Anal. Chem. 2002, 74, 6073-6079
High-Basicity Determination in Mixed Water-Alcohol Solutions by a Dual Optical Sensor Approach T. Andrew Canada and Ziling Xue*
Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996-1600
The activity of NaOH is known to be significantly affected by the presence of an alcohol in aqueous solutions. A novel linear relationship between (DA/DCalcohol) and Cbase was found in the highly alkaline, mixed H2O-ROH solutions (R ) Me, Et, i-Pr). The use of this linear relationship led to a dual-transducer approach to decompose the optical signals of optical base sensors and to give base and alcohol concentrations in concentrated NaOH-H2OROH solutions ([OH-] ) 0.05-3.6 M). The scope of the new dual-sensor approach was evaluated, and errors in Cbase and Calcohol were analyzed. The optical base sensors consist of sol-gel SiO2-ZrO2-organic polymer composites doped with high-pKa indicators. The pKas of the indicators encapsulated in the composite films were determined and found to be affected by the composition of the sol-gel composites. Optical sensors and their uses in multicomponent systems are of intense current interest.1-7 In the multicomponent systems, the activity of the analyte and sensor response are often affected by change in ionic strength. For optical sensors that are based on indicator equilibria involving the analyte as their transducing mechanism, such effect is particularly significant. The concentrations of both the analyte and other chemicals affect ionic strength, and the sensor response to concentration of the analyte is thus often indistinguishable from those of other chemicals. An accurate measurement of each component in these multicomponent systems is actively studied. Several approaches have been developed to correct ionic strength in optical sensing for the pH region and solutions of low-to-medium ionic strength.1-9 We recently reported a dual-transducer approach to measure acid concentrations (2-9 M HCl) in salt-containing, concentrated strong acids such as MClx-HCl (M ) Li, Ca, Al) solutions.10 This approach was shown to reduce the error in Cacid from, for example, * Corresponding author. E-mail:
[email protected]. (1) Edmonds, T. E.; Flatters, N. J.; Jones, C. F.; Miller, J. N. Talanta 1988, 35, 103. (2) Wolfbeis, O. S.; Offenbacher, H. Sens. Actuators 1986, 9, 85. (3) Lavigne, J. J.; Savoy, S.; Clevenger, M. B.; Ritchie, J. E.; McDoniel, B.; Yoo, S.-J.; Anslyn, E. V.; McDevitt, J. T.; Shear, J. B.; Neikirk, D. J. Am. Chem. Soc. 1998, 120, 6429. (4) Opitz, N.; Luebbers, D. W. Sens. Actuators 1983, 4, 473. (5) Aussenegg, F. R.; Brunner, H.; Leitner, A.; Lobmaier, C.; Schalkhammer, T.; Pittner, F. Sens. Actuators, B 1995, 29, 204. (6) Zhang, L.; Langmuir, M. E.; Bai, M.; Seitz, W. R. Talanta 1997, 44, 1691. (7) McCurley, M. F.; Seitz, W. R. Anal. Chim. Acta 1991, 249, 373. (8) Shamsipur, M.; Azimi, G. Anal. Lett. 2001, 34, 1603. (9) Noire, M. H.; Couston, L.; Douarre, E.; Pouyat, D.; Bouzon, C.; Marty, P. J. Sol-Gel Sci. Technol. 2000, 17, 131. 10.1021/ac0202987 CCC: $22.00 Published on Web 10/31/2002
© 2002 American Chemical Society
60 to 13 become “nonideal” media, and the traditional pH scale cannot adequately reflect alkalinity in these solutions. The Hammett acidity function in eq 1 was introduced for these highly alkaline media.16,17,23 In the
H• ) pKw + log COH- - log aw + log(γHIndγOH-/γInd-) (1) relationship in eq 1, a weakly acidic indicator was used to address severe deviations due to the nonlinearity between [OH-] and activity aOH- in concentrated alkaline solutions.23 The activity coefficient term in eq 1 makes an important contribution to the H• value.23 Individual activity coefficients cannot be directly determined experimentally. Yagil and Anbar slightly modified eq 1 to give eq 2 for H• calculation.21 The term,
H• ) pKw + log COH- - (n + 1) log Cw
(2)
Cw, is the concentration of “free water” and is defined to be the amount of water that is not bound to OH- in hydration. Cw can be determined from eq 3, where d is the density of the aqueous
Cw ) d - 0.001(MW + 18.0n)COH-
(3)
NaOH solution, MW is the molecular weight of NaOH, and COHis the molar concentration of NaOH.21 The hydroxide hydration number, n, is taken to be 3. The assumption is that the two different forms of indicator are equally hydrated.21 H• values calculated by this method agree well with the experimental results by Schwarzenbach and Sulzberger up to 7 M NaOH concentrations.24 Equations 2 and 3 were used in the current studies for the determination of pKas of TY and AY encapsulated in our sensor matrixes. Equations 2 and 3 were, however, not used in the empirical approach developed in the current studies to determine Cbase and Calcohol. These issues are discussed below. H• was found to strongly depend on the solvent.17 For instance, H• was found to equal 12.66, 14.57, and 16.95 for nonaqueous methanol, ethanol, and 2-propanol solutions of 0.10 M NaOH, respectively.17 The solvent dielectric constants at 25 °C for MeOH, EtOH, and i-PrOH are 32.6, 24.3, and 18.3, respectively.17,25 In other words, at a constant concentration of NaOH, the OH- activity is greater in a protic solvent of a lower dielectric constant.17 Solvents of low dielectric constants are generally nonpolar hydrocarbons that are poor at solvating ions because of the diminished ability to hydrogen bond, thus leading to higher OH- activity.26 H• values in various nonaqueous alcoholic NaOH solutions were reviewed by Bowden.17 In a NaOH aqueous-organic mixed solvent system, the basicity of such a ternary system appears to be a function of the (21) Yagil, G.; Anbar, M. J. Am. Chem. Soc. 1963, 85, 2376. (22) Robinson, R. A.; Harned, H. S. Chem. Rev. 1941, 28, 419. (23) Rochester, C. H. Acidity Functions; Academic Press: New York, 1970; pp 234-261. (24) Schwarzenbach, G.; Sulzberber, R. Helv. Chim. Acta 1944, 27, 348. (25) Carey, F. A. Organic Chemistry, 2nd ed.; McGraw-Hill: New York, 1992; pp 323-324 and 937. (26) McMurry, J. Organic Chemistry, 3rd ed.; Wadsworth, Inc.: Belmont, CA, 1992; pp 384-386.
