Anal. Chem. 2002, 74, 2535-2540
High-Acidity Determination in Salt-Containing Acids by Optical Sensors. The Scope of a Dual-Transducer Approach and the Hammett Acidity Function T. Andrew Canada,† Leonardo R. Allain,† David B. Beach,‡ and Ziling Xue*,†
Department of Chemistry, The University of Tennessee, Knoxville, Tennessee 37996-1600, and Chemical Sciences Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831-6101
A dual-transducer approach based on sol-gel optical sensors was recently reported to measure acid and salt concentrations, Cacid and Csalt, in concentrated aqueous LiCl-HCl, CaCl2-HCl, and AlCl3-HCl solutions (Cacid at 5-6 M; Csalt e 2 M).1 The scope of this new approach has been studied in salt-containing HCl solutions with Cacid at 2-9 M, and factors that influence sensor responses and accuracy have been investigated. A linear relationship between (DA/DCsalt)Cacid and (dA/dCacid)Csalt)0, which is the basis of this dual-transducer approach, was found to lead to an empirical linear relationship between (∆H0)Cacid and (∆Csalt)Cacid (H0: Hammett acidity function of the indicator encapsulated in the sensor). Optical sensors constitute one major category of chemical sensors, and they are often used in systems containing more than one chemical.1-8 In these multicomponent systems, sensor response is often affected by changes in ionic strength by chemicals other than the analyte. This is particularly significant for optical sensors that are based on indicator equilibria as their transducing mechanism. In addition, the sensor response to changes in ionic strength (by chemicals other than the analyte) is often indistinguishable from that by the analyte. An accurate measurement of each component in these multicomponent systems is of intense current interest. Several approaches have been developed to correct ionic strength in optical sensing for the pH region and solutions of lowto-medium ionic strength.2-8 We recently reported a dualtransducer approach to measure acid concentrations in saltcontaining, concentrated strong acids, such as LiCl-HCl, CaCl2†
The University of Tennessee. Oak Ridge National Laboratory. (1) Allain, L. R.; Canada, T. A.; Xue, Z. Anal. Chem. 2001, 73, 4592. (2) Edmonds, T. E.; Flatters, N. J.; Jones, C. F.; Miller, J. N. Talanta 1988, 35, 103. (3) Wolfbeis, O. S.; Offenbacher, H. Sens. Actuators 1986, 9, 85. (4) 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. (5) Opitz, N.; Lubbers, D. W. Sens. Actuators 1983, 4, 473. (6) Aussenegg, F. R.; Brunner, H.; Leitner, A.; Lobmaier, C.; Schalkhammer, T.; Pittner, F. Sens. Actuators B 1995, 29, 204. (7) Zhang, L.; Langmuir, M. E.; Bai, M.; Seitz, W. R. Talanta 1997, 44, 1691. (8) McCurley, M. F.; Seitz, W. R. Anal. Chim. Acta 1991, 249, 373. ‡
10.1021/ac0200623 CCC: $22.00 Published on Web 04/24/2002
© 2002 American Chemical Society
HCl, and AlCl3-HCl solutions.1 This approach in the solutions of 5 or 6 M HCl (with a salt contribution of up to 5.5 M to ionic strength) was shown to reduce the error in Cacid from, for example, 60% to 0.1 M.13 Other quantitative scales are needed to express the acidity (or basicity) in the more concentrated solutions. The work of Hammett and Deyrup in the early 1930s provided a quantitative scale.14 In concentrated acid, for example, Hammett and Deyrup suggested a convenient measure of acidity by the spectrophotometric determination of the extent of protonation of weak basic indicators in acid solution (eq 2).
