Prediction of Retention for Halide Anions and Oxoanions in

Chem. , 1995, 67 (2), pp 434–441. DOI: 10.1021/ac00098a032. Publication Date: January 1995. ACS Legacy Archive. Cite this:Anal. Chem. 67, 2, 434-441...
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Anal. Chem. 1995,67, 434-441

Prediction of Retention for Halide Anions and Oxoanions in Suppressed ion Chromatography Using Multiple Species Eluent Peter Haj&,*,t Otto Horv&th,*and Villo Denket Departments of Analytical Chemistry and General and Inorganic Chemistry, University of Veszprem, P.O. Box 158, 820 1 Veszprem, Hungary

The retention behavior of inorganic halide and oxoanions is studied as a function of changing eluent composition. The model developed for separation of C1-, Br-, c103-, BrOs-, Se032-, Se042-, and P043- ions with eluent containingHC03-, C032-, and OH- anions is utilized for determination of selectivity coefficients for sample and eluent species. It can also take into account the protonation of the sample ions. The model effectiveh characterizes the behavior of the analytes under elution conditions of practical importance. The predicted and measured retentions are in rather good agreement. The capacity factors determined for these anions make possible a reliable planning for IC separation of them with carbonate eluent in relatively wide ranges of concentration and pH. The different retention behaviors of mono-, di-, and trivalent anions as a function of pH are also interpreted in this eluent system. Anion separation by suppressed and nonsuppressed ion chromatography has became a routine analytical procedure in the past This technique offers a reliable methodology for simultaneous determination of ions and has been found to be useful in many applications. The most effective utilization of ion chromatography requires accurate characterization of the solute retention and development of a predictive capability. The versatility of IC has been significantly enhanced by the application of multiple species eluents. These eluents contain more than one type of competing anion, in many cases different dissociated forms of the same weak acid. Thus, the composition of such an eluent can be easily governed by its pH. Phthalate, benzoate, phosphate, citrate, and carbonatebuffer eluents were most frequently utilized for this purpose.134-6 In alkaline solutions, the OH- anion can also operate as an eluent species. OH- is the weakest eluting anion and, consequently, is usually used at higher concentrations than the other eluents. In suppressed IC, however, the higher load of suppressors needs more powerful regeneration. When bicarbonate and carbonate eluent anions are used together, the resulting eluent Department of Analytical Chemistry. Department of General and Inorganic Chemistry. (1) Small, H.; Stevens, T.;Bauman, W. Anal. Chem. 1975,47,4801. (2)Small, H. Zon Chromatography; Plenum Press: New York, 1989. (3)Haddad, P. R;Jackson, P. E. Zon Chromatographj-Principles and Applications; Elsevier: Amsterdam, 1990. (4)Gjerde, D. T.;Fritz, J. S. Anal. Chem. 1981, 53, 2324. (5) Gjerde, D.T.;Schmuckler, G.; Fritz, 5. S. J. Chromatogr. 1980, 35, 187. (6)Jenke, D.R; Pagenkopf, G. IC /. Chromatogr. 1983,269,202. +

t

434 Analytical Chemistry, Vol. 67, No. 2,January 15, 1995

is buffered and has an elution strength which can be varied easily by varying the ratio of the two anions. The analytes could be eluted with fewer microequivalents of carbonate than hydroxide. Carbonate buffer systems are the most widely used eluents for suppressed IC.7 The protonation of solutes can play a considerable role in the retention behavior, which can be sigrdicantly sensitive to the pH in a domain where the species are partially protonated. Thus, in order to plan a separation of anionic samples with a multiple species eluent, a suitable model is necessary, by means of which a reliable prediction of the retention volumes can be made. The aim of this work was the development and application of a theoretical model for the retention of inorganic anions in suppressed IC with carbonate eluent. Such a model must involve, beside the usual ionexchange equilibria, the protonation of not only the carbonate but also some of the sample ions. Inorganic oxoanions were chosen for separation because of their practical importance. Some halide ions were also studied for comparison. A critical evaluation of this model as a predictive tool for retention behavior is also presented in this paper. THEORY

