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Autoprotolysis constants and standardization of the glass electrode in acetonitrile-water mixtures. Effect of solvent composition
183
Analytica Chimica Acta, 244 (1991) 183-191 Elsevier Science Publishers B.V.. Amsterdam
Autoprotolysis constants and standardization of the glass electrode in acetonitrile-water mixtures. Effect of solvent composition J. Barbosa * and V. Sanz-Nebot Department
of Analytical
Chemistry,
University of Barcelona, 08028 Barcelona (Spain)
(Received
3rd August
1990)
Abstract Standard e.m.f.s for the cell GE/HCl/AgCl/Ag/Pt (GE = glass electrode) in acetonitrile-water mixtures containing O-7056 (w/w) of acetonitrile were obtained. Values of the autoprotolysis constant, K,, of these mixed solvents were also determined from e.m.f. measurements of the cell GE/KC1 + KS/AgCl/Ag/Pt. The influence of variations in values was evaluated. Over the whole of the composition range studied the pK,, the solvent composition on pK, values were linearly correlated with the mole fraction of acetonitrile and with the reciprocal of the relative permittivity values vs. the Kamlet-Taft R* polarizability/diof solvent mixtures. Linear relationships were also obtained for pK, polarity parameter in the range O-504; (w/w). Keywords:
Voltammetry;
Autoprotolysis
constant;
Glass electrode:
A recent IUPAC document on autoprotolysis constants in non-aqueous solvents and aqueous organic solvents [l] points out the importance of the autoprotolysis constant, Kap, of each solvent. The conclusions in this document indicate that the present availability of pK,, data is highly unsatisfactory, especially for binary aqueous-organic solvent mixtures, and confirm the necessity for the rapid acquisition and analysis of the relevant pK,, data. The autoprotolysis constant of each solvent determines the so-called “normal range of pH” (as given by pK,, = -log K,,) in such solvents [2,3]. A solvent HS (a pure solvent or a binary aqueous-organic solvent mixture, HS = H,O + HZ), capable of being both a proton donor and a proton acceptor, can undergo autoprotolysis according to the general process HS + HS = H,S++
S-
The general equilibrium
(1) constant
for Eqn. 1 is
Acetonitrile
called the autoprotolysis defined by [l]
constant,
Kap, and is
K,, = au2s+as-/&s (2) = mH2S+YH2s+ms~Ys-/(mO)211flS where aHzS+ and a,- are ionic activities and and ys- the activity coefficients at the YH2S+ molahties m&s+ and MS-, respectively; m, = 1 mol kg-’ and aHs is the activity of the undissociated species HS at the mole fraction xus. Hence K,, is a dimensionless thermodynamic quantity which is a composite function of the intrinsic acidic and basic strength of the solvent and its relative permittivity. The recommended IUPAC method for the determination of pK, values in solvent mixtures [l] is based on e.m.f. measurements of the typical reversible cell Pt/Ag/AgCl/KS (m,-) + KC1 (m,,-) in HS/H+-sensing electrode
184
J. BARBOSA
where S- is the lyate ion and ms- and m,,- are the molalities of the lyate and chloride ions, respectively. With acetonitrile-water mixtures, the use of the hydrogen electrode is not appopriate because of the delicacy of its behaviour in contact with acetonitrile [4,5]. Also, as the method requires measurements in basic media, the e.m.f. quinhydrone electrode cannot be used as an H +sensing electrode [6]. The measurements of pH utilize, in most instances, the convenient and versatile glass electrode (GE). Thanks the modern technology, the potential of the external surface of this membrane electrode parallels to a remarkable extent that of the hydrogen gas electrode [7], the primary reference for hydrogen ion measurements. Other reference electrodes, especially the silver/silver chloride electrode, may constitute the left-hand element of the cell. This electrode is employed extensively in the determination of thermodynamic data by the e.m.f. method. From the above, the basic cell used in this work is Pt/Ag/AgCl/KS + KC1 in acetonitrile-water/GE
(A)
This cell permits reliable measurements of pH in acetonitrile-water mixtures used extensively in both voltammetry and reversed-phase liquid chromatography. In fact, the functional expression for the e.m.f. of the cell, E, is E = E o + g log( a,+ac&
(3)
where g = (In lO)RT/F and E o is the standard e.m.f. of the cell in the appropriate acetonitrilewater solvent mixture. Equation 3 requires a knowledge of the standard e.m.f. of cell A. The relevant E o values covering those acetonitrile-water mixture containing up to 70% (w/w) acetonitrile at 298.15 K were determined in this work from e.m.f. measurements of the reversible cell Pt/Ag/AgCl/HCl
in acetonitrile-water/GE (B)
AND
V. SANZ-NEBOT
The standard potential in cell B, which is, of course, the same as for cell A, is indispensable to the determination of pK,, values, but it is also needed for pH measurements in acetonitrile-water mixtures using the glass electrode. The need for reliable pH measurements in mixed solvents such as acetonitrile-water has become increasingly obvious in recent studies of the chromatographic behaviour of substances as a function of pH [8,9]. However, investigation into the importance of pH changes for the interpretation of the ionization effect in non-aqueous mobile phases in liquid chromatography has been restricted by the limited validity of pH measurements made with conventional electrodes calibrated in aqueous solutions. The highest reproducibility in pH measurements cannot be achieved if the electrodes are immersed in an aqueous medium for standardization and then moved suddenly to a medium of different composition such as acetonitrile-water, as is clearly explained by Mussini and Mazza [3]. On the other hand, considering the unlimited number of possible binary solvent acetonitrilewater mixtures, it is evident that an absurdly large number of experiments would be needed to determine all the corresponding pK,, values. Clearly, some procedure for predicting pK,, values, including pure water as the extreme case, is highly desirable. To explain the influence of solvent composition on the autoprotolysis constant of acetonitrilewater mixtures, Born’s model, being purely electrostatic in nature, could be insufficient. Bulk measurements of a solvent, such as dielectric constant, E, could be insufficient to describe or characterize the solute-solvent interactions. It is for these reasons that a number of empirical solvatochromic solvent scales have been developed, based primarily on spectroscopic measurements
DOI. For pure solvents the multiparametric equation of Kamlet and Taft [ll] in its more complete form includes terms which measure the hydrogen-bonding capacity by proton donation (a) or by proton acceptance (p), the polarity (m*), the polarizability (S), Hildebrand’s solubility parameter (6,) and the coordinated covalence (5). Also, simpler
EFFECTS
OF SOLVENT
COMPOSITION
ON GLASS
ELECTRODES
scales of solvent polarity have been defined as a function of empirical parameters such as r* [12] or the parameter ET” of Dimroth and Reichardt [lo]. The aim of this study was the determination of standard e.m.f. E” and pK,, values according to the criteria recently endorsed by IUPAC [1,13] in acetonitrile-water mixtures containing 0, 10, 30, 40, 50 and 70% (w/w) acetonitrile. Also, relationships between the autoprotolysis constant of the medium and different characteristics of the solvent mixtures (l/e, E,, +rr*, CYand /3) were examined.