B + H+ ) BH+
(2)
In dilute acid solutions, the protonation of B will be related to pH by the equilibrium
KBH+ )
{H+}{B} +
{BH }
pH ) pKBH+ - log
)
{H+}[B] fB [BH+] fBH+
( ) ( ) fB [BH+] + log fBH+ [B]
(3)
(4)
where [S] is the molar concentration of a chemical species S, {S} (11) Hisham, M. W. M.; Bommaraju, T. V. In Encyclopedia of Chemical Technology, 4th ed.; John Wiley & Sons: New York, 1995; Vol. 13, p 894. (12) Greenwood, N. N.; Earnshaw, A. Chemistry of the Elements, 2nd ed.; Pergamon Press: Boston, 1997; pp 811-812.
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Analytical Chemistry, Vol. 74, No. 11, June 1, 2002
is its activity, and fS is the activity coefficient for species S, defined by the expression {S} ) fS[S]. At low ionic strength, fB approaches unity, and fBH+ can be calculated using the Hu¨ckel-Debye approximation. However, in concentrated solutions with ionic strength over 0.1 M, fB deviates from unity by over 25%, and this approach will produce large errors. The Hammett acidity function, H0, as defined in eq 5, was introduced as a quantitative measurement of acidity in concentrated solutions.
H0 ) pKBH+ - log
( )
( )
{H+}fB [BH+] ) -log fBH+ [B]
(5)
H0 is independent of the bases (indicators) used to measure it, provided that (fB/fBH+) is identical for all bases in the same acid solution. Bases (indicators) with similar structures usually have close ratios fB/fBH+, but deviations often occur if bases with different structures are used. At low ionic strengths, H0 approaches pH, and is identical to pH at infinite dilution. For pure water, H0 ) pH ) 7.00 at 25 °C and 1 atm, and for solutions of increasing acidity, H0 decreases. In the acidity function defined in eq 5, the ionization ratio ([BH+]/[B]) is usually measured spectrophotometrically. The pKBH+ is derived from the plot of ([BH+]/[B]) as a function of acid concentration. At infinite dilution, all activity coefficients approach unity, and eq 5 becomes eq 6. Thus, extrapolating the function defined by eq 5 to [H+] ) 0 will give pKBH+, the thermodynamic dissociation constant that refers to the pure solvent as a standard state.
pKBH+ ) log
( )
[BH+] -log [H+] [B]
(6)
When the acidity function concept was first introduced, it was hoped that there would be a unique H0 function, applicable to a specific acid, which would be independent of the bases used to measure it. This acidity function would be the universal standard for this specific acid. The condition for such universal standard acidity function is that the ratio fB/fBH+ (eq 5) is the same for all neutral bases. It is recognized now that this condition is seldom satisfied, and structurally diverse bases give (fB/fBH+) ratios that differ from that of the primary amine series used by Hammett.13 Indicator Selection. We used two criteria in our selection of indicators for sensors in concentrated strong acids: (1) They are stable in solutions such as 1-11 M HCl; (2) There is at least one equilibrium between different forms of the indicator in these highly acidic solutions, and these forms of indicators can be observed by visible spectroscopy. Several indicators were tested in the range of 1-11 M H+. Bromocresol purple (BCP), bromocresol green (BCG), and neutral red (NR) were found to be stable while having a large sensitivity. The use of BCP was studied earlier.9a We, thus, focused on BCG and NR in the current work. Bromocresol green (BCG) is a member of the sulfonephthalein dyes. Sulfonephthalein indicators contain the sulfonic group and are very soluble in aqueous solutions. These indicators exist in (13) Rochester, C. H. Acidity Functions; Academic Press: New York, 1970. (14) (a) Hammett, L. P.; Deyrup, A. J. J. Am. Chem. Soc. 1932, 54, 2721. (b) Paul, M. A.; Long, F. A. Chem. Rev. 1957, 57, 1.
