J. CHEM. SOC. FARADAY TRANS., 1994, 90(21), 3287-3292 3287 Preferential Solvation in Acetonitrile-Water Mixtures Relationship between Solvatochromic Parameters and Standard pH Values Jose Barbosa' and Victoria Sanz-Nebot Department of Analytical Chemistry, University of Barcelona, Diagonal, 647.08028, Barcelona, Spain Standard pH values; pH(s), for five reference buffer solutions, KH tartrate, KH, citrate, KH phthalate, acetate buffer and phosphate buffer in acetonitrile-water mixtures containing 10, 30, 40, 50, 70 and 100 wt.% acetonitrile at 298.15 K have been determined using the IUPAC standardization rules. The relationship between pH(s) and solvent composition, expressed as a fraction, have been studied, with a view to assessing the presence of preferential solvation effects. In order to obtain pH(s) values for all possible acetonitrile-water mixtures, the linear solvation energy relationships method, LSER, has been applied. The pH(s) values were then correlated with the Kamlet-Taft, K*, a and /3 solvatochromic parameters of the acetonitrile-water mixtures. The equation obtained permits the standardization of potentiometric sensors in these mixtures. Solvent mixtures have attracted interest because of their fre- quent use and wide field of applications. A prominent binary mixture is acetonitrile-water. Aqueous acetonitrile is used in many branches of chemistry, ranging from hydrometallurgy to liquid chromatography, from reaction media for synthesis to electrochemistry, and the properties of these mixture are therefore of considerable interest. Accurate pH measurements in the more widely used binary acetonitrile-water mixtures are needed, since pH is potentially useful for optimizing methods. Accurate determination of the pH of reference buffer solu- tions for standardization of potentiometric sensors is the key to the pH-metric problem in aqueous organic solvent mix- tures such as acetonitrile-water.' *' The internationally recog- nized operational equation used for electrometric pH measurement3 is (E, - Ex) pH(x) = pH(s) + - 9 where Ex and E, denote the emf measurements, in cell A, in the sample solutions at unknown pH(x) and in the reference standard buffer solution at known pH(s), respectively, and g = log(RT/F) The reference pH values of the standard buffer solutions are influenced by the nature of the solvent and in acetonitrile-water mixtures they vary with solvent composi- tion in a manner that is not easily understood. Preferential solvation in binary solvent mixtures is impor- tant in solution chemistry for explaining spectroscopic, equi- librium and kinetic In general, preferential solvation is a composite effect determined by solute-solvent inter- actions and solvent-solvent interactions. The quasi-lattice quasi-chemical (QLQC) theory of prefer- ential solvation developed by Marcusg*'* can be applied to quantify the preferential solvation of the hydrogen ions in acetonit rile-w ater mixtures . The main quantity obtained from the theoretical approaches is the local mole fraction of one of the components of the mixtures, say water, around hydrogen ions, xf; . For the QLQC method 'local' means nearest-neighbour. Another way to express this is the preferential solvation, i.e. the excess or deficiency of the local mole fraction relative to the corre- sponding bulk quantity: 6, = x4 - x, is the preferential sol- vation of water around ions. The QLQC method permits the calculation of the preferential solvation parameter as a func- tion of the composition of the solvent, on the basis of infor- mation that is independent of the transfer of the ions to the solvent mixture. Central to the study of pH(s) in acetonitrile-water mixtures is the problem of how the solvated species reacts to changes in the environment. Certain microscopic phenomena of solutes are influenced by the solvent that forms their solva- tion sphere. This does not normally have the same properties as the bulk solvent, or even the same composition. In order to characterize this zone of the solvent, a group of solvatoch- romic parameters has been proposed. Recently' ' the polarity and ability to form hydrogen bonds in binary aqueous mix- tures of acetonitrile have been measured by the Kamlet-Taft solvatochromic parameters n*, a and /3."