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Standard pH values in non-aqueous mobile phases used in reversed-phase liquid chromatography
320
Anulytica Chimica Acta, 283 (1993) 320-325 Elsevier Science Publishers B.V., Amsterdam
Standard pH values in non-aqueous mobile phases used in reversed-phase liquid chromatography J. Barbosa and V. Sanz-Nebot Department of Analyticul Chemistry, University of Barcelona, Avda. Diagonal 647, 08028 Barcelonu (Spain) (Received 8th September 1992; revised manuscript received 28th January 1993)
Abstract Standard pH, values for three reference buffer solutions (0.05 mol kg’ potassium dihydrogencitrate; 0.1 mol I-’ acetic acid + 0.1 mol I-’ sodium acetate: 0.03043 mol kg’ disodium hydrogenphosphate + 0.008695 mol kg-’ potassium dihydrogenphosphate) in 10, 30, 40, 50 and 70% (w/w) acetonitrile-water mixtures at 298.15 K were determined from e.m.f. measurements of the reversible cell Pt/Ag/AgCl/standard buffer + KCI, in acetonitrilewater/glass electrode. In order to obtain pH, values in each of the unlimited number of possible acetonitrile-water mixtures, pH, values were correlated with mole fraction, % (w/w) and % (v/v) of acetonitrile in solvent mixtures and the methodology of linear solvation energy relationship, based on the Kamlet-Taft multiparametric scales, was applied and pH, data were correlated with rr*, a and p solvatochromic parameters of the acetonitrile-water mixtures. Keyworuk Liquid chromatography; Acetonitrile; pH; Standard pH values
Mixed aqueous-organic solvents are widely used in chemistry to enhance the reactivities, solubilities, biological absorption properties and chromatographic properties of a wide variety of chemical substances. As in aqueous solutions, the pH of the solvent will be affected by solutes and its control will often be necessary in order to obtain optimum chemical results. The solvent system chosen in this study was acetonitrile-water because of its wide use in reversed-phase liquid chromatography (RPLC). Many different methods have been devised for optimizing the selectivity of chromatographic separations [l-3]. Usually, the methods focus on the optimization of the mobile phase composition, i.e., on the concentrations of water and organic Correspondence to: J. Barbosa, Department of Analytical Chemistry, University of Barcelona, Avda. Diagonal 647,08028 Barcelona (Spain). 0003-2670/93/$06.00
solvents. However, for separating ionic or ionogenie solutes, variations in the mobile phase pH may easily lead to dramatic variations in selectivity [4]. The degree of ionization of solutes, stationary phases (e.g., ion exchangers) and mobile phase additives (e.g., ion-pairing reagents) may be affected by the pH. Hence pH is potentially a very powerful parameter for optimizing selectivity in RPLC. However, the optimization of the mobile phase pH is complicated as the problem of pH measurements in aqueous-organic mixtures has not been solved [5]. Usually, the operational pH in mixed aqueous-organic solvents is measured assuming that the mobile phase pH is the same on that of the aqueous fraction, in which case errors due to the medium effects contribute to the uncertainty in the true pH. In acetonitrile-water mixtures the influence of the co-solvent on the pH is substantial [6,7].
0 1993 - Elsevier Science Publishers B.V. All rights reserved
I. Barbosa and V: SawNebot/AnaL
From the point of view of practical chromatography, it is possible to measure the activity of the hydronium ion in mixed aqueous-organic solvents if reference pH values of standard buffer solutions in these solvents are known. The conventional electrometric technique for pH measurements is dependent on an operational definition of pH: PH, =pH,+-
321
Chim. Acta 283 (1993) 320-325
Es-Ex g
where X denotes the solution of unknown pH and S the standard reference solution of known or assigned pH, E is the electromotive force of a suitable galvanic cell consisting of an electrode reversible to hydrogen ions (usually a glass electrode) coupled with a suitable reference electrode (commonly a silver/silver chloride electrode) and g = (ln10) RT/F. The aim of this present work was the assessment of pH, values for three standard buffer solutions (citrate, acetate and phosphate buffers) in acetonitrile-water mixtures containing 10, 30, 40, 50 and 70% (w/w> acetonitrile, according to the criteria recently endorsed by IUPAC [5,8]. Also, considering the unlimited number of possible binary acetonitrile-water mixtures, relationships between pH svalues and different characteristics of the solvent mixtures were examined and the methodology of linear solvation energy relationship (USER) [g-11] were used to correlate pH, values with solvent dipolarity/ polarizability (‘rr*>, solvent hydrogen bond-donating acidity (cu) and solvent hydrogen bond-accepting basic&y (/I) 112,131.
EXPERIMENTAL
E.m.f. values were measured with a Crison 2002 potentiometer ( f 0.1 mV) using a radiometer G202C glass electrode and a reference Ag/AgCl electrode prepared according to the electrolytic method [14]. The cell was thermostated externally at 25 f O.l”C. All of the potentiometric assembly was automatically controlled with a Stronger AT microcomputer.