EXPERIMENTAL
Apparatus Values of the e.m.f. of the potentiometric cell were measured with a Crison 2002 potentiometer ( + 0.1 mv), using a Radiometer G202C glass electrode and a reference Ag/AgCl electrode prepared according to the electrolytic method [14]. Its base was a smooth platinum wire, 1 mm in diameter. This platinum wire, after cleaning in concentrated nitric acid, was repeatedly washed in triply distilled water, then silver plated in a ILAg( bath (10 g 1-i) at a current density of 0.4 mA cm-’ for 5 h. After prolonged washing in water, the silver-plated wire was chloridized in 0.1 M HCl at a current density of 0.6 mA cm-* for 30 min and subsequently washed for a long period in triply distilled water. The cell was thermostated externally at 25 + 0.1” C. Test solutions were stirred magnetically under a continuous stream of purified nitrogen [washed with vanadium(I1) perchlorate solution, sodium hydroxide and distilled water and dried with soda-lime]. For potentiometric titrations, the titrant (KOH) was added from a Metrohm E415 Multidosimat autoburette equipped with an anti-diffusion tip. All the potentiometric assembly was automatically controlled with a Stronger AT microcomputer. The stabilization criterion for the e.m.f. readings was 0.2 mV within 120 s; if this stabilization is not achieved after 15 min, a new addition of titrant was made.
185
Reagents Analytical-reagent grade chemicals were used unless indicated otherwise. Stock 0.1 M potassium hyroxide (Carlo Erba, RPE grade) solutions were prepared with an ionexchange resin [15] to avoid carbonation and were standardized volumetrically with potassium hydrogenphthalate (Merck). Hydrochloric acid solutions were prepared from concentrated hydrochloric acid (Merck) and standardized volumetrically with tris(hydroxymethyl)aminomethane (Merck). Potassium nitrate (Merck) and potassium chloride (Merck) solutions were also prepared. All these solutions were prepared by mixing doubly distilled, freshly boiled water and acetonitrile (Merck, for chromatography grade).
Procedures The standard e.m.f., E O, of the cell with 0, 10, 30, 40, 50 and 70% (w/w) of acetonitrile in the solvent mixture was evaluated by two similar methods: the classical method [16,17] by series of e.m.f. measurements with cell B of HCl concentrations f 0.1 M, and the method of Gran [18] from titrations of diluted HCl solutions in the desired solvent using KOH solutions in the same solvent as the titrant, and evaluation of the calibration parameters using a multiparametric data-fitting procedure or Gran plots. These titrations were carried out with and without simultaneous additions of 0.3 M KNO, or 0.3 M KC1 solutions in the same mixed solvent, to take into account the influence of changes in ionic strength. From Gran plots before the equivalence point, using concentrations, c, of E-g
log cut-
g log ccl--
where y is the molar the basic side of E + g log css-
2g log y vs. aH+
activity
coefficient,
g log cc,- vs. a,-
(4)
and on
(5)
it was shown that the liquid junction potential of the cell remained constant and negligible. Thus, the E o value was calculated from the Gran function at each point of the titration. The latter method has the advantage that it permits the simultaneous determination of the au-
186
J. BARBOSA
AND
V. SANZ-NEBOT
expressed for log yf through a form of the Debye-Htickel equation [6,16]:
toprotolysis constant of the medium, which was calculated from the expression:
py * = AZ”Z/( 1 + a,BZ”2) + log(1 + 0.002MA,)
where g = 59.157 mV at 25” C and E o and Et are the standard potentials in acidic and basic medium, respectively. In a similar way, the e.m.f. measurements after the equivalence point of the titrations were used for the determination of the autoprotolysis constant [l].
or the classical Debye-Htickel
(8)
equation: (9)
where A and B are the Debye-Htickel constants, a0 is the ion size, b is the interaction parameter in the solvent mixture considered, MAW is the “molecular weight” of the acetonitrile-water mixed solvent and the ionic strength Z is the HCl molarity c. In compliance with IUPAC rules [2,13], the value of the product a,B is assigned at the appropriate temperature T by an extension of the Bates-Guggenheim convention [13,17] in terms of
RESULTS AND DISCUSSION
E.m.f. measurements for cell B at various concentrations of hydrochloric acid in the acetonitrile-water solvent mixtures studied were made for various series of HCl solutions and their values for one series in each solvent mixture are given in Table 1. The Nernstian expression with the assumption yc, = y, (which is reliable for an ionic strength Q 0.1 mol 1-l) is E= E” + 2g log(cy/c”)uc,
- bZ
(a,B),=
1.5[cw~s,‘(eSpW)]~
where the superscripts W and S refer to pure water and to the appropriate solvent mixture, respectively. Values of the dielectric constant, e, and densities, p, involved in the calculation of the Debye-Htickel constants A and a,B in Eqns. 8 and 9 were taken from data in the literature [6,16,19,20] and are quoted in Table 2 for readers’ convenience.
(7)
The dependence of the activity coefficients y, on the HCl concentration c can be appropriately
TABLE 1 Measured e.m.f. values of cell B for various acetonitrile-water
mixtures at 298.15 K
Acetonitrile in admixture with water (S, w/w) 0
10
30
40
50
70
CHCl
E
CHCl
E
CHCl
E
CHCl
E
CHCl
(Mx10e4)
(mV)
(Mx10m4)
(mv)
(MX 10m4)
(mv)
(MX10m4)
(mv)
(MX
6.04
9.6
6.13
26.1
4.20
23.3
8.03 10.0 17.9 23.7 35.2 42.6 57.3 66.2 83.6
23.4 35.3 65.0 79.5 99.2 108.8 123.5 130.6 142.2
8.14 10.2 18.2 29.9 43.3 58.4 67.2 76.1 84.9
40.7 51.6 81.4 106.1 124.4 139.2 146.2 152.2 157.6
9.00 13.3 17.4 21.0 27.5 33.0 35.5 41.0 85.7
60.8 80.7 93.8 103.3 116.6 125.7 129.2 135.3 172.7
8.06 16.0 23.8 31.5 39.1 46.5 53.9 61.1 75.3 83.9
10m4)
71.7
3.78
105.5 125.6 139.7 150.4 159.0 166.1 172.2 185.4 187.6
7.54 11.3 18.6 22.3 29.7 33.2 38.0 81.4 120
E
CHCl
E
(mv)
(MX10m4)
(mv)
47.7 81.2 101.8 127.0 136.0 150.0 155.9 162.5 199.0 218.1
4.04 8.05 12.0 16.0 20.0 23.8 27.6 31.4 35.2 39.0
108.6 143.0 163.0 177.0 187.6 196.4 203.7 209.9 215.2 220.2
EFFECTS
OF SOLVENT
COMPOSITION
ON
GLASS
TABLE 2 Values of dielectric constants, densities and Debye-Hiickel parameters A and a,B at 25OC and weight percentages of acetonitrile in admixture with water Acetonitrile concentration
z ;g ml-‘)
A (kg”’ mol-‘/2)
a,B (kg”’ mol-1/2)
0.9971 0.9809 0.9389 0.9150 0.8912 0.8465
0.5103 0.5404 0.6476 0.7227 0.8197 1.0181
1.5 1.5206 1.5918 1.6369 1.6859 1.7859
(% w/w) 0 10 30 40 50 70
78.36 75.01 65.52 60.38 55.44 46.82
+ 2g log(1 + 2cM,,)
+ a&/*) (11)
+ a&“*)
= E, + 2gbc
The classical Debye-Htickel equation is recommended by IUPAC for calculating the activity coefficient [2]. Consequently, Eqn. 9 was also tried as an alternative path to determine the E” values. Taking into account Eqn. 9, by insertion of PYi in Eqn. 7 the function for E, takes the simpler form E“ = E - 2g log c + 2gAc”*/(l
Taking into account Eqn. 8 by insertion of py, Eqn. 7 can be rearranged to define the extrapolation function @ [6] a= E - 2g log c + 2gAc”*/(l
187
ELECTRODES
(10)
Plotting Q, vs. c should produce a straight line whose intercept at c = 0 gives E” and from the slope of which the value of the interaction parameter b can be obtained [6]. Figure 1 shows the data obtained for the acetonitrile-water mixtures studied at 25 o C. As can be seen from the plots in Fig. 1, the slopes of the straight lines obtained have very small values and as a consequence the values obtained for b in such a series showed a high degree of dispersion, although very close to zero.