~'~ The polarity and polarizability of these solvents are measured by n*, the hydrogen-bond accepting ability is measured by fi, and the ability to donate a hydrogen atom for the formation of a hydrogen bond is measured by a. On the other hand, the solvatochromic parameter EJ30), proposed by Dimroth and Reichardt14 and the normalized EA30) parameter, E;, in ref- erence to sulfolane (EY = 0) and water (EY = I), have been used to study preferential solvation in binary solvent mix- ture~.~.' '." E: values are already known for acetonitrile- water mixtures." The purposes of the present study were: (a) to assess pH(s) values for five standard buffer solutions: 0.05 mol kg-' pot- assium dihydrogen citrate (KH, citrate); 0.1 mol 1-' acetic acid-0.1 mol 1-' sodium acetate (acetate buffer); 0.025 mol kg- ' potassium dihydrogen phosphate-0.025 mol kg- sodium hydrogen phosphate (phosphate buffer); a saturated solution, at 25"C, at potassium hydrogen tartrate (KH tartrate) and 0.05 mol kg- potassium hydrogen phthalate (KH phthalate), in acetonitrile-water mixtures containing 10, 30, 40, 50, 70 and 100 wt.% acetonitrile, according to the criteria recently endorsed by IUPAC;'v2 (b) to apply the QLQC theory to the study of the preferential solvation of the hydrogen ions in acetonitrile-water mixtures in order to clarify the acid-base behaviour of the solutes and (c) to study the correlation of pH(s) values with the solvatochromic parameters n*, a and fi for the acetonitrile-water mixtures by the LSER method with a view to determining the pH(s) values of the buffer reference solution studied in any of the binary solvent acetonitrile-water mixtures. The equations obtained allow calculation of the pH(s) values of the standard Downloaded by George Washington University on 16/04/2013 17:01:05. Published on 01 January 1994 on http://pubs.rsc.org | doi:10.1039/FT9949003287 View Article Online / Journal Homepage / Table of Contents for this issue
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J. CHEM. SOC. FARADAY TRANS., 1994, 90(21), 3287-3292 3287
Preferential Solvation in Acetonitrile-Water Mixtures Relationship between Solvatochromic Parameters and Standard pH Values
Jose Barbosa' and Victoria Sanz-Nebot Department of Analytical Chemistry, University of Barcelona, Diagonal, 647.08028, Barcelona, Spain
Standard pH values; pH(s), for five reference buffer solutions, KH tartrate, KH, citrate, KH phthalate, acetate buffer and phosphate buffer in acetonitrile-water mixtures containing 10, 30, 40, 50, 70 and 100 wt.% acetonitrile at 298.15 K have been determined using the IUPAC standardization rules. The relationship between pH(s) and solvent composition, expressed as a fraction, have been studied, with a view to assessing the presence of preferential solvation effects. In order to obtain pH(s) values for all possible acetonitrile-water mixtures, the linear solvation energy relationships method, LSER, has been applied. The pH(s) values were then correlated with the Kamlet-Taft, K*, a and /3 solvatochromic parameters of the acetonitrile-water mixtures. The equation obtained permits the standardization of potentiometric sensors in these mixtures.
Solvent mixtures have attracted interest because of their fre- quent use and wide field of applications. A prominent binary mixture is acetonitrile-water. Aqueous acetonitrile is used in many branches of chemistry, ranging from hydrometallurgy to liquid chromatography, from reaction media for synthesis to electrochemistry, and the properties of these mixture are therefore of considerable interest. Accurate pH measurements in the more widely used binary acetonitrile-water mixtures are needed, since pH is potentially useful for optimizing met hods.
Accurate determination of the pH of reference buffer solu- tions for standardization of potentiometric sensors is the key to the pH-metric problem in aqueous organic solvent mix- tures such as acetonitrile-water.' *' The internationally recog- nized operational equation used for electrometric pH measuremen t3 is
(E, - Ex) pH(x) = pH(s) + - 9
where E x and E, denote the emf measurements, in cell A, in the sample solutions at unknown pH(x) and in the reference standard buffer solution at known pH(s), respectively, and g = log(RT/F)
The reference pH values of the standard buffer solutions are influenced by the nature of the solvent and in acetonitrile-water mixtures they vary with solvent composi- tion in a manner that is not easily understood.