autoprotolysis constant and the proton affinity of the organic solvent.17 Insufficient organic solvate molecules or solvate molecules of a lower dielectric constant than water can both contribute to the generation of fewer hydrated hydroxide ions.17,27 Two factors that affect the OH- activity have been considered in these NaOHH2O-organic solvent ternary systems.17 First, solvation effects involving “good hydrogen bonders” lower hydroxide activity. If solvents of low dielectric constants and poor hydrogen bond acceptors such as 2-propanol are present, rapid elevations in the concentration of nonsolvated hydroxide occur.17,20 In some cases, the added solvent can compete with hydroxide for hydrogen bonding, therefore removing water from the solution that would normally hydrogen bond to hydroxide.17 The second factor is the reduction in the number of solvent molecules in mixed H2Oorganic solvents. In dilute aqueous hydroxide solutions, there are adequate water molecules to readily solvate OH- ions. However, when water is replaced by an organic solvent, a deficiency in solvate molecules may arise. For example, an equal volume of ethanol contains fewer moles than that of water. Therefore, there exist fewer available solvating molecules in mixed H2O-organic solvents, thereby increasing the OH- activity.27 The effect of the organic solvent on alkalinity in NaOH-H2Oorganic systems is also shown in acidity function H•. Equation 2 indicates that, as Cwater is reduced (while increasing Calcohol) at constant COH, H• inherently increases.17 For example, H• incrementally rises from 11.74 to 15.71 when i-PrOH concentration increases from 0 to 100% at a constant 0.005 M NaOH.17 In the base sensors studied here, an increase in A was observed when Cbase or Calcohol was increased in mixed aqueous-alcohol solutions. If no correction for organic solvent is performed in mixed aqueous-organic solvent systems, we found that measurements in Cbase by our optical sensors gave errors as large as 99.4%. As an example, Figure 1 shows errors in Cbase measurements by sensors TY2 and AY2 in NaOH-H2O-EtOH solutions.20 Dual Optical Transducer Approach. We have chosen NaOH-H2O-ROH (R ) Me, Et, i-Pr) ternary systems to demonstrate our dual optical transducer approach to accurately measure Cbase and Calcohol. The solubility of NaOH and water in the alcohol is an important criterion in choosing these media. Methanol and water are mixable, and the solubility of NaOH in methanol is high (23.9 g/100 mL or ∼6 M).28 Ternary phase diagrams of NaOH-H2O-EtOH and NaOH-H2O-i-PrOH solutions have been reported.29, 30 This dual optical transducer approach is based on a novel linear relationship that we observed in the NaOH-H2O-ROH ternary systems. An optical sensor that bases its transducing mechanism on an indicator chemical equilibrium (e.g., eq 4) may show a
HInd + OH- ) Ind- + H2O
(4)
nonlinear relationship between its analytical signal and analyte concentration.10 When no alcohol is present, absorbance (A) is a function of Cbase. Nonlinear relationships between A and Cbase were observed in the current studies. At a fixed Cbase, A was found to (27) O’Ferrall, R. A. M.; Ridd, J. H. J. Chem. Soc. 1963, 5030. (28) Murray, A. G. J. Assoc. Off. Agric. Chem. 1929, 12, 309. (29) Peyronel, G. Gazz. Chim. Ital. 1949, 79, 792. (30) Mills, A. L.; Hughes, F. Chem., Eng. Data Ser. 1957, 2, 35.
