Selectivity Character istics of a CaIcium-Selective Ion- Exchange Electrode in the System Calcium( 11)-Sodium(1)-Chloride(1)-Water Michael Whitfield and J. V. Leyendekkers Division of Fisheries and Oceanography, CSIRO, Cronulla, N.S. W.2230. Australia Experimental selectivity isotherms are presented for the above system over a range of solution ionic strengths (0.03-6 molal) for the Orion Calcium Activity electrode (92-20). The electrode selectivity shows considerable variation over this range and is a function of solution composition as well as ionic strength. The whole family of isotherms could be predicted reasonably well by fitting the data to a function based on simple ion-exchange theory and regular solution theory. FEW,IF ANY, liquid ion-exchange electrodes are specific for one ion so that in mixed solutions their usefulness can be severely limited unless their selectivity characteristics are known. The data regarding “interference” commonly given in manufacturers’ handbooks, while useful as a guide, are not precise enough for many studies and sometimes tend to be confusing, as pointed out by Shatkay (1). Eisenman (2) has examined the effects on selectivity of variations in the solvent and concentration of the exchanger (fixed, in a commercial electrode) and variations in the solution composition. He shows that the parameters controlling electrode specificity reduce to ratios of classically measurable quantities such as conductances, distribution coefficients, and equilibrium constants. However, even for the case of monovalent cations any changes in the state of aggregation of the exchanger would complicate treatment of the experimental results considerably. In this paper we adopt a different criterion for describing selectivity-viz., the mole fraction of exchange sites occupied by competing ions us. the solution composition. The considerable diversity of interpretation of selectivity of ionexchange materials that exists in the literature (3, 4) has not yet been transferred to analogous interpretations for liquid ion-exchange electrodes. Selectivity isotherms, for example, concisely summarize the selectivity properties of an exchanger and should be useful in characterizing liquid ion-exchangers over a wide range of compositions and ionic strengths. Essentially, we equate the selectivity with the ion-exchange reaction and illustrate the relation between the thermodynamic exchange constant and the empirical selectivity parameter which may be used to calculate the mole fractions so that the isotherms can be constructed. Alternatively, the mole fractions could be measured directly by tracer techniques or other suitable methods. A theory that enables prediction of selectivity to be made without the need for a great deal of experimental work would be very valuable. During a study of activity ioerlicients for the above system, over a range 0.03-0.7M, wI*obta,ned data on the selectivity of a liquid ion-exchange electrode (Orion Calcium Activity electrode). The selectivity of this electrode at higher concentrations (1-6M) was recently investigated (5) and we have combined the two sets of data to draw up (1) A. Shatkay, ANAL.CHEM., 39, 1056 (1967). (2) G. Eisenrnan, ibid., 40, 310 (1968). (3) F. Helfferich, “Ion Exchange,” McGraw-Hill, New York, 1962. (4) J. A. Marinsky, “Ion Exchange,” Vol. I, Edward Arnold, London, 1966. ( 5 ) Rima Huston and J. N. Butler, ANAL.CHEM., 41, 200 (1969). 444
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
isotherms and attempt to find a general relationship valid over the whole concentration range which could form a basis of prediction for other systems. For consistency we use the empirical selectivity parameter common in the literature (5, 6) and represented here by K’. This parameter may be defined by
E = const.
+ S log ( a c , a c ~+~ K r a ~ a z a c ~ z )
(1)
where E is the potential of the cell I Reversible chloride CaCl2(ml),NaCl(mz) Reversible electrode HzO calcium electrode ~
az represents the activity of ion X , and S the Nernst slope. K’ may be related to the solution and resin compositions via simple ion-exchange theory, which has already been used to simplify the analysis of potentiometric titrations in mixed electrolyte solutions (7), viz. U C J ~ N ~=’
K‘y/(l
- Y)
(2)
where y represents the mole fraction of sites occupied by calcium ions and (1 - y) the mole fraction of sites occupied by sodium ions. The cell potential may therefore be expressed
E
=
const.