Reagents Analytical-reagent grade chemicals were used unless indicated otherwise. All the solutions were prepared by mixing doubly distilled, freshly boiled water and acetonitrile (Merck, chromatography grade). The concentrations of the standard reference solutions used in this work were chosen as those recommended by IUPAC [8]. The compositions of the buffer solutions prepared for standardization were as follows: 0.05 mol kg-’ potassium dihydrogencitrate (citrate buffer), 0.1 mol 1-l acetic acid + 0.1 mol 1-i sodium acetate (acetate buffer) and 0.03043 mol kg-’ disodium hydrogenphosphate + 0.008695 mol kg-’ potassium dihydrogenphosphate (phosphate buffer). Procedures Reference pH values of the standard buffer solutions in acetonitrile-water mixtures containing 10, 30, 40, 50 and 70% (w/w) acetonitrile, PI-L were assigned by using the procedure adopted by the IUPAC [5]. This procedure involves three steps. The first step is the measurement of the e.m.f. of the cell Pt/Ag/AgCl/standard
buffer
+ KC1 in acetonitrile-water/glass
electrode
(cell A) where the reference standard buffer solutions contains potassium chloride at different and accurately known concentration. The e.m.f., E, of this cell is directly related to the activities of the hydrogen ions and chloride ions in solution: E = E” + g log( aH+aCI-)
(1)
where E” is the standard e.m.f. of the cell, values of which are essential and have been determined in previous work [14]. The second step is the determination of the different pH values for each concentration of potassium chloride, ccI-, examined using the Nemst expresison of e.m.f., E, for cell A: P(an+Yei-)
= PH +wcl=[(E'-EM+PC,-
(2)
where p(a,+y,,-1 is a thermodynamic quantity that can be determined in thermodynamically ex-
322
I. Barbara and K Sam-Nebot /Ad
a temperature T = 298.15 K by an extension of the Bates-Guggenheim convention [5,8] in terms of,
act terms, but to obtain pH values for the mixed electrolyte in the cell it is essential calculate the molar activity coefficient, p_v,-, thought an extra-thermodynamic assumption, i.e., a form of the classical Debye-Hiickel equation: PYCl--=
(a,&.=
1.5[ew~s/(eSpW)J~
(4)
where E is the dielectric constant, p the density and the superscripts W and S refer to pure water and to the appropriate solvent mixture, respectively. Calculation of pyc,- through Eqn. 3 requires a
(3)
(1 + a,,1”2)
Chim. Acta 283 (1993) 320-325
In compliance with IUPAC rules [5,151, the value of the product a,B in Eqn. 3 is assigned at
TABLE 1 Measured e.m.f. values of cell A, E, molar activity coefficients of monoprotonated concentrations, cm-, in various acetonitrile-water mixtures at 298.15 K Acetonitrile concentration (o/o, w/w)
Buffer solution Citrate
Acetate
C,(mM)
E (mV)
’
10
6.7 9.9 16.2 22.2 28.1 39.1
37.3 47.6 60.6 69.1 75.4 84.4
0.799 0.795 0.789 0.784 0.779 0.769
30
9.5 15.5 21.3 26.9 34.8 42.4
18.0 30.9 39.3 45.6 52.7 58.1
40
7.7 12.6 19.6 24.0 28.3 32.5
50
5.6 10.8 17.9 22.3 28.2 33.7
70
species (y) and pH values at different KC1
3.89 4.48 5.56 6.05 6.95 7.37
PH
Phosphate pH
C,(mM)
E (mV)
’
4.902 4.901 4.898 4.895 4.893 4.892
7.4 11.1 18.3 21.8 28.8 35.7
-
180.9 170.2 156.7 151.9 144.2 138.3
0.763 0.760 0.756 0.754 0.750 0.746
7.682 7.675 7.661 7.656 7.645 7.636
0.723 0.718 0.714 0.710 0.706 0.701
5.535 5.531 5.527 5.523 5.522 5.517
7.8 11.6 22.6 33.0 39.6 49.0
-
186.8 176.3 158.4 147.8 142.6 136.4
0.730 0.727 0.719 0.713 0.709 0.704
8.137 8.130 8.110 8.092 8.081 8.066
47.5 30.0 16.3 10.2 - 3.3 0.3
0.701 0.697 0.692 0.689 0.685 0.682
5.870 5.865 5.860 5.856 5.850 5.847
6.3 12.4 21.1 29.3 34.5 39.5
-
194.5 176.6 162.1 152.7 148.0 144.0
0.707 0.703 0.696 0.691 0.687 0.684
8.421 8.409 8.390 8.371 8.360 8.350
- 72.0 -55.1 - 45.6 - 39.0 -34.1 -28.6
0.674 0.671 0.667 0.664 0.661 0.657
6.272 6.268 6.265 6.262 6.259 6.256
4.7 9.11 13.2 20.5 25.4 28.4
-
214.3 197.2 187.3 174.8 168.2 164.9
0.685 0.681 0.678 0.672 0.669 0.667
8.622 8.615 8.606 8.583 8.562 8.553
CCI(mM)
E (mV)
’
3.987 3.982 3.973 3.964 3.956 3.940
7.8 15.4 33.1 43.0 49.3 52.3
- 15.0 2.2 21.7 28.4 21.9 33.5
0.760 0.755 0.745 0.740 0.737 0.736
0.765 0.758 0.752 0.747 0.740 0.733
4.444 4.436 4.428 4.420 4.409 4.399
7.6 14.9 21.9 28.7 35.2 44.6
-33.9 - 16.5 -6.5 0.54 5.75 11.9
32.4 45.2 57.0 62.5 67.0 70.7
0.748 0.741 0.733 0.729 0.724 0.720
4.696 4.689 4.677 4.670 4.663 4.657
5.5 10.7 18.3 23.0 29.9 34.3
-
7.1 24.3 37.6 43.4 50.2 55.2
0.726 0.719 0.710 0.705 0.699 0.693
4.979 4.969 4.958 4.950 4.935 4.924
5.4 10.5 15.2 19.5 23.6 29.2
24.7 31.8 36.5 38.3 41.2 42.4
0.687 0.686 0.683 0.682 0.680 0.679
5.657 5.665 5.678 5.683 5.693 5.697
PH
.I. Barbosa and V. SamNebot/Anal.