The average E” values obtained using Eqn. 11 for each HCl solution do not differ significantly from the data obtained from the extrapolation of the function @ (Eqn. lo), the average deviation being as low as 0.1 mV. Hence it can be concluded that the classical Debye-Htickel equation (Eqn. 9) can be used as a convenient approximation for the y, values of electrolytes in acetonitrile-water mixtures with up to 70% (w/w) acetonitrile. Evaluation of E” values by the Gran method [18], from titration of HCl solutions in the desired solvent mixture using KOH solution in the same solvent as the titrant, involves E values obtained in the acidic medium of the titrations and Eqn. 11 itself for cells without liquid junction potential. The Gran plots show that the liquid junction potential of the cell used is negligible and the E” values obtained are not significantly different from the data obtained previously. The E“ values obtained are summarized in Table 3. Table 4 gives the E“ values obtained for 40% (w/w)
TABLE 3 Values of the standard e.m.f., E“, in acetonitrile-water mixtures at 25’C and mole fraction x of acetonitrile as obtained elaborating measured E values of cell B and of titrations of HCl solutions with 0.1 M KOH solution Acetonitrile concentration
x
EO(mV)
0 0.0465 0.1583 0.2264 0.3051 0.5059
400.59 405.62 422.97 439.59 454.78 511.17
(% w/w)
0
0.002
o.oM
0.006
C
o.wII
0.01
0.012
0.01,
0.016
Fig. 1. Plot of extrapolation function @ vs. HCl concentration, c.
0 10 30 40 50 70
E” (Eqn. 12)
E0 (Eifn. 13)
(mv)
(mv)
400.01 406.15 424.29 437.69 455.37 511.20
400.32 406.17 423.29 437.50 456.59 510.85
188
.I. BARBOSA
TABLE 4 Values of the standard e.m.f., E O, in 40% (w/w) acetonitrilewater mixtures at 25 o C as obtained by the Gran method V
E
(ml)
(mv)
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20
194.9 193.5 191.9 190.2 188.4 186.5 184.4 182.1 179.8 177.2 174.3 171.1
E”
PH
@VI 2.08 2.10 2.13 2.16 2.19 2.22 2.25 2.28 2.32 2.36 2.41 2.46
1.02x10-2 1.01 x10-2 1.01 x10-2 1.00x10-* 9.96~10-~ 9.91x10-3 9.86~10-~ 9.82~10-~ 9.77x10-3 9.72~10-~ 9.68~10-~ 9.63~10-~
439.40 439.59 439.66 439.71 439.75 439.80 439.77 439.68 439.75 439.72 439.62 439.51
AND V. SANZ-NEBOT
termination was based on e.m.f. measurements for the reversible cell A. Eliminating an+ in Eqn. 3, taking into account Eqn. 2 and ~~,~+=a~+ for simplicity, uHS = 1, and using concentrations, c, gives (E” - E)/g
+ log(cc,-/cs-) K,,
= -log
- lodYc,-/Ys-)
Expressing the simple-ion activity through an extended Debye-Htickel type 1: py, = AZ”2/(
1 + a,Bz”*)
= (E” - E)/g = pK,,
coefficients equation of
- b;Z
then from Eqn. 14 one can define tion function pK&: PK,,
(14)
05) the extrapola-
+ log&/cs-)
+ (b,--
bc,-)Z
(16)
acetonitrile-water, obtained from E values of HCl titrations with 0.0998 M KOH solution. To provide a test of internal consistency of the E” results, they were averaged by fitting all the data to a secondor third-order least-squares polynomial [19]. If the mole fraction x of nonaqueous component (acetonitrile) is the independent variable, the following equation is obtained:
Plotting pK& vs. Z and extrapolating to Z = 0, the intercept gives the pK,, value. In this work, for the acetonitrile-water mixtures, the classical Debye-Htickel equation was also tried as an alternative path to determine pK,, values. From Eqn. 9, the following simpler equation was obtained:
E” = 400.04 + 122.06x
PK,,
+ 195.00x2
(12)
and if the usually used concentration by volume, % (v/v), u, is the independent variable, the equation E” = 400.30 + 0.48 u - 3.38 x 1O-3 u* + 2.13
x 1o-4
u3
= (E“ - E)/g
+ log&/css)
(17)
The E measurements were made in solutions which correspond to the basic side of titrations of HCl solutions in the desired solvent mixture using KOH solutions in the same solvent as the titrant
(13)
is obtained. Equations 12 and 13 lead to the E” values with the quoted errors in Table 3. These equations can be used for interpolation of E” values at 298.15 K in the experimental range of x (from 0 to 0.5059). On the other hand, the normal pH scale or normal pH range in any solvent is conventionally defined as pK,,, where K,, is the autoprotolysis constant of the solvent at 298.15 K, a quantity that, unlike pH, is determinable in thermodynamically exact terms [3]. According to the criteria recently endorsed by IUPAC [l], and replacing the hydrogen electrode for a glass electrode for the practical reasons explained previously, pK,, de-
TABLE
5
Values of the extrapolation function pK,6 (Eqn. 16) for 10% (w/w) acetonitrile-water mixtures at 25 o C
vw
E (mV)
PS
I CM)
pK,‘p
2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10
- 415.5 - 419.4 - 422.9 - 425.9 - 428.7 -431.2 - 433.3 - 435.3 - 437.3 - 439.2 -440.7
2.61 2.55 2.49 2.45 2.40 2.36 2.33 2.30 2.27 2.24 2.21
9.46~10-~ 9.87~10-~ 1.03x10-2 1.07x10-2 1.11 x10-2 1.15x10-* 1.18x10-* 1.22x10-2 1.26~10-~ 1.30x10-* 1.34x10-2
14.28 14.27 14.28 14.28 14.28 14.28 14.28 14.27 14.28 14.28 14.28
EFFECTS
TABLE
OF SOLVENT
COMPOSITION
ON GLASS
ELECTRODES
TABLE
6
Values of autoprotolysis constants on a logarithmic acetonitrile-water mixtures at 25 o C Mole fraction of acetonitrile
scale for
pK,,
pK,, (Eqn. 18)
PK, (Eqn. 19)
PK,, (Eqn. 20)
14.00 14.27 14.93 15.32 15.71 16.76 33.58
14.03 14.29 14.90 15.27 15.70 16.79 -
14.07 14.26 14.86 15.27 15.74 16.78
14.04 14.23 14.94 15.32 15.71 -
7
Solvatochromic parameters mixtures studied Mole fraction of acetonitrile
values
for the acetonitrile-water
ET”
r*
a
P
1.00 0.93 0.84 0.81 0.79 0.76
1.17 1.14 1.03 0.97 0.91 0.84
1.084 0.973 0.870 0.855 0.859 0.866
0.47 0.40 0.41 0.40
(x)
(x) 0.0000 0.0465 0.1583 0.2264 0.3051 0.5059 1.0000
189
with and without simultaneous addition of a salt solution. The data obtained for a titration in 10% (w/w) acetonitrile-water are shown in Table 5, where pS = -log a,-. Comparison of the values of pK& given in the last column of Table 5 shows that the values of the extrapolation function PK.&, are not very sensitive to the values of I, and as a consequence the values of pK,, calculated with or without the use of the b values are not appreciably different. This implies that for acetonitrile-water mixtures, Eqn. 17 can be used for pK,, determination, which is the same equation as used for the Gran plots. Then, in acetonitrile-water mixtures, the use of Gran’s method permits the determination of sets of E” values in acidic medium and of pK,, values after the equivalence point for each titration performed in the desired mixture. The pK,, values obtained for all the acetonitrile-water mixtures studied are given in Table 6, where the previously obtained pK,, value for pure acetonitrile solvent is also given [21]. Relationships between the autoprotolysis constant of the medium and different characteristics of the solvent medium were examined. Thus, pK,, values were plotted against the mole fraction, X, %I (w/w), 54;(v/v), l/r, Ey, 7~*, a and p values. The ET values [22-241 and the Kamlet-Taft r* [25] and p [24] values for acetonitrile-water mixtures over the entire range of composition are known. The literature ET” and r* values permit an estimate of (Y values, the hydrogen bond acidity parameter, for acetonitrile-water mixtures [25].
