Retention of Ionizable Compounds on HPLC. pH Scale in Methanol

Oct 15, 1996 - The chromatographic retention of any solute can be thus related to the real pH value of the mobile phase used. This procedure is more r...
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Anal. Chem. 1996, 68, 3651-3657

Retention of Ionizable Compounds on HPLC. pH Scale in Methanol-Water and the pK and pH Values of Buffers Elisabeth Bosch,* Pilar Bou, Hille Allemann, and Martı´ Rose´s*

Departament de Quı´mica Analı´tica, Universitat de Barcelona, Diagonal 647, 08028 Barcelona, Spain

Several properties of methanol-water mixtures (molar volume, molar refractivity, Debye-Hu1 ckel parameters, pH scale, HPLC-useful pH range, dissociation constants of acids) are studied. Some macroscopic properties are used to calculate the extent of the methanol-water interaction. Solute properties, such as pKa values, depend on the preferential solvation of the solute by the three solvents that coexist in the mixture (methanol, water, methanol-water aggregrates). Based on this preferential solvation and on the methanol-water interaction, equations that relate the pKa values of acids with the solvent composition are derived. The equations are applied to several acids widely used to prepare HPLC buffers. The pKa of an acid and the pH of a buffered solution at any methanol-water composition can be easily calculated from the proposed equations. The chromatographic retention of any solute can be thus related to the real pH value of the mobile phase used. This procedure is more rigorous and should give better results than the usual method of relating the retention to the pH value of the aqueous buffer before mixing it with methanol. The acid-base equilibria in nonaqueous and mixed solvents have been a constant subject of study this century.1-6 During the last decades, the pH scales of many solvents have been established, the pK values of many compounds measured, and the pH of many buffered solutions determined. Nowadays, knowledge of the acid-base behavior in solution allows one to achieve complete and effective pH standardization in almost any solvent of analytical interest. Nevertheless, pH standardization in the solvent used is often not performed in some widespread analytical applications. In particular, the pH of the mobile phases used in liquid chromatography is taken, calculated, and measured as aqueous pH, although water alone is almost never used as an HPLC mobile phase. It may be argued that some of the most used HPLC mobile phases (acetonitrile-water, tetrahydrofuran-water, 2-propanolwater) have not been adequately studied because their analytical (1) Kolthoff, I. M., Elving, P. J., Eds. Treatise on Analytical Chemistry; Wiley: New York, 1959; Vol. 1, Part I. (2) Kolthoff, I. M., Elving, P. J., Eds. Treatise on Analytical Chemistry, 2nd ed.; Wiley: New York, 1979; Vol. 2, Part I. (3) Bates, R. G. Determination of pHsTheory and Practice, 2nd ed.; Wiley: New York, 1954. (4) Serjeant, E. P. Potentiometry and Potentiometric Titrations; Wiley: New York, 1984. (5) Safarik, L.; Stransky, Z. Titrimetric Analysis in Organic Solvents; Wilson and Wilson’s Comprehensive Analytical Chemistry, XXII; Elsevier: Amsterdam, 1986. (6) Rose´s, M. Anal. Chim. Acta 1994, 285, 391-399, and references cited therein. S0003-2700(96)00104-7 CCC: $12.00