The most straightforward model in ionexchange chromatography is that in which the eluent contains a single type of competing i ~ n . *Linear ~ ~ plots of the logarithm of adjusted retention time against the logarithm of the eluent composition were obtained in all cases. These straight line plots can be predicted by considering the equilibrium of an ionexchange system (see later). Many separations in ionexchange chromatography use an eluent which contains more than one type of species. For modeling the retention of ions with such eluents, two approaches have been proposed. When the two eluent species are in rapid protolytic equilibrium,we can use the effective charge approach. It is assumed in this approach that the competing ions have similar selectivities for the solute ion.5J0J1 (7) (a) Reference 3,pp 106-109 and 543-733. (b) Walton, H. F.; Rocklin, R D.Ion Exchange in Analytical Chemistry; CRC Press: B o a Raton, FL, 1990; pp 63-65. (c) Smith, R E. Zon Chromatography Applications; CRC Press: Boca Raton, FL, 1988; pp 48-64 and 115-161. (d) Dionex ZC Symposium Workshop Handbook 1994;Dionex Corp.: Sunnyvale, CA; 1994;pp 16-29; LPN 0422435M 7/94 USA. (e) Karmashar, S. V.; Tatabai, M. A Chromatographia 1992,11,643.(f) Rabin, S.; Stillian,J.; Barreto, V.; Friedman, IC; Toofan, M. J. Chromatogr. 1993, 640, 97. Cp) Frankenberger, W. T.; Mehra, H. C.; Gjerde, D. T. J. Chromatogr. 1990,504, 211. (8)Strelow, F. W. E.; Walt, T. N. Anal. Chem. 1975,47, 2272. (9)Hajos, P.; Inczedy, J. In Zon-Exchange Technoloo; Naden, D., Streat, M., Eds.; Ellis Honvood Chichester, 1 9 W p 450. (10)Haddad, P. R;Cowie, C. E. J. Chromatogr. 1984, 303, 321. 0003-2700/95/0367-0434$9.00/0 0 1995 American Chemical Society

The multiple eluent species model was proposed as a means of consideringall competing eluent ions by taking into account their differing ionexchange sele~tivities.~~-~~ However, no attempt has been made so far to model the retention behavior of analytes which can undergo partial protonation or other side reactions. Earlier retention m o d e l ~ are ~ ~ unable J~ to model accurately the retention behavior of a system that contains different forms of analytes (phosphate, selenite, carbonate, etc.) which show changes in charge by eluent pH. In order to have a reliable retention model, all the forms of analytes in the system must be considered at the same time. Such a completion of the multiple eluent species approach makes it applicable for sample anions, too, which themselves can be protonated in the pH range used. The system that contains several ionic species in the eluent and Werent forms of analytes in the sample is rather complicated. This is probably due to its theoretical complexity and the lack of a commonly accepted mathematical model to describe solute retention. The ionexchange equilibria are complex, and there has been much effort to account for different effects. Theoretical and practical treatments of retention behavior of ionic and ionizable components in liquid chromatography have been reported extensively in the recent literature.16-19 Ion-ExchangeEquilibria of Sample Ions. The general ionexchange equilibrium for binding of an analyte anion to a stationary phase that has been conditioned with an eluent containing a competing anion Ex- is given by

y&-E

+ xAy-

xR,,-A

+ yEx-

DA= KA/HCO,CYHCO,Q)~[HC~~-]-~ =K~co,(1/~co,Q)3~2[CO~~l~3’2 = K A / ~ H&&>[OH-] -3

(6)

The symbol XE (E = HCOB-, Cos2-, and OH-) represents the molar fraction of the eluent species in the stationary phase. Since any of the expressions in eqs 4, 5, and 6 is suitable for the description of the ionexchange equilibrium, one with a monovalent eluent species is chosen. Thus, the ionexchange processes for A3-, HA2-, and HA- analyte ions in the separation are given by eqs 7, 8, and 9, the equilibrium constants for which are expressed in eqs 10, 11, and 12, respectively.

+ A3- 3 R3-A + 3E-

(7)

+ HA--KH*A/E R-HA + E-

(9)

3R-E

R-E

(1)

where R denotes the stationary phase. In the expression of the equilibrium constant for this reaction, parentheses and square brackets refer to the concentrations in the stationary and the mobile phases, respectively (eq 2): KA/E

=

(Ay-)”[E”-Iy [Ay-]”(E”-)y

The volumetric distribution coefficient of Ar can be given in terms of KMEand the ion-exchange capacity, &, of the column (eq 3):

The volumetric distribution coefficient can be given as follows:

D A + ~ + H=+ Since in alkaline carbonate buffer, HCOB-, Cos2-, and OH- all act as competing anions, any of them can be used in the expressions of D for mono- (DHA, eq 41, di- (Dm, eq 5), and trivalent (DA, eq 6) solute ions.