0.0000 0.0465 0.1583 0.2264 0.3051 0.5059
Table 7 gives the relevant solvatochromic parameter values for the mixtures studied. When the data at a particular composition could not be located, the existing data were interpolated by a cubic splines method. When more than one data set was available, they were averaged by fitting all of the data to a third-order polynomial least-squares regression. When the values of pK,, are plotted against the mole fraction of acetonitrile, x, in the solvent mixture or against values of the reciprocal of the relative permittivity, l/e, of the solvent mixture, linear relationships are obtained (Figs. 2 and 3) over the whole experimental range of acetonitrile contents studied, up to 70% (w/w). The linear segments show slopes of 5.46 f 0.09 (r = 0.999) vs. x and of 314.84 +_ 8.30 (r = 0.998) vs. l/c and can be expressed by the following equations: pK,, = 14.03 + 5.46x
Fig. 2. Plot of pK,,
vs. mole fraction
(18)
of acetonitrile,
X.
190
J. BARBOSA
AND
V. SANZ-NEBOT
It is of practical interest to note that pK,, values are related to u (W, v/v) and w (W, w/w) by a second order polynomial of the types pK,, = 14.02 + 1.44 x lo-$I + 2.78 x 1O-4 u2 (21) and pK,, = 14.01+ 2.36 x 1O-2 w + 2.22 x 1O-4 w* (22)
Fig. 3. Plot of pKap vs. reciprocal of solvent mixtures, l/c.
of the relative
permittivity
and pK,, = 10.06 + 314.84/c
(19)
Equations 18 and 19 can be used for interpolation of PK,, values at 298.15 K in the experimental range of x (from 0 to 0.5059) (Table 6). These equations cover the whole set of experimental points, even those obtained in mixtures richer in acetonitrile. Plots of pK,, vs. the solvatochromic parameters ET, a and j3 show no zone of linearity for up to 70% (w/w) acetonitrile-water mixtures. If the results obtained for pK,, values are plotted against the ?r* values, only one zone of linearity is obtained (Fig. 4) in the range from 0 to 50% (w/w). This linear part shows a slope of -6.42 f 0.13 (r = 0.999) and can be expressed by pK,, = 21.55 - 6.42~*
Fig. 4. Plot of pK,, vs. Kamlet-Taft dipolarity parameters of solvent mixtures.
(20)
r*
polarizability/
Analysis of the plots shows that the autoprotolysis constant of the acetonitrile-water solvent mixtures decreases with increasing acetonitrile content in the medium and, as the plot vs. l/e shows, this decrease is that expected according to the electrostatic model. The optimum linearity of the plot of PK, vs. l/e indicates that the simple model in which only electrostatic interaction is considered explains the changes in pK,, values of acetonitrile-water mixtures over the full range of solvent compositions. This implies that electrostatic interactions are more important to consider than solute-solvent interactions such as those derived from hydrogen-bond formation and those derived from modifications in the solvation shell. The linearity of pK,, vs. 7~* plots up to 50% (w/w) acetonitrile is in accordance with the interpretation that Cheong and Carr [25] gave for the significant qualitative similarity in the shape of the plots of 7~* and E vs. volume fraction of the organic cosolvent in acetonitrile-water mixtures up to an acetonitrile content of ca. 50% (w/w). They pointed out that the principal effect of changing the solvent composition on the observed r* values operates through the dielectric properties of the local medium around the solute, taking into account that the dielectric constant is a bulk property of the mixture as a whole and the solvatochromic properties can only reflect the interaction of a solute with its immediate surroundings. It must be emphasized that each pK,, value for an acetonitrile-water mixture defines the normal pH scale or normal pH range in this mixture [26] and p&S (H+), the primary medium effect upon H+ [27], represents the acidic end of the normal pH scale in each distinct solvent mixture S with ultimate reference to the familiar aqueous pH
EFFECTS
OF SOLVENT
COMFQSITION
ON GLASS
ELECTRODES
scale and with physical comparability latter [3].
with the
REFERENCES 1 S. Rondinini, P. Longhi, P.R. Mussini and T. Mussini, Pure Appl. Chem., 59 (1987) 1693. 2 T. Mussini, A.K. Covington, P. Longhi and S. Rondinini, Pure Appl. Chem., 57 (1985) 865. 3 T. Mussini and F. Mazza, Electrochim. Acta, 32 (1987) 855. 4 P. Giammario, P. Longhi and T. Mussini, Chim. Ind. (Milan), 53 (1971) 347. 5 S. Rondinini and A. Nese, Electrochim. Acta, 32 (1987) 1499. 6 S. Rondinini, C. Confalonieri, P. Longhi and T. Mussini, Electrochim. Acta, 30 (1985) 981. 7 R.G. Bates, CRC Crit. Rev. Anal. Chem., 10 (1981) 247. 8 P.P. Pashankov, P.S. Zikdov and O.B. Budevsky, J. Chromatogr., 209 (1981) 149. 9 F. Szokoli, Zs. Nemeth and J. Inczedy, Chromatographia, 90 (1990) 265. 10 C. Reichardt, Solvents and Solvent Effects in Organic Chemistry, VCH, Weinheim, 1988. 11 M.J. Kamlet, J.M.K. Abboud, M.H. Abraham and R.W. Taft, J. Org. Chem., 48 (1983) 2877.