© 1996 American Chemical Society

interest is as recent as their use in HPLC. However, several authors have reported acid-base studies in these mixed solvents7-14 that can be used for pH standardization. The argument also fails for methanol-water, by far the most used HPLC mobile phase together with acetonitrile-water. The acid-base behavior in methanol-water mixtures has been studied for a long time.15 It is likely the most studied binary system, its acid-base properties are well known, and the acidity or basicity constants of a host of compounds have been determined for many solvent compositions.16 In this paper we investigate several properties (molar volume, molar refractivity, autoprotolysis) of methanol-water mixtures that depend on methanol-water interactions. These affect on one hand, the pH scale of the medium, and on the other, the solvation of solutes by the mixed solvent. These two factors have a strong influence on the pKa values of solutes and, therefore, on the retention of ionizable solutes in reversed phase liquid chromatography. From the interaction constant, determined from the macroscopic properties of methanol-water, we derive an equation (similar to the previously used for 2-propanol-water)14 that relates the pKa values of acids in methanol-water with the solvent composition. The parameters of the equations have been determined for the acids most used to prepare pH-buffered mobile phases from literature pKa data. With the proposed equation and parameters, the calculation of the pKa value (or values) of the acid for any methanol-water composition is straightforward. Then, the pH value of the methanol-water mobile phase used can be easily calculated from the pK values and the concentrations of the acid and the conjugated base mixed. This procedure is much simpler than the potentiometric measurement of the pH value on the binary solvent used. In fact, it is even easier than the usual procedure of measuring the pH value of the aqueous buffer before the mixing with the organic modifier and is indeed much more rigorous. It is well known that the dissociation of electrolytes in binary solvents depends strongly on their preferential solvation, (7) Mussini, T.; Longhi, P.; Rondinini, S; Tettamanti, M. Anal. Chim. Acta 1985, 174, 331-337. (8) Rondinini, S.; Nese, A. Electrochim. Acta 1987, 32, 1499-1505. (9) Rondinini, S.; Longhi, P.; Mussini, P. R.; Nese, A.; Pozzi, M.; Tiella, G. Anal. Chim. Acta 1988, 207, 211-223. (10) Barbosa, J.; Sanz-Nebot, V. Anal. Chim. Acta 1993, 283, 320-325. (11) Barbosa, J.; Beltra´n, J. L.; Sanz-Nebot, V. Anal. Chim. Acta 1994, 288, 271278. (12) Niazi, M. S. K.; Hassan, A.; Khan, M. Z. I.; Shah, S. S.; Ali, J. J. Chem. Eng. Data 1992, 37, 470-473. (13) Niazi, M. S. K.; Khan, M. Z. I.; J. Solution Chem. 1993, 22, 437-456. (14) Bosch, E.; Ra`fols, C.; Rose´s, M. Anal. Chim. Acta 1995, 302, 109-119. (15) Mizutani, M. Z. Phys. Chem. 1925, 118, 318-327. (16) Palm, V., Ed. Tables of Rate and Equilibrium Constants of Heterolytic Organic Reactions; Viniti: Moscow, 1975-1976; Supplements, Tartu (Estonia), 19841985.

Analytical Chemistry, Vol. 68, No. 20, October 15, 1996 3651

and this is different for each solute.14,17 Therefore, the variation between the HPLC mobile phase and pure water pK values of the acid used to prepare the buffer and the chromatographied ionizable solute is different. The use of the pH value in the mobile phase used instead of the pH value in water should give better fits of the retention of the solute to the pH variation models proposed, as will be shown in part 2 of this series. METHANOL-WATER INTERACTIONS The methanol-water system is not really a binary system. Methanol and water interact by hydrogen bonding to form structures different from the ones of pure water or methanol. Therefore, the system must be considered at least ternary (methanol, water, methanol-water). For 2-propanol-water mixtures,14 we have proposed an interaction model that can be also applied to the similar methanolwater mixtures. The two solvents mixed, represented by S1 and S2 (water and alcohol, respectively), interact to form a mixed structure S12 (or alcohol-water solvent) according to the equilibrium

S1 + S2 a 2 S12

KfS12 ) x212/x1x2

(1)

where KfS12 is the formation constant of the methanol-water solvent in the mole fraction scale and x1, x2, and x12, are the mole fractions of the three solvents that may coexist in the mixture. In this approach, water-alcohol mixtures are regarded as systems where two types of molecules (water and alcohol) interact to from three different structures (S1, S2, S12). Thus, the solvent is composed of clusters of water (S1), alcohol (S2), and wateralcohol (S12), which are in equilibrium. The water and alcohol clusters have molecular properties (molar volume, molar refractivity, etc.) equal to those of pure water or alcohol, respectively. But, when water interacts with the alcohol through hydrogen bonding, a new structure (S12) with properties different from those of water or alcohol is formed. When water is mixed with many alcohols, a volume contraction is observed because the new structure formed is more dense than the simple average of the water and alcohol structures. The number 2 on the right-hand side of equilibrium 1 is to keep the number of solvent molecules constant, because this number does not change when the alcohol is mixed with water. Only a new structure is formed, but not new molecules. The mole fractions in equilibrium can be related to the initial mole fractions of solvents 1 and 2 mixed (x01 and x02) according to

x01 ) x1 + x12/2

(2)

x02 ) x2 + x12/2

(3)

x01 + x02 ) x1 + x2 + x12 ) 1

(4)

The mole fraction of the mixed solvent S12 can be calculated by (17) Marcus, Y. Ion Solvation; Wiley: New York, 1985.

