Anal. Chem. 1981, 53, 2244-2246
2244
LITERATURE CITED (1) Albert, Ph. “Le Dosage de l’azote dans les metaux refractaires”, Cahler 90, Bureau Eurlsotop. Brussels, 1974. (2) Ortner, H. M. Tabnta 1979, 26, 629-640. (3) Grallath, E.; Ortner, H. M. Tabnta 1978, 25, 195-202. (4) Olivler, C.; Pelsach, M.; Pierce, T. B. J. Radioanal. Chem. 1976, 32, 71-63. (5) Gihwala, D.; Glles, I. S.; Oliver, C.; Peisach, M. J . Radioanal. Chem. 1978, 46, 333-341. (6) Marschal, A.; Gosset, J.; Engelmann, Ch. J. Radioanal. Chem. 1971, 8, 243-255. (7) Nozakl, T.; Yatsurugl, Y.; Akiyama, N. J . Radloaflal. Chem. 1970, 4 , 87-98. (8) Kuln, P. N.; Reynders, J. P. J . Radioanal. Chem. 1973, 16, 403-411. (9) Sellschop, J. P. F.; Keddy, R. J.; Mlngay, D. W.; Renan, M. J.; Schuster, D. J. rnt. J . ~ p p l Radiat. . rsot. 1975, 26, 640-647. (IO) Strljckmans, K.; Vandecasteele, C.; Hoste, J. Anal. Chim. Acta 1977, 89, 255-256.
(1 1) Glovagnoll, A.; Valladon, M.;Koemmerer, C.; Blondiaux, G.; Debrun, J. L. Anal. Chim. Acta 1979, 109, 41 1-418. (12) Clemenson, M.; Novakov, T.; Markowitz, S. S. Anal. Chem. 1979, 51, 572-575. (13) Rook, H. L.; Schweikert, E. A.; Walnerdl, R. E. Anal. Chem. 1968, 40, 1194-1 196. (14) Sastri, C. S.; Caletka, R.; Krivan, V. Anal. Chem. 1961, 53, 765-770. (15) Ricci, E.;Hahn, R. L. Anal. Chem. 1965, 37, 742-748. (16) Inoue, T.; Tanaka, S. J. Inorg. Nucl. Chem. 1976, 38, 1425-1427. (17) Sastri, C. S.; Ney, J.; Moiler, P. Nucl. Instrum. Methods 1979, 159, 369-374.
RECEIVED for review March 16,1981. Accepted August 4,1981. Financial assistance for this project was provided by Bundesministerium fur Forschung und Technologie, Bonn.
Coulometric Study of Cadmium Iodate Solubility Equilibria Richard W. Ramette Department of Chemistry, Carleton College, Northfield, Minnesota 55057
The solubillty of recrystalllred cadmium iodate in solutlons of cadmium perchlorate was determlned by controlled cathode potential coulometry in an acidlc chlorlde/iodide electrolyte. At 25 O C and lonlc strength 1.0 the solublllty product constant is (6.94 f 0.02) X lo-’, the CdIOS+ formation constant Is 3.27 f 0.01, and the intrlnslc solubility is (2.4 f 0.1) X lo-’ mol/L. Improved techniques for saturatlon and sampling are descrlbed.