Preferential solvation in binary solvent mixtures is impor- tant in solution chemistry for explaining spectroscopic, equi- librium and kinetic In general, preferential solvation is a composite effect determined by solute-solvent inter- actions and solvent-solvent interactions.
The quasi-lattice quasi-chemical (QLQC) theory of prefer- ential solvation developed by Marcusg*'* can be applied to quantify the preferential solvation of the hydrogen ions in ace t oni t rile-w ater mixtures .
The main quantity obtained from the theoretical approaches is the local mole fraction of one of the components of the mixtures, say water, around hydrogen ions, xf; . For the QLQC method 'local' means nearest-neighbour. Another way to express this is the preferential solvation, i.e. the excess or deficiency of the local mole fraction relative to the corre-
sponding bulk quantity: 6, = x4 - x, is the preferential sol- vation of water around ions. The QLQC method permits the calculation of the preferential solvation parameter as a func- tion of the composition of the solvent, on the basis of infor- mation that is independent of the transfer of the ions to the solvent mixture.
Central to the study of pH(s) in acetonitrile-water mixtures is the problem of how the solvated species reacts to changes in the environment. Certain microscopic phenomena of solutes are influenced by the solvent that forms their solva- tion sphere. This does not normally have the same properties as the bulk solvent, or even the same composition. In order to characterize this zone of the solvent, a group of solvatoch- romic parameters has been proposed. Recently' ' the polarity and ability to form hydrogen bonds in binary aqueous mix- tures of acetonitrile have been measured by the Kamlet-Taft solvatochromic parameters n*, a and / 3 . " ~ ' ~ The polarity and polarizability of these solvents are measured by n*, the hydrogen-bond accepting ability is measured by f i , and the ability to donate a hydrogen atom for the formation of a hydrogen bond is measured by a. On the other hand, the solvatochromic parameter EJ30), proposed by Dimroth and Reichardt14 and the normalized EA30) parameter, E;, in ref- erence to sulfolane (EY = 0) and water (EY = I), have been used to study preferential solvation in binary solvent mix- tu re~ .~ . ' '." E: values are already known for acetonitrile- water mixtures."
The purposes of the present study were: (a) to assess pH(s) values for five standard buffer solutions: 0.05 mol kg-' pot- assium dihydrogen citrate (KH, citrate); 0.1 mol 1-' acetic acid-0.1 mol 1-' sodium acetate (acetate buffer); 0.025 mol kg- ' potassium dihydrogen phosphate-0.025 mol kg- sodium hydrogen phosphate (phosphate buffer); a saturated solution, at 25"C, at potassium hydrogen tartrate (KH tartrate) and 0.05 mol kg- potassium hydrogen phthalate (KH phthalate), in acetonitrile-water mixtures containing 10, 30, 40, 50, 70 and 100 wt.% acetonitrile, according to the criteria recently endorsed by IUPAC;'v2 (b) to apply the QLQC theory to the study of the preferential solvation of the hydrogen ions in acetonitrile-water mixtures in order to clarify the acid-base behaviour of the solutes and (c) to study the correlation of pH(s) values with the solvatochromic parameters n*, a and f i for the acetonitrile-water mixtures by the LSER method with a view to determining the pH(s) values of the buffer reference solution studied in any of the binary solvent acetonitrile-water mixtures. The equations obtained allow calculation of the pH(s) values of the standard
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buffer solutions in any acetonitrile-water mixture up to 70 wt.% acetonitrile and thus permit the standardization of potentiometric sensors in these mixtures.
