(23-25), Andermann (26), Holland and Brindle (27), Claisse and Quintin (28), and McKinney and Rosenberg (22). The proposed equations all ultimately reduce, after substantial peregrination, to equations similar to Equation 12 or functionally like those of Criss and Birks ( I I ) , the main difference being that the coefficients are deduced from absorption coefficients rather than estimated by regression techniques or found by the simultaneous equation method. The statistical ability to decide which variates are really important is, of course, lost in the process, and the increased complexity of these techniques greatly enhances the possibility of obtaining an artificially good fit to the data. Before resorting to such procedures, it is wise to determine if ordinary regression analysis might yield sufficiently accurate results since, in principle, regression techniques will suffice if the data are both accurate and sufficiently numerous, In any case, quantitative measures do exist to help decide between the alternatives. The clear distinction between empirical and theoretical methods of Xray emission analysis made by Criss and Birks (11) seems entirely justified. The method of choice is naturally the one that yields correct answers the majority of the time in the actual analysis of unknowns, and any equation that fulfills ~
~
~
(23) R. J. Traill and G. R. Lachance, Geol. Survey Can., Pup. 64-57 (1964). (24) G. R . Lachance and R. J. Traill, ibid., 11,43 (1966). (25) R. J. Traill and G. R. Lachance, ibid., p 63. 38,82 (1966). (26) G. Andermann, ANAL.CHEM., (27) J. G. Holland and D. W. Brindle, Specfrochim.Acfu,22, 2083 (1966). (28) F. Claisse and M. Quintin, Can. Spectrosc., 12, 129 (1967).
this, whether physically or statistically realistic or not, may be used. The regression technique described here is oriented toward minimizing the variance of predicted concentrations. The possibility does exist that the equations may be biased. The most serious bias error likely to arise is that the assumed quadric model is really cubic. Since variance, in almost all cases, is the overriding source of imperfection in the models, the choice of an all-variance design is the most logical, and the least-squares minimization of the residuals between theoretical and calculated concentrations should give satisfactory equations. If we also postulate normality for all the errors, the least-squares method is also equivalent to maximum likelihood methods. The greatest source of difficulty is the confounding correlations between the independent variates. While substantially more accurate results might obtain by eliminating such correlations through a linear transformation of the variates via component or canonical analysis of the data according to the principles nicely described by Kendall(29), the added effort probably should be directed toward seeking a solution to the absorption and enhancement problem through first physical principles, although advanced statistical analysis of the data is not intractable. RECEIVED for review October 5, 1970. Accepted November 25, 1970. (29) M. G. Kendall, “A Course in Multivariate Analysis,” Charles Griffin and Co., Ltd., London (1957).
Spectrophotometric Determination of Traces of Thallium in Tungsten The Extraction of Thallium Diethyldithiocarbamate Karoly Vadasdi, Piroska Buxbaum, and Andras Salamon Research Institute for Technical Physics of the Hungarian Academy of Sciences, Budapest, Upesr I., PJ 76, Hungary A spectrophotometric method i s presented for the determination of thallium in tungsten metal. The Samples are dissolved in the mixture of hydrofluoric and nitric acids. The thallium i s separated from tungsten by extraction with sodium diethyldithiocarbamate into chloroform between pH 8-11 and the Methyl Violet method was used for its determination at 605 nm. Interference effects of some diverse ions are reported ~ ~ ~ ~ interference ( l l l ) is prevented with EDTA. Th; method is suitable for the determination of 0.1-10 ppm thallium in tungsten metal with a precision of 10-20%. The equilibrium constants in the TI(I)-diethyldithiosystem have also been determined by means of EDTA competition as well as the stability constant of TI(I)-EDTA by tentiometric methods.