DH+ = K H ~ A / H C O , C X H C O , Q )[HCO3-1-’

[A3-]

+ [HA2-] + [HA-]+ [H3Al (13)

Substitution of eqs 10,11, and 12 into eq 13 results in

(A3-) + (HA2-> + @Id-) DA+HA+H+ = [A3-] [HA2-] [HA-]+ [H3Al

+

(11) Hajbs, P.; Kecskemkti, T.; Inczkdy, J. React. Polym. 1988, 7,239. (12) Hoover, T.B. Sep. Sci. Tecknol. 1982, 17, 295. (13) Jenke, D. R; Pagenkopf, G. K Anal. Ckem. 1984,56, 85. (14)Maruo, M.; Hirayama, N.; Kuwamoto, T. ]. Chromatop. 1989, 481, 315. (15) Jenke, D. R; Pagenkopf, G. IC Anal. Chem. 1984,56,88. (16) Hajbs, P.; Rkv&sz,G.; Sarzanini, C.; Sacchero, G.; Mentasti, E.]. Chromatop. 1993, 640, 15. (17) Rodgers, k H.; Khaledi, M. G. Anal. Chem. 1994,66, 327. (18)Stahlberg, J. Anal. Chem. 1994, 66, 440. (19)F6ti, G.; Hajds, P.;KovAts, sz. E. Talanta 1994, 7, 1073.

+

(14)

which can be rewritten as

The symbols @A, @ p ~ ~ 1and @HA denote the partial molar fractions Analytical Chemistry, Vol. 67, No. 2, January 15, 1995

435

F CI\

p’~” HPOIf

pH = 10,5

, 20

10

0

30

40

50

I

RETENTION VOLUME,cm3

Figure 1. Chromatogram of halide anions and oxoanions obtained by using carbonate eluent (Celuent = [HC03-] [C03*-] = 2 mM, pH = 9.62; sample volume, 50 pL; conductivity detection).

‘r

Figure 3. Chromatogram of phosphate-containingsample (Celuent = [HC03-] [C032-] = 2 mM, pH = 10.58; sample volume, 50 pL; conductivity detection).

+

+

applied for divalent anions which are partially protonated. The behavior of deprotonated m o m or divalent anions of strong acids such as C1-, C103-, or Sod2-can be described by one term of eq 15 (by the third or second one, respectively) because the values of the partial mole fractions for protonated species are 0. Ion-ExchangeEquilibria of Eluent Ions. Choosing HC03as the basic eluent component, the following ion-exchange equilibria are considered between the competing anions: 0

I

I

3

6

I I 9 1 2 1 5

Cot-

RETENTION VOLUME, cm3 Figure 2. Chromatogram of halide anions and Oxoanions obtained by using carbonate buffer eluent (Celuent = [HC03-] + [C032-] = 2 mM, pH = 11.5; sample volume, 50 pL; conductivity detection).

+ 2R-HCO,

OH-

+ R-HCO,

‘%OQ/HCOQ

KOH/HCO~

R,-CO, R-OH

+ 2HC0,-

+ HCOS-

(16)

(17)

The intereluent ion-exchange equilibrium constants for these processes are

of deprotonated and partially protonated forms of the analyte ion. They can be calculated from the three protonation constants of A3- at the pH of the mobile phase. Of course, eq 15 can also be

( C o t - ) [HC0,-12 KC0,/HC03

=

[c0,2-1(HC0J2

(18)

Table 1. Ion-Specific (K-q or K-0,) and Intereluent ( K c o ~ n c oand ~ K,.w,Hco,) Chromatographic Ion-Exchange Selectivity Constants for Halide Anions and Oxoanions, Determined at Different Eluent Concentrations eluent concn