Experimental Apparatus
The emf values of the potentiometric cell were measured with a CRISON 2002 potentiometer (k0 . l mV) using a Radi- ometer G202C glass electrode and a reference Ag/AgCl elec- trode prepared according to the electrolytic method17 and directly inmmersed in the solution to avoid the residual liquid-junction potentials. This electrode system gave stable and reproducible potentials within 5 min. The glass electrode was stored in water when not in use and soaked for 15-20 min in acetonitrile-water mixture before potentiometric mea- surements. The E" values used here are the average of at least 15 standardizations. l7 The standardization of the electrode system was carried out each time the solvent medium or elec- trodes were changed, and the constancy of E" values was assured by continual surveillance by means of periodic cali- brations. The cell was thermostatted externally at 25 0.1 "C. All the potentiometric assembly was automati- cally controlled by a Stronger AT microcomputer.
Reagents
Analytical reagent grade chemicals were used, unless other- wise indicated.
All of the solutions were prepared by mixing doubly dis- tilled, freshly boiled water, the conductivity of which did not exceed 0.05 pS cm-', and acetonitrile (Merck, chromatog- raphy grade). The concentrations of the standard reference solutions were chosen as recommended by IUPAC.3 Primary standards (potassium hydrogen tartrate, potassium dihydro- gen citrate, disodium hydrogen phosphate, potassium dihy- drogen phosphate and potassium hydrogen phthalate) were Merck reagents for preparation of pH standard buffer solu- tions according to DIN 19266. Chemicals were dried at 110 "C before use. Anhydrous sodium acetate and anhydrous acetic acid were Carlo Erba Reagents, RPE-ACS and RS grade, respectively.
Stock 0.1 mol I - ' potassium hydroxide (Carlo Erba, RPE grade) solutions were prepared with an ion-exchange resin' to avoid carbonation and standardized volumetrically against potassium hydrogen phthalate.
Procedures
Reference pH values of standard buffer solutions in acetonitrile-water mixtures with 10, 30, 40, 50 and 70 wt.% acetonitrile, pH(s), were assigned using the procedure adopted by IUPAC.2 This procedure involves different steps:I8 (i) measurement of the emf of the cell:
standard buffer + KCl in acetonitrile-water
glass electrode
where the reference standard buffer solution contains pot- assium chloride at different and accurately known concentra- tions. The emf, E , of this cell is directly related to the activities of the hydrogen and chloride ions in solution:
E = E" + log(aH+ + I - ) (2) where E" is the standard emf of the cell. E" values were deter- mined as in a previous study.17
(ii) Determination of the pH values for each concentration of potassium chloride, eel-, examined using the Nernst expression of emf, E , for cell (A):
P(aH+ycl-) is a thermodynamic quantity that can be deter- mined in thermodynamically exact terms, but to obtain pH values for the mixed electrolyte in cell (B) it is essential to calculate the molar activity coefficient, pycl-, through an extra-thermodynamic assumption, i.e. a form of the classical Debye-Huckel equation
(4)
In compliance with IUPAC rule^,^,'^ the value of a, B in eqn. (4) is assigned at T = 298.15 K by an extension of the Bates-Guggenheim convention :2i3
(a, B)T = 1.5[(&wps)/(&spw)];'2
where E is the relative permittivity, p the density and the superscripts W and S refer to pure water and to the approp- riate solvent mixture, respectively.
Calculation of pycl- from eqn. (4) requires knowledge of the ionic strength, I , of the standard buffer-KC1 mixed elec- trolyte solutions
1 = I , + cc1-
but I is, in turn, a function of the H + concentration cH+, which is expressed by
(7)
and of the ionization constants, pK, corresponding to the equilibria involved in the standard buffer solutions in acetonitrile-water mixtures. These pK values were deter- mined previously."
Then, calculation of pycl - values proceeds by successive iterations. Initially one takes I = c, + ccl- and obtains pycl- from eqn. (4), for subsequent insertion in eqn. (7) to obtain pcH+ and a better value of I by eqn. (6). Thus, one calculates again the pycl- value by eqn. (4), and so on, until constancy of I is obtained.
Inserting pycl- in eqn. (3), a distinct pH value is obtained for each concentration ccl- examined. The standard value, pH(s), for standard buffer alone at the fixed concentration recommended as International pH Standards3 can finally be obtained as the intercept at ccl- = 0 from the pH us. ccl- linear regression at each mole fraction, x, of acetonitrile studied.