A GREAT NUMBER of methods have been described in the literature for the determination of different impurities and doping materials in tungsten. One of the recently introduced doping materials is thallium ( I ) . For this reason a sensitive (1) T. Millner and J. Neugebauer, Hungarian Patent 155.352 (1969); French Patent 1.536.155 (1969). 318
ANALYTICAL CHEMISTRY, VOL. 43,
NO. 3, MARCH 1971
method has been needed for the determination of small quantities of thalliumin tungsten metal, For the separation and determination of thallium from different elements, sensitive and accurate methods are known (2, 3). Thallium can be determined with the highest sensitivity by means of inverse polarography. Among the colorimetric methods, the Rhodamine B and Methyl Violet methods are well known(4-6). The main problem which occurs during the determination ofdifferent ions in tungsten is the selection of a suitable separation method because the tungstate ion may form heteropolyacid complexes with the considerable part Of the elements of the periodic table. These complexes usually are much more (2) E. B. Sandell, “Colorimetric Determination of Traces of Metals,” Interscience, New York, N. Y., 1959. (3) 0.G. Koch, Koch, and G. A. Dedic, “Handbuch der Spurenanalyse,” Springer, Heidelberg, Germany, 1964. (4) H. Onishi, Bull. Chem. SOC.Japan, 29, 943 (1956). (5) N. T.Voskresenskaya, J. Anal. Chem. USSR,11, 585 (1956). (6) M. E. Campbell, C . Millingan, and A. Lindsay, Amer. Ind. H y g . Ass. J., 20, 23 (1959).
stable than the customary metallic ion-organic reagent complexes and can only be destroyed in alkaline medium. For the determination of thallium in the presence of tungsten or for the separation of thallium from tungsten, no method can be found i n the literature. No data are available about the existence of heteropolyacid complexes formed either thallium(1) or thallium (111) and tungsten, like aluminium and gallium (7, 8).
Table I. Summarization of Extraction Data
CN~DDTC 1 x 10-1M 5 . 2 ; -2.87, CTI 1 x 10PM 7 . 2 ; -0.46, Medium 1 x 10-1MNaC104 8 . 9 ; 1.81, Temperature 20 'C 10.1; 2.53, Time of extr. 24 hours 11.5; 2.48, Method Isotope 12.6; 1 . 3 1
Author
EXPERIMENTAL
(7) T. Millner and J. Neugebauer, Magy. Kem. Fuly., 57, 321 (1951). (8) K . G. Vadasdi, Chem. Anal. (Warsaw),14,733 (1969). (9) J. Kinnunen and B. Wennestrand, Chemist-Analyst, 46, 92 (1957).
Schweitzer-Norton (12)
Apparatus and Reagents. All absorbance measurements were made with a Beckman D U spectrophotometer in matched 1.000-cm cuvettes. The pH measurements were made with a Radelkisz OP-205 and Radiometer pHM 26 precision pH meters. The pH standards were 0.05M potassium acid phthalate and 0.05M borax. SODIUMDIETHYLDITHIOCARBAMATE (NaDDTC). Reagent grade (98.5% min) NaDDTC.3H20 was used to prepare a 2 % aqueous solution which was adjusted to about pH 9-10 with alkali. METHYLVIOLET(Standard Fluka, C.I. 69710). A 0.1% aqueous solution was mixed with diluted sulfuric acid to prepare fresh daily a 0.05% working solution (0.05N in sulfuric acid). ETHYLENEDIAMINETETRAACETIC ACID AND DISODIUM SALT (EDTA), reagent grade. CHLOROFORM, reagent grade with 1 % ethanol content was used without further purification. BENZENE, reagent grade. GLYCINE BUFFER. From reagent grade material, a 0.1M solution of glycine was prepared adjusting its pH to 10 i 0.2 with alkali. BORATEBUFFER. Reagent grade borax (Na2B407.10H20) was twice recrystallized from water. A 0.2M solution was prepared adjusting its pH with alkali to the desired value. PHOSPHATE BUFFER. A 0.2M solution was prepared from reagent grade K H 2 P 0 4and Na,HPO4 2H20. THALLIUM(I) NITRATE AND THALLIUM(" CHLORIDE solutions were prepared from reagent grade salts and the metal content was determined complexometrically by the thorium nitrate-xylenol orange methanol (9). Other materials used in this work were reagent grade. Preparation of the Calibration Curve. Add 0, 1 , 2, 4, 7, 10 pg Tl(1)- or Tl(II1)-containing solution into a 150-ml beaker, add 1.8 ml concentrated sulfuric acid and 20 ml of 30% hydrogen peroxide and evaporate to sulfuric acid fumes. (After cooling down, wash down the sides of the beaker with a little water and evaporate again.) Dilute with 20 ml of water, add 2 ml of 1:9 hydrobromic acid and 10 drops of bromine water. Boil the solution for a few minutes to expel the excess bromine. After cooling down, complete the volume to 49 ml, pour the solution into a separatory funnel. Add to the solution 5.0 ml of benzene and 1.0 ml of diluted working Methyl Violet solution, and immediately after shake for 1 minute. Allow the layers to separate completely, discard the aqueous layer, and obtain the transmittance of the organic layer at 605 nm in 1-cm cuvette. Pure benzene is used in the reference cells. Recommended Procedure for the Determination of 0.1-10 ppm Thallium. IF 1-10 PPM THALLIUM PRESENT. Add 2 ml of 38% hydrofluoric acid in a Teflon (Du Pont) vessel to 1 gram of powdered tungsten metal and add dropwise 6 5 x nitric acid until the complete dissolution of the sample.