selectivity constant

KCIO~/HCO~

KCO~/HCO~ KOH/HCO~ KS~O~/HCO~ KHS~O~IHCO~ KC03/HC03

KOH/HCO~ K%04/HC03

KCO,/HCO~

KOH/HCO~ KPOd‘HC03

KHPO~/HCO~ KCO,/HCO~ KOH/HCO~

([C032-l + [HCOs-]), m M

2

3

4

5

7

mean f SD

3.17 19.94 1.48

3.07 13.86 1.05

3.02 14.05 1.53

3.02 13.55 1.88

2.74 12.09 1.05

3.00 f 0.16 13.50 f 0.81 1.40 f 0.35

0.930 13.69 1.13

0.934 13.98 1.45

0.883 12.55 1.18

0.920 14.05 1.75

0.922 i 0.023 13.68 f 0.65 1.44 f 0.29

0.734 13.89 1.06

0.672 12.03 1.01

0.729 13.98 1.03

0.943 14.12 1.71 0.729 13.83 1.37

0.720 13.91 1.97

0.717 f 0.026 13.53 f 0.84 1.28 f 0.41

3.29 13.66 1.43

3.14 13.23 1.05

3.17 13.87 1.05

3.11 13.89 1.01

2.86 12.05 1.60

5.04 8.71 13.95 1.78 18.84 13.95 2.21 138.5 7.92 14.89 1.57

4.80 6.17 13.97 1.55 17.71 14.17 1.97 87.5 10.14 14.91 1.57

4.75 4.05 13.84 1.75 17.57 14.21 2.15 125.4 9.74 14.99 1.50

4.43 5.09 13.72 1.70 16.70 13.89 2.08 113.5 8.48 14.95 1.64

4.35 3.93 13.97 1.75 15.99 14.26 1.89 93.9 8.11 14.92 1.90

436 Analytical Chemistty, Vol. 67, No. 2,Januaty 15, 1995

3.11 f 0.16 13.34 f 0.77 1.22 f 0.27 4.67 f 0.28 5.59 f 1.97 13.89 f 0.11 1.71 f 0.10 17.36 f 1.08 14.10 f 0.17 2.06 f 0.13 111.8 f 21.3 8.88 i 1.00 14.93 i 0.04 1.64 If 0.16

Table 3. Comparison of Predicted and Observed Retention Volumes of Br-

eluent concn, PH mM

I

IF I

r.

I

i I

Figure 4. Chromatogram of phosphate-containingsample (C,l,t = [HC03-] [Cos2-] = 2 mM, pH = 115;sample volume, 50 pL; conductivity detection.

+

Table 2. Ion-Specific ( K ~ oor, K n m o a ) and intereluent (K&~nco, and &H,WCO,) Chromatographic ion-Exchange Selectlvity Constants for Halide Anions and Oxoanions*

analyte

mean of KA(HA)IHCO, KCO~HCO,KOH/HCO, errors, %

(A or HA) Br-

3.00 f 0.16 0.922 f 0.023 0.717 f 0.026 3.11 i0.16

C1BrO3-

C103-

* ] 111‘8 * 21’3 ] 8.88 f 1.00

903’H903904’-

4’67 o’28 5.59 f 1.97 17.36 f 1.08

Pod3HP02-

mean value

13.50 f 0.81 13.68 f 0.65 13.53 f 0.84 13.34 f 0.77

1.40 f 0.35 1.44 f 0.29 1.28 f 0.41 1.22 f 0.27

2.15 1.78 1.16 2.44

13.89 f 0.11 1.71 & 0.10

3.76

14.10 f 0.17 2.06 f 0.13

7.34

14.93 f 0.04

1.64 f 0.16

12.17

2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0 a

9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50

retention volumes, mL calc meas 12.40 8.60 6.77 5.93 5.51 5.25 10.33 7.35 5.90 5.22 4.90 4.70 9.09 6.60 5.37 4.80 4.53 4.37 8.24 6.09 5.01 4.51 4.27 4.14 7.13 5.42 4.54 4.13 3.94 3.83

difference,a %

12.95 9.11 6.90 6.20 5.82 5.45 10.49 7.32 6.03 5.30 5.00 4.91 9.09 6.56 5.36 4.92 4.62 4.47 8.07 6.21 5.09 4.55 4.28 4.14 6.75 5.27 4.55 4.20 4.01 3.86

4.24 5.58 1.86 4.43 5.28 3.70 1.54 0.43 2.23 1.50 2.06 4.23 0.00 0.65 0.19 2.48 2.03 2.27 2.15 1.92 1.54 0.91 0.19 0.06 5.61 2.75 0.26 1.73 1.87 0.78

Mean of errors, 2.15%.