Chh
323
Acta 283 (1993) 320-325
TABLE 2 Values of standard e.m.f., E”, of cell A, dielectric constants, 6, densities, p, and solvatochromic Kamlet-Taft parameters at various concentrations of acetonitrile in acetonitrile-water mixtures Acetonitrile concentration (%, w/w) 0
10 30 40 so 70
EO (mV)
c
401.03 466.44 426.87 442.64 458.57 515.43
78.36 75.01 65.52 60.38 55.44 46.82
P
0.9971 0.9809 0.9389 0.9150 0.8912 0.8465
knowledge of the ionic strength Z of the standard buffer + KC1 mixed electrolyte solutions: z=zs+
cc,-
(5) but Z is, in turn, a function of the H+ concentration, c n+, which is expressed by (E”-E) pcH+= g
?r*
a
B
1.17 1.14 1.03 0.97 0.91 0.84
1.285 1.137 0.971 0.919 0.891 0.859
0.47 0.30 0.37 0.40 0.41 0.40
(g mol-‘1
-PC,--P(Y.+Y,,-)
(6)
and of the ionization constants, pK, corresponding to the equilibria involved in the standard buffer solutions in acetonitrile-water mixtures. These pK values required were determined previously [ 161. Calculation of pyc,- values must proceed by succesive iterations. Initially one takes Z = cs + C,- and obtain py,- by Eqn. 3 for their subsequent insertion in Eqn. 6 to obtain pcH+ and a better value of Z by Eqn. 5. Thus, one calculates again the pyc,- value by Eqn. 3, and so on until constancy of Z is obtained. Inserting py,in Eqn. 2, one distinct pH value is obtained for each concentration cc,examined. The standard value, pH,, for standard buffer alone at the fixed molality recommended for International pH Standards [8] can finally be obtained, step (iii), as the intercept at cc,-= 0 of the pH vs. ccl- linear regression at each mole fraction x of acetonitrile studied.
each standard buffer as recommended [8] constant concentration solutions in 10, 30, 40, 50 and 70% (w/w) acetonitrile-water mixtures at 298.15 K. At each solvent composition and for each pH reference material studied, various series of measurements were made, giving total of 560 independent measurements over the solvent interval explored. To simplify the tabulation, E values for only one series of different ccl- concentrations in each standard reference solutions are quoted in Table 1. Table 1 also reports the corresponding values of molar activity coefficients of monoprotonated species and pH. Values of the dielectric constants, E, and densities, p, involved in the calculation of the Debye-Hiickel parameters A and a,B in Eqn. 3, were taken from the literature [17-201 and are given in Table 2. The determination of standard
RESULTS AND DISCUSSION
E.m.f. measurements different concentrations
for cell A were made at of KCl, ccI-, added to
Fig. 1. Variation of pH with concentration of chloride added to acetate buffer in acetonitrile-water mixtures. Acetonitrile concentrations in % (w/w) are given adjacent to the lines.