-
6 . 1 ; -1.60, 8 . 1 ; 0.79, 9 . 7 ; 2.44, 10.5; 2.49, 1 2 . 1 ; 1.82,
TI (1) CN~DDTC 1 x 10-2M 2.5 x 1 0 - 4 ~ Medium 2 X 10-lM, W as
C TI
3.8; 1 . 1 8 , 4 . 8 ; 1 . 8 4 , 5 . 8 ; 2.29,7.0; 2.22,7.2;2.32, 7 . 6 ; 2.34, 8 . 2 ; 2 . 3 3
NazW04 2 X 10-IM tartaric
acid Temperature 25 i 2 "C Time of extr. 3 minutes Method Isotope, zo4T1, 3.56 years Author This work Tl(II1) CN~DDTC 1 x 10-2M CTI 2.5 x 1 0 - 4 ~ Medium 2 X lO-lM, W as
Na2W04 2 X IO-lMtartaric
2 . 7 ; -1.07, 3 . 2 ; -0.49, 3.8; 0.31,4.8; 1.78,5.8; 2 . 1 1 , 7 . 0 ; 2 . 4 8 , 7 . 3 ; 2.70, 8 . 2 ; 2.94, 1 0 . 5 ; 3.16, 12.5; 3 . 2 4
acid Temperature 25 i 2 "C Time of extr. 3 minutes Method Isotope, z04TI,3 , 5 6 years Author This work
After this add 4 ml of 3 0 z tartaric acid and adjust the pH of the solution between 8-1 1 with 20% potassium hydroxide. Add 1 ml of 2 % NaDDTC solution (and EDTA solution if necessary calculating the amount according to Equation 11). Pour the solution which has a volume of about 25-30 ml into a separatory funnel and shake twice with 20 ml of chloroform for 2 minutes. Wash the combined chloroform layers twice with 2-3 ml of 10 pH glycine buffer. Discard the aqueous layers. Evaporate the chloroform on a water bath and destroy the organic residue with 1.8 ml of sulfuric acid and 20 ml of hydrogen peroxide evaporating to sulfuric acid fumes and determine the thallium as described under the preparation of the calibration graph. IF 0.1-1.0 PPM THALLIUM PRESENT.Add 25 ml of 3 8 x hydrofluoric acid in a Teflon vessel to 10 grams of finely powdered tungsten sample and dropwise 6 5 x nitric acid until the sample completely dissolves. Add 40 ml of 30% tartaric acid, 2 ml of 0.05N EDTA solution, and adjust the pH between 8-11 with 60% potassium hydroxide. After cooling down, add 10 ml of 2 % NaDDTC and pour the solution which has a volume between 200-300 ml into a 500ml separatory funnel and shake four times with 20 ml of chloroform for 2 minutes. Wash the combined organic phases with 10 pH glycine buffer; evaporate it on a water bath, destroy the residue, and determine the thallium as described above. RESULTS AND DISCUSSION
Extraction of Thallium(1) and Thallium(II1) Diethyldithiocarbamates. Bode carried out the first systematic study on the extraction of thallium diethyldithiocarbamates ( I O , 11). (10) H. Bode, Z . Anal. Clzem., 142, 414 (1954). (11) Ibid., 144, 165 (1955). ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
319
100
ap
K n
50
-
n I-
10-5
10-8
10-4
10-2
CEDTA
Figure 1. Equilibrium concentration of the TlDDTC in the chloroform phase as the function of EDTA concentration at different pH values 0 pH 9.30 JZ 0.03 (0.1M borate buffer) x pH 9.88 i 0.03 (0.1M borate buffer) 0 p~ 10.14 f 0.03 (0.1M glycine buffer) CTIIll= 4.9 x 10-6M; CN,DDTC = 1.0 X lO-'M; t = 25 i 2 " C ; extraction time 10 minutes