13.85 f 1.34 1.54 f 0.49

aThe means of differences between the predicted (V& and measured (Vmed retention volumes, ElVdc - Vmeasl/Vmeas)/N, are also given (see Tables 3-7 and the corresponding text). The expressions for (HCOs-) can be substituted into eq 15, and the final form of the model is obtained The ion-exchange capacity of the separator column is given by

Q = 2(C0,2-)

+ (HC03-) + (OH-)

+ *H+@HZ,

DA+HA+H+ = DA@A +

(20)

Substitution of eqs 18 and 19 into eq 20 leads to the following quadratic equation: 2-

Q=

2KC03/HC03[C03 [HC03-12

(Hco- 2 + 3 )

I

\

where

4 = ~Kco,/Hco,Q where a=

and

2KC0,/HC0,

[‘O,2-1

[HC03-12

The molar concentrations of the three competing anions in the eluent can be easily calculated from the two protonation constants of C032- (log j31 = 10.1, log j 3 ~= 16.4)20at pH of the mobile phase. Activities instead of concentrations were used in the actual data processing. Activity coefficients were calculated by the extended Debye-Huckel equation.’l Analytical Chemistry, Vol. 67, No. 2, January 15, 7995

437

Table 4. Comparison of Predicted and Observed Retention Volumes of Br03-

Table 5. Comparison of Predicted and Observed Retention Volumes of SeO~*-klSe0~-

eluent

eluent

concn,

mM

PH

2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0

9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50

retention volumes, mL meas calc 4.18 3.27 2.83 2.63 2.53 2.47 3.68 2.97 2.62 2.46 2.39 2.34 3.39 2.79 2.50 2.36 2.30 2.26 3.18 2.67 2.41 2.29 2.24 2.21 2.92 2.51 2.30 2.20 2.16 2.13

4.13 3.35 2.85 2.67 2.61 2.51 3.63 2.97 2.66 2.49 2.42 2.40 3.32 2.79 2.51 2.39 2.33 2.30 3.14 2.69 2.42 2.33 2.25 2.22 2.85 2.51 2.30 2.22 2.18 2.15

difference," %

concn,

mM

PH

2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0

9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50

1.12 2.38 0.57 1.42 2.94 1.58 1.36 0.00 1.39 1.11 1.43 2.54 2.01 0.12 0.42 1.13 1.37 1.72 1.42 0.70 0.26 1.55 0.56 0.66 2.41 0.00 0.04 0.77 1.05 0.84

Mean of errors, 1.16%.

EXPERIMENTAL SECTION Reagents and Solutions. Eluents were prepared by using analytical grade NaHCO3, Na2C03, and NaOH (Merck). Triply distilled water was purified by a Milli-Q system (Millipore) containiig a 0.45pm Millistack filter at the outlet. Sample solutions of chloride, bromide, chlorate, bromate, selenite, selenate, and phosphate were prepared by dissolution of analytical grade salts (NaCl, NaC103, NaBr, and Na3P04 from Merck, and NaE%r03,and NazSeO3, Na2SeO4 from Aldrich). The concentrations of the anions in the samples varied in the range of 4.7 x 10-5-1.8 x M. The actual pH was monitored after the sample was degassed with argon, and the pH was controlled by addition of diluted NaOH. The samples were analyzed at five eluent concentrations ([HC032-l + [COS~-I= 2, 3, 4, 5, and 7 mM) andsixpHvalues (9.1,9.62, 10.1,10.58, 11.1,and 11.5),i.e., at 30 different eluent compositions. Instrumentation. The chromatographic system consisted of a Dionex Series 201Oi ion chromatograph (Dionex Co., Sunnyvale, CA), a Dionex AS4A anion separator column (250 x 4 mm), a Dionex AMMSl suppressor membrane, a Dionex CDM conductivity detector, and a Carlo Erba SP 4270 data module integrator. (20) (a) Martell, A E.; Sillkn, L. G. Stability Constants of Metal-Ion Complexes; Special Publication 17; The Chemical Society: London, 1964. @) Martell, A E.; Sillkn, L. G. Stability Constants of Metal-Ion Complexes; Special Publication 25; The Chemical Society: London, 1971. (c) HBgfeldt, E. Stability Constants of Metal-Ion Complexes, Part A: Inorganic Ligands; Pergamon Press: Oxford, 1982. (21) Inczkdy, J. Analytical Application of Complex Equilibria; Akadkmia Kiad6: Budapest, 1976; p 22.

438 Analytical Chemistry, Vol. 67, No. 2, January 15, 1995

a

retention volumes, mL calc meas 26.24 12.59 7.60 5.77 4.99 4.55 18.31 9.15 5.77 4.53 4.01 3.73 14.28 7.38 4.83 3.88 3.50 3.29 11.85 6.32 4.26 3.49 3.18 3.02 9.05 5.08 3.59 3.03 2.81 2.70

29.84 13.74 8.12 5.94 5.27 4.65 18.86 9.45 5.85 4.55 4.05 3.83 13.67 7.29 4.83 3.81 3.47 3.29 11.30 6.21 4.08 3.41 3.08 2.96 8.03 4.82 3.38 2.88 2.72 2.60

%

12.07 8.38 6.38 2.89 5.25 2.24 2.90 3.21 1.33 0.49 0.98 2.66 4.43 1.27 0.03 1.95 0.74 0.05 4.88 1.76 4.35 2.45 3.28 2.08 12.65 5.42 6.20 5.37 3.28 3.77

Mean of errors, 3.76%.