This work is directed toward the improved use of solubility behavior as a chemical probe for determining metal-ligand complex stability constants. The goal is to establish techniques and a general approach that is more accurate than the traditional methods of potentiometry, polarography, and spectrophotometry (1). To find reliable p values from measurements on a metal-ligand system involving several successive complexes, it is essential that the analytical data are accurate with relative errors of 0.1% or less in the determined concentrations. It is not possible for the traditional methods to provide this accuracy. Although solubility approaches have been used (2) they have not been designed for the best possible accuracy. Consider a slightly soluble salt MA2 (cadmium iodate in the present work) that is largely dissociated into its ions. The solubility of MA2will be higher in the presence of a complexing ligand L because of the formation of a series of complexes ML, ML2,etc. Given a set of solubilities corresponding to a range of ligand concentrations, the data may be used to find the successive p values for the MLi species, but only if there is accurate knowledge of the equilibria between M and A. This work deals with the solubility of cadmium iodate in the absence of any complexing ligand. Anticipating that the later M-L studies will be carried out in a constant ionic strength medium, we made all measurements at I = 1.00 using sodium perchlorate as the inert salt. Thus activity coefficients are considered to be unity, using a thermodynamic reference state of 1.00 M sodium perchlorate. The simple strong electrolyte model is not adequate to describe the solubility of cadmium iodate. By interpreting the shift in peak potential of AC polarograms, using varying
iodate concentration in solutions from which cadmium iodate was slowly precipitating, Bond and Hefter (3) showed that two homogeneous equilibria are involved
M + A P MA MA + A s MA2
K1 = 3.1 f 0.2 K2 = 10.5 f 0.5
where ionic charges have been omitted for simplicity. These values were obtained in sodium perchlorate solutions having I = 1. In addition to the uncertainties shown, there are unknown effects of varying diffusion coefficients, the liquid junction potential in the cell, and the likely deviation of electrode response from the theoretical value of 29.58 mV per 10-fold change in Cd2+concentration. Therefore for systems a t equilibrium with solid cadmium iodate, the chemical model is MA2(s) ~t MA2(aq) F? A
+ MA
MA*A+M The corresponding equilibrium constants are
KO= [MA2]/Xs (the intrinsic solubility) Ki = [MA1/[MI [AI K2 = [MA,I/[MAl[Al The mole fraction of the solid Xs is presumed to be unity. The intrinsic solubility is the minimum solubility even if the dissociation steps are repressed. The familiar solubility product constant is not independent and may be expressed in terms of the above
K,, = [Ml[A12/Xs = KO/KlK2 The value of KBphas not been previously determined at I = 1but its value for the reference state of pure water is 2.3 x 10-8 ( 4 ) . The present approach to a study of these equilibria is to determine with high accuracy the solubility S of cadmium iodate in a set of solutions containing varying concentrations C of cadmium perchlorate. For a saturated solution we may write two material balance expressions 2 s = 2[MAz]
0003-2700/81/0353-2244$01.25/00 1981 American Chemical Society
+ [MA] + [A]
(1)
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981 2245 which states that the rmount of iodate in the solution will be twice the amount of cadmium iodate that dissolves, and
S
+ C =: [MA,] + [MA] + [MI
(2)
which states that the total amount of cadmium in solution can be traced to the two sources, C mol/L from cadmium perchlorate and S mol/’L from solubility of cadmium iodate. With substitutions from the equilbrium constant expressions and rearrangement, eq 1 takes the forim
2(S -KO)
K1Kap1/2[M]1/2 + K,p1/2/[M]’/2
(3)
The experimental data (S and C values) must be interpreted by an iterative approach. As a first approximation, [MI -- S C and KO= 0. A least-squares fit in accord with eq 3 yields tentative values of Kl and KBp,which in turn lead to improved estimates of [MA,] = KO= Kas1KZ(using Bond and Hefter’s value of K z = 10.5). The [A] = (KBp/1[M])1/2, and [MA] = K,[M][A], and the iterative step is completed by refining [MI = S C - [MA] - [MA,]. The loop is repeated until there is no significant change in the values of K1 and Ksp. The reason for relying on the known value of KZ for the estimation of KOis that the intrinsic solubility is too small, only about 0.2% of S , t o be determined independently in the present work. Therefore it is best to treat it as a small correction to S as shown in eq 3. The BASIC program KSPKlFIT used for these calculations is available upon request.
+
+
EXPERIMENTAL SECTION Preparation of Cadmium Iodate. Cadmium iodate was first precipitated by dropwiiJe and simultaneous addition, from separatory funnels, of 500 mL of 0.40 M cadmium nitrate and 500 mL of warm 0.8 M sodium iodate to 200 mL of gently boiling 1 M nitric acid. During the precipitation the mixture was stirred vigorously with a magnetic stirrer. The product was washed four times by decantation with distilled water before being placed in a Soxhlet extraction thimble. Distilled water was used in the boiling flask, and over a period of 3 weeks the hot water Soxhlet extraction transferred the cadmium ioda1,e to the boiling flask. Microscopic examination showed this recrystallized material to be small and transparent individual crystals, in striking contrast to the white opaque “snowballs” of the original precipitate. The goal of the recrystallization was to prepare a solid phase that is thermodynamically stable, and the fact that the recrystallized salt wm about 30% less soluble than the original precipitated form was encouraging. Preparation of Cadimium Perchlorate Solutions. Reagent grade cadmium perchlorate was dissolved in distilled water to make a 0 2 M solution. The density of this solution, and of the other solutions )usedin this work, was determined by weighing a portion delivered by a calibrated siliconized 5-mL pipet. The pipet had been treated by immersion in i i 10% solution of trimethylchlorosilane in carbon tetrachloride. The hydrophobic surface resulted in a flat meniscus and total drainage except at the tip. Standardization using distilled water was reproducible to fO.OO1 mL. The solution was standardized on a mass basis by controlled potential coulometry using a mercury cathode (5), both by deposition at -0.67 V vs. ElCE and by stripping from the amalgam at -0.3 V. The density was 1.0445 g/mL (not corrected For buoyancy) and the cadmium concentration was 0.1976 & 0.0002 mol/L. The five solutions for the solubility study were prepared by mass, adding portions of the stock cadmium perchlorate solution to the appropriate aniount of sodium perchlorate solution (to make the final ionic strength LOO) and diluting in volumetric flasks. These solutions had densities of 1.0743 f 0.0002 g/mL at 25 “C. After saturation with cadmium iodate the densities were 1.0756 i 0.0002 g/mL. Saturation and Sarmpling. Fine-porosity sealing tubes (Corning 39570) were cut so that 3 cm remained below the fritted disk. About 7 g of air-dried cadmium iodate was added to each tube and stirred with a few milliliters of cadmium perchlorate/sodium perchlorate solution, while being heated to
Figure 1. Equilibration tubes.