Scheme 1. Equilibria of the Different Protonated Forms of (a) Bromocresol Green and (b) Neutral Red
three different protonated forms and experience two color change sequences (Scheme 1a).15 The phenolic form III predominates in slightly acidic to basic solutions (pH > 5.4). III is converted to the hydroquinonic form II in the acidic pH range. Several pKa2 (4.35-4.90) determinations have been reported.16-18 II is converted to the sulfonic form I in extremely acidic conditions. A pKa1 of -4.4 ( 0.1 on the Hammett acidity scale has been reported recently by Aragoni and co-workers.19 They chose HCl to study the pKa1 of BCG for the non-oxidizing nature of HCl, even though HCl does not completely produce the diprotonated form of the dye.19 Determination of the pKa1 of BCG was found to be difficult because of the upper limits of the acidity of HCl.20 In addition, it was not clear whether the dye exists in the fully protonated form in highly concentrated HCl. Therefore, H0 was extrapolated using the scale reported by Paul and Long.14b Another study did not give the pKa1 of BCG, but the value was predicted to be approximately -2.7 on the Hammett acidity scale.20 III f II f I chemical changes result in a color sequence of blue f yellow f violet.15,17 We were able to spectrometrically monitor (Figure 1) the change from II to I in bromocresol green (BCG) encapsulated in a sol-gel matrix in concentrated HCl solutions. This measurement gave a plot (Figure 2) of scaled absorbance versus CHCl for two distribution curves for the first ionization of sol-gel-encapsulated BCG. The absorbances at 450 nm (II) were scaled with those at 560 nm (I) in order to eliminate extinction coefficient differences between the two forms of BCG. The two curves intersected at (15) Bates, R. G. Determination of pH: Theory and Practice, 2nd ed.; John Wiley & Sons: New York, 1973; pp 136-139. (16) Casula, R.; Crisponi, G.; Cristiani, F.; Nurchi, V. Talanta 1993, 40, 1781. (17) Dean, J. A. E. Lange’s Handbook of Chemistry, 14th ed.; McGraw-Hill: New York, 1992; p 8.116. (18) (a) Kolthoff, I. M.; Rosenblum, C. Acid-Base Indicators; The MacMillan Co.: New York, 1937, pp 120-124. (b) Bishop, E. Indicators; Pergamon Press: Oxford, 1972, pp 104-106, 127.
Figure 1. Typical spectra of a bromocresol green (BCG) sol-gel sensor in aqueous HCl solutions.
9.81 ( 0.48 M HCl, and this corresponded to a pKa1 of -3.60 ( 0.10 on the Hammett acidity scale (-0.99 ( 0.02 using theoretical pH).14 The pKa1 of -3.60 ( 0.10 on the Hammett acidity scale for bromocresol green (BCG) encapsulated in sol-gel matrix in the current study falls between -4.4 ( 0.119 and -2.7,20 two values reported earlier for the indicator dissolved in solution. The solgel films of the BCG sensors were prepared with a small amount of the surfactant cetyltrimethylammonium bromide [Me(CH2)15NMe3+Br-, CTAB; CTAB/Si molar ratio ) 8.1 × 10-3:1; CTAB/ BCG ratio ) 1:7]1, which was found to enhance the film strength and, thus, BCG sensor durability.9a Recently, Avnir and co-workers studied in detail the effect of doped surfactants on the properties (19) Aragoni, M. C.; Massilmiliano, A.; Guido, C.; Valeria, M. N.; Silvagni, R. Talanta 1995, 42, 1157. (20) Gupta, V. D.; Reed, J. B. J., Jr. Pharm. Sci. 1970, 59, 1683.
Analytical Chemistry, Vol. 74, No. 11, June 1, 2002
2537
Figure 2. Distribution curves (scaled absorbance vs concentration) for the first ionization of BCG3 in a sol-gel matrix. The curves were fitted with a third-degree polynomial.