Moreover, pH(s) values were obtained in pure acetonitrile solvent for the three standard buffers that are soluble in this medium. For this purpose, the potentiometric system described previously2' was used and the standard potential of the cell was determined by titration of picric acid solutions in acetonitrile with tetrabutylammonium hydroxide as in pre- vious
Results and Discussion The emf, E, of cell B was measured at different concentrations ccl- of KCl added to the constant concentration of each stan- dard buffer in 10, 30, 40, 50 and 70 wt.% acetonitrile-water solvent. For each standard buffer solution various series of measurements were performed, for a total of 560 independent measurements over the solvent interval explored. When the acidity function, pH, for each buffer solution was plotted us. ccl-, straight lines of small slope were obtained. Typical
regression lines are shown in Fig. 1 for the KH tartrate in the acetonitrile-water mixtures studied.
The statistical analysis of variance was applied to the various independent sets of measurements. The variances that we can hope to estimate are s;, the variance within sets of data or series of measurements and s i , the variance between sets of data. If applying the F-test for a 5% level of signifi- cance we can conclude that the two variances do not differ significantly, then, for a given primary standard buffer, all the points of every data set belong to the same population and it should be permissible to calculate the total average, pH,, and the standard deviation, s, by fitting all the points together and carrying our least-squares analysis. If this hypothesis is rejected, then most of the error derives from the variability between data series, the pH(s) value is obtained by averaging the different intercepts and the total variance s2 = s; + s; can be calculated.
Table 1 shows the pH(s) values determined for the KH tar- trate, KH, citrate, phosphate buffer, KH phthalate and acetate standard buffer solutions in 10, 30, 40, 50 and 70 wt.% acetonitrile-water mixtures and the respective standard deviations, s, together with standard pH(s) values reported in water24 that can be used for standardization of poten- tiometric sensors in these solvents. Table 1 also shows the pH(s) values in neat acetonitrile obtained in the present work. pH(s) values of acetate and phosphate buffers cannot be obtained in 70 wt.% acetonitrile-water mixtures or in neat acetonitrile, since these substances are not soluble in these media.
Although the variation of the pH(s) values obtained in acetronitrile-water mixtures with xAN is approximately linear in the mixtures studied (Fig. 2) these pH(s) are lower than the expected values considering the high pH(s) in the neat solvent acetonitrile, (Table 1). Thus, preferential solvation by one of
2 -0.05 0.05 0.15 0.25 0.35 0.45 0.55
X A N
Fig. 2 pH(s) as a function of the mole fraction of acetonitrile, xAN in the acetonitrile-water mixtures. V, KH tartrate; +, KH, citrate; +, KH phthalate; 0, acetate buffer; A, phosphate buffer.
the solvents is expected. If a solute interacts with one solvent more strongly than with the other, the solute will be prefer- entially solvated by the former. Preferential solvation in acetonitrile-water mixtures produce lower pH(s) than expected if the 'preferred' solvent is water.
As a consequence of the mixture nature of the Dimroth and Richardt solvatochromic parameter, E,(30), which is sen- sitive to many solvent-solvent interactions, it has been used to study preferential solvation in many binary mix- tUres.4,8,15,25 The normalized EF values for acetonitrile- water mixtures ' 3 6 v 2 7 are given in Table 2. Krygowsky et ~ 1 . ' ~ studied the contribution of the transition energy of pyri- dinium betaine due to specific interactions (E;) in aqueous binary solvent mixtures. A plot of EY values of the acetonitrile-water mixture us. the mole fraction of water is shown in Fig. 3. For these mixtures there is preferential sol- vation of betaine by acetonitrile in the water-rich region. The strong self-association interactions between the water mol- ecules makes them less available for solvation. However, as more dipolar aprotic solvent is gradually added it breaks the self-associated structure of water and the resulting 'free' water molecules then interact with the solute.4*" Thus, the solute is preferentially solvated by water in the acetonitrile-
Table 2 Solvatochromic parameter values for the acetonitrile-water mixtures studied
x w Fig. 3 ,!$ values of acetonitrile-water mixtures us. the mole fraction of water, x,
rich region. The transition occurs at an intermediate solvent composition around xAN z 0.35 or ca. 55 wt.% acetonitrile. The solvation of the betaine used to establish the E , scale of solvent polarity may, however, be different from that of inor- ganic ions since it is large and hydrophobic. Moreover, in water-acetonitrile mixtures, the specific solvation of iodide and chloride ions has been studied by UV and NMR, respec- t i ~ e l y . ~ ~ , ~ ~ The results showed that iodide and chloride are preferentially solvated by water in acetonitrile-water solvent mixtures. In a parallel manner to the E , scale, halide ions, n-alkylpyridinium iodides' or several alkyl halide^,^ the solutes in the buffer solutions studied are likely to undergo preferential solvation in acetonitrile-water mixtures.