about 95 “C in a water bath. This preconditioning step was found to improve the internal consistency of the results, as measured by adherence to eq 3. After being cooled the tubes were allowed to drain and were refilled with about 6 mL of the solution at 25 “C. Each fritted tube was placed in a screw-capped test tube (Kimble 45066), and the assemblies were totally immersed in a water bath controlled at 25.06 f 0.005 “C, using a low-wattage heater to minimize temperature overshoot from the heating cycle. Over a period of 12 h the solution seeped through the bed (about 3 cm deep) of cadmium iodate and collected in the bottom of the test tube as shown in Figure 1. The first output solution was discarded and the tubes were reflled with fresh portions of solutions. Samples for coulometric analysis were withdrawn with a weighed pipet fitted with a rubber bulb. This pipet was made from a standard 5-mL transfer pipet, cut to a length of 6 cm, drawn to a fine delivery tip, and was siliconized to facilitate sample transfer. This technique provided not only an accurate sample size (&O.OOOl g) but also a convenient way to inject the sample into the coulometer cell. Sample sizes were typically 2.5 g and contained about 25 kequiv of iodate. Apparatus and Coulometric Determination. A Model 3 coulometer system (M-T Electronics Co., San Leandro, CA), consisting of a potentiostat and an integrator module (61, was housed in a thermal insulation cabinet. Nevertheless the temperature within the integrator module, monitored by a probe connected to a Markson Model 70 digital meter, varied from 33 to 39 “C over the course of this work. The precise temperature dependence of the integrator performance was determined by calibrations over the temperature range. Calibration was accomplished by using the potentiostat to apply a precise voltage to a standard 99.9964 resistor for a period of 400-500 s measured by a quartz millisecond clock. This voltage, and also the resulting integrator output voltage, was measured with a Hewlett-Packard Model 3455A digital voltmeter, and corrections for capacitor leakage were applied as described by Frazzini et al. (7). The electrical calibration was the basis for calculating the iodate content of the samples. The coulometer cell assembly was the PARC 377A with a KO027 platinum gauze electrode. The cell current was monitored by Simpson 364 multimeter only for the purpose of judging when the current had dropped sufficiently close to the background value. The cell electrolyte contained 2 M sodium chloride, 0.02 M sodium iodide, and 0.02 M hydrochloric acid. By use of low iodide and acid concentrations the effect of air oxidation was virtually eliminated, and the background current at +0.2 V vs. SCE was typically only 4 HA. There was no need to remove oxygen from the solution by passing nitrogen over the solution, which probably would have caused significant loss of iodine by volatilization. A current-voltage curve is shown in Figure 2. Each determination began with a timed period (50-100 s) of background current, giving a background voltage accumulation rate for the individual run. The timer was reset to zero and upon injection of the iodate sample there was rapid chemical reduction to form 12/I;, followed by controlled potential reduction to iodide ion. The timer yas read when the current approached the
2246
ANALYTICAL CHEMISTRY, VOL. 53, NO. 14, DECEMBER 1981
Table I. Results of Solubility Measurements of Cadmium Iodate in Cadmium Perchlorate Solutions at 25 "C a 200-
[MA]/S
[MI
9.814
0.069
11.024
1.3016
19.839
0.126
20.691
0.9796
29.587
0.179
30.272
0.8340
39.382
0.231
39.953
0.7471
49.165
0.278
49.660
0.6891
C
2
110-
I
103
I
I
1
02
0 1
0
,,,,,,,E,
~ G L T Evs
I
-01
I
-32
S ( e q 3) S(obsd)
SZE
Figure 2. Current-voltage curve in coulometer cell.