+ S log
- S log y
(3)
which is a useful form for mixed solutions since the interference effects are confined to the last term. We note here that in practice this last term might include other quantities deriving from nonideal behavior of the electrodes-e.g., if the response slope is not Nernstian but equals (S - n) where n could be a variable, the last term of Equation 3 would equal
.s log [(aCaaC12)nY~-nl This would complicate the interpretation of K’. However, on the basis of Eisenman’s investigations (2), it seems that n is likely to be quite small, at least for 1-1 ion exchange. We assume here that n is also small for 1-2 ion exchange. It has been shown that n is small in pure solutions of calcium chloride up to about 6 M ( 5 ) . K’ is related to the thermodynamic equilibrium constant, Kt, of the exchange reaction by K’
K,Yi/T,
(4)
where represents the rational activity coefficient (3, p 156) of an exchange-site species. The suffixes 1 and 2 refer to calcium and sodium species, respectively. Since the exchanger is a mixture of weakly polar molecules with large aliphatic components dissolved in a weakly polar (6) G. Eisenman, Ed., “Glass Electrodes for Hydrogen and Other Cations,” Marcel Dekker, New York, 1967. (7) M. Whitfield and J. V. Leyendekkers, Anal. Chim. Acta., 46, 63 (1969).
oh
I.S. C a C I ,
Figure 1. Selectivity isotherms for Orion calcium activity electrode in aqueous CaC12-NaCI solutions at constant ionic strength, at 25 “C and pH = 8 Experimental curves;
- - - - derived from Equation 9 and Figure 3.
AB is the
diagonal.
solvent, regular solution theory (8) is applicable, whereby (799) In 71 = (B/R7‘) (1
- y)’
In72 = (B/RT)y2
(5)
B is a constant and R and T have their usual meaning. Equations 2, 4, and 5 together yield log [ U C ~ / ~ Z N~ . y~ )] /[ ~( ~l= log Ki - B‘ ( 2 ~ 1)
(6)
where B‘ = 2.303B/RT. Evaluation of this function over a range of values of and B’. (2y - 1) should enable an estimate of log Ki: EXPERIMENTAL
Calcium chloride and sodium chloride solutions were prepared as described previously (IO). A small quantity (ca. lO-5M) of tetraethylammonium hydroxide was added to the calcium chloride solutions to bring the pH to around 8. The solution compositions used cover most of the ionic strength and ion-ratio ranges of natural waters. The electrodes used were Orion liquid ion-exchange calcium (Cat. 92-20) with 0.1M internal filling solution as supplied by the manufacturer, and Orion liquid ion-exchange chloride (Cat. 92-17). The potential of each electrode was measured in turn, via a pH switch (Cary model 4010750), against a
Jenaer thalamide reference electrode (Cat. B183) using a Dynamco digital voltmeter (DM2022) described previously (10).
The electrodes were immersed in a pure solution of calcium chloride, and sodium chloride solution of the same ionic strength was titrated in to give progressively greater ionic strength fractions of sodium chloride (1SFNsci) in the mixture. The titration was done in sections--i.e., the first section covered the ISFN~CI range 0-0.2, the second section 0.15-0.3, the third 0.25-0.4, and so on up to an ISFNaCl of approximately unity. This technique enabled us to minimize errors arising from the sudden shifts in potential (unrelated to the changes in solution composition) that sometimes occurred when the electrodes were transferred from one solution to another. A second titration was performed in a similar manner but commencing with an I S F N ~close C ~ to 1 and adding became very small. The calcium chloride until ISFN~CI response of each Orion electrode was checked regularly by calibration in pure solutions. Magnetic stirring was employed and the temperature was 25.0 0.1 “C. The experimental data were analyzed on the basis of Cell I. This procedure minimized errors caused by variations in the liquid junction potential. Mean molal activity coefficients (yk) are used throughout because there is, as yet, no consistent convention for the definition of single-ion activities in mixed electrolyte solutions.
*
RESULTS AND DISCUSSION (8) J. H. Hildebrand and R. L. Scott, “Regular Solutions,” Prentice-Hall, Englewood Cliffs, N. J., 1962. (9) R. M. Garrels and C. L. Christ, “Solutions, Minerals and
Equilibria,” Harper and Row, New York, 1965.
(10) M. Whitfield, J. V. Leyendekkers, and J. D. Kerr, Anal. Chim. A c t a , 45, 399 (1969).
