are summarized in Table 11. Concentrations of ionic species were obtained from the measured lead ion activities using mass balance and electroneutrality expressions (8). The thermodynamic association constant, K, was obtained by successive approximations for the ionic strength. The standard deviations of the K values are given in Tables I and I1 and it is seen that the agreement between the results of the two methods is satisfactory. The values obtained by the potentiometric method in these dilute solutions are particularly susceptible to uncertainties since a change of -1.0.2 mV in the measured emf results in a difference of approximately *70 1. mole-’ in the calculated K value. Hydrolysis of the lead ion in these studies was considered to be negligible since no drifts were ob(7) H. S . Harned and B. B. Owen, “Physical Chemistry of Electrolyte Solutions,”Reinhold, New York, N.Y., 1958. (8) G. H. Nancollas “Interactions in Electrolyte Solutions,” Elsevier Publishing Co., Amsterdam, 1966.
K
x
105
ohm-’ cm-l 3.9327 4.8268 5.2870 5.8645 7.0631 8.4992 5.0064 5.9782 6.8932 7.4513 4.6113 5.5930 6.3870
I
x103~ 1.684 1.728 1.617 1.659 1.578 1.558 1.612 1.736 1.576 1,692 1.433
K 1. mole-’ 544 547 580 566 571 586 518 549 586 577 531 560 576
K 1. mole-’
519 553 467 493 482 429 493 433 459 528 596
served in the conductance readings and previous conductance measurements with lead nitrate (9, IO) lead chloride, and lead bromide (IZ) at similar pH values had indicated that such effects were negligible. Likewise, in the potentiometric measurements, the agreement of the calculated K(PbS04) with conductance value, and its insensitivity to changes of pH of about ~ k 0 . 2unit from the normal 5.8, pointed to the absence of appreciable hydrolysis. The mean value of K (PbSOd), 531 1. mole-’, may be compared with the value, 420 1. mole-’, estimated from the results of conductivity measurements of appreciably more supersaturated solutions of lead sulfate than those used in the present work ( I ) . The only other literature value of K(PbS04) with which to compare our data is 8.5 X l o 31. mole-’, based upon the results of solubility determinations (ZI). On the basis of comparison of similar cadmium and lead complexes (ZZ), K (CdN03+) = 3 1. mole-’, K(PbN03+) = 15 1. mole-’, the association constant for CdS04, 200 1. mole-‘, would suggest that a value of 8.5 X loa 1. mole-’ for the corresponding lead complex is appreciably too large.
RECEIVED for review February 19, 1970. Accepted April 2, 1970. Work supported by grants from the National Science Foundation and Office of Saline Water, Department of the Interior. (9) E. C. Righellato and C. W. Davies, Trans. Faraday SOC.,26,592 (1930). (10) G. H. Nancollas, J. Chem. SOC.,1955,1458. (11) I. M. Korenman, Izuest VUZ Khim., 4, 554 (1961). (12) “Stability Constants of Metal-Ion Complexes,” L. G. Sillen, Ed., J. Clzem. SOC.(London),Special Publ. No. 17, 1964. ANALYTICAL CHEMISTRY, VOL. 42, NO. 7, JUNE 1970
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