He stated that the extraction of Tl(DDTC), was not interfered with by tartarate, citrate, phosphate, borate, glycine, cyanide, or EDTA between pH 8-11, whereas that of TIDDTC was hindered by EDTA. Later Schweitzer and Norton investigated the extraction of TIDDTC into chloroform and they gave the pH function of the distribution constant (12). Since no data are available for the extraction of TIDDTC and TI(DDTC)3in the presence of tungstate and fluoride ions, we have investigated their influence. Results in the case of tungstate ion were summarized in Table 1. (Tartaric acid was added to prevent the precipitation of tungstic acid in lower pH regions.) No remarkable effect of these ions was observed. In the following, the influence of EDTA on the extraction of TIDDTC was investigated in order that its hindering effect could be minimized, because it was found that the presence of EDTA was needed to mask iron. Determination of Extraction Equilibrium Constant of TIDDTC Complex by EDTA Competition. Figure 1 shows the effect of EDTA concentration on the extraction of TIDDTC at different pH values from 0.1 M borate or 0.1 M glycine buffers. Ten-minute oxtraction periods were used at 25 f 2 "C. The concentration of TlDDTC in the chloroform phase was determined by spectrophotometric measurements at 245 nm. Since from the literature is known the formation constant of [Tl (I)-EDTAJ3- complex (Z.?)-in the following denoted as TIY 3--the calculation of extraction equilibrium constant of TIDDTC became possible, with the help of the following relations: TIY 3-
+ (HDDTC),,,
$
(TlDDTC),,,
+ HY
3-
The two phase formation constant of TIDDTC: T1+ + DDTC- e (TlDDTC),,, [TIDDTCor,I K2 = [Tl+][DDTC-J (12) G. K. Schweitzer and A. D. Norton, Anal. Chim. Acta., 30, 119 (1964).
320
ANALYTICAL CHEMISTRY, VOL. 43,
NO. 3, MARCH 1971
where the three times and four times ionized fractions of EDTA were denoted as HY 3-, Y 4-; the diethyldithiocarbaminic acid as HDDTC and its anion as DDTC-; the thallium (I) diethyldithiocarbamate and EDTA complexes as TIDDTC and TIY a-. The following equilibriums also were needed, the constants of which are known from the literature: (Z3-15). TI+
+Y
4-
e TIY3-
[TlY K -____ - [TI+][Y4-] HY 3- s Y *H+
(3)
+
Kd, =
[H+3[Y4-l [HY 3-]
(4)
~
Here it should be mentioned that the formation constant of TIY a-, K3, was determined formerly by a polarographic method by Bouten, Verbeek, and Eckaut who found log K = 5.81 =k 0.05 in 0.2M sulfate medium at 20 "C (I.?), and recently by Koch and Kupsch with extraction method log K = 6.1 + 0.2 (15). During this work we redetermined this value by a pH titration method with KOH in 0.1N K N 0 3 at 25 OC, and the so-called stoichiometric constant was found log K = 6.38 i 0.02. The ionization constants of EDTA measured under these conditions are in agreement with the values reported in the literature, pK8 = 6.15; pK4 = 10.24 (14). The two-phase ionization constant of diethyldithiocarbamic acid was also needed. H+
+ DDTCK'
=
s (HDDTC),,,
[HDDTCd [H+][DDTC-]
(5)
The K ' was determined by Bode in the case of carbon tetrachloride, We have also determined this constant by the method of Bode for chloroform at 25 i 2 "C from 0.1M phosphate buffer (ZZ). (13) J. Bouten, F. Verbeek, and J. Eckaut, Anal. Chim. Acta., 17, 339 (1957). (14) R. Shockdopole and S . Chaberek, J. Inorg. Nucl. Chem., 11, 222 (1959). (15) H. Koch and H. Kupsch, 2.Nutrrrforsch. B., 24, 398 (1969).