background current to within 1-2 PA, typically requiring about 10 min. A plot of In i vs. time was linear from i = 100 mA to 100 FA with a time constant of 45 s. Background corrections were typically 0.1% of the total voltage and were calculated simply by multiplyingthe background voltage accumulation rate by the time used for the coulometric reduction step. The overall procedure was tested with a solution of recrystallized potassium iodate, resulting in an assay of 99.96 k 0.02%.
RESULTS OF THE EQUILIBRIUM STUDY In Table I there are three values of observed solubility for each of the five cadmium perchlorate solutions. The first S value in each group is the result of a single pass of solution through the cadmium iodate bed, while the second and third results were obtained by using solutions that had been recycled through the bed once and twice, respectively. There is no trend corresponding to recycling, and a single pass seems sufficient to saturate the solution. The 15 values were used in the iterative calculation proK1 cedure described earlier, giving Ksp= (6.94 f 0.02) X = 3.27 f 0.01, and KO= (2.4 f 0.1) X lo4. The uncertainties shown for and K1 are in accord with the relative average deviation (0.0018) of the results in Table I. The larger uncertainty in KOis in accord with the use of K z = 10.5 f 0.5. The value for K1 agrees with the literature value (3) but is more accurate. Table I shows that the ion pair species CdI03' is a significant fraction of the total solubility in solutions containing cadmium perchlorate. The calculated solubilities shown in column 4 of Table I were found by using the K values and [MI values in eq 3 and are in close agreement with the observed results. CONCLUSIONS Controlled potential coulometry, using a platinum cathode in an acidic chloride/iodide medium, serves very well for the rapid and highly accurate determination of dissolved iodate. The cadmium iodate recrystallized by the Soxhlet technique was not only less soluble than the precipitated material but showed better reproducility in reaching equilibrium, especially after conditioning with hot solution. Together with the use
1.3031 1.3022 1.2995 0.9776 0.9794 0.9782 0.8378 0.8367 0.8368 0.7461 0.7462 0.7450 0.689'7 0.6882 0.6889
re1 dev 0.0012 0.0004 -0.0018 -0.0021 -0.0002 -0,0016 0.0046 0.0033 0.0033 -0.0013 -0.0025 -0.0028 0.0009 -0.0013 -0.0003
Concentrations are i n units of mmol/L. of fritted tubes, total immersion in the water bath, and the use of weighed samples, these techniques are recommended for future solubility studies. Nevertheless, the results obtained still show deviations of a few parts per thousand from theoretical behavior, while the estimated errors due to equilibration, sampling, and coulometry are lower than 0.05%. This is probably due to some type of instability of the solid phases and more work must be done to prepare a totally reliable crystalline material. Considering that an error of only 0.5 mV in the potential of a cell using a cadmium or cadmium amalgam electrode corresponds to a 4% error in the inferred cadmium ion concentration, it appears that the use of a solubility probe as described in this research will be more reliable than either potentiometry or polarography in studies of certain metalligand complex equilibria.
ACKNOWLEDGMENT Exploratory work on this project was performed by Michael G. Werdick and Brian D. Smith. I am grateful to Michael K. Holland and to the New Brunswick Laboratory, U.S. Department of Energy, for advice and for the loan of the coulometry system. LITERATURE CITED Hartley, F. R.; Burgess, C.; Alcock, R. M. "Solution Equilibria"; Ellis Horwood Limited: Chichester, 1980. Johansson, L. Coord. Chem. Rev. 1988, 3, 293-318. Bond, A. M.; Hefter, G. J . Nectroanal. Chem. 1972, 34, 227-237. Saegusa, F. Nlppon Kagabukal Pure Chem Sect SHI 1950, 223-228. Segatto, P. R. J. Am. Cerarn. SOC. I M P , 45, 102-104. Harrar, J. E.; Behrin, E. Anal. Chem. 1967, 39, 1230-1237. Frazzlnl, T. L.; Holland, M. K.; Weiss, J. R.; Pletri, C. E. Anal. Chem. 1980, 52,2112-2116.
RECEIVED for review July 17, 1981. Accepted September 18, 1981. Support from a Shell Foundation Grant to Carleton College is acknowledged.