324
.I. Barbma and K SamNebot /Anal. Chim. Acta 283 (1993) 320-325
TABLE 3 pH, values for standard reference solutions and pK values of the involved equilibria in various acetonitrile-water 298.15 K Primary standard
Parameter
mixtures at
Acetonitrile concentration (%, w/w) 0
10
30
40
50
70
PK,
3.776 3.13 4.76 6.40
3.994 3.40 5.01 6.68
4.470 3.81 5.50 7.29
4.702 4.06 5.81 7.63
4.995 4.31 6.08 7.91
5.610 5.00 7.03 8.86
Acetate buffer
PH, PK,
4.644 4.75
4.898 4.97
5.532 5.63
5.875 5.99
6.275 6.41
5.57
Phosphate buffer
PH, PK,
7.413 7.20
7.697 7.46
8.151 8.02
8.436 8.24
8.646 8.53
9.42
PH, PKI
Citrate buffer
pK2
e.m.f. values, E”, for the glass electrode, silver/ silver chloride electrochemical cell A containing mixtures of acetonitrile and water has been described previously [141. The E” values obtained are stable, the average deviation being as low as 0.2 mV. Also, the ionization constant values required for the iterative calculations (pK,, pK, and pK, of citric acid, pK of acetic acid and pK, of phosphoric acid) where determined previously [16]. All these values, given in Tables 2 and 3, now permit the assignment of standard pH values to reference solutions in acetonitrile-water mix-
tures by using procedures and conventions described. When the pH for each buffer solution in each acetonitrile-water mixture was plotted as a function of ccl-, straight lines of small slope were obtained. Typical regression lines are shown in Fig. 1 for the acetate buffer in acetonitrile-water mixtures studied. Table 3 gives the pH, values determined for the citrate, acetate and phosphate buffers, standard reference solutions in 10, 30, 40, 50 and 70% (w/w) acetonitrile-water mixtures together
TABLE 4 Relationships between pH, values and weight(w) and volume (u) percentages and mole fraction of acetonitrile in acetonitrile-water mixture and linear solvation energy relationships for pH, values Buffer solution
Relationship
r
n
Citrate
pH pH pH pH
= = = =
3.775 + 2.18 x 1O-2 w - 1.24 x 1O-5 w2 + 7.13 x 1O-6 w3 3.775 + 1.74 x 1O-2 u - 2.72 x lo-’ u2 + 1.15 x 10W6u3 3.777 + 4.803 x - 3.348 x2 + 2.011 x3 10.917 - 7.416 W* + 1.824 a - 1.733 /3
0.999 0.999 0.999 0.991
6 6 6 6
Acetate
pH pH pH pH
= = = =
4.642 + 2.42 x 1O-2 w + 1.81 x 1O-4 w2 - 2.45 x lo-’ w3 4.643 + 1.88 x 1O-2 u + 1.26 x 1O-4 v2 - 7.23 x lo-’ u3 4.641 + 5.692 x - 0.355 x2 - 2.505 x3 12.310 - 6.741~ * + 0.422 (I - 0.685 B
0.999 0.999 0.999 0.9%
5 5 5 5
Phosphate
pH = 7.418 + 2.78 x 1O-2 w - 1.21 x 1O-4 w2 + 1.19 x 10W6w3 pH = 7.417 + 2.23 x 1O-2 v + 8.29 x 1O-5 u2 + 1.23 x 1O-6 u3 pH=7.422+5.880~-8.080x2+6.588x3 pH = 12.837 - 3.852 w * + 0.531 (Y- 0.500 /3
0.999 0.999 0.999 0.993
5 5 5 5
325
J. Barbosa and I! Sam-Nebot /Anal. Chim. Acta 283 (1993) 320-325
with the literature
standard pH, values in water
D1l. Determination of pH, values must be carried out at each distinct composition of the solvent but, considering the unlimited number of possible binary acetonitrile-water mixtures, some procedure for predicting pH, values, including pure water as the extreme case, is highly desirable. To this end, the different sets of results for the various solvent mixtures investigated were analysed in terms of a multilinear regression procedure. The usually used concentration by volume, % (v/v), U, the mole fraction of acetonitrile, x, and concentration by weight, % (w/w), W, are the independent variables and the third-order polynomials shown in Table 3 were obtained. To provide an independent interpretation of the pH, results, the linear solvation energy relationship (LSER) method based on the KamletTaft multiparameter scales [93 was utilized. The solvatochromic UER approach of Kamlet and Taft seeks to relate a pH, value or a dissociation constant value, XYZ, with three types of terms as shown below, based on the differential evaluation of solvent dipolarity/ polarizability, r *, solvent hydrogen bond-donating acidity, a, and solvent hydrogen bond accepting basicity, p: XYZ=xYz,+aa+b/3+s?T*
(4)
where a, b and s represent the susceptibilities of XYZ to changes in the solvent solvatochromic properties [22]. Values of the Kamlet-Taft solvatochromic parameters r * [lo], (Y[12] and p [13] for acetonitrile-water mixtures are known. As a result of the application of the ISER method to pH, values determined in this work, the relationships shown in Table 4 were obtained. These equations allow the pH, value of a primary standard buffer in any acetonitrile-water mixture to be calculated.
The financial support of the DGICYT ject PB91-0262) is gratefully acknowledged.