The composition of the immediate surroundings of a solute may be different from the composition of the bulk mixture. Preferential solvation is attributable to an excess or a defi- ciency of molecules of one of the solvents in these surround- i n g ~ . ~ ~ If the solute has no preference between the solvent molecules, the solvent composition in the cybotactic zone, in the immediate neighbourhood of the solute, is the same as in the bulk. For such cases:
where pH(s), and pH(s), represent the standard pH(s) values in solvents 1 and 2, respectively.
The deviation from the ideal dependence on the composi- tion of the mixture, pH(s) us. x1 plot (Fig. 4) indicates that the solvent composition in the neighbourhood of the solute may be different from that in the bulk. Fig. 4 shows the pH(s) values as a function of xl , the bulk mole fraction of water. pH(s) us. x1 plots are not linear but a dotted line indicating linearity over the entire range (henceforth referred to as the ideal line) is also shown.
The results from the QLQC method at 25 "C for the prefer- ential solvation by water, a,, and for the local mole fraction of water, x i , around a hydrogen ion are shown in Table 3 and plotted in Fig. 5 and 6, respectively, as functions of the composition of the binary mixtures of water and acetonitrile. The preferential solvation of hydrogen ions by water is posi- tive, i.e. water molecules show a greater tendency to be in the immediate vicinity of a given hydrogen ion than acetonitrile molecules. This preference is a maximum at x, z 0.25. The results, in terms of preferential solvation by water, d,, Fig. 5 and Table 3, are similar to those also obtained for chloride ions in aqueous acetonitrile" with a similar At G*(Cl-, W + AN)kJ mol-' = 42.1.31
Therefore, as the preferential solvation of hydrogen ions by water is positive, the standard pH(s) values in these mixtures are more similar to the standard pH(s) values in water than to the pH(s) in acetonitrile (Fig. 4). This is different from com-
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I I I I 1 I I I I 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
xw Fig. 4 pH(s) us. mole fraction of water, x,, in acetonitrile-water mixtures. +, KH tartrate; 0, KH, citrate; f , KH phthalate. The dashed straight lines correspond to the ideal variation of the pH(s) values for the three buffer solutions.
Fig. 5 Preferential solvation of hydrogen ions by water in acetonitrile-water mixtures, a,, as a function of the solvent composi- tion. The dashed straight line corresponds to total preference for water.