of pH indicators.21 CTAB was found to form micellar aggregates (at CTAB/Si molar ratio ) 4.8 × 10-3:1) within the SiO2 sol-gel glass. At CTAB/BCG ) 2950-590:1 ratios,21a the pH indicating range of BCG was found to shift from 3.8-5.4 in CTAB-free solution18 to 1.5-3.8 in the CTAB micellar aggregates-SiO2. In the current studies, the effect of encapsulated CTAB on pKa1 of BCG was investigated. A CTAB-free BCG sensor (BCG4) was prepared in a procedure similar to the procedure to give BCG1-3 sensors except that CTAB was not used. The intersection for the scaled absorbance versus CHCl for two distribution curves for the first ionization of CTAB-free BCG4 was 9.64 M HCl.22 The difference between two intersection values of the CTAB-containing BCG sensor and CTAB-free BCG is ∼0.17 M, which is within the standard deviation (( 0.48 M HCl) of the trials. We were thus not able to determine whether CTAB in our sensor BCG3 has a noticeable effect upon the pKa1 value of encapsulated BCG in highly acidic media, perhaps because of a small CTAB/BCG ratio in the BCG3 sensor. There is, on average, one CTAB molecule/7 molecules of BCG indicator in our BCG3 sensor. Neutral red (NR) is a readily water soluble aminophenazine derivative. As many as five forms of NR can exist from pH 13 to -8.4 on the H0 acidity scale (Scheme 1b).23 From pH 7.4 to 13, the yellow uncharged NR V exists.15,23-27 Around pH 7.5 to 0, the red NR+ IV predominates.23-25,27 The pKa4 of IV to V conversion has been determined from a range of 6.75-7.40.16,23-26 The conversion of IV to the blue NR2+ III has been reported at a range of pKa3 values (0.20 to -0.7 or 0.63 to 5 M {H+}).14,23,28 Upon conversion to the Hammett acidity scale, pH 0.20 and -0.7 are approximate to 0.08 and -1.75.14 Bisset and Dines were able to provide supporting Raman and NMR data in order to confirm the structure of III.26 (21) (a) Rottman, C.; Grader, G.; De Hazan, Y.; Melchior, S.; Avnir, D. J. Am. Chem. Soc. 1999, 121, 8533. (b) Rottman, C.; Avnir, D. J. Am. Chem. Soc. 2001, 123, 5730. (22) Additional plots are provided in the Supporting Information. (23) Bartels, P. Z. Phys. Chem. (Frankfort, N.F.) 1956, 9, 74. (24) Dutta, R. K.; Bhat, S. N. Can. J. Chem. 1993, 71, 1785. (25) Moulik, S. P.; Paul, B. K.; Mukherjee, D. C. J. Colloid Interface Sci. 1993, 161, 72. (26) Bisset, A.; Dines, T. J. J. Raman Spectrosc. 1991, 22, 101. (27) Singh, M. K.; Pal, H.; Bhasikuttan, A. C.; Sapre, A. V. Photochem. Photobiol. 1999, 69, 529. (28) Meretoga, A. Suom. Kemistil. B 1948, 21, 24.
2538 Analytical Chemistry, Vol. 74, No. 11, June 1, 2002
Figure 3. Distribution curves for the first ionization of NR3 in a solgel matrix. The curves were fitted by third-degree polynomial.
NR2+ can be converted to NR2++ II (green) and then to NR2+++ I is reportedly difficult to observe.23 The corresponding pKa2 and pKa1 values, as determined in concentrated H2SO4 solutions, are -3.38 ( 0.04 (7.10 M H2SO4) and -9.5, respectively.14b,23 The determination of pKa1 involved a theoretical approximation.23 The change from IV to III for a NR sensor in concentrated HCl (Figure 3) was evaluated in a procedure similar to that for the BCG sensors. The two maximums, 450 nm (IV) and 680 nm (III) were used to give an intersection at CHCl ) 5.88 ( 0.29 M, therefore giving a pKa3 of -2.07 ( 0.1 on the H0 acidity scale (-0.77 ( 0.02 using theoretical pH).14 A noticeable transition occurred from red to blue, both in soluble NR and the NR composite using HCl solutions ranging from 0 to 10 M. Our NR sensors were prepared with Nafion, a hydrophilic poly(tetrafluoroethylene) polyphenylene ether sulfonate resin, which was found to shorten the NR sensor response time and enhance the sensor durability. No CTAB or other surfactant was used in the preparation of the NR sensors. When compared to NR dissolved in solution, a shift to higher acidity (lower pKa) was observed for the indicator encapsulated with Nafion in our solgel sensor matrix. The presence of the organic