(Pro-
REFERENCES 1 P.J. Shoenmakers, Optimization of Chromatographic Selectivity: a Guide to Method Development, Elsevier, Amsterdam, 1986. 2 W.J. Cheong and P.W. Carr, Anal. Chem., 61(1989) 1524. 3 D.W. Armstrong, G.L. Bertrand, KD. Ward, T.J. Ward, H.S. Secor and J.I. Seeman, Anal. Chem., 61 (1990) 332. 4 P.J. Shoemnakers, S. van Molle, C.M.G. Hayes and L.C.M. Uunk, Anal. Chii. Acta, 250 (1991) 1. 5 S. Rondinini, P.R. Mussini and T. Mussini, Pure Appl. Chem., 59 (1987) 1549. 6 S. Rondinini and A. Nese, Electrochim. Acta, 32 (1987) 1499. I T. Mussini, AK. Covington, P. Longhi, S. Rondinini and S. Tettamanti, Anal. Chim. Acta, 174 (1985) 331. 8 A.K. Covington, R.G. Bates and R.A. Durst, Pure Appl. Chem., 57 (1985) 531. 9 M.J. Kamlet, J.M.L. Abboud, M.H. Abraham and R.W. Taft, J. Org. Chem., 48 (1983) 2877. 10 W.J. Cheong and P.W. Carr, Anal. Chem., 60 (1988) 820. 11 J. Barbosa and V. Sanz-Nebot, Talanta, submitted for publication. 12 J.H. Park, M.D. Jang, D.S. Kim and P.W. Carr, J. Chromatogr., 513 (1990) 107. 13 T.M. Krygowski, PK. Wrona, U. Zielkowska and C. Reichardt, Tetrahedron, 41(1985) 4519. 14 J. Barbosa and V. Sanz-Nebot, Anal. Chim. Acta, 244 (1991) 183. 15 T. Mussini, AK. Covington, P. Longhi and S. Rondinini, Pure Appl. Chem., 57 (1985) 865. 16 J. Barbosa and V. Sanz-Nebot. Anal. Chim. Acta., submitted for publication. 17 S. Rondinini, C. Confalonieri, P. Longhi and T. Mussini, Electrochim. Acta, 30 (1985) 981. 18 T. Mussini, P. Longhi and P. Giammario. Chim. Ind. (Milan), 53 (1971) 1124. 19 P. Longhi, T. Mussini, F. Penotti and S. Rondinini, J. Chem. Thermodyn., 17 (1985) 355. 20 C. Moreau and G. Douheret, J. Chem. Thermodyn., 8 (1976) 403. 21 R.G. Bates, CRC Crit. Rev. Anal. Chem., 10 (1981) 247.
Anulytica Chimica Acta, 283 (1993) 320-325 Elsevier Science Publishers B.V., Amsterdam
Standard pH values in non-aqueous mobile phases used in reversed-phase liquid chromatography J. Barbosa and V. Sanz-Nebot Department of Analyticul Chemistry, University of Barcelona, Avda. Diagonal 647, 08028 Barcelonu (Spain) (Received 8th September 1992; revised manuscript received 28th January 1993)
Abstract Standard pH, values for three reference buffer solutions (0.05 mol kg’ potassium dihydrogencitrate; 0.1 mol I-’ acetic acid + 0.1 mol I-’ sodium acetate: 0.03043 mol kg’ disodium hydrogenphosphate + 0.008695 mol kg-’ potassium dihydrogenphosphate) in 10, 30, 40, 50 and 70% (w/w) acetonitrile-water mixtures at 298.15 K were determined from e.m.f. measurements of the reversible cell Pt/Ag/AgCl/standard buffer + KCI, in acetonitrilewater/glass electrode. In order to obtain pH, values in each of the unlimited number of possible acetonitrile-water mixtures, pH, values were correlated with mole fraction, % (w/w) and % (v/v) of acetonitrile in solvent mixtures and the methodology of linear solvation energy relationship, based on the Kamlet-Taft multiparametric scales, was applied and pH, data were correlated with rr*, a and p solvatochromic parameters of the acetonitrile-water mixtures. Keyworuk Liquid chromatography; Acetonitrile; pH; Standard pH values
Mixed aqueous-organic solvents are widely used in chemistry to enhance the reactivities, solubilities, biological absorption properties and chromatographic properties of a wide variety of chemical substances. As in aqueous solutions, the pH of the solvent will be affected by solutes and its control will often be necessary in order to obtain optimum chemical results. The solvent system chosen in this study was acetonitrile-water because of its wide use in reversed-phase liquid chromatography (RPLC). Many different methods have been devised for optimizing the selectivity of chromatographic separations [l-3]. Usually, the methods focus on the optimization of the mobile phase composition, i.e., on the concentrations of water and organic Correspondence to: J. Barbosa, Department of Analytical Chemistry, University of Barcelona, Avda. Diagonal 647,08028 Barcelona (Spain). 0003-2670/93/$06.00
solvents. However, for separating ionic or ionogenie solutes, variations in the mobile phase pH may easily lead to dramatic variations in selectivity [4]. The degree of ionization of solutes, stationary phases (e.g., ion exchangers) and mobile phase additives (e.g., ion-pairing reagents) may be affected by the pH. Hence pH is potentially a very powerful parameter for optimizing selectivity in RPLC. However, the optimization of the mobile phase pH is complicated as the problem of pH measurements in aqueous-organic mixtures has not been solved [5]. Usually, the operational pH in mixed aqueous-organic solvents is measured assuming that the mobile phase pH is the same on that of the aqueous fraction, in which case errors due to the medium effects contribute to the uncertainty in the true pH. In acetonitrile-water mixtures the influence of the co-solvent on the pH is substantial [6,7].
0 1993 - Elsevier Science Publishers B.V. All rights reserved
I. Barbosa and V: SawNebot/AnaL
From the point of view of practical chromatography, it is possible to measure the activity of the hydronium ion in mixed aqueous-organic solvents if reference pH values of standard buffer solutions in these solvents are known. The conventional electrometric technique for pH measurements is dependent on an operational definition of pH: PH, =pH,+-
321
Chim. Acta 283 (1993) 320-325
Es-Ex g
where X denotes the solution of unknown pH and S the standard reference solution of known or assigned pH, E is the electromotive force of a suitable galvanic cell consisting of an electrode reversible to hydrogen ions (usually a glass electrode) coupled with a suitable reference electrode (commonly a silver/silver chloride electrode) and g = (ln10) RT/F. The aim of this present work was the assessment of pH, values for three standard buffer solutions (citrate, acetate and phosphate buffers) in acetonitrile-water mixtures containing 10, 30, 40, 50 and 70% (w/w> acetonitrile, according to the criteria recently endorsed by IUPAC [5,8]. Also, considering the unlimited number of possible binary acetonitrile-water mixtures, relationships between pH svalues and different characteristics of the solvent mixtures were examined and the methodology of linear solvation energy relationship (USER) [g-11] were used to correlate pH, values with solvent dipolarity/ polarizability (‘rr*>, solvent hydrogen bond-donating acidity (cu) and solvent hydrogen bond-accepting basic&y (/I) 112,131.