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Analytical Chemistry, Vol. 68, No. 20, October 15, 1996

x12 ) k - xk2 - 4kx02 (1 - x02)

(5)

where k is a constant depending on KfS12

k ) KfS12/(KfS12 - 4)

(6)

The equilibrium for formation of the methanol-water solvent can be expressed in terms different from those of equilibrium 1. Katz et al.18,19 have proposed an equilibrium of the type

S1 + S2 a S12 that they applied19 to the study and comparison of the solventsolvent interactions in the most important HPLC mobile phases (methanol-water, acetonitrile-water, tetrahydrofuran-water). However, if the number of moles on both sides of the equilibrium is not the same, the resulting expression is more complex. If the model is then applied to the preferential solvation of solutes (as we did for pKa values in 2-propanol-water and will do here in methanol-water), the final expression becomes too complex to be easily solved. Although the constant values obtained for the two equilibrium can be quite different, they lead to very similar solvent compositions, as it will be shown later (Figure 1). The interaction constant KfS12 can be evaluated from some properties of the solvent mixtures. For an additive property (Y)

Y ) x1Y1 + x2Y2 + x12Y12

(7)

and replacing the preceding expressions and rearranging terms

Y ) Y1 + (Y2 - Y1)x02 + Y12(k - xk2 - 4kx02 (1 - x02))

(8)

The equation shows that the observed property is a function of the properties of the three “pure” solvents (Y1, Y2, Y12), the interaction constant (KfS12 or k), and the solvent composition (x02). All these parameters can be evaluated by nonlinear regression from the measured Y values. However, the property used to calculate the interaction constant has to be additive or transformed to an additive property. So, density (d) or refractive index (n) are not additive, but molar volume (VM) or molar refractivity (RM) are. A further requirement for the property is that it must be a solvent property. Equation 8 cannot be applied to solute properties (e.g., pKa) because these are subject to preferential solvation. Katz and Scott18,19 determined the constant of the equilibrium they proposed from volume change on mixing, density, and refractive index data. We have used the data for the same properties transformed to molar volume and molar refractivity to estimate the value of the constant of equilibrium 1. The results obtained are presented in Table 1. The molar properties of the associated methanol-water are intermediate between those of methanol and water. The molar refractivity of the associate is practically equal to the average of the molar refractivities of methanol and water. The molar volume is slightly lower than (18) Katz, E. D.; Ogan, K.; Scott; R. P. W. J. Chromatogr. 1986, 352, 67-90. (19) Katz, E. D.; Lochmu ¨ ller, C. H.; Scott; R. P. W. Anal. Chem. 1989, 61, 349355. (20) Arroyo, A. Rev. Roum. Chim. 1990, 35, 523-533.

Table 1. Parameters for Macroscopic Properties of Methanol-Water property

Y1

Y2

Y12

log KfS12

SD

N

T (°C)

ref

molar volume molar volume molar refractivity A Ba0

18.107 ( 0.002 18.071 ( 0.005 3.710 ( 0.001 0.53 ( 0.02 1.50 ( 0.01

40.713 ( 0.027 40.489 ( 0.011 8.231 ( 0.003 1.87 ( 0.02 2.31 ( 0.01

27.561 ( 0.130 27.430 ( 0.038 5.948 ( 0.008 0.83 ( 0.03 1.85 ( 0.01

0.809 ( 0.147 0.795 ( 0.044 0.840 ( 0.817 0.8 0.8

0.046 0.014 0.003 0.02 0.01

33 44 44 11 11

25 23 23 25 25

18, 19 20 20 3 3

Table 2. Macroscopic Properties and Composition of Methanol-Water Mixtures % MeOHa

0 b xMeOH

xMeOH-H2O

% MeOH-H2Oa (% S12)

VM

RM

d

n

A

Ba0

pKap

silica columns pH range

0 10 20 30 40 50 60 70 80 90 100

0.000 0.047 0.100 0.160 0.229 0.308 0.400 0.509 0.640 0.800 1.000

0.000 0.090 0.183 0.275 0.363 0.442 0.500 0.521 0.479 0.328 0.000

0.0 13.1 25.1 31.7 44.3 50.2 52.5 50.1 41.6 25.4 0.0

18.11 19.01 20.03 21.22 22.61 24.25 26.23 28.65 31.69 35.58 40.71

3.714 3.925 4.162 4.431 4.739 5.094 5.510 6.002 6.594 7.320 8.230

0.9948 0.9826 0.9693 0.9548 0.9388 0.9209 0.9008 0.8780 0.8518 0.8216 0.7870

1.3319 1.3344 1.3367 1.3386 1.3400 1.3408 1.3408 1.3398 1.3373 1.3330 1.3267

0.530 0.560 0.596 0.643 0.702 0.779 0.881 1.019 1.211 1.481 1.870

1.500 1.533 1.571 1.615 1.665 1.725 1.797 1.884 1.992 2.130 2.310

14.00 14.08 14.08 14.07 14.09 14.14 14.23 14.39 14.63 15.04 16.77

1-8.0 1-8.1 1-8.1 1-8.1 1-8.1 1-8.1 1-8.2 1-8.4 1-8.6 1-9.0 1-10.8

a All percentages in volume. b Calculated by x MeOH ) VM(H2O)(% MeOH)/[(VM(H2O)(% MeOH) + VM(MeOH)(% H2O)] ) % MeOH/[% MeOH + 2.25(100 - % MeOH)].

