Anal. Chem. 1999, 71, 741-746
Conductometric Detection of Anions of Weak Acids in Chemically Suppressed Ion Chromatography: Critical Point Concentrations Arety Caliamanis, Malcolm J. McCormick, and Peter D. Carpenter*
Department of Applied Chemistry, Royal Melbourne Institute of Technology, City Campus, GPO Box 2476V Melbourne, Victoria 3001, Australia
Previously we demonstrated that the conductometric determination of anions of weak acids in chemically suppressed ion chromatography could be enhanced, by conversion of the acid to a conjugate salt, if the anion was present above what we termed the critical point concentration (CPC). In this paper we have developed a simple theoretical model for the calculation of CPCs for weak acid/conjugate salt pairs. The CPC was found to be dependent on the acid ionization constant Ka and the molar ionic conductivities (MICs) of the ions present. For monovalent anions with a MIC in the common range 2575 S cm2 mol-1, with sodium or potassium as cations, the CPCs could be estimated from the expression pC ≈ pKa - 1, where pC ) -log CPC. For formate, benzoate, and acetate, excellent agreement was found between the calculated and experimental CPCs, with a mean deviation of 0.05 mM. For fluoride, the calculated and experimental CPCs were 7.4 and 9.2 mM, respectively. Experimental CPCs could not be determined for other anions as their calculated CPCs were below the detection limits of the IC system. The simple theoretical model could also be used to estimate the expected conductivity enhancement for the conversion of weak acid to a particular conjugate salt. The effects of detector linearity and dispersion in the IC system on the use of CPCs are also discussed. Ion chromatography is a well-established method for determining ion concentrations in solution and is particularly popular for anions.1 In chemically suppressed ion chromatography, anions are converted from a salt to their conjugate acid just prior to detection, which is usually conductometric.2 The conductivity of the final solution is dependent on the molar ionic conductivities and concentrations of the ions present.3 For an anion of a strong acid, the conversion results in an acid that is essentially completely ionized.3 As the replacement of any cation with hydrogen ions will result in the solution having a higher conductivity than the preceding salt solution,4 the conversion has effectively increased * To whom correspondence should be addressed. E-mail Carpenter@ RMIT.edu.au. (1) Weiss, J. Ion Chromatography, 2nd ed.; VCH: Weinheim, 1995; Chapter 1. (2) Weiss, J. Ion Chromatography, 2nd ed.; VCH: Weinheim, 1995; Chapter 6. (3) Atkins P. W. Physical Chemistry, 4th ed; Oxford University Press: Oxford, 1990; Chapter 25. (4) Weiss, J. Ion Chromatography, 2nd ed.; VCH: Weinheim, 1995; Chapter 3. 10.1021/ac9807767 CCC: $18.00 Published on Web 12/30/1998
© 1999 American Chemical Society
detector sensitivity. However, for a weak acid, the ion concentrations are dependent on the degree of ionization (R) of the acid,3 which in turn is dependent on the formal concentration and pKa of the acid.3 Hence, under conditions where the degree of ionization is high (low concentration and/or pKa3), the conversion from salt to acid will still result in a solution having a higher conductivity than the preceding salt solution and vice versa. As the degree of ionization of a weak acid decreases with increasing formal concentration,3 it is possible for a weak acid solution to show higher conductivity than the preceding salt solution at low concentrations and vice versa at higher concentrations. We have previously termed the concentration where the acid and conjugate salt solutions have the same conductivity the critical point concentration (CPC).5 Thus, chemical suppression will result in a decrease in conductivity and hence detector sensitivity for anions present above their CPCs. This problem has been recognized by several researchers who have attempted to convert the weak acids back to higher conducting salts by a variety of means.6-14 We recently trialed a novel approach to this problem, using a second micromembrane suppressor as an ion-exchange reactor (IER) to convert weak acids to salts.5,15 This approach worked well for boric acid, where converting a 5.0 mM solution of boric acid to the sodium salt produced 250- and 1400-fold increases in conductometric peak height and peak area, respectively.5,15 Knowledge of the CPC for particular acid/conjugate salt combinations is of practical importance because it allows prediction of whether the proposed conversion from acid to salt will enhance sensitivity or not in the analytical concentration range of interest. In this paper, we have developed a simple theoretical model which allows CPC values to be calculated and compared the results obtained with some experimentally determined CPCs. (5) Caliamanis, A.; McCormick, M. J.; Carpenter, P. D. Anal. Chem. 1997, 69, 3272-3276. (6) Okada, T.; Kuwamoto, T. Anal. Chem. 1985, 57, 829-833. (7) Rocklin, R. D.; Slingsby, R. W.; Pohl, C. A. J. Liq. Chromatogr. 1986, 9 (4), 757-775. (8) Tanaka, K.; Fritz, J. S. Anal. Chem. 1987, 59, 708-712. (9) Tanaka, S.; Yasue, K.; Katsura, N.; Tanno, Y.; Hashimoto, Y. Bunseki Kagaku 1988, 37, 665-670. (10) El Khatib, E. A. Z. Pflanzenernaehr. Bodenkd. 1990, 153 (3), 201-205. (11) Okada, T.; Dasgupta, P. K. Anal. Chem. 1989, 61, 548-554. (12) Berglund, I.; Dasgupta, P. K. Anal. Chem. 1991, 63, 2175-2183. (13) Berglund, I.; Dasgupta, P. K. Anal. Chem. 1992, 64, 3007-3012. (14) Berglund, I.; Dasgupta, P. K.; Lopez, J. L.; Nara, O. Anal. Chem. 1993, 65, 1192-1198. (15) Caliamanis A. B. App. Sc. (Honours) Thesis, RMIT, Melbourne, 1995.