accordance with the low values of 6 , in acetonitrile-water mixtures with xAN < 0.15, Fig. 5. In the range 0.15 d xAN < 0.75 there are clusters of molecules of the same kind sur- rounded by regions where molecules of the two kinds are near each other. In this middle range of compositions prefer- ential solvation of hydrogen ions by water is high, Fig. 5, this could explain the low slope of the linear variations of the pH(s) us. x, plots (Fig. 4). At xAN 2 0.75 the number of water clusters is low, and water-acetonitrile interactions that could be discounted in the middle range now become important. One may consider this region as 6, decreases, Fig. 5, and then a concave variation of the pH(s) us. x, plot as represent- ed by the dotted line for KH phthalate in Fig. 4 could be expected. The boundaries of the regions are, of course, not sharp.' '
On the other hand, it is not self-evident that solvatochro- mic parameters would be valid to represent generalized solutes in binary solvent mixtures with regard to the proper- ties they are supposed to measure. Preferential solvation in such mixtures may interfere more seriously with the ability of indicators to represent generalized solutes than in the case of single solvents. Progress has been made' 1*36 and although this problem has not been solved unequivocally, these investi- gations, provide significant evidence that the solvatochromic parameters seem to have general validity. It is therefore, of interest to examine the LSER which explain any solute pro- perty varying with solvent composition as a linear com- bination of the microscopic parameters of the solvent responsible. The Kamlet-Taft ' expression states :
(21)
where a, /? and n* are the microscopic parameters previously described, X Y Z is the solute property, X Y Z , the value of this property for the same solute in a hypothetical solvent for which a = /? = n* = 0 and a, b and c are the susceptibilities to changes in a, /3 and n*, respectively, of the solute property studied. This equation can include additional terms or some of its terms can become equal to zero, depending on the pro- perty of the solute to be described.37 Values of the Kamlet- Taft solvatochromic parameters n*,' 1.38 a' 1*39 and / ? " 7 ' 5 for acetonitrile-water mixtures over the entire range of composi- tion are known. Table 2 gives the relevant solvatochromic parameter values for the mixtures studied.
Several attempts were made to find the best form of the Kamlet-Taft equation to describe the variation of stan- dard pH(s) values in acetonitrile-water mixtures. Multiple regression analysis was applied to our pH(s) data. All pos- sible combinations of solvatochromic parameters were checked. The best fit was obtained when the three solvatoch- romic parameters a, #? and 7r* are used, yielding the general equations shown in Table 4. From a practical point of view these equations enable us to know the standard pH(s) values of the buffer reference solutions studied in any binary solvent acetonitrile-water mixture up to 70 wt.% acetonitrile, and thus permit the standardization of potentiometric sensors in these mixtures.
X Y Z = ( X Y Z ) , + aa + b/? + s7r*
f /
/ ,
x w
Fig. 6 Local mole fraction of water, xk, near hydrogen ion as a function of its bulk mole fraction, x w , according to the QLQC method
positions close to the acetonitrile pure where x, < 0.25 and the preferential solvation by water decreases quickly, Fig. 5.
The pH(s) values obtained could be explained in terms of the structural features of the acetonitrile-water mixtures. The structure of mixtures of water and acetonitrile was explored by Marcus and Migron" using the QLQC and the inverse Kirkwood-Buff integral (IKBI) methods. These authors con- cluded that these methods indicate strong microheterogeneity in a middle range of compositions in mixtures of water and acetonitrile, i.e. preference for neighbours of the same kind, which extends over several concentric shells around a given molecule. Thus, there is a preference of a given water mol- ecule for water molecules rather than acetonitrile molecules. This preference is a maximum at xAN x 0.75. The same applies to the preference of acetonitrile molecules to be in the vicinity of a given acetonitrile molecule. Thus, the plot of pH(s) values us. x,, Fig. 4, can be explained by taking into account that in acetonitrile-water mixtures there are three regions.7.1 1.33.34 On the water-rich side there is a region in which the water structure remains more or less intact and the acetonitrile molecules gradually occupy the cavities between water molecules without disrupting the water s t ruc t~re .~ ' The limit of xAN beyond which the acetonitrile can no longer be accommodated within the cavities of the structure of water is CQ. 0.15." The variation of the pH(s) values for KH phthal- ate over the whole composition range is shown in Fig. 4, where the dotted line represents the expected varation of pH(s) between xAN = 0.5 and pure acetonitrile solvent. pH(s) values vary linearly with x, with an inflection point at xAN x 0.15. The slope of the pH(s) us. x, plot is greater in the water- rich region, xAN < 0.15, than in the regions where water- acetonitrile mixtures show microheterogeneity, which is in
Table 4 Linear solvation energy relationships for pH(s) values
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