Our experimental data (ionic strength range 0.03-0.7M) were analyzed on the basis of Equation 3. Since log y is it was possible to determine the negligible at low ISFN~CI, functional relationship between log yice~ll and solution composition. Fortunately, this was linear and y could be ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
445
,
r
I
1
21- I
Figure 2. Least-squares fit of experimental data R represents log
[aC&Ns']
YCo/YNo'
=
[(l - y ) / y ] with the approximation f CaCl@ f NaCl
simply estimated. Values of y at higher ionic strengths were calculated from the results of Huston and Butler ( 5 ) using Equation 2 and activity coefficient data of Robinson and Bower (11). These values of y were plotted as a function of the percentage ionic fraction of calcium chloride in the solution and a family of selectivity isotherms was obtained (Figure 1). The pattern of isotherms, up to an ionic strength of 2M, is consistent with that of an electroselective exchanger whose selectivity characteristics are controlled primarily by electrostatic effects (3). The enhancement of divalent ion selectivity in dilute solutions is more pronounced for the calcium resin [0.1Mcalcium didecyl phosphate in di-n-octyl phenyl phosphonate (S)] than for Dowex 50-X8 where the active exchange group (sulfonic acid) is less polarizable (12). Since the calcium resin is a liquid, there are no sieve effects or swelling effects to mask this simple behavior. At higher ionic strengths (greater than 2M) the isotherms become S-shaped, indicating the onset of heterofunctional ion-exchange behavior. However, the effect is not very pronounced and it may be attributed to the formation of micelles or islands of associated exchanger molecules. This sort of behavior has been observed in analogous liquid ion-exchangers-e.g., di(2-ethyl(11) R.A. Robinson and V. E. Bower. J. Res. Nut. Bur. Stand.., A ,. . 70,313 (1966). (12) H. C. Subba Rao and M. M. Davis, A.1.Ch.E. J., 3, 187 (1957). 446
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
hexyl)-phosphoric acid, D2EHPA-as the percentage in the sodium form increases (13, 14). It is interesting to note that the electrode actually becomes sodium selective at ionic strengths greater than 3 M . A great deal of experimental work would be required to complete the family of curves. An attempt at prediction has therefore been made, using the data already available and the simple ion-exchange theory discussed above. Equation 6 is based on the simple reaction CaX,
+ 2Na+ e NazXz + Ca2+
(7)
where X represents an exchanger group. However, there is evidence (13, 14) that the reaction CaX, .2HX
+ 4Na+ e Ca2+ + 2HC + (NaX)4
(8)
might be more appropriate. In this case Equation 6 would become log [~c~/ahi.'l[(l - y)/yl = log K'i
- B'(2y
- 1)
(9)
(Pibeing proportional to the thermodynamic equilibrium constant for the reaction, since the pH is constant), and, in fact, this equation gave a linear (least squares) fit to the data (13) D. E. Horner, D. J. Crouse, K. B. Brown, and B. Weaver, Nucl. Sei. Eng., 17,234(1963). (14) D. F. Peppard, W. J. Driscoll, R. J. Sironen, and S. McCarty, J. Inorg. Nucl. Chem., 4,326 (1957).
+2
I
I
I
I
Figure 4. Selectivity curves based on estimates
of K' Experimental values of K' are represented by A (3molal) 0 (1 molal)
molal) (0.1 molal)
0 (6
+
0 o/o
I.S. N a C I
(Figure 2). We were thus able simply to determine log K'$ and B' for a number of ionic strengths, and, by drawing smooth curves (Figure 3), to estimate their values over the whole range. This, in turn, enabled us to estimate y for a larger number of ionic strengths (dashed curves in Figure 1). Equation 2 is still valid, irrespective of the interpretation
of the reaction. K' is an empirical quantity and might be thought of as a conditional equilibrium constant. On the basis of our interpretation, K' = K'iaNa2yl/y2
(10)
The estimated values of y were used in conjunction with ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
447
Equation 2 to calculate K’. The experimental and calculated values are compared in Figure 4. Calculations and numerical analyses were run on a CDC 3600 computer. In general, K’ is underestimated but the trend in values is predicted reasonably well considering the wide range of ionic strengths and solution compositions covered. The pattern of selectivity isotherms, including the onset of heterofunctional behavior above 2M, is fairly accurately reproduced. The equilibrium process may involve a number of reactions and our simple treatment gives only an average behavior of the system. When y = 0.5 then, from Equation 2 acs/aNeZ= K’
This value of K’ is frequently used as an average value of the corrected selectivity coefficient at a particular ionic strength (4, p 235) and can be estimated from Figures 1 and 4-e.g., at 2M, KtaVhas the value 0.039 and at 0.75M the value 0.011. At low ionic strength the value becomes relatively small (about 10-3. KIav corresponds to the selectivity ratio determined by the standard titration procedure (6, p 304; 9, p 296) and has proved a useful parameter for glass electrodes; it is even possible to determine B of Equation 5 from the form of the titration curve (6, p 298). However, for the liquid
ion-exchanger used here, this parameter is inadequate, particularly for the more concentrated solutions. A limiting value of K’ could be defined by comparing the value of K’ at y = 1 with the value at y = 0. Recently (15) an investigation of the selectivity characteristics of a number of Orion selective electrodes, of the liquid membrane type, has been made over an ionic strength range 0.1 to 1 0 - 4 ~ . Three useful methods of evaluating K’ were described. The first two were based on comparisons of pure solutions of the salts of the two counter ions. The K’ value from the first method roughly corresponds to the limiting value of K’ and that of the second to KIaV. In the third method K’ was measured over a range of solution compositions. Although the measurements were not made on the basis of constant ionic strengths the data could be interpreted uia the simple ion-exchange theory outlined in this paper, whence some of the apparent anomalies might be resolved. RECEIVED for review October 6, 1969. Accepted December 29, 1969. (15) K. Srinivasan and G. A. Rechnitz, ANAL.CHEM.,41, 1203 ( 1969).