Analytical Chemistry, Vol. 71, No. 3, February 1, 1999 741
THEORETICAL MODEL In the following treatment, the effects of water ionization and ionic strength are neglected, and activity coefficients are assumed to be unity. For a weak monoprotic acid HA which has a formal (total) concentration C (i.e. C ) [HA] + [A-]) in water, we can write
HA(aq) + H2O ) H3O+(aq) + A-(aq) O+,
[H3O+][A-] [HA]
)
C ) Ka[1 - (λM+ + λA-)/(λH+ + λA-)]/ [(λM+ + λA-)/(λH+ + λA-)]2 (10)
(1) A-
At equilibrium, the concentrations of HA, H3 and will be C - x, x, and x, respectively, so the acid ionization constant Ka is equal to3
Ka )
The CPC can also be readily calculated if we again assume that the MICs of the ions at concentrations x or C are not significantly different from those at infinite dilution.
x2 C-x
(2)
The conductivity of this solution κHA at formal concentration C will be given by
κHA ) xλH+x + xλA-x
(3)
For a diprotic acid H2A being fully reconverted to the dimetallic salt M2A, eq 2 can be used with the first acid ionization constant. An implicit and reasonable assumption here is that ionization of the monoprotic anion in a solution of the diprotic acid is negligible.16 Equation 5 becomes
xλH+x + xλHA-x ) 2CλM+2c + CλA2-c
(11)
assuming again that hydrolysis of the anion A2- is negligible. Following the steps described earlier gives
x/C ) R ) (2λM+2c + λA2-c)/(λH+x + λHA-x)
(12)
C ) Ka[1 - (2λM+2c + λA2-c)/(λH+x + λHA-x)]/ where λH+x represents the molar ionic conductivity (MIC) of hydrogen ions at concentration x (and similarly for the other λ). Similarly, the conductivity of a conjugate salt MA of the same formal concentration will be given by
κMA ) CλM+c + CλA-c
(4)
[(2λM+2c + λA2-c)/(λH+x + λHA-x)]2 (13) and, with the same assumptions as for eq 9, eq 13 becomes
C ) Ka[1 - (2λM+ + λA2-)/(λH+ + λHA-)]/ [(2λM+ + λA2-)/(λH+ + λHA-)]2 (14)
Hydrolysis of the anion A- in the salt solution is assumed to be negligible. When C is equal to the CPC, the conductivity of the two solutions will, by definition, be equal; hence, we can equate eqs 3 and 4, giving
xλH+x + xλA-x ) CλM+c + CλA-c
(5)
Rearranging eq 5 gives
x/C ) (λM+c + λA-c)/(λH+x + λA-x)
(6)
x/C ) R
(7)
where R is the degree of ionization of the weak acid at concentration3 C and hence at the CPC. The degree of ionization can be readily calculated if we assume that the MICs of the ions at concentrations x or C are not significantly different from those at infinite dilution. Rearranging eq 7 and substituting into eq 2 gives the wellknown relationship3
C ) Ka(1 - R)/R2
(8)
Thus, the CPC can be calculated provided R is known. By combining eqs 6-8, we obtain an overall expression for the CPC in terms of Ka and the MICs:
C ) Ka[1 - (λM+c + λA-c)/(λH+x + λA-x)]/ [(λM+c + λA-c)/(λH+x + λA-x)]2 (9) 742
Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
Similar equations can be derived for higher protic acids. EXPERIMENTAL SECTION Apparatus. A Dionex 4500i ion chromatograph was used with two Dionex anion micromembrane suppressors (AMMS-II, P/N 043074) placed in series just before the conductivity detector. The detector was operated with a default factor of 1.7 for the automatic temperature compensation mode. An eluent flow rate of 1.0 mL/ min was used throughout. Delta chromatography computer software (Version 5.0) was used to acquire peak heights and peak areas. Samples were filtered through 0.2-µm PTFE membrane filters (Alltech Assoc. Aust. Pty. Ltd.) into a 20-µL injection loop. Three replicate injections of each sample were made and the results averaged. Regenerant