nonaqueous and mixed solvents have dielectric constants lower than that of water, and the ionic activity coefficients (y) should be considered. The Debye-Hu¨ckel equation is often used in these media:

log y ) -

Az2xI 1 + Ba0xI

(9)

where z is the charge of the ion, I is the ionic strength of the solution, and A and B are the Debye-Hu¨ckel parameters, which can be calculated from the equations

A ) (1.8246 × 106)/(T)3/2

(10)

B ) 50.29/(T)1/2

(11)

Figure 1. Composition of methanol-water mixtures.

the average; log KfS12 values close to 0.8 have been obtained from the different properties, and this value has been used in all the further calculations. The most important methanol-water properties calculated from this value are presented in Table 2 for volume percentages. The value of the interaction constant is quite high, and it reflects a strong interaction between methanol and water. Therefore, methanol-water is in fact a ternary solvent, as can be observed in Figure 1, where the volumetric composition of methanol-water mixtures is represented. The values obtained by Katz and Scott are different from those of Table 1 because they used a different interaction equilibrium. The value of the constant is specially different because they expressed it in molarity, and we express it in mole fraction. However, the composition of methanol-water in Figure 1, obtained from our constant and model, matches very well the compositions obtained by Katz and Scott with their constant and model.18,19 The constant obtained can be used to fit properties not strictly additive to the solvent composition by the proposed model. Many

Since the Bates-Guggenheim convention assigns a constant value of 4.56 Å to the a0 parameter,3,4 we have fitted the A and Ba0 parameters to the model proposed. The results given in Table 1 allow an easy estimation of the activity coefficient for any methanol-water composition and simplify the calculation of pH values. A and Ba0 values for some common particular methanolwater compositions are also directly given in Table 2. PREFERENTIAL SOLVATION OF SOLUTES IN MIXED SOLVENTS The model proposed for macroscopic properties can be applied to dissociation constants of acids with some modification. When a solute is solved in a mixed solvent, it interacts to a different degree with the solvents of the mixture, and thus, it is preferentially solvated by some of them. In other words, the solvent composition on the microsphere of solvation of the solute is different from the composition of the bulk solvent. We have defined14 preferential solvation parameters (f2/1, f12/1, etc.) that relate the proportion of mole fractions in the microsphere Analytical Chemistry, Vol. 68, No. 20, October 15, 1996

3653

of solvation (xS) with the proportion of mole fractions in the bulk solvent (x).

f2/1 )

xS2 /xS1 x2/x1

(12)

f12/1 )

xS12/xS1 x12/x1

(13)

These preferential solvation parameters are also equivalent to the constants of the solvent exchange processes

A(S1) + S2 a A(S2) + S1 A(S1) + S12 a A(S12) + S1 where A(S1), A(S2), and A(S12) indicate the solute (A) solvated by water (S1), methanol (S2), and associated methanol-water (S12), respectively. Acidity pK values are proportional to ∆G°, which can be considered additive, and an equation similar to eq 7, but considering the composition of the solvation sphere, can be written for pK

pK ) xS1 pK(S1) + xS2 pK(S2) + xS12pK(S12)

(14)

where pK(S1), pK(S2), and pK(S12) are the pK values of the solute in water, methanol, and methanol-water, respectively. Putting eqs 12, 13, and 2-5 into eq 14 gives14

pK ) pK(S1) +

ax02 + c[k - xk2 - 4k(1 - x02)x02] 1 + bx02 + d[k - xk2 - 4k(1 - x02)x02] (15)

a ) f2/1(pK(S2) - pK(S1))

(16)

b ) f2/1 - 1

(17)

c ) f12/1(pK(S12) - pK(S1)) d ) f12/1 -

f2/1(pK(S2) - pK(S1)) 2

(1 + f2/1) 2

(18)

(19)

It can be easily observed that if

f12/1 ) (1 + f2/1)/2 pK(S12) )

pK(S1) + f2/1pK(S2) 1 + f2/1

(20) (21)

the c and d terms become zero, and eq 15 is simplified to

pK ) pK(S1) + ax02/(1 + bx02)

(22)

It has been also demonstrated14 that if KfS12 is high enough, eq 15 can be simplified to two different equations (eq 22), one applicable for x02 e 0.5 and the other for x02 g 0.5. 3654