The injection loop was 50 pL. The separator column was based on a 15pm polystyrene-divinylbenzene copolymer agglomerated with completely aminated anion-exchange latex. The ionexchange capacity of the column was 0.0128 mequiv/mL. All samples were analyzed in triplicate with a flow rate of 1.5 mL/ min. RESULTS AND DISCUSSION Both the concentration (IHC03-I [C032-1) and the pH of the eluent have been varied in a relatively wide range; therefore, 30 retention data were obtained for each analyte ion: Figures 1-4 show typical chromatograms for the separation of the seven anions studied. Phosphate was analyzed in samples containing other analyte ions which were not subject of this study (Figures 3 and 4). On the basis of eq 25, the ion-specific selectivity constants, KA/HCO~, KWHQ, and KH~A/HCO~, and the intereluent selectivity constants, Kco3/~co3and KOHIHCO~, were determined from the experimental data by iterative calculations. During the computation, the difference between the calculated and measured retention volumes was minimized. Simplex method (due to Nelder and Mead)22*23 was applied to solve this multiple nonlinear regression problem. In the actual data processing, the selectivity constants were calculated from six retention volumes (measured at differentpH values) belonging to the same eluent concentration, and then the values obtained in this way were averaged. Table 1

+

(22) Nelder, J. A; Mead, R Comput. /. 1965, 7, 308. (23) Ebert, IC; Ederer, H.; Isenhour, T. L. Computer Application in Chemistty; V C H Weinheim, 1989; p 387.

Table 6. Comparison of Predlcted and Observed Retention Volumes of SeOe2-

eluent concn, PH mM 2.0 2.0 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3..0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0 (I

9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 8.62 10.10 10.58 11.10 11.50

retention volumes, mL CalC meas 97.28 41.81 23.54 16.95 14.15 12.51 64.1 28.73 16.73 12.35 10.51 9.49 47.62 22.13 13.26 9.99 8.62 7.88 37.76 18.12 11.13 8.53 7.45 6.87 26.64 13.52 8.67 6.83 6.07 5.67

113.63 44.76 24.03 16.59 14.04 12.06 68.4 28.95 16.16 11.63 9.95 9.15 47.81 21.50 12.54 9.18 9.72 7.25 38.06 17.34 10.11 7.64 6.57 6.12 25.20 12.48 7.62 5.85 5.31 4.94

difference,u %

14.39 6.59 2.05 2.17 0.80 3.69 6.29 0.75 3.54 6.21 5.66 3.68 0.39 2.94 5.76 8.81 11.30 8.73 0.79 4.51 10.14 11.66 13.33 12.28 5.73 8.37 13.81 16.80 14.24 14.80

Mean of errors, 7.34%.

shows the results of this process for all the anions studied. Table 2 summarizes the averaged data for each analyte ions. The standard deviations of these constantsare relatively low, indicating that they are independent of the eluent concentration. The uncertainties of the Kvalues given in Table 2 involve the effect of all the 30 data evaluated. Among the anions studied, selenite and phosphate undergo partial protonation within the pH range applied. Since the protonation constant of the former is not too high (log PI= 8.5),20occurrence of HSeO3- is significant only at the lower pH values ( ~ 1 0 ) .Therefore, the uncertainty of the selectivity constant for this ion is rather high (see also Table 1). For a similar reason (log P2 = 18.9),20H2PO4- does not exist in any significant amount under these conditions (less than 2% even at pH 9.1), thus no selectivity constant could be estimated for it. While the selectivity constant for Br- is considerably higher than that for C1-, as is expected on the basis of size and polarizability, BrO3- is eluted much earlier than C103-; moreover, it was the first ion in the sample to elute. ?is phenomenon may be attributed to a shielding effect of the oxygens, resulting in a more compact ion with lower charge density and polarizability. The selectivity constants for Se032- and Sod2-as well as P043and HP042- are rather high, basically due to their charge and size. Of course, such an order of the K values strongly depends on the physical and chemical structure of the separator column. The intereluent selectivity constantsdetermined at the different analyte ions do not significantly deviate from one another, especially in the case of KCO~/HCO~, contirming the expectation that the constants are independent of the ions to be separated. The