solution was forced through two micromembrane suppressors in line, under 5 psi pressure (1.2 mL/min). Conductivity measurements were carried out using an Activon model 301 conductivity meter and an Activon Cond-Probe (dip epoxy K ) 1 each 7A6L carbon plates, 10 µS-100 mS range). Three readings were taken of each solution and the results averaged. Reagents. Reagent grade water was obtained from a Milli-Q system (Millipore Corp.). All chemicals were analytical reagent grade, unless otherwise specified, and all glassware was A grade. All standard solutions, eluents, and reagents were prepared in Milli-Q water, degassed under vacuum, and filtered through 0.2µm membrane filters (PTFE) prior to use. Standard solutions (16) Harris, D. C. Quantitative Chemical Analysis, 4th ed.; W. H. Freeman & Co.: New York, 1995; Chapter 11.
Table 1. Theoretical Critical Point Concentrations Calculated from Eqs 10 and 14 for a Range of Weak Acid/Conjugate Salt Pairs salt cation acid anion
pKa19
MICID19
Li+, 38.7
FHCOOC6H5COOCH3COOHCO3CO32CNB(OH)4-
3.17 3.74 4.20 4.76 6.35 6.35 9.22 9.24
55.4 44.6b 37.2b 40.9 44.5 118.6 82.0 74.4b
2.02 2.49 2.80 3.48 5.10 6.04 8.26 8.23
Na+, 50.1
K+, 73.5
NH4+, 73.5
2.13 2.62 2.95 3.61 5.23 6.19 8.35 8.33
2.34 2.85 3.20 3.84 5.46 6.49 8.53 8.51
2.34 2.85 3.20 3.84 5.46 6.49 8.53 8.51
a The CPCs have been expressed as pC ) -log(CPC). b Molar ionic conductivities at infinite dilution of formate, benzoate, and borate were determined experimentally at 22 °C.
Table 2. Values of L Calculated from the Expression pC ) pKa - L (Eq 16) for a Range of Monovalent Anions and for the Common MICID Range of 50 ( 25 S cm2 mol-1 salt cation acid anion
MICID19
Li+
Na+
K+
NH4+
FHCOOC6H5COOCH3COOHCO3CO32CNB(OH)4-
55.4 44.6b 37.2b 40.9 44.5 118.6 82.0 74.4b
1.15 1.25 1.40 1.28 1.25 0.77 0.97 1.01
1.04 1.12 1.25 1.15 1.12 0.69 0.87 0.91
0.83 0.89 1.00 0.92 0.89 0.55 0.69 0.73
0.83 0.89 1.00 0.92 0.89 0.55 0.69 0.73
1.19
1.07
0.84
0.84
25 50 75
1.46 1.20 1.01
1.30 1.08 0.91
1.03 0.86 0.73
1.03 0.86 0.73
1.22
1.10
0.87
0.87
meanc
mean
included sodium fluoride (BDH, as dried NaF, 20 mM and 0.5 M), acetate (BDH, as crystalline CH3COONa, 2 and 10 mM), hydrogen carbonate (BDH, as NaHCO3, 2.5 mM), carbonate (BDH, as Na2CO3‚10H2O, 0.5 mM), acetic acid (BDH, as CH3COOH, 0.5 M), and hydrochloric acid (BDH, as HCl, 0.1 M). Regenerant used for the suppressors was sulfuric acid (12.5 or 50 mM). Milli-Q water was used to flush suppressors in some experiments. RESULTS AND DISCUSSION Theoretical Critical Point Concentrations. Theoretical CPC values were calculated for a range of exchange cations and monovalent anions using eq 10 and for carbonate using eq 14. The results (Table 1) show CPC values varying from 3.0 nM for ammonium cyanide up to 9.6 mM for LiF. Calculated CPCs above about 10 mM are expected to be increasing in error as assumptions made in the calculations become increasingly invalid.17 This, however, was not seen as a problem, as most analytical IC work is done at concentrations lower than 10 mM.18 Potassium, with a higher MIC, is expected to be a better cation to use for exchange than sodium, and this is reflected in the lower CPC values calculated for potassium (Table 1). The calculation of CPC values of other anions is somewhat restricted by the limited availability of MIC data. However, most of the available MIC data for monovalent anions fall within the range 50 ( 25 S cm2 mol-1,19 and this allows us to estimate the CPC range expected for anions of different Ka, even if MIC data are not known. Taking the negative logarithm of eq 10 yields