Analytical Chemistry, Vol. 68, No. 20, October 15, 1996

Equations 15 and 22 allow calculation of the pK value of an electrolyte in a binary solvent if the appropriate parameters are known. Equation 15 has been already checked for the pKa values of some acids in 2-propanol-water.14 Equation 22 has been tested for some dissociation pK values in tert-butyl alcohol-cosolvent mixtures21 and for polarity ET(30) values in a variety of binary systems.22 Both equations will be used here to fit the pKa values of several acids used to prepare HPLC buffered solutions in methanol-water. DISSOCIATION OF ACIDS IN METHANOL-WATER The proposed equations have been applied to the available literature data on pKa values of the acids most employed to prepare HPLC buffers. Literature data on pKa values of phosphoric, citric, succinic, formic, acetic, trichloroacetic, and ammonium acids have been analyzed and the results are given in Table 3. The pKa values of some acids (citric, succinic, and pKa2 of phosphoric) covered up to ∼50% of methanol only (in volume), and they can be fitted to the simplified eq 22. The lack of pKa data for these solutes in methanol-rich mixtures restricts the applicability range of the parameters to 50-60% methanol approximately, although we have obtained acceptable results even for 80% methanol. Of course, the determination of some pKa values of these solutes in methanolrich mixtures would improve the accuracy of the estimations. This is not so easy because of the limited solubility of the inorganic salts in methanol-rich mixtures. For formic, acetic, trichloroacetic, ammonium, and the first pK of phosphoric acids, the derived parameters can be applied to the full mobile phase composition range of practical interest. Table 3 also presents the results for benzoic and anilinium acids. These two test compounds represent ionizable solutes with chromatographic retention strongly affected by the pH of the mobile phase. Benzoic acids and aniline are neutral acids and (21) Rose´s, M.; Rived, F.; Bosch, E. J. Chem. Soc., Faraday Trans. 1993, 89, 1723-1728. (22) Bosch, E.; Rose´s, M. J. Chem. Soc., Faraday Trans. 1992, 88, 3541-3546. (23) Bhattacharyya, A.; Maandal, A. K.; Lahiri S. C. Electrochim. Acta 1980, 25, 559-561. (24) Ender, F.; Teltschik, W.; Scha¨fer, K. Z. Elektrochem. 1957, 61, 775-781. (25) Paabo, M.; Robinson, R. A.; Bates, R. G. J. Am. Chem. Soc. 1965, 87, 415418. (26) Bates, R. G.; Pinching, G. D. J. Am. Chem. Soc. 1949, 71, 1274-1283. (27) Papanastasiou, G.; Ziogas, I. Talanta 1989, 36, 977-983. (28) Voznˇakova, Z.; Strafelda, F. Collect. Czech. Chem. Commun. 1971, 36, 29933003. (29) Papanastasiou, G.; Stalidis, G.; Jannakoudakis, D. Bull. Soc. Chim. Fr. 1984, 255-259. (30) Tabagua, I. D. Tr. Sukhumsk. Gos. Ped. Inst. 1962, 119-133; Chem. Abstr. 1964, 60, 14373d. (31) Tabagua, I. D. Zh. Fiz. Khim. 1963, 37, 1545-1548. (32) Juriaado, T.; Palm, V. Reakts. Sposobn. Org. Soedin. 1975, 12, 123-131; Chem. Abstr. 1976, 85, 32281p. (33) Shedlovsky, T.; Kay, R. L. J. Phys. Chem. 1956, 60, 151-155. (34) Douheret, G. Bull. Soc. Chim. Fr. 1967, 1412-1419. (35) Ong, K. C.; Robinson, R. A.; Bates R. G. Anal. Chem. 1964, 36, 19711972. (36) Bacarella, A. L.; Grunwald, E.; Marshall, H. P.; Purlee, E. L. J. Phys. Chem. 1958, 62, 856-857. (37) Niazi, M. S. K. Bull. Chem. Soc. Jpn. 1989, 62, 1253-1257. (38) Juillard, J. Bull. Soc. Chim. Fr. 1964, 3069-3071. (39) Juillard, J.; Simonet N. Bull. Soc. Chim. Fr. 1968, 1883-1899. (40) Bacarella, A. L.; Marshall, H. P.; Purlee, E. L.; Grunwald, E. J. Org. Chem. 1955, 20, 747-762. (41) Afanas’ev, V. N.; Shormanov, V. A.; Krestov, G. A. Tr. Ivanov. Khim.-Tekhnol. Inst. 1972, 36-39; Chem. Abstr. 1973, 78, 164978m. (42) Paabo, M.; Bates, R. G.; Robinson, R. A. J. Phys. Chem. 1966, 70, 247-251. (43) Kolthoff, I. M.; Guss, L. S. J. Am. Chem. Soc., 1938, 60, 2516-2522. (44) Goodhue, L. A.; Hixon, R. M. J. Am. Chem. Soc. 1934, 56, 1329-1333.