Table 7. Comparlson of Predlcted and Observed Retentlon Volumes of P04a-/HP042-

eluenr concn, mM PH 2.0 2.0 2.0 2.0 3.0 3.0 3.0 3.0 3.0 4.0 4.0 4.0 4.0 4.0 4.0 5.0 5.0 5.0 5.0 5.0 5.0 7.0 7.0 7.0 7.0 7.0 7.0

10.10 10.58 11.10 11.50 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50 9.10 9.62 10.10 10.58 11.10 11.50

retention volumes, mL calc meas 15.42 13.52 16.1 22.49 16.84 10.94 9.56 10.98 13.08 25.98 13.10 8.73 7.65 8.58 10.07 20.77 10.86 7.42 6.53 7.19 8.33 14.93 8.32 5.93 5.28 5.68 6.43

15.42 13.52 16.10 22.49 19.62 12.26 9.21 9.72 15.18 31.13 14.25 7.94 6.99 8.24 11.75 24.35 9.59 6.59 5.66 6.43 9.23 17.67 9.43 5.27 4.67 5.01 7.55

difference,b %

14.25 12.11 10.46 15.12 14.19 10.79 3.78 12.85 13.85 16.54 8.12 10.00 9.47 4.15 14.30 14.69 13.22 12.65 15.36 11.67 9.78 15.50 11.79 12.48 12.96 13.38 14.90

When eluents with concentration-pH combinations of 2 mMand 3 mM-9.1 were used, no retention could be detected within a reasonable range (up to 35 cm13) because of the toolow elution power. Mean of errors, 12.17%. (I

9.1, 2 mM-9.62,

uncertainty of KOH/HCO, is relatively high because of its rather deviating value at Se0d2-. This, however, does not affect the applicability of these values, because the intereluent selectivity constant for C032- is 1 order of magnitude higher than that for OH-, i.e., the system is much less sensitive to the latter anion. Thus, the averages of the values for K c o 3 ~ c o(13.85 3 f 1.34) and KOH/HCO~ (1.54 f 0.49) can be taken as universal intereluent selectivity constants for all the ions to be separated. Using these values involving the effect of all the data evaluated and the actual ion specific selectivity constants, predicitions can be made for the retention volumes of each analyte ion at different concentrations and pH values of the carbonate eluent. Tables 3-7 show the individual deviations between the measured (Vme3 and predicted (calculated, V& retention volumes for Br-, BrO3-, Se032-/ HSe03-, Sod2-,and P043-/HP042- ions as typical examples. The errors are given as absolute values of the relative differences, according to the expression lVdC - Vmeal/Vmeap The mean of errors is indicated at the bottom of the tables. These values are given in the last column of Table 2 for each analyte ions. These results confirm the validity of the proposed model and the reliability of the selectivity constants determined. However, it should be mentioned that signillcantly bigger error belongs to higher selectivity constants in the case of the analyte ions. This phenomenon is probably the consequenceof ignored effects, such as, e.g., nonexchange adsorption, which are stronger for di- and trivalent ions. Hence, this effect is very pronounced for phosphate ions. Besides, the higher number of independent variables in this case increases the uncertainty of the calculated results. Analytical Chemisfty, Vol. 67, No. 2, January 15, 1995

439

0.8 1.0

8

0.6

Y

-1.0

PH

1

yH

.^ IL

Figure 7. Calculated retention surface for selenite ions eluted with HC03--C03*- buffer (C = [HC03-] [C032-]). Partial molar fractions of HCO3- and C03*- (together with the OH- concentration) in HC03--C032- buffer and those of selenites are also illustrated as functions of pH.

+

For describing of the retention behavior, the capacity factor, k', of the analyte ion is more suitable than the distribution coefficient (0) , because the k' eliminates the instrument-specific void volume, VO,

where VRis the brutto retention volume and Vsatis the volume of the stationary phase. Figures 5-8 show the calculated retention surfaces for the oxoanions studied in this work. These well demonstrate the common effect of the concentration and pH of the eluent. The former can be easily interpreted by using eq 3. The effect of pH is based on the change in the concentrations of the eluent components. Since pH applied in the separation was varied in the range 9.1-11.5, the decrease in the molar fraction of HC03- in the eluent 440 Analytical Chemistry, Vol. 67, No. 2, January 15, 1995