191 12 M.J. Kamlet, T.N. Hall, J. Boykin and R.W. Taft, J. Am. Chem. Sot., 101 (1979) 3734. 13 S. Rondinini, P.R. Mussini and T. Mussini, Pure Appl. Chem., 59 (1987) 1549. 14 D.J.G. Ives and G.J. Jam, Reference Electrodes, Academic, New York, 1961, p. 204. 15 J.E. Powell and M.A. Hiller, J. Chem. Educ., 34 (1957) 330. 16 T. Mussini, P. Longhi, P. Giammario, Chim. Ind. (Milan), 53 (1971) 1124. 17 A.K. Covington, R.G. Bates and R.A. Durst, Pure Appl. Chem., 57 (1985) 531. 18 G. Gran, Analyst, 77 (1952) 661. 19 P. Longhi, T. Mussini, F. Penotti and S. Rondinini, J. Chem. Thermodyn. 17 (1985) 355. 20 C. Moreau and G. Douhbret, J. Chem. Thermodyn., 8 (1976) 403. 21 J. Barbosa and V. Sam-Nebot, Talanta, 36 (1989) 837. 22 J.G. Dorsey and B.P. Johnson, Chimicaoggi, (1986) 23. 23 S. Balakrishnan and A.J. Easteal, Aust. J. Chem., 34 (1981) 943. 24 T.M. Krygowski, P.K. Wrona, U. Zielkowska and C. Reichardt, Tetrahedron, 41 (1985) 4519. 25 W.J. Cheong and P.W. Carr, Anal. Chem., 60 (1988) 820. 26 R.G. Bates, Determination of pH - Theory and Practice, Wiley, New York, 2nd edn, 1973, p. 227. 27 Y. Marcus, Pure Appl. Chem., 55 (1983) 977.
Analytica Chimica Acta, 244 (1991) 183-191 Elsevier Science Publishers B.V.. Amsterdam
Autoprotolysis constants and standardization of the glass electrode in acetonitrile-water mixtures. Effect of solvent composition J. Barbosa * and V. Sanz-Nebot Department
of Analytical
Chemistry,
University of Barcelona, 08028 Barcelona (Spain)
(Received
3rd August
1990)
Abstract Standard e.m.f.s for the cell GE/HCl/AgCl/Ag/Pt (GE = glass electrode) in acetonitrile-water mixtures containing O-7056 (w/w) of acetonitrile were obtained. Values of the autoprotolysis constant, K,, of these mixed solvents were also determined from e.m.f. measurements of the cell GE/KC1 + KS/AgCl/Ag/Pt. The influence of variations in values was evaluated. Over the whole of the composition range studied the pK,, the solvent composition on pK, values were linearly correlated with the mole fraction of acetonitrile and with the reciprocal of the relative permittivity values vs. the Kamlet-Taft R* polarizability/diof solvent mixtures. Linear relationships were also obtained for pK, polarity parameter in the range O-504; (w/w). Keywords:
Voltammetry;
Autoprotolysis
constant;
Glass electrode:
A recent IUPAC document on autoprotolysis constants in non-aqueous solvents and aqueous organic solvents [l] points out the importance of the autoprotolysis constant, Kap, of each solvent. The conclusions in this document indicate that the present availability of pK,, data is highly unsatisfactory, especially for binary aqueous-organic solvent mixtures, and confirm the necessity for the rapid acquisition and analysis of the relevant pK,, data. The autoprotolysis constant of each solvent determines the so-called “normal range of pH” (as given by pK,, = -log K,,) in such solvents [2,3]. A solvent HS (a pure solvent or a binary aqueous-organic solvent mixture, HS = H,O + HZ), capable of being both a proton donor and a proton acceptor, can undergo autoprotolysis according to the general process HS + HS = H,S++
S-
The general equilibrium
(1) constant
for Eqn. 1 is
Acetonitrile
called the autoprotolysis defined by [l]
constant,
Kap, and is
K,, = au2s+as-/&s (2) = mH2S+YH2s+ms~Ys-/(mO)211flS where aHzS+ and a,- are ionic activities and and ys- the activity coefficients at the YH2S+ molahties m&s+ and MS-, respectively; m, = 1 mol kg-’ and aHs is the activity of the undissociated species HS at the mole fraction xus. Hence K,, is a dimensionless thermodynamic quantity which is a composite function of the intrinsic acidic and basic strength of the solvent and its relative permittivity. The recommended IUPAC method for the determination of pK, values in solvent mixtures [l] is based on e.m.f. measurements of the typical reversible cell Pt/Ag/AgCl/KS (m,-) + KC1 (m,,-) in HS/H+-sensing electrode
184
J. BARBOSA
where S- is the lyate ion and ms- and m,,- are the molalities of the lyate and chloride ions, respectively. With acetonitrile-water mixtures, the use of the hydrogen electrode is not appopriate because of the delicacy of its behaviour in contact with acetonitrile [4,5]. Also, as the method requires measurements in basic media, the e.m.f. quinhydrone electrode cannot be used as an H +sensing electrode [6]. The measurements of pH utilize, in most instances, the convenient and versatile glass electrode (GE). Thanks the modern technology, the potential of the external surface of this membrane electrode parallels to a remarkable extent that of the hydrogen gas electrode [7], the primary reference for hydrogen ion measurements. Other reference electrodes, especially the silver/silver chloride electrode, may constitute the left-hand element of the cell. This electrode is employed extensively in the determination of thermodynamic data by the e.m.f. method. From the above, the basic cell used in this work is Pt/Ag/AgCl/KS + KC1 in acetonitrile-water/GE
(A)
This cell permits reliable measurements of pH in acetonitrile-water mixtures used extensively in both voltammetry and reversed-phase liquid chromatography. In fact, the functional expression for the e.m.f. of the cell, E, is E = E o + g log( a,+ac&
(3)
where g = (In lO)RT/F and E o is the standard e.m.f. of the cell in the appropriate acetonitrilewater solvent mixture. Equation 3 requires a knowledge of the standard e.m.f. of cell A. The relevant E o values covering those acetonitrile-water mixture containing up to 70% (w/w) acetonitrile at 298.15 K were determined in this work from e.m.f. measurements of the reversible cell Pt/Ag/AgCl/HCl
in acetonitrile-water/GE (B)
AND
V. SANZ-NEBOT
The standard potential in cell B, which is, of course, the same as for cell A, is indispensable to the determination of pK,, values, but it is also needed for pH measurements in acetonitrile-water mixtures using the glass electrode. The need for reliable pH measurements in mixed solvents such as acetonitrile-water has become increasingly obvious in recent studies of the chromatographic behaviour of substances as a function of pH [8,9]. However, investigation into the importance of pH changes for the interpretation of the ionization effect in non-aqueous mobile phases in liquid chromatography has been restricted by the limited validity of pH measurements made with conventional electrodes calibrated in aqueous solutions. The highest reproducibility in pH measurements cannot be achieved if the electrodes are immersed in an aqueous medium for standardization and then moved suddenly to a medium of different composition such as acetonitrile-water, as is clearly explained by Mussini and Mazza [3]. On the other hand, considering the unlimited number of possible binary solvent acetonitrilewater mixtures, it is evident that an absurdly large number of experiments would be needed to determine all the corresponding pK,, values. Clearly, some procedure for predicting pK,, values, including pure water as the extreme case, is highly desirable. To explain the influence of solvent composition on the autoprotolysis constant of acetonitrilewater mixtures, Born’s model, being purely electrostatic in nature, could be insufficient. Bulk measurements of a solvent, such as dielectric constant, E, could be insufficient to describe or characterize the solute-solvent interactions. It is for these reasons that a number of empirical solvatochromic solvent scales have been developed, based primarily on spectroscopic measurements
DOI. For pure solvents the multiparametric equation of Kamlet and Taft [ll] in its more complete form includes terms which measure the hydrogen-bonding capacity by proton donation (a) or by proton acceptance (p), the polarity (m*), the polarizability (S), Hildebrand’s solubility parameter (6,) and the coordinated covalence (5). Also, simpler
EFFECTS
OF SOLVENT
COMPOSITION
ON GLASS
ELECTRODES
scales of solvent polarity have been defined as a function of empirical parameters such as r* [12] or the parameter ET” of Dimroth and Reichardt [lo]. The aim of this study was the determination of standard e.m.f. E” and pK,, values according to the criteria recently endorsed by IUPAC [1,13] in acetonitrile-water mixtures containing 0, 10, 30, 40, 50 and 70% (w/w) acetonitrile. Also, relationships between the autoprotolysis constant of the medium and different characteristics of the solvent mixtures (l/e, E,, +rr*, CYand /3) were examined.