Table 3. Parameters for Dissociation of Acids in Methanol-Water range studied acid phosphoric pKa1 pKa2 citric pKa1 pKa2 pKa3 succinic pKa1 pKa2 trichloroacetic formic acetic benzoic anilinium ammonium a

N

SD

xMeOH

% MeOH

pK(50%MeOH)

10 6

0.03 0.02

0-0.8 0-0.4

0-90 0-56

3.21 8.24

1.10 1.05

23 24, 25

0.224 0.308 0.471

6 6 6

0.01 0.02 0.01

0-0.3 0-0.3 0-0.3

0-48 0-48 0-48

3.98 5.70 7.59

0.85 0.92 1.20

16, 26-28 16, 26-28 16, 26-28

0.502 0.319 -0.641 -0.878 -0.859 -0.859 -0.874 -0.953

6 7 9 12 56 36 16 16

0.02 0.03 0.16 0.04 0.05 0.08 0.05 0.04

0-0.3 0-0.3 0-1.0 0-1.0 0-1.0 0-1.0 0-1.0 0-1.0

0-48 0-48 0-100 0-99 0-100 0-100 0-100 0-100

5.00 6.71 1.61 4.35 5.54 5.23 4.23 8.76

0.80 1.11 0.96 0.62 0.77 1.04 -0.37 -0.48

pK(H2O)

a

b

c

2.11 7.19

27.0 3.13

6.67 -0.279

-9.54

3.13 4.78 6.39

2.95 3.29 4.47

4.20 5.60 0.65 3.73 4.77 4.19 4.60 9.24

3.00 3.95 1.53 0.549 0.68 0.731 0.152 0.073

0.807 0.597 0.907 1.403 -0.650 -0.957

d 0.971

0.176 -0.021 0.139 0.235 -0.099 0.385

∆pKa

ref

16, 29 16, 29 16, 30-32 16, 28 16, 28, 29, 33-36 28, 37-40 16, 34, 40 16, 41-44

pK ) pK(50%MeOH) - pK(H2O).

Figure 2. Variation of pKa values of polyprotic acids with the methanol-water composition: (b) pKa1 of phosphoric acid, (3) pKa1 of citric acid, (9) pKa1 of succinic acid, ()) pKa2 of citric acid, (0) pKa2 of succinic acid, (4) pKa3 of citric acid, and (O) pKa2 of phosphoric acid. Symbols are experimental data, and the lines are computed by eq 15 from the parameters of Table 3.

base, respectively, with aqueous pKa values inside the usual HPLC pH ranges. The variation in the pK values of the acids with the solvent composition is presented in Figures 2 and 3. This variation is different for each acid, although the pKa values increase when the methanol content increases, except for anilinium and ammonium. This behavior can be explained from the different nature of the acids. Dissociation of neutral acids in methanol-water is ruled by electrostatic interactions, and also specific solute-solvent interactions (solvation effects). In the dissociation of neutral or anionic acids, charges are created (HA a H+ + A- or HAn- a H+ + A(n+1)-), and the dissociation process is disturbed when the dielectric constant of the medium decreases with the increase in methanol content. Therefore, the pKa values of these acids increase when the methanol content increases. However, in the dissociation of a cationic acid (such as anilinium and ammonium ions), there is no change in the number of charges (HAn+ a H+ + HA(n-1)+) and the change in the dielectric constant of the medium does not affect the dissociation

Figure 3. Variation of pKa values of acids with the methanol-water composition: (O) trichloroacetic acid, (4) formic acid, ()) benzoic acid, (0) acetic acid, (9) anilinium, and (b) ammonium. Symbols are experimental data, and the lines are computed by eq 15 from the parameters of Table 3.

process. In this instance, the dissociation depends only on the solvation of the different species by the three solvents of the mixture (water, methanol, methanol-water). The pK(S12) values are lower than the average of pK(S1) and pK(S2), and this fact shows that solvation by the methanol-water solvent favors dissociation of the acids. For neutral and anionic acids, the electrostatic interactions overwhelm the specific solvation and the pKa value increases with the percentage of methanol. However, for the cationic acids, the decrease of the pKa value by solvation by methanol-water is not balanced by the change on the dielectric constant, and the pKa value decreases with the formation of the methanol-water complex at intermediate methanol compositions. Since anilinium and ammonium are preferentially solvated by water, the minimum of the pKa value (Figure 3) is not observed at the maximum of methanol-water (Figure 1), but at lower water concentrations. The result is a minimum in pKa values observed at 80-90% methanol in volume. Because the electrostatic and solvation effects depend on many different solute properties (charge, volume, polarity, hydrogen bond abilities, etc.), the variation of the dissociation constant with Analytical Chemistry, Vol. 68, No. 20, October 15, 1996