is more than 20 times upon increasing the pH, Le., the ratio [C032-]/[HC03-] is 250 times higher at pH 11.5 than at pH 9.1. Besides, [OH-] also increases several orders of magnitude; thus it reaches the concentration range of the other two eluent ions. This situation is well-demonstrated in Figures 7 and 8. The dramatic change in the concentrationsof the eluent components as a function of pH results in a significant change in the retention volumes. The chromatograms in Figures 1and 2 belong to the same eluent concentration ([HC03-] + [C032-l = 2 mM) but different pH values (9.62 and 11.5). The range of the retention volumes at the higher pH is about 3 times smaller than that at the lower pH. This effect can be attributed to the stronger eluent power, i.e., higher selectivity constants, of C02- and/or OH- than that of HC03-. Since the selectivity constants of HC03- and OHare rather close (see Table 2), the change in the [C032-1/[HC03-l ratio is the main reason for this effect. The increase of [C032-] diminishes all three terms in eq 25, because it is found exclusively in the denominators. A further consequence of this is that the distribution coefficients, and thus the retention volumes for the di- and trivalent ions, decrease faster (because of the powers of 2 and 3) than those for monovalent ions with increasing pH. Comparing the ratios of the net retention volumes (reduced by Vo, see water dip) in F i r e s 1 and 2, they are about 2 for the monovalent and 4 for the divalent ions. As a consequence of this, even the order of the separated ions can be changed, e.g., !+2032-, which is the next to the last to elute at pH 9.62, is eluted before Br- and C103- at pH 11.5. As is demonstrated in Figure 7, HSeO3exists at pH below 10, and it markedly affects the retention surface

3

$

s

2 1

0

0.5 1 1.5 2 LOG k’ MEASURED Figure 9. Relationship of measured and calculatedcapacity factors for oxoanions eluted with carbonate buffer (slope, 0.986 f 0.007; correlaton coefficient, 0.996for 147 data pairs). -0.5

Figure 8. Calculated retention surface for phosphate ions eluted with HC03--C0a2- buffer (C = [HCOs-] [C032-]). Partial molar fractions of HC03- and C032- (together with the OH- concentration) in HC03--CO3*- buffer and those of phosphates are also illustrated as functions of pH.

+

only at pH below 9. A more pronounced pH effect can be observed on analysis of phosphate ( F i i r e s 3 and 4). In this case, however, the change in the elution order is reversed, namely at pH 10.58, phosphate eluted before SO+- and Sod2-,while at pH 11.5, its peak was the last one. This phenomenon is in accordance with Figure 8, which shows a concave surface, i.e., the log k’ vs pH functions (at different eluent concentrations) have their minima in the range 10.3-10.7. This is the consequence of the difference between the protonation constants of Cos2- and Pod3-. The capacity factor of phosphate and thus its retention volume steadily decrease, as the partial mole fraction of C032-, which is the strongest eluent component,increases with increasing pH values (up to ca. 10.3-10.5). In this range the mole fraction of Pod3- is not signifmnt (less than 6%),while that of Cos2- reaches about 80%. Upon increasing the pH to 11.5, the relative change in the

0

carbonate concentration ([C032-]) is rather low (from 80%to 97%), while that for Pod3- increases by more than 5fold (from 7%to 38%), as is demonstrated in Figure 8. Since the latter ion (being trivalent) has an extremely high selectivity coefficient (see Table 2), k’ and thus the retention volume steadily increase in this range with increasing pH values. These examples also confirm the reliability and applicability of the proposed model both for prediction and for interpretation of retention behavior of halide anions and oxoanions in ionexchange chromatographic separation with carbonate eluent. This conclusion is also supported by the good agreement between the measured and calculated capacity factors for all the oxoanions in this study (Figure 9). The slope of the log k’dc vs log k’,,, function is 0.986 f 0.007. The correlation coefficient calculated for the 147 data pairs is 0.996. It is clear from the above discussion that, although not all physicochemical aspects are included in our model, it contains a useful methodology by a phenomenological description. ACKNOWLEDGMENT Financial support from the Hungarian National Science Foundation (Grant No. OTKA-2562) is gratefully acknowledged. V.D. thanks Prof. Dr. J. F. K Huber (University of Vienna) for making all of his facilities available for a part of the experimental work. O.H. is indebted to the Alexander von Humboldt Foundation for the book donation helping the software development. Received for review July 29, 1994. Accepted October 24, 1994.a AC940749Q @

Abstract published in Advance ACS Abstracts, November 15, 1994.

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