pC ) pKa - log{[1 - (λM+ + λA-)/(λH+ + λA-)]/ [(λM+ + λA-)/(λH+ + λA-)]2} (15) pC ) pKa - L
(16)
where pC represents the -log(CPC) and L is dependent on the (17) Laidler, K. J.; Meiser, J. H. Physical Chemistry, Benjamin/Cummings Pub. Co.: Menlo Park, CA, 1982; Chapter 7. (18) Weiss, J. Ion Chromatography, 2nd ed.; VCH: Weinheim, 1995; Chapter 8. (19) Alward, G. H.; Findlay, T. J. V. SI Chemical Data, 2nd ed.; Wiley Ltd.: New York, 1991.
a pC ) -log(CPC). b Molar ionic conductivities at infinite dilution of formate, benzoate, and borate were determined experimentally at 22 °C. c Means exclude values for carbonate.
MIC of the anion and exchange cation. Table 2 shows the values of L for lithium, sodium, and potassium paired with some common anions and with anions with nominal MICs of 25, 50, and 75 S cm2 mol-1. The values of L obtained for sodium and potassium with the nominal MIC anions were 1.1 ( 0.2 and 0.87 ( 0.15, respectively. Figure 1 shows eq 15 plotted for lithium, sodium, and potassium with some common anions. Although the data for each cation appear slightly curved, they fit a straight line well (r2 in each case > 0.999), with a mean slope (half-range) of 1.034(6) and an intercept of 1.2(2). Thus, as a rule of thumb, we can estimate the CPC for sodium or potassium ion exchange with a weak monoprotic acid by using the simple expression
pC ≈ pKa - 1 or
CPC ≈ 10Ka
(17) (18)
Experimental Critical Point Concentrations. The theoretical model was initially tested by measuring the conductivities of acetic acid and sodium acetate solutions over the concentration range expected to encompass the CPC. The results (Figure 2) show that the curves cross over at a formal concentration of 0.27 mM, in excellent agreement with the calculated theoretical CPC of 0.25 mM (Table 1). Even the rule-of-thumb value (0.17 mM) calculated from eq 17 was adequate for most analytical purposes. As a comparison, the IC system was then used in an attempt to determine the CPCs of several weak acids. Sodium acetate and fluoride solutions were pumped directly through two anion micromembrane suppressors (AMMS) in series and then through to the detector (i.e., the system did not have a column). The conductivities of the sodium salts were measured when using Milli-Q water as regenerant in both suppressors, while the conductivities for the acids were measured when using sulfuric acid regenerant in one or both suppressors, as shown in Table 4. It was found that 12.5 mM sulfuric acid regenerating both suppressors gave the highest conversion of the salts to their acids Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
743
Figure 1. Graph of pC ()-log CPC) versus the pKa for a range of weak acid/conjugate salt combinations (as shown in Table 1) calculated using eq 15. Lithium, 2; sodium, 9; potassium, [; (and ammonium, ×).
Figure 2. Conductivity of acetic acid (9) and sodium acetate (b) solutions as a function of formal concentration. The conductivities were measured with a conductivity meter. The crossover point corresponds to the critical point concentration (CPC). Table 3. Comparison of Experimental with Theoretical Critical Point Concentrations (mM) Calculated from Eqs 10 and 17 for a Range of Weak Acid/Sodium Salt Pairs CPC
b
acid anion
pKa19
eq 10
eq 17
exptl
method
fluoride formate benzoate acetate
3.17 3.74 4.20 4.76
7.39 2.40 1.12 0.25
6.76 1.82 0.63 0.17
9.2 2.35 1.23 0.26(7)
ICa CMb CMb CM (IC)
a Determined using the IC system and conductivity detector. Determined using the conductivity meter.