Analysis of Inorganic Sulfur Compounds by Flame Ionization Detector B. A. Schaefer Department of Chemistry, Royal Australian Air Force Academy (University of Melbourne), Point Cook, Victoria, Australia
By selecting appropriate conditions of operation, certain inorganic sulfur compounds could be determined using the normal flame ionization detector in gas chromatography. Carbon disulfide gave positive peaks of optimum response under conditions similar to those for hydrocarbons, requiring 20% equivalent hydrogen in the flame gases. These positive peaks inverted to negative with a high background current of hydrocarbon origin and nonoptimum conditions of 24% equivalent H P . Sulfur dioxide, H S , and SCO gave large negative peaks in the ratio of l i 3 i 3 approximately with high hydrogen, and l i l i l with low hydrogen (or high oxygen) in the flame. These negative responses were superior to responses from the katharometer, especiallywhen hydrocarbon at about10 p.p.m. was present in the flame. The response was proportional to the carbon added, and optimum responses were obtained with about 24% equivalent Hz. Positive peaks were observed from all four compounds when the burner jet became heated to redness, caused by high Hzor low Nzflow rates. The results were applied to the analysis of partially oxidized C S z . A mechanism is proposed to account for the negative peaks, involving the reaction of sulfur radical and sulfur oxide with flame radicals, particularly oxygen atom.
COLUMNS FOR SEPARATING sulfur compounds have been described (1-6), but the hydrogen flame ionization detector (FID)is generally regarded as unsuitable for inorganic substances (7). Condon, Scholly, and Averill (8) reported no response to CS2 with cold electrodes, and little or no response 448
~
ANALYTICAL CHEMISTRY, VOL. 42, NO. 4, APRIL 1970
~~
to SOn,H2S, or SCO. Perkins et ai. (9), and Andreatch and Feinland (10) reported no response for CS2. Sternberg, Gallaway, and Jones ( I I ) , Phillips (12), McWilliam (13), and Walker (14) have separately examined CS2, obtaining limited (1) C. T. Hodges and R. F. Matson, ANAL.CHEM., 37, 1065 (1965). (2) E. L. Obermiller and G. 0. Charlier, J. Gas Chromntogr., 6 , 446 (1968). (3) S. Pennington and C. E. Meloan, ANAL.CHEM., 39, 119 (1967). (4) H. L. Hall, ibid., 34,61 (1962). (5) C. N. Jones, ibid., 39, 1858 (1967). (6) R. J. Liebrand, J. Gus Chromntogr.,5,518 (1967). (7) “Manufacturer’s Handbook of the F.I.D. Instrument,” Beck-
man Instruments Inc., Fullerton, Calif. (8) R. D. Condon, P. R. Scholly, and W. Averill, “Gas Chromatography,” R. P. W. Scott, Ed., Butterworth, Bethesda, Md., 1960, p 31. (9) G. Perkins, G. M. Rouayheb, L. D. Lively, and W. C . Hamilton in “Gas Chromatography Third International Symposium,” N. Brenner, J. E. Callen, and M. D. Weiss, Eds., Academic Press, New York, 1962, pp 269-83. (10) A. J. Andreatch and R. Feinland, ANAL.CHEM.,32, 1021 (1960). (11) J. C. Sternberg, W. S. Gallaway, and D. T. L. Jones, “Gas Chromatography Third International Symposium,” N. Brenner, J. E. Callen and M. D. Weiss, Eds., Academic Press, New York, 1962, p 231. (12) T. R. Phillips, “Gas Chromatography,” R. P. W. Scott, Ed., Butterworth, Bethesda, Md., 1960, pp 132-4, 317. (13) I. G. McWilliam, J. Chromntogr.,6, 110 (1961). (14) B. L. Walker, J. Gus Chromntogr.,4, 384 (1966).