Table 11. Summarization of Used or Calculated Equilibriums and Constants Process Equilibrium constant Reference TlY 3(HDDT&, = (TIDDTC),r, + HY KI = (4.0 f 0.9) X lo3 This work; 25 f 2 'C 0.1M T1+ + DDTC= (TlDDTC),,, K2 = K,K' K3 Kdr = ( 5 . 2 i 1.1) X lo6 ! glycine or borate T1+ Y4=~ 1 ~ 3 K3 = ( 2 . 4 + 0.1) X lo6 This work; 25 "C 0.1 M KNOI HY3= Y4- + H+ (5.37 f , .x. 10-11 f14) This work; 25 31 2 OC CHC13 (1.0 o, 1) 107 H+ DDTC= (HDDTC),,, 0.1Mphosphate (1.6 + ) X lo6 Bode (IO); CClr 18-20 "C
+ +
'1
*
+
Table 111. Accuracy of Method Thallium found, pg Procedure Procedure Thallium 1-10 ppm 0.1-1.0 pprn added, Diverse ions added, pg (1 g W) (10 g W) rg ... 0 0 0 ... 1.9 1 . 7 i0.4 2.0 (std dev) ... 5.6 5.0 2 0 . 7 5.0 (std dev) ... 10.1 ... 10.0 As(V), SWIII), Sn(IV) 5.0 ... 5.0 100 pg each 5.6 ,.. 5.0 Fe(III), Co(II), Ni(JI), 8.8s 4 . 3b ... Bi(II1) 100 pg each 1 7 . 9 4.7b ... 5.0 Bi(II1) 100 pg 4.70 4.53 5 . 0 4.9b ~ ... Without EDTA. b With addition of 5.0 ml 0.01M EDTA.
X
r 40
. I .
PO
0
P
6
4 xx104
a
+
Figure 2. Determination of Kl K'(K,, [H+]) at different p H values. Calculated from the data of Figure 1 0
pH 9.30
0
pH 10.14
x pH
9.88
Y
The distribution of thallium between the aqueous and organic phases:
The following approaching equations can also be described which are valid only under the experimental circumstances (between p H 8-1 1): CTLC- [TlDDTCorg]
CN~DDTC C- [TIDDTCJ CEDTA
= [TIY 3-]
+ [TlY "1
+ IDDTC-1
+ [Y"1 + [HY "1
(7) (8)
[TlDDTC,,,] D
=
CEDTA -
[TlDDTC,,,] D
Figure 2 displays the Y us. X at three different pH values. In Table I1 the measured and those constants were summarized which were taken from the literature for the calculations. In that case, when the concentration of sodium diethyldithiocarbamate and EDTA is considerably higher than that of thallium, the distribution ratio of the thallium between chloroform and aqueous phases can be calculated from the following equation at given p H values (between pH 8-1 1):
-D1 _ - Q1
CEDTA - + KlK'(Kd41+ [H+l) X - CN~DDTC
(11)
(9)
Combining Equations 1, 4-6, 8, and 9, the following simple connection can be derived giving us the possibility for the calculation of K , from experimental data. CEDTA -
where CTI,CN~DDTC, C E D T A are the total analytical concentrations of thallium, sodium diethyldithiocarbamate, and EDTA. From extraction experiments at constant pH values, the Y 6s. X function gives straight lines with different slopes, where the
where Q is the distribution constant of TlDDTC in the absence of EDTA. Interfering Effect of Different Ions. According to the literature the color reaction between TI(1II) and Methyl Violet is interfered by the following ions: Au(III), B(III), Fe(III), Bi(III), Sb(III), Sn(II), Cd(II), Hg(II), and Cr(V1). From these ions, the boron cannot be extracted by diethyldithiocarbamate, and the Au, Sb, Fe, Cd, H g can be masked with EDTA and cyanide between pH 8-11 (2, 3). The inANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
* 321
terfering effect of Bi cannot be eliminated in such a way but according to our experiences the interfering effect of lOO/pg of Bi may be neglected for 5/pg of T1 (Table 111). Precision of the Method. Table 111 shows the accuracy of our method both for 1-10 ppm and for 0.1-1.0 ppm ranges. Even in the lower range, the relative standard deviation doesn’t exceed 20% which is general at the determination of such a small amount of impurities.
ACKNOWLEDGMENT
The authors are indebted to Prof. Dr. T. Millner and Dr. L. Bartha for encouraging and helpful advice in the course of this work. RECEIVED for review April 27, 1970. Accepted August 10, 1970.