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the solvent composition must be different for each acid. Table 3 presents the pKa values of the studied acids in pure water and in 50% methanol (in volume). The variation in pKa (∆pKa) is different for each acid, ranging from -0.48 for ammonium to 1.20 for the third dissociation of citric acid. For example, we can deduce from Figure 3 that aniline must be protonated in a formic-formate buffer at water-rich mixtures. Therefore, it must be poorly retained when it is chromatographed in this buffer in a waterrich mobile phase. However, if the same buffer is used in a methanol-rich mobile phase, aniline must be relatively quite retained because it is poorly protonated in this medium. This example shows that the use of the aqueous pH value, instead of the pH value in the mobile phase used, can lead to erroneous conclusions that may not agree with the experimental results. The use of the true pH value must give a better agreement between the expected and the observed HPLC results. The true pH of the mobile phase can be easily calculated by the proposed equations and the data of Table 3. First, eq 15 is used to estimate the pKa value of the acid in the methanol-water mixture used as mobile phase. And second, the pH value of the buffer is calculated from the pKa value and the concentrations of the acid and conjugated base mixed. Because methanol has good hydrogen bond properties and a relative high dielectric constant ( ≈ 32), homoconjugation, heteroconjugation, and ion pair formation in methanol-water mixtures can be neglected at the usual working range of concentration (except perhaps for ionpair chromatography). In this instance, the acid-base equilibria in methanol-water are similar to the acid-base equilibria in water and the same procedures can be used to calculate the pH of a solution. However, the activity coefficients should be considered because of the lower dielectric constant of the medium (eqs 10 and 11). pH SCALE IN METHANOL-WATER AND USEFUL pH RANGE FOR HPLC The pH scale of any amphiprotic solvent (pure or mixed) is the pH range limited by the zero and pKap values,2,45 where Kap is the autoprotolysis constant of the medium. In a binary solvent, namely, methanol-water, the autoprotolysis is defined by four different proton transfer equilibria:45

Figure 4. pH scale in methanol-water and useful pH ranges for different material-based HPLC columns.

refers to the hydrogen ion solvated by either water or methanol, and S- to the hydroxide or methanolate ions. It must be noted that, in the above equilibria, methanol-water is considered a binary system rather than a ternary system as it has been considered in the Methanol-Water Interactions section. This contradiction is only apparent because methanol-water is a system with three solvent structures (S1, S2, and S12) but only two types of molecules (MeOH, H2O). The properties studied in the previous sections depend on solvent structure, but autoprotolysis depends on proton transfer between individual methanol and water molecules. Therefore, for autoprotolysis, methanolwater is in fact a binary system. We have derived equations45 that relate the pKap values of binary solvents with the composition. For methanol-water mixtures the equation is

Kap ) 10-(14.00xH2O+20.82xMeOH)x2H2O + 2 10-(12.98xH2O+14.56xMeOH)xH2OxMeOH + 10-16.77xMeOH (24)

In this equation, a and y stand for activity and ionic molar activity coefficient, respectively, of the subscripted species. According to the usual convention in aqueous binary solvents, H+

This equation defines the pH scale in methanol-water for any solvent composition. The pH scale is presented in Figure 4 for the whole range of solvent compositions and in Table 2 for some selected compositions (at 10% volume intervals). The pKap value of the mixtures increases slightly from pure water to 10% methanol and then keeps almost constant up to 40% methanol. For higher contents of methanol, the pKap value increase is steeper, especially after 90% methanol. However, the pH range for the buffered solutions used in HPLC is more restricted than the solvent pH range. The packings of most HPLC columns are silica-based bonded phases that are unstable outside the pH range 1-8.46 Of course, this pH range refers to the pH value of the aqueous buffer and it must be properly modified if it is referred to the pH scale of the binary solvent used. At low pH values the packing is hydrolyzed by the high H+ activity. Therefore, the same limit of pH ) 1 that corresponds to aH+ ) 10-1 can be used for the whole range of methanol-water mixtures. However, the basic limit of pH ) 8 (aH+ ) 10-8 but aS- ) 10-6 for pure water) is defined by the Sactivity (much higher than the H+ activity) and the limiting pH value corresponding to this S- activity is pH ) pKap - 6.

(45) Rose´s, M.; Ra`fols, C.; Bosch, E. Anal. Chem. 1993, 65, 2294-2299.

(46) Poole, C. F.; Poole, S. K. Chromatography Today; Elsevier: Amsterdam, 1991.