EXPERIMENTAL
Apparatus Values of the e.m.f. of the potentiometric cell were measured with a Crison 2002 potentiometer ( + 0.1 mv), using a Radiometer G202C glass electrode and a reference Ag/AgCl electrode prepared according to the electrolytic method [14]. Its base was a smooth platinum wire, 1 mm in diameter. This platinum wire, after cleaning in concentrated nitric acid, was repeatedly washed in triply distilled water, then silver plated in a ILAg( bath (10 g 1-i) at a current density of 0.4 mA cm-’ for 5 h. After prolonged washing in water, the silver-plated wire was chloridized in 0.1 M HCl at a current density of 0.6 mA cm-* for 30 min and subsequently washed for a long period in triply distilled water. The cell was thermostated externally at 25 + 0.1” C. Test solutions were stirred magnetically under a continuous stream of purified nitrogen [washed with vanadium(I1) perchlorate solution, sodium hydroxide and distilled water and dried with soda-lime]. For potentiometric titrations, the titrant (KOH) was added from a Metrohm E415 Multidosimat autoburette equipped with an anti-diffusion tip. All the potentiometric assembly was automatically controlled with a Stronger AT microcomputer. The stabilization criterion for the e.m.f. readings was 0.2 mV within 120 s; if this stabilization is not achieved after 15 min, a new addition of titrant was made.
185
Reagents Analytical-reagent grade chemicals were used unless indicated otherwise. Stock 0.1 M potassium hyroxide (Carlo Erba, RPE grade) solutions were prepared with an ionexchange resin [15] to avoid carbonation and were standardized volumetrically with potassium hydrogenphthalate (Merck). Hydrochloric acid solutions were prepared from concentrated hydrochloric acid (Merck) and standardized volumetrically with tris(hydroxymethyl)aminomethane (Merck). Potassium nitrate (Merck) and potassium chloride (Merck) solutions were also prepared. All these solutions were prepared by mixing doubly distilled, freshly boiled water and acetonitrile (Merck, for chromatography grade).
Procedures The standard e.m.f., E O, of the cell with 0, 10, 30, 40, 50 and 70% (w/w) of acetonitrile in the solvent mixture was evaluated by two similar methods: the classical method [16,17] by series of e.m.f. measurements with cell B of HCl concentrations f 0.1 M, and the method of Gran [18] from titrations of diluted HCl solutions in the desired solvent using KOH solutions in the same solvent as the titrant, and evaluation of the calibration parameters using a multiparametric data-fitting procedure or Gran plots. These titrations were carried out with and without simultaneous additions of 0.3 M KNO, or 0.3 M KC1 solutions in the same mixed solvent, to take into account the influence of changes in ionic strength. From Gran plots before the equivalence point, using concentrations, c, of E-g
log cut-
g log ccl--
where y is the molar the basic side of E + g log css-
2g log y vs. aH+
activity
coefficient,
g log cc,- vs. a,-
(4)
and on
(5)
it was shown that the liquid junction potential of the cell remained constant and negligible. Thus, the E o value was calculated from the Gran function at each point of the titration. The latter method has the advantage that it permits the simultaneous determination of the au-
186
J. BARBOSA
AND
V. SANZ-NEBOT
expressed for log yf through a form of the Debye-Htickel equation [6,16]:
toprotolysis constant of the medium, which was calculated from the expression:
py * = AZ”Z/( 1 + a,BZ”2) + log(1 + 0.002MA,)
where g = 59.157 mV at 25” C and E o and Et are the standard potentials in acidic and basic medium, respectively. In a similar way, the e.m.f. measurements after the equivalence point of the titrations were used for the determination of the autoprotolysis constant [l].
or the classical Debye-Htickel
(8)
equation: (9)
where A and B are the Debye-Htickel constants, a0 is the ion size, b is the interaction parameter in the solvent mixture considered, MAW is the “molecular weight” of the acetonitrile-water mixed solvent and the ionic strength Z is the HCl molarity c. In compliance with IUPAC rules [2,13], the value of the product a,B is assigned at the appropriate temperature T by an extension of the Bates-Guggenheim convention [13,17] in terms of
RESULTS AND DISCUSSION
E.m.f. measurements for cell B at various concentrations of hydrochloric acid in the acetonitrile-water solvent mixtures studied were made for various series of HCl solutions and their values for one series in each solvent mixture are given in Table 1. The Nernstian expression with the assumption yc, = y, (which is reliable for an ionic strength Q 0.1 mol 1-l) is E= E” + 2g log(cy/c”)uc,
- bZ
(a,B),=
1.5[cw~s,‘(eSpW)]~
where the superscripts W and S refer to pure water and to the appropriate solvent mixture, respectively. Values of the dielectric constant, e, and densities, p, involved in the calculation of the Debye-Htickel constants A and a,B in Eqns. 8 and 9 were taken from data in the literature [6,16,19,20] and are quoted in Table 2 for readers’ convenience.