EXPERIMENTAL
E.m.f. values were measured with a Crison 2002 potentiometer ( f 0.1 mV) using a radiometer G202C glass electrode and a reference Ag/AgCl electrode prepared according to the electrolytic method [14]. The cell was thermostated externally at 25 f O.l”C. All of the potentiometric assembly was automatically controlled with a Stronger AT microcomputer.
Reagents Analytical-reagent grade chemicals were used unless indicated otherwise. All the solutions were prepared by mixing doubly distilled, freshly boiled water and acetonitrile (Merck, chromatography grade). The concentrations of the standard reference solutions used in this work were chosen as those recommended by IUPAC [8]. The compositions of the buffer solutions prepared for standardization were as follows: 0.05 mol kg-’ potassium dihydrogencitrate (citrate buffer), 0.1 mol 1-l acetic acid + 0.1 mol 1-i sodium acetate (acetate buffer) and 0.03043 mol kg-’ disodium hydrogenphosphate + 0.008695 mol kg-’ potassium dihydrogenphosphate (phosphate buffer). Procedures Reference pH values of the standard buffer solutions in acetonitrile-water mixtures containing 10, 30, 40, 50 and 70% (w/w) acetonitrile, PI-L were assigned by using the procedure adopted by the IUPAC [5]. This procedure involves three steps. The first step is the measurement of the e.m.f. of the cell Pt/Ag/AgCl/standard
buffer
+ KC1 in acetonitrile-water/glass
electrode
(cell A) where the reference standard buffer solutions contains potassium chloride at different and accurately known concentration. The e.m.f., E, of this cell is directly related to the activities of the hydrogen ions and chloride ions in solution: E = E” + g log( aH+aCI-)
(1)
where E” is the standard e.m.f. of the cell, values of which are essential and have been determined in previous work [14]. The second step is the determination of the different pH values for each concentration of potassium chloride, ccI-, examined using the Nemst expresison of e.m.f., E, for cell A: P(an+Yei-)
= PH +wcl=[(E'-EM+PC,-
(2)
where p(a,+y,,-1 is a thermodynamic quantity that can be determined in thermodynamically ex-
322
I. Barbara and K Sam-Nebot /Ad
a temperature T = 298.15 K by an extension of the Bates-Guggenheim convention [5,8] in terms of,
act terms, but to obtain pH values for the mixed electrolyte in the cell it is essential calculate the molar activity coefficient, p_v,-, thought an extra-thermodynamic assumption, i.e., a form of the classical Debye-Hiickel equation: PYCl--=
(a,&.=
1.5[ew~s/(eSpW)J~
(4)
where E is the dielectric constant, p the density and the superscripts W and S refer to pure water and to the appropriate solvent mixture, respectively. Calculation of pyc,- through Eqn. 3 requires a
(3)
(1 + a,,1”2)
Chim. Acta 283 (1993) 320-325
In compliance with IUPAC rules [5,151, the value of the product a,B in Eqn. 3 is assigned at
TABLE 1 Measured e.m.f. values of cell A, E, molar activity coefficients of monoprotonated concentrations, cm-, in various acetonitrile-water mixtures at 298.15 K Acetonitrile concentration (o/o, w/w)
Buffer solution Citrate
Acetate
C,(mM)
E (mV)
’
10
6.7 9.9 16.2 22.2 28.1 39.1
37.3 47.6 60.6 69.1 75.4 84.4
0.799 0.795 0.789 0.784 0.779 0.769
30
9.5 15.5 21.3 26.9 34.8 42.4
18.0 30.9 39.3 45.6 52.7 58.1
40
7.7 12.6 19.6 24.0 28.3 32.5
50
5.6 10.8 17.9 22.3 28.2 33.7
70
species (y) and pH values at different KC1
3.89 4.48 5.56 6.05 6.95 7.37
PH
Phosphate pH
C,(mM)
E (mV)
’
4.902 4.901 4.898 4.895 4.893 4.892
7.4 11.1 18.3 21.8 28.8 35.7
-
180.9 170.2 156.7 151.9 144.2 138.3
0.763 0.760 0.756 0.754 0.750 0.746
7.682 7.675 7.661 7.656 7.645 7.636
0.723 0.718 0.714 0.710 0.706 0.701
5.535 5.531 5.527 5.523 5.522 5.517
7.8 11.6 22.6 33.0 39.6 49.0
-
186.8 176.3 158.4 147.8 142.6 136.4
0.730 0.727 0.719 0.713 0.709 0.704
8.137 8.130 8.110 8.092 8.081 8.066
47.5 30.0 16.3 10.2 - 3.3 0.3
0.701 0.697 0.692 0.689 0.685 0.682