(Figure 3), while 50 mM sulfuric acid in the first or both suppressors gave marginally lower results. The results obtained for acetate with 12.5 mM sulfuric acid regenerating the first suppressor only (Figure 3a) are not consistent with the other results shown here (or the preliminary work done earlier), and this is under investigation. The CPC for acetate determined from 744 Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
Figure 3. Conductivity of (A) acetic acid and sodium acetate solutions and (B) hydrofluoric acid and sodium fluoride solutions as a function of formal concentration. Conductivities were measured by continuous pumping of the solutions through the IC system with two membrane suppressors in series. The suppressors had Milli-Q water or either 12.5 or 50 mM sulfuric acid as regenerant, as shown in Table 4.
a graph of conductivity versus concentration (Figure 4A) was 0.26 mM, which was not significantly different from the calculated value of 0.25 mM (Table 1) and the value obtained using the conductivity meter (0.27 mM). For fluoride, a CPC of 9.2 mM was determined (Figure 4B), which was ∼25% higher than the calculated value of 7.4 mM (Table 1). This difference could be due to a number of factors, including the simple nature of the theoretical model, assumptions made in the calculations,17 the neglect of aqueous species such as HF2in the model, or just the inherent uncertainty in determining the point at which two lines, constructed from experimental data and at an angle much less than 90° will intersect. Whatever the cause, the difference is not large enough to negate the usefulness of calculated CPCs to an analyst wishing to decide whether to convert weak acids to their conjugate salts in order to maximize detector sensitivity. It should be remembered that the major advantage of conversion would occur when working well above the CPC. If analysts were working within 25% of the CPC, there would be little benefit in conversion to a conjugate salt. The conductivities of the sodium fluoride solutions were significantly higher, and the plots showed much more curvature than was observed for sodium acetate, suggesting that the IC
Figure 5. Comparison of the measured conductivity of sodium fluoride solutions with formal concentration measured by using a conductivity meter (9) and by using the IC system (b) with direct pumping of the fluoride solutions.
However, for these very weak acids, it is possible to extend the theory to determine the conductivity enhancement E expected at some concentration above the CPC. If we define E as the ratio of the conductivity of a salt MA at formal concentration C to the conductivity of the weak acid HA at the same formal concentration, then by combining eqs 3 and 4, we obtain
E ) κHA/κMA ) [CλM+c + CλA-c]/[xλH+x + xλA-x]
Figure 4. Conductivity of (A) acetic acid and sodium acetate solutions and (B) hydrofluoric acid and sodium fluoride solutions as a function of formal concentration. Conductivities were measured by continuous pumping of the solutions through the IC system with two membrane suppressors in series. Both suppressors had 12.5 mM sulfuric acid as regenerant. The crossover point in each graph corresponds to the critical point concentration (CPC).
(19)
which, with the usual assumptions employed earlier, would simplify to
E ) [CλM+ + CλA-]/[xλH+ + xλA-] E ) C[λM+ + λA-]/x[λH+ + λA-]
(20)
By combining eqs 2 and 20 and assuming x , C, we obtain conductivity detector may give nonlinear responses at higher conductivities. This was tested by measuring the conductivities of sodium fluoride, acetate, and chloride solutions (over the same concentration range) with both the IC detector and a conductivity meter. The results for fluoride (Figure 5) were typical of the other anions and showed that the IC detector was far more nonlinear than the other meter. This curvature is not a reflection on the quality of the detector, which was designed to be used at lower conductivities where most analytical IC work is done.18 No attempt was made to determine experimental CPCs for acids stronger than fluoride as these would lie at concentrations above 10 mM, well above the concentrations at which most analytical IC work is done.18 Experimental CPCs for formate and benzoate, determined using the external conductivity meter, show excellent agreement with the calculated values, differing by only 0.5 and 0.1 mM, repsectively (Table 3). The calculated CPCs for the other anions listed in Table 1 are in the micromolar (e.g., hydrogen carbonate) and nanomolar (e.g., borate) range, which, despite our best efforts, remained below our IC detection limits. Hence, it was not possible to determine experimental CPCs for these anions.