H2O + H2O a H3O+ + OHH2O + MeOH a H3O+ + MeOMeOH + H2O a MeOH2+ + OHMeOH + MeOH a MeOH2+ + MeOThe autoprotolysis constant is defined as

Kap ) aH+aS- ) ([H3O+]yH3O+ + [MeOH2+]yMeOH2+) × ([OH-]yOH- + [MeO-]yMeO-) (23)

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Therefore, the useful pH on HPLC for silica-based columns is defined by the pH range from 1 to the pKap - 6 value. In pure water it corresponds to the 1-8 pH range, but in pure methanol it is 1-10.8. Figures 2-4 show these pH ranges for all the methanol-water compositions. The pKa values of the acids used to prepare the HPLC buffer should lie inside or very close to this range. Any acid or base with a pKa value much higher or lower than the limits of the pH range should not be employed as an HPLC buffer because it will attack the column in a very short time.46 However, if the feasibility of a potential buffer is checked only from the aqueous pKa value and useful pH range, once again one may arrive at wrong conclusions. For example, it is commonly believed that ammonia buffers are too basic to be used in silicabased columns, although extensive use of them in methanol-rich mixtures (80-90%) has been reported with no apparent attack of the silica column.46-55 This mobile phase is particularly useful for many basic drug separations. Figure 3 clearly shows that the pKa of ammonium is outside the useful pH range for most methanol-water compositions, but inside for methanol contents higher than 75%. On one hand, the pKa of ammonium decreases with the increase of methanol content in the 0-90% range. On the other, the useful pH range increases with the methanol content increase. Hence, a buffer with an equal concentration of ammonia and ammonium will give a pH value of 9.24 and [OH-] ) 1.7 × 10-5 in pure water, but a pH value of 8.51 and [OH-] + [MeO-] ) 3 × 10-7 in 90% methanol. That is to say, the same buffer will be 200 times less basic. The same procedure used for silica-based columns can be applied to other supports. Alumina supports are stable in the aqueous pH range 2-12,46 which corresponds to [H+] ) 10-2 and [S-] ) 10-2. In pure methanol the stable pH range will be 2-14.8. (47) Jane, I. J. Chromatogr. 1975, 111, 227-233. (48) Wheals, B. B. J. Chromatogr. 1976, 122, 85-105. (49) Achari, R. G.; Theimer, E. E. J. Chromatogr. Sci. 1977, 15, 320-321. (50) Achari, R. G.; Balridge, J. L.; Koziol, T. R.; Yu, L. J. Chromatogr. Sci. 1978, 16, 271-273. (51) Wherli, A.; Hildenbrand, J. C.; Keller, H. P.; Stampfli, R.; Frei, R. W. J. Chromatogr. 1978, 149, 199-210. (52) Atwood, J. G.; Schmidt, G. J.; Slavin, W. J. Chromatogr. 1979, 171, 109115. (53) Wheals, B. B. J. Chromatogr. 1980, 187, 65-85. (54) Smith, R. G.; Rabour, J. O. J. Chromatogr. 1989, 464, 117-123. (55) Law, B.; Chan, P. F. J. Chromatogr. 1989, 467, 267-271. (56) Tanaka, N.; Araki, M. Adv. Chromatogr. 1989, 30, 81-122.

Polymer-based columns are usually stable from pH 1 or 2 to pH 12-14 in water.46,56 This will correspond to pH values from 1-2 to 14.8-16.8 in pure methanol. The variation of the pH limits of these columns with the methanol-water composition is also presented in Figure 4. CONCLUSIONS The methanol-water mixtures used as mobile phase in many HPLC separations are in fact, at least ternary mixtures with methanol, water, and methanol-water aggregrates. Solutes solved in these mixtures are differently solvated by the three components of the mixtures and this may lead to chromatographic behaviors in methanol-rich mixtures different from those expected in water-rich mixtures. In particular, the pH value of an HPLC buffer, the dissociation constants of many ionizable solutes, and the pH scale of the medium change with the mobile phase composition to a different degree. Preferential solvation models can be applied to describe the variation of the dissociation pKa value of acids in methanol-water mixtures. Application of these models to the acids used to prepare HPLC pH buffers allows computation of the pH value of the buffer for any methanol-water mobile phase. The use of this pH value to relate the retention of ionizable solutes with the solvent properties (pH and composition) must give better results than the use of the pH value of the aqueous part of the buffer. The different variation of the pH scale of the medium and of the pKa value of ammonium ion explains why ammonium buffers can be used at high methanol compositions without signifficant attack of silica-based columns. ACKNOWLEDGMENT We thank Professor Colin F. Poole for reading the manuscript and making helpful comments. This work was supported by the DGICYT of the Spanish Government (Projects PB91-0262 and PB94-0833). The work of H. A. was supported by an EC-Tempus grant (JEP-06125), which is gratefully acknowledged. Received for review February 1, 1996. Accepted July 15, 1996.X AC960104L X

Abstract published in Advance ACS Abstracts, August 15, 1996.

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