5.870 5.865 5.860 5.856 5.850 5.847
6.3 12.4 21.1 29.3 34.5 39.5
-
194.5 176.6 162.1 152.7 148.0 144.0
0.707 0.703 0.696 0.691 0.687 0.684
8.421 8.409 8.390 8.371 8.360 8.350
- 72.0 -55.1 - 45.6 - 39.0 -34.1 -28.6
0.674 0.671 0.667 0.664 0.661 0.657
6.272 6.268 6.265 6.262 6.259 6.256
4.7 9.11 13.2 20.5 25.4 28.4
-
214.3 197.2 187.3 174.8 168.2 164.9
0.685 0.681 0.678 0.672 0.669 0.667
8.622 8.615 8.606 8.583 8.562 8.553
CCI(mM)
E (mV)
’
3.987 3.982 3.973 3.964 3.956 3.940
7.8 15.4 33.1 43.0 49.3 52.3
- 15.0 2.2 21.7 28.4 21.9 33.5
0.760 0.755 0.745 0.740 0.737 0.736
0.765 0.758 0.752 0.747 0.740 0.733
4.444 4.436 4.428 4.420 4.409 4.399
7.6 14.9 21.9 28.7 35.2 44.6
-33.9 - 16.5 -6.5 0.54 5.75 11.9
32.4 45.2 57.0 62.5 67.0 70.7
0.748 0.741 0.733 0.729 0.724 0.720
4.696 4.689 4.677 4.670 4.663 4.657
5.5 10.7 18.3 23.0 29.9 34.3
-
7.1 24.3 37.6 43.4 50.2 55.2
0.726 0.719 0.710 0.705 0.699 0.693
4.979 4.969 4.958 4.950 4.935 4.924
5.4 10.5 15.2 19.5 23.6 29.2
24.7 31.8 36.5 38.3 41.2 42.4
0.687 0.686 0.683 0.682 0.680 0.679
5.657 5.665 5.678 5.683 5.693 5.697
PH
.I. Barbosa and V. SamNebot/Anal.
Chh
323
Acta 283 (1993) 320-325
TABLE 2 Values of standard e.m.f., E”, of cell A, dielectric constants, 6, densities, p, and solvatochromic Kamlet-Taft parameters at various concentrations of acetonitrile in acetonitrile-water mixtures Acetonitrile concentration (%, w/w) 0
10 30 40 so 70
EO (mV)
c
401.03 466.44 426.87 442.64 458.57 515.43
78.36 75.01 65.52 60.38 55.44 46.82
P
0.9971 0.9809 0.9389 0.9150 0.8912 0.8465
knowledge of the ionic strength Z of the standard buffer + KC1 mixed electrolyte solutions: z=zs+
cc,-
(5) but Z is, in turn, a function of the H+ concentration, c n+, which is expressed by (E”-E) pcH+= g
?r*
a
B
1.17 1.14 1.03 0.97 0.91 0.84
1.285 1.137 0.971 0.919 0.891 0.859
0.47 0.30 0.37 0.40 0.41 0.40
(g mol-‘1
-PC,--P(Y.+Y,,-)
(6)
and of the ionization constants, pK, corresponding to the equilibria involved in the standard buffer solutions in acetonitrile-water mixtures. These pK values required were determined previously [ 161. Calculation of pyc,- values must proceed by succesive iterations. Initially one takes Z = cs + C,- and obtain py,- by Eqn. 3 for their subsequent insertion in Eqn. 6 to obtain pcH+ and a better value of Z by Eqn. 5. Thus, one calculates again the pyc,- value by Eqn. 3, and so on until constancy of Z is obtained. Inserting py,in Eqn. 2, one distinct pH value is obtained for each concentration cc,examined. The standard value, pH,, for standard buffer alone at the fixed molality recommended for International pH Standards [8] can finally be obtained, step (iii), as the intercept at cc,-= 0 of the pH vs. ccl- linear regression at each mole fraction x of acetonitrile studied.
each standard buffer as recommended [8] constant concentration solutions in 10, 30, 40, 50 and 70% (w/w) acetonitrile-water mixtures at 298.15 K. At each solvent composition and for each pH reference material studied, various series of measurements were made, giving total of 560 independent measurements over the solvent interval explored. To simplify the tabulation, E values for only one series of different ccl- concentrations in each standard reference solutions are quoted in Table 1. Table 1 also reports the corresponding values of molar activity coefficients of monoprotonated species and pH. Values of the dielectric constants, E, and densities, p, involved in the calculation of the Debye-Hiickel parameters A and a,B in Eqn. 3, were taken from the literature [17-201 and are given in Table 2. The determination of standard
RESULTS AND DISCUSSION
E.m.f. measurements different concentrations
for cell A were made at of KCl, ccI-, added to
Fig. 1. Variation of pH with concentration of chloride added to acetate buffer in acetonitrile-water mixtures. Acetonitrile concentrations in % (w/w) are given adjacent to the lines.