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Figure 1. Error in CNaOH using (a) sensor TY2 and (b) sensor AY2 in NaOH-H2O-EtOH solutions before correction via the dual-sensor approach.
increase with increased alcohol concentration Calcohol. Experimental 3-D plots of A versus Cbase and CROH for the Thiazole Yellow GGM sensors TY1-3 are given in Figure 2. Several different empirical mathematical curve fittings may be used for the calibration plots in the aqueous, alcohol-free solutions (Figure 3). A sigmoidal curve-fitting function, which we reported earlier for acid sensors in acid-salt-H2O ternary systems,10 gave an average value of (0.990 for the curve-fitting correlation factor (R2) in the current aqueous NaOH solutions. A logarithmic curvefitting function (eq 5) was found to give slightly better fitting with average R2 values of (0.999 and could be applied to all six sensors (TY1-3 and AY1-3). We would like to emphasize that both mathematical curve-fitting models are empirical, and in the current work, the logarithmic curve-fitting function in eq 5 was employed with different curve fitting constants a, b, and c for all six sensors.20
A ) f(Cbase) ) c + a ln(Cbase - b)
(5)
Figure 2. 3-D plots of the response of the TY sensors: (a) TY1 in NaOH-H2O-MeOH; (b) TY2 in NaOH-H2O-EtOH; (c) TY3 in NaOH-H2O-i-PrOH solutions.
We found that, in these NaOH-H2O-ROH ternary systems, there is a novel linear relationship as shown in eq 7 for 0-70
(∂A/∂Calcohol)Cbase ) dCbase + e
(7)
vol % Calcohol. (∂A/∂Calcohol)Cbase, the slope of absorbance change with respect to Calcohol at a fixed Cbase, is a linear function of Cbase. This linear relationship in various NaOH-H2O-ROH solutions is shown in Figure 4.20 We found that this novel linear relationship (eq 7) could be used to calculate Calcohol and Cbase. The change ∆A in mixed aqueous-organic solvents can be represented by eq 8.
In NaOH-H2O-ROH ternary systems, the total sensor absorbance At was found to be functions of both base and alcohol concentrations, as shown in Figure 2.20 In such mixed solvent systems, the use of organic solvent leads to an absorbance increase ∆A from A in aqueous, alcohol-free NaOH solution. The total absorbance At is thus
Substituting the linear curve-fitting eq 7 into eq 8 gives ∆A in eq 9.
At ) A + ∆A
∆A ) (e + dCbase)Calcohol
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(6)
Analytical Chemistry, Vol. 74, No. 23, December 1, 2002
∆A ) (∂A/∂Calcohol)CbaseCalcohol
(8)
(9)
Figure 3. Calibration plot of A vs Cbase for (a) sensor TY2 and (b) sensor AY2 in aqueous solutions. Figure 5. Errors in Cbase measurements after the corrections: (a) NaOH-H2O-MeOH; (b) NaOH-H2O-EtOH; (c) NaOH-H2O-iPrOH.
When two independent transducers are used, we have the following two independent equations (eqs 11 and 12).
At1 ) c1 + a1 ln(Cbase - b1) + (e1 + d1Cbase)Calcohol (11) At2 ) c2 + a2 ln(Cbase - b2) + (e2 + d2Cbase)Calcohol (12)
Figure 4. Plots of (∂A/∂Calcohol) vs CNaOH in NaOH-H2O-ROH ternary systems: (a) R ) Me (sensor TY1); (a′) R ) Me (sensor AY1); (b) R ) Et (sensor TY2); (b′) R ) Et (sensor AY2); (c) R ) i-PrOH (sensor TY3); (c′) R ) i-PrOH (sensor AY3).
and thus At in eq 10.
At ) c + a ln(Cbase - b) + (e + dCbase)Calcohol
(10)
Solving eqs 11 and 12 for the two independent sensors gives Cbase and Calcohol. In essence, this approach converts (∂A/∂Calcohol)Cbase, an unknown function of Cbase, into a linear function (dCbase + e). The parameters d and e could be determined experimentally and, thus, lead to the computed solutions for Cbase and Calcohol. This empirical approach was found to substantially reduce the errors in Cbase after the corrections and give predictions for the Calcohol (Figures 5 and 6), a subject to be discussed below. Error Analysis. In the current work, an extended range of Cbase (∼0.05-3.6 M) in NaOH-H2O-ROH was probed to investigate the impact of alcohol on the errors in Cbase measurements. The concentration range of MeOH, EtOH, and i-PrOH was 0-70 vol %. Sensors TY1-3 and AY1-3 were tested in several NaOHH2O-ROH solutions. The dual-sensor approach here leads to substantial increases in the Cbase accuracy, as a comparison of Figures 1 and 5 demonstrates. In the range of mixed methanol and ethanol solutions tested, errors in Cbase were reduced from Analytical Chemistry, Vol. 74, No. 23, December 1, 2002
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Scheme 1. Equilibria of the Different Forms of (a) Thiazole Yellow GGM and (b) Alizarin Yellow R
Figure 6. Validation plots of predicted vs actual Calcohol in NaOHH2O-alcohol solutions: (a) CMeOH in NaOH-H2O-MeOH (TY1 and AY1); (b) CEtOH in NaOH-H2O-EtOH (TY2 and AY2); (c) Ci-Pr-OH in NaOH-H2O-i-PrOH (TY3 and AY3).
as much as 95.0% to e15.0% (