E≈
C λM+ + λAKa λH+ + λA-
x
(21)
Thus, it is possible to estimate the conductivity enhancement expected at a concentration C by the conversion of the acid to a specified conjugate salt. E will, of course, be equal to 1 at the CPC. Further work in this area is continuing. The experimental results obtained by pumping the sodium salt solutions continually were then compared with results obtained when the salt solutions were injected into a system that used Milli-Q water as mobile phase to carry the solutions through two anion micromembrane suppressors (AMMS) to the detector. Again, the system did not have a column. The conductivities of salt and acid solutions were measured as described earlier (Table 4). For acetate and fluoride, the highest conductivity was again obtained when using 12.5 mM H2SO4 regenerating both suppressors, while 50 mM (first) and 50 mM (both) gave similar responses. Thus, despite the salt now passing through the suppressor in a transitory manner rather than continually as Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
745
Table 4. Set of Experiments Used to Determine Conductivity of Salt and Conjugate Acid Solutions (a) by Using Continuous Pumping of the Salt Solutions and (b) by Injection of the Salt Solutions (20 µL) into Milli-Q Water Mobile Phasea regenerant and H2SO4 concn (mM)
1 2 3 4 5
sodium salt acid form
[ 9 2 ×
suppressor 1
suppressor 2
Milli-Q 12.5 12.5 50 50
Milli-Q Milli-Q 12.5 Milli-Q 50
aIn both cases, the IC was set up without a separation column and with two anion micromembrane suppressors in series.
Figure 6. Conductivity of acetic acid (9) and sodium acetate (b) solutions as a function of formal concentration. The conductivities were measured by injection of the solutions into the IC system with two membrane suppressors in series. The mobile phase was Milli-Q water. Both suppressors had 12.5 mM sulfuric acid as regenerant.
before, the use of 12.5 mM sulfuric acid in the first suppressor only was still not sufficient to effect the same conversion to acid as was obtained using 12.5 mM H2SO4 regenerating both suppressors, or 50 mM in the first suppressor. The graphs of conductivity versus concentration for acetate (Figure 6), and similarly for fluoride, did not exhibit the expected crossover points, and hence CPCs could not be calculated. It was clear that these results were significantly different from those produced using direct conductivity measurements (Figure 2) or by continuous pumping of the salt solutions (Figure 4A). The most likely cause of these differences was dispersion of the analyte plugs between injection and detection. The dispersion of the system, estimated from the ratio of the conductivities obtained for the sodium acetate solutions from injection (Figure 6) and
746
Analytical Chemistry, Vol. 71, No. 3, February 1, 1999
continuous pumping (Figure 4a), was 90%. This compares with 20% found previously with a column present in the system.5 CONCLUSIONS A simple theoretical model has been developed for the calculation of critical point concentrations for weak acid/conjugate salt pairs. The CPC was found to be dependent on the acid ionization constant Ka and the molar ionic conductivities of hydrogen ions, the salt cation, and the anion (eqs 9 and 10). A lack of MIC data for anions limited the number of acid/conjugate salt pairs for which CPCs could be calculated. However, for anions with a MIC in the range 25-75 S cm2 mol-1, it was found that, with sodium or potassium as cations, the CPCs could be estimated from the expression pC ≈ pKa - 1 (or CPC ≈ 10Ka). For formate, benzoate, and acetate, excellent agreement was found between the calculated and experimental CPCs (Table 3), with a maximum deviation of 0.1 mM (mean 0.05 mM). For fluoride, the agreement was not as good, with a calculated CPC of 7.4 mM compared with an experimental value determined by continuous pumping of 9.2 mM. The difference could have been due to limitations in the model, or increased experimental uncertainty in the determination of the crossover point, enhanced by nonlinearity in the IC detector. The theoretical CPCs for other anions were in the nanomolar to micromolar range and could not be experimentally determined. Given the simple nature of the theory, we believe the agreement obtained is more than adequate for the proposed purpose of giving analysts an indication of the magnitude of CPCs of weak acids of interest. It should be remembered that the major advantage of converting a weak acid to its conjugate salt occurs when working with concentrations well above the CPC. If analysts were working within 25% of the CPC, there would be little benefit in converson to a conjugate salt. The model could also be used by the analyst to estimate the expected conductivity enhancement E in a particular concentration range for the conversion of weak acid to a particular conjugate salt (eq 21). Results from this study indicate that analysts would need to combine this information with knowledge of the detector linearity and dispersion in their IC system in order to have an indication as to whether the conversion from acid to salt will be an advantage for their specific application. ACKNOWLEDGMENT A.C. would like to acknowledge financial support given by an RMIT Postgraduate Research Scholarship. We thank Carolyn Toomey for her careful determination of some MICIDs. Received for review July 14, 1998. Accepted November 3, 1998. AC9807767