(7)
The dependence of the activity coefficients y, on the HCl concentration c can be appropriately
TABLE 1 Measured e.m.f. values of cell B for various acetonitrile-water
mixtures at 298.15 K
Acetonitrile in admixture with water (S, w/w) 0
10
30
40
50
70
CHCl
E
CHCl
E
CHCl
E
CHCl
E
CHCl
(Mx10e4)
(mV)
(Mx10m4)
(mv)
(MX 10m4)
(mv)
(MX10m4)
(mv)
(MX
6.04
9.6
6.13
26.1
4.20
23.3
8.03 10.0 17.9 23.7 35.2 42.6 57.3 66.2 83.6
23.4 35.3 65.0 79.5 99.2 108.8 123.5 130.6 142.2
8.14 10.2 18.2 29.9 43.3 58.4 67.2 76.1 84.9
40.7 51.6 81.4 106.1 124.4 139.2 146.2 152.2 157.6
9.00 13.3 17.4 21.0 27.5 33.0 35.5 41.0 85.7
60.8 80.7 93.8 103.3 116.6 125.7 129.2 135.3 172.7
8.06 16.0 23.8 31.5 39.1 46.5 53.9 61.1 75.3 83.9
10m4)
71.7
3.78
105.5 125.6 139.7 150.4 159.0 166.1 172.2 185.4 187.6
7.54 11.3 18.6 22.3 29.7 33.2 38.0 81.4 120
E
CHCl
E
(mv)
(MX10m4)
(mv)
47.7 81.2 101.8 127.0 136.0 150.0 155.9 162.5 199.0 218.1
4.04 8.05 12.0 16.0 20.0 23.8 27.6 31.4 35.2 39.0
108.6 143.0 163.0 177.0 187.6 196.4 203.7 209.9 215.2 220.2
EFFECTS
OF SOLVENT
COMPOSITION
ON
GLASS
TABLE 2 Values of dielectric constants, densities and Debye-Hiickel parameters A and a,B at 25OC and weight percentages of acetonitrile in admixture with water Acetonitrile concentration
z ;g ml-‘)
A (kg”’ mol-‘/2)
a,B (kg”’ mol-1/2)
0.9971 0.9809 0.9389 0.9150 0.8912 0.8465
0.5103 0.5404 0.6476 0.7227 0.8197 1.0181
1.5 1.5206 1.5918 1.6369 1.6859 1.7859
(% w/w) 0 10 30 40 50 70
78.36 75.01 65.52 60.38 55.44 46.82
+ 2g log(1 + 2cM,,)
+ a&/*) (11)
+ a&“*)
= E, + 2gbc
The classical Debye-Htickel equation is recommended by IUPAC for calculating the activity coefficient [2]. Consequently, Eqn. 9 was also tried as an alternative path to determine the E” values. Taking into account Eqn. 9, by insertion of PYi in Eqn. 7 the function for E, takes the simpler form E“ = E - 2g log c + 2gAc”*/(l
Taking into account Eqn. 8 by insertion of py, Eqn. 7 can be rearranged to define the extrapolation function @ [6] a= E - 2g log c + 2gAc”*/(l
187
ELECTRODES
(10)
Plotting Q, vs. c should produce a straight line whose intercept at c = 0 gives E” and from the slope of which the value of the interaction parameter b can be obtained [6]. Figure 1 shows the data obtained for the acetonitrile-water mixtures studied at 25 o C. As can be seen from the plots in Fig. 1, the slopes of the straight lines obtained have very small values and as a consequence the values obtained for b in such a series showed a high degree of dispersion, although very close to zero.
The average E” values obtained using Eqn. 11 for each HCl solution do not differ significantly from the data obtained from the extrapolation of the function @ (Eqn. lo), the average deviation being as low as 0.1 mV. Hence it can be concluded that the classical Debye-Htickel equation (Eqn. 9) can be used as a convenient approximation for the y, values of electrolytes in acetonitrile-water mixtures with up to 70% (w/w) acetonitrile. Evaluation of E” values by the Gran method [18], from titration of HCl solutions in the desired solvent mixture using KOH solution in the same solvent as the titrant, involves E values obtained in the acidic medium of the titrations and Eqn. 11 itself for cells without liquid junction potential. The Gran plots show that the liquid junction potential of the cell used is negligible and the E” values obtained are not significantly different from the data obtained previously. The E“ values obtained are summarized in Table 3. Table 4 gives the E“ values obtained for 40% (w/w)
TABLE 3 Values of the standard e.m.f., E“, in acetonitrile-water mixtures at 25’C and mole fraction x of acetonitrile as obtained elaborating measured E values of cell B and of titrations of HCl solutions with 0.1 M KOH solution Acetonitrile concentration
x
EO(mV)
0 0.0465 0.1583 0.2264 0.3051 0.5059
400.59 405.62 422.97 439.59 454.78 511.17
(% w/w)
0
0.002
o.oM
0.006
C
o.wII
0.01
0.012
0.01,
0.016
Fig. 1. Plot of extrapolation function @ vs. HCl concentration, c.
0 10 30 40 50 70
E” (Eqn. 12)
E0 (Eifn. 13)
(mv)
(mv)
400.01 406.15 424.29 437.69 455.37 511.20
400.32 406.17 423.29 437.50 456.59 510.85
188
.I. BARBOSA
TABLE 4 Values of the standard e.m.f., E O, in 40% (w/w) acetonitrilewater mixtures at 25 o C as obtained by the Gran method V
E
(ml)
(mv)
0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20
194.9 193.5 191.9 190.2 188.4 186.5 184.4 182.1 179.8 177.2 174.3 171.1
E”
PH
@VI 2.08 2.10 2.13 2.16 2.19 2.22 2.25 2.28 2.32 2.36 2.41 2.46
1.02x10-2 1.01 x10-2 1.01 x10-2 1.00x10-* 9.96~10-~ 9.91x10-3 9.86~10-~ 9.82~10-~ 9.77x10-3 9.72~10-~ 9.68~10-~ 9.63~10-~
439.40 439.59 439.66 439.71 439.75 439.80 439.77 439.68 439.75 439.72 439.62 439.51
AND V. SANZ-NEBOT
termination was based on e.m.f. measurements for the reversible cell A. Eliminating an+ in Eqn. 3, taking into account Eqn. 2 and ~~,~+=a~+ for simplicity, uHS = 1, and using concentrations, c, gives (E” - E)/g
+ log(cc,-/cs-) K,,
= -log
- lodYc,-/Ys-)
Expressing the simple-ion activity through an extended Debye-Htickel type 1: py, = AZ”2/(
1 + a,Bz”*)
= (E” - E)/g = pK,,
coefficients equation of
- b;Z
then from Eqn. 14 one can define tion function pK&: PK,,
(14)
05) the extrapola-
+ log&/cs-)
+ (b,--
bc,-)Z
(16)
acetonitrile-water, obtained from E values of HCl titrations with 0.0998 M KOH solution. To provide a test of internal consistency of the E” results, they were averaged by fitting all the data to a secondor third-order least-squares polynomial [19]. If the mole fraction x of nonaqueous component (acetonitrile) is the independent variable, the following equation is obtained:
Plotting pK& vs. Z and extrapolating to Z = 0, the intercept gives the pK,, value. In this work, for the acetonitrile-water mixtures, the classical Debye-Htickel equation was also tried as an alternative path to determine pK,, values. From Eqn. 9, the following simpler equation was obtained:
E” = 400.04 + 122.06x
PK,,
+ 195.00x2
(12)
and if the usually used concentration by volume, % (v/v), u, is the independent variable, the equation E” = 400.30 + 0.48 u - 3.38 x 1O-3 u* + 2.13
x 1o-4
u3
= (E“ - E)/g
+ log&/css)
(17)
The E measurements were made in solutions which correspond to the basic side of titrations of HCl solutions in the desired solvent mixture using KOH solutions in the same solvent as the titrant
(13)
is obtained. Equations 12 and 13 lead to the E” values with the quoted errors in Table 3. These equations can be used for interpolation of E” values at 298.15 K in the experimental range of x (from 0 to 0.5059). On the other hand, the normal pH scale or normal pH range in any solvent is conventionally defined as pK,,, where K,, is the autoprotolysis constant of the solvent at 298.15 K, a quantity that, unlike pH, is determinable in thermodynamically exact terms [3]. According to the criteria recently endorsed by IUPAC [l], and replacing the hydrogen electrode for a glass electrode for the practical reasons explained previously, pK,, de-