324
.I. Barbma and K SamNebot /Anal. Chim. Acta 283 (1993) 320-325
TABLE 3 pH, values for standard reference solutions and pK values of the involved equilibria in various acetonitrile-water 298.15 K Primary standard
Parameter
mixtures at
Acetonitrile concentration (%, w/w) 0
10
30
40
50
70
PK,
3.776 3.13 4.76 6.40
3.994 3.40 5.01 6.68
4.470 3.81 5.50 7.29
4.702 4.06 5.81 7.63
4.995 4.31 6.08 7.91
5.610 5.00 7.03 8.86
Acetate buffer
PH, PK,
4.644 4.75
4.898 4.97
5.532 5.63
5.875 5.99
6.275 6.41
5.57
Phosphate buffer
PH, PK,
7.413 7.20
7.697 7.46
8.151 8.02
8.436 8.24
8.646 8.53
9.42
PH, PKI
Citrate buffer
pK2
e.m.f. values, E”, for the glass electrode, silver/ silver chloride electrochemical cell A containing mixtures of acetonitrile and water has been described previously [141. The E” values obtained are stable, the average deviation being as low as 0.2 mV. Also, the ionization constant values required for the iterative calculations (pK,, pK, and pK, of citric acid, pK of acetic acid and pK, of phosphoric acid) where determined previously [16]. All these values, given in Tables 2 and 3, now permit the assignment of standard pH values to reference solutions in acetonitrile-water mix-
tures by using procedures and conventions described. When the pH for each buffer solution in each acetonitrile-water mixture was plotted as a function of ccl-, straight lines of small slope were obtained. Typical regression lines are shown in Fig. 1 for the acetate buffer in acetonitrile-water mixtures studied. Table 3 gives the pH, values determined for the citrate, acetate and phosphate buffers, standard reference solutions in 10, 30, 40, 50 and 70% (w/w) acetonitrile-water mixtures together
TABLE 4 Relationships between pH, values and weight(w) and volume (u) percentages and mole fraction of acetonitrile in acetonitrile-water mixture and linear solvation energy relationships for pH, values Buffer solution
Relationship
r
n
Citrate
pH pH pH pH
= = = =
3.775 + 2.18 x 1O-2 w - 1.24 x 1O-5 w2 + 7.13 x 1O-6 w3 3.775 + 1.74 x 1O-2 u - 2.72 x lo-’ u2 + 1.15 x 10W6u3 3.777 + 4.803 x - 3.348 x2 + 2.011 x3 10.917 - 7.416 W* + 1.824 a - 1.733 /3
0.999 0.999 0.999 0.991
6 6 6 6
Acetate
pH pH pH pH
= = = =
4.642 + 2.42 x 1O-2 w + 1.81 x 1O-4 w2 - 2.45 x lo-’ w3 4.643 + 1.88 x 1O-2 u + 1.26 x 1O-4 v2 - 7.23 x lo-’ u3 4.641 + 5.692 x - 0.355 x2 - 2.505 x3 12.310 - 6.741~ * + 0.422 (I - 0.685 B
0.999 0.999 0.999 0.9%
5 5 5 5
Phosphate
pH = 7.418 + 2.78 x 1O-2 w - 1.21 x 1O-4 w2 + 1.19 x 10W6w3 pH = 7.417 + 2.23 x 1O-2 v + 8.29 x 1O-5 u2 + 1.23 x 1O-6 u3 pH=7.422+5.880~-8.080x2+6.588x3 pH = 12.837 - 3.852 w * + 0.531 (Y- 0.500 /3
0.999 0.999 0.999 0.993
5 5 5 5
325
J. Barbosa and I! Sam-Nebot /Anal. Chim. Acta 283 (1993) 320-325
with the literature
standard pH, values in water
D1l. Determination of pH, values must be carried out at each distinct composition of the solvent but, considering the unlimited number of possible binary acetonitrile-water mixtures, some procedure for predicting pH, values, including pure water as the extreme case, is highly desirable. To this end, the different sets of results for the various solvent mixtures investigated were analysed in terms of a multilinear regression procedure. The usually used concentration by volume, % (v/v), U, the mole fraction of acetonitrile, x, and concentration by weight, % (w/w), W, are the independent variables and the third-order polynomials shown in Table 3 were obtained. To provide an independent interpretation of the pH, results, the linear solvation energy relationship (LSER) method based on the KamletTaft multiparameter scales [93 was utilized. The solvatochromic UER approach of Kamlet and Taft seeks to relate a pH, value or a dissociation constant value, XYZ, with three types of terms as shown below, based on the differential evaluation of solvent dipolarity/ polarizability, r *, solvent hydrogen bond-donating acidity, a, and solvent hydrogen bond accepting basicity, p: XYZ=xYz,+aa+b/3+s?T*
(4)
where a, b and s represent the susceptibilities of XYZ to changes in the solvent solvatochromic properties [22]. Values of the Kamlet-Taft solvatochromic parameters r * [lo], (Y[12] and p [13] for acetonitrile-water mixtures are known. As a result of the application of the ISER method to pH, values determined in this work, the relationships shown in Table 4 were obtained. These equations allow the pH, value of a primary standard buffer in any acetonitrile-water mixture to be calculated.
The financial support of the DGICYT ject PB91-0262) is gratefully acknowledged.
(Pro-
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