ElectroI yte SoIutions J. V. Leyendekkers and Michael Whitfield Dicision of Fisheries and Oceanography, CSIRO,Cronuffa,Sydney, 2230, Australia Two liquid ion exchange electrodes (Orion Calcium 9220 and Chloride 92-17) were used to monitor changes in the activity coefficient of calcium chloride in the two aqueous systems CaCI2-MgCl2 and CaCI2-SrCl2 over the ionic strength range 0.1-6 molal at 25 OC. On the basis of comparison with isopiestic data, it is considered that useful estimates of Harned’s coefficients can be made with these electrodes provided the selectivity characteristics are not too unfavorable and depending on the complexity of the ionic interactions. Experimental selectivity isotherms are presented for both systems. Parameters are derived, on the basis of simple ion exchange theory and regular solution theory, which facilitate interpolation over the experimental range.
A THOROUGH AND VERY USEFUL review of ion-selective electrodes has recently become available (I). Among the important points discussed are two which are relevant here. The first concerns the need for more thermodynamic studies made on a basis of comparison with other, unrelated, methods. For example, how useful are electrodes of the liquid-ion exchange type for measuring activities in mixed electrolyte solutions as compared with isopiestic studies? The second point concerns electrode selectivity. This is of general interest, as many natural systems contain appreciable concentrations of different counterions. Even in the analysis of single electrolyte solutions, complexing reagents and buffers can introduce significant levels of interfering ions. In short, the behavior of the electrode in a mixed electrolyte solution is often the main concern. Since the electrode measures activities, data on the activity coefficients of the electrolytes in mixed solutions will be needed. Data for around 30 twoelectrolyte systems are available ( 2 , 3), and a number of theories and empirical relationships (2-6) enable reasonable (1) “Ion-Selective Electrodes,” Richard A. Durst, Ed., Nat. Bur. Stand. (US.) Spec. Pubi., 314, 474 pp (1969). (2) H. S. Harned and R. A. Robinson, “Multicomponent Elec-
trolyte Solutions,” in The International Encyclopedia of Physical Chemistry and Chemical Physics, Topic 15, Vol. 2, Pergamon Press, London, 1968. (3) R. M. Rush, Oak Ridge National Laboratory Report ORNG 4402, UC-4-Chemistry, 1969. (4) G. Scatchard, J . Amer. Chem. Soc., 90, 3124 (1968). ( 5 ) J. Leyendekkers, J. Phys. Chem., 74, 2225 (1970). (6) Y . C . Wu, R. M. Rush, and G. Scatchard, ibid., 13, 2047 (1969). 322
ANALYTICAL CHEMISTRY, VOL. 43, NO. 3, MARCH 1971
estimates of activity coefficients in multicomponent systems to be made; however, many more experimental data are needed. In this paper, results are given of measurements of activity coefficients of calcium chloride in the presence of strontium(I1) or magnesium(I1) over the ionic-strength range 0.1-6 molal. Isopiestic data are available for these two systems and these are used as a guide to the usefulness of the electrodes for such measurements. The selectivity characteristics of the Orion calcium activity electrode in these systems are also given. This electrode has an acidic organophosphorus exchanger, and from the considerable amount of study on this type of extractant over the past few years (7), it has been shown that in general the cation exchange reactions are more complicated than those of exchange resins. However, even though the actual mechanism of the reaction is unknown, the distribution can always be described in terms of a convenient chemical reaction through which meaningful and useful information can be obtained concerning the system studied, We adopted this attitude in a previous paper (8) where, by means of a simple theory, the composition of an exchange site was derived. This enabled an estimate to be made of the parameters A and B in the equation log (amcs*+/an.wz+)[(l - y)/yl = A - B(2 Y - 1) (1) where a represents the activity of the ion in the aqueous phase, M the interfering counterion (of charge z ) , y the mole fraction of exchange sites occupied by calcium(II), and rn and n are integers related to the exchange reaction [A and B were formerly represented by log K, and B’, respectively (S)]. This facilitated interpolation so that the ionic strength range 0-6 molal was completely covered. The same procedure is adopted here, with some limited extrapolation to extend the range to an ionic strength of 7.5 molal. EXPERIMENTAL
The same equipment and technique were used as described previously (8). The additional reagents used were AR grade (7) Y . Marcus and A. S. Kertes, “Ion Exchange and Solvent Extraction of Metal Complexes,” Wiley-Interscience, London,
1969.
(8) Michael Whitfield and J. V. Leyendekkers, ANAL.CHEM., 42, 444 (1970).