TABLE
5
Values of the extrapolation function pK,6 (Eqn. 16) for 10% (w/w) acetonitrile-water mixtures at 25 o C
vw
E (mV)
PS
I CM)
pK,‘p
2.10 2.20 2.30 2.40 2.50 2.60 2.70 2.80 2.90 3.00 3.10
- 415.5 - 419.4 - 422.9 - 425.9 - 428.7 -431.2 - 433.3 - 435.3 - 437.3 - 439.2 -440.7
2.61 2.55 2.49 2.45 2.40 2.36 2.33 2.30 2.27 2.24 2.21
9.46~10-~ 9.87~10-~ 1.03x10-2 1.07x10-2 1.11 x10-2 1.15x10-* 1.18x10-* 1.22x10-2 1.26~10-~ 1.30x10-* 1.34x10-2
14.28 14.27 14.28 14.28 14.28 14.28 14.28 14.27 14.28 14.28 14.28
EFFECTS
TABLE
OF SOLVENT
COMPOSITION
ON GLASS
ELECTRODES
TABLE
6
Values of autoprotolysis constants on a logarithmic acetonitrile-water mixtures at 25 o C Mole fraction of acetonitrile
scale for
pK,,
pK,, (Eqn. 18)
PK, (Eqn. 19)
PK,, (Eqn. 20)
14.00 14.27 14.93 15.32 15.71 16.76 33.58
14.03 14.29 14.90 15.27 15.70 16.79 -
14.07 14.26 14.86 15.27 15.74 16.78
14.04 14.23 14.94 15.32 15.71 -
7
Solvatochromic parameters mixtures studied Mole fraction of acetonitrile
values
for the acetonitrile-water
ET”
r*
a
P
1.00 0.93 0.84 0.81 0.79 0.76
1.17 1.14 1.03 0.97 0.91 0.84
1.084 0.973 0.870 0.855 0.859 0.866
0.47 0.40 0.41 0.40
(x)
(x) 0.0000 0.0465 0.1583 0.2264 0.3051 0.5059 1.0000
189
with and without simultaneous addition of a salt solution. The data obtained for a titration in 10% (w/w) acetonitrile-water are shown in Table 5, where pS = -log a,-. Comparison of the values of pK& given in the last column of Table 5 shows that the values of the extrapolation function PK.&, are not very sensitive to the values of I, and as a consequence the values of pK,, calculated with or without the use of the b values are not appreciably different. This implies that for acetonitrile-water mixtures, Eqn. 17 can be used for pK,, determination, which is the same equation as used for the Gran plots. Then, in acetonitrile-water mixtures, the use of Gran’s method permits the determination of sets of E” values in acidic medium and of pK,, values after the equivalence point for each titration performed in the desired mixture. The pK,, values obtained for all the acetonitrile-water mixtures studied are given in Table 6, where the previously obtained pK,, value for pure acetonitrile solvent is also given [21]. Relationships between the autoprotolysis constant of the medium and different characteristics of the solvent medium were examined. Thus, pK,, values were plotted against the mole fraction, X, %I (w/w), 54;(v/v), l/r, Ey, 7~*, a and p values. The ET values [22-241 and the Kamlet-Taft r* [25] and p [24] values for acetonitrile-water mixtures over the entire range of composition are known. The literature ET” and r* values permit an estimate of (Y values, the hydrogen bond acidity parameter, for acetonitrile-water mixtures [25].
0.0000 0.0465 0.1583 0.2264 0.3051 0.5059
Table 7 gives the relevant solvatochromic parameter values for the mixtures studied. When the data at a particular composition could not be located, the existing data were interpolated by a cubic splines method. When more than one data set was available, they were averaged by fitting all of the data to a third-order polynomial least-squares regression. When the values of pK,, are plotted against the mole fraction of acetonitrile, x, in the solvent mixture or against values of the reciprocal of the relative permittivity, l/e, of the solvent mixture, linear relationships are obtained (Figs. 2 and 3) over the whole experimental range of acetonitrile contents studied, up to 70% (w/w). The linear segments show slopes of 5.46 f 0.09 (r = 0.999) vs. x and of 314.84 +_ 8.30 (r = 0.998) vs. l/c and can be expressed by the following equations: pK,, = 14.03 + 5.46x
Fig. 2. Plot of pK,,
vs. mole fraction
(18)
of acetonitrile,
X.
190
J. BARBOSA
AND
V. SANZ-NEBOT
It is of practical interest to note that pK,, values are related to u (W, v/v) and w (W, w/w) by a second order polynomial of the types pK,, = 14.02 + 1.44 x lo-$I + 2.78 x 1O-4 u2 (21) and pK,, = 14.01+ 2.36 x 1O-2 w + 2.22 x 1O-4 w* (22)
Fig. 3. Plot of pKap vs. reciprocal of solvent mixtures, l/c.
of the relative
permittivity
and pK,, = 10.06 + 314.84/c
(19)
Equations 18 and 19 can be used for interpolation of PK,, values at 298.15 K in the experimental range of x (from 0 to 0.5059) (Table 6). These equations cover the whole set of experimental points, even those obtained in mixtures richer in acetonitrile. Plots of pK,, vs. the solvatochromic parameters ET, a and j3 show no zone of linearity for up to 70% (w/w) acetonitrile-water mixtures. If the results obtained for pK,, values are plotted against the ?r* values, only one zone of linearity is obtained (Fig. 4) in the range from 0 to 50% (w/w). This linear part shows a slope of -6.42 f 0.13 (r = 0.999) and can be expressed by pK,, = 21.55 - 6.42~*
Fig. 4. Plot of pK,, vs. Kamlet-Taft dipolarity parameters of solvent mixtures.
(20)
r*
polarizability/
Analysis of the plots shows that the autoprotolysis constant of the acetonitrile-water solvent mixtures decreases with increasing acetonitrile content in the medium and, as the plot vs. l/e shows, this decrease is that expected according to the electrostatic model. The optimum linearity of the plot of PK, vs. l/e indicates that the simple model in which only electrostatic interaction is considered explains the changes in pK,, values of acetonitrile-water mixtures over the full range of solvent compositions. This implies that electrostatic interactions are more important to consider than solute-solvent interactions such as those derived from hydrogen-bond formation and those derived from modifications in the solvation shell. The linearity of pK,, vs. 7~* plots up to 50% (w/w) acetonitrile is in accordance with the interpretation that Cheong and Carr [25] gave for the significant qualitative similarity in the shape of the plots of 7~* and E vs. volume fraction of the organic cosolvent in acetonitrile-water mixtures up to an acetonitrile content of ca. 50% (w/w). They pointed out that the principal effect of changing the solvent composition on the observed r* values operates through the dielectric properties of the local medium around the solute, taking into account that the dielectric constant is a bulk property of the mixture as a whole and the solvatochromic properties can only reflect the interaction of a solute with its immediate surroundings. It must be emphasized that each pK,, value for an acetonitrile-water mixture defines the normal pH scale or normal pH range in this mixture [26] and p&S (H+), the primary medium effect upon H+ [27], represents the acidic end of the normal pH scale in each distinct solvent mixture S with ultimate reference to the familiar aqueous pH
EFFECTS
OF SOLVENT
COMFQSITION
ON GLASS
ELECTRODES
scale and with physical comparability latter [3].
with the
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