polymer phase has been known to significantly lower an indicator pKa value, much more so than the oxide phase.9c It is plausible that the shift to higher acidity for NR infers that Nafion polymer acts as a proton sponge.21 In other words, protons are being adsorbed by the sulfonate groups of the Nafion molecules. In our current studies, an error analysis revealed that the standard deviations (random errors of trials of each sensor) for NR, BCP, and BCG sensors were 0.02-0.05, 0.03-0.07, and 0.070.10 M HCl, respectively. The standard deviations of the Nafioncontaining NR sensors are within the same proximity as the Nafion-free BCG and BCP sensors. It is, thus, not clear if the presence of Nafion in the NR sensors noticeably contributes to the standard deviation under highly acidic conditions. Salt Selection. The three main criteria for the selection of salts to be used in conjunction with HCl were cation valence, solubility, and optical transparency of the salt-HCl solutions. By using chloride salts we were able to have a three-component system in each case: Cl-, H+, and metal (Li+, Ca2+, or Al3+) ions. Univalent, divalent, and trivalent salts were investigated individually. Because of the common-ion effect, salt solubility was crucial I.23
Table 2. Comparisons for the LiCl-HCl Solutions22,a
Table 1. BET Results of the Bulk Samples sensor bulk Davisil-635 silica standard SiO2 blank (1) SiO2-CTAB blank (2) SiO2-CTAB-BCG (3) SiO2-Nafion (4) SiO2-Nafion-NR (5)
surface area (m2/g)
av pore diam (Å)
total pore vol (cm3/g)
475
61
0.72
238 226 227 7 14
26 25 25 36 43
0.22 0.14 0.14 0.0062 0.015
to having monophase solutions concentrated in acid and salt. LiCl, CaCl2, and AlCl3 were chosen for their relatively high aqueous solubilities (1 g/1.3 mL, 1 g/1.5 mL, and 1 g/0.9 mL, respectively).29 In addition, the solutions of these salt-HCl solutions have little or no color to minimize visible spectral interference. Characterization of the Sensor Materials. Profilometry measurements showed that the sensor film thickness ranged from 3.4 to 5.0 µm. In these measurements, a diamond stylus was scanned over the film surface. The stylus was attached to an arm that rotates about a flexure pivot to give smooth and stable scanning across the film surface. The aberrations were recorded by a detector and plotted. There were two baselines, film surface and substrate surface, and they were separated by a step that gave the film thickness. These surface profilers have a resolution of 1 Å in a range of thickness from 100 Å to 0.3 mm. The Brunauer-Emmett-Teller (BET) method was used to examine the surface area, average pore distribution, and total pore volume of the sol-gel materials.30 Because of the limited mass of the sensor film, we used the bulk sol-gel samples for the BET measurements (Table 1). These bulk materials were prepared by procedures similar to those to give the sensor films except that the sol-gel was not cast to films. The blank and BCG-encapsulated sol-gel samples 1-3 were found to be mesoporous on the basis of their isotherm plots. The surface area of 1-3 ranged from 226 to 238 m2/g, with an average pore size distribution of 25-26 Å. The total pore volume ranged from 0.14 to 0.22 cm3/g. In the NR sensor materials containing Nafion and SiO2 (4-5, Table 1), much lower surface areas and pore volumes were obtained. This suggests that Nafion either covered the SiO2 surface extensively or formed a Nafion/SiO2 polymer blend, thus reducing the ability of the SiO2 polymer to absorb N2 on its surface. Scope of the New Dual-Sensor Approach and Error Analysis. In our previous paper on accurate Cacid measurement in concentrated salt-containing acids, one acid concentration (5-6 M HCl) was studied for each salt to demonstrate the new approach.1 In the current work, an extended range of Cacid (∼2-9 M) with LiCl, CaCl2, and AlCl3 was probed to extend the scope of the approach and to investigate the impact of acid concentration on the errors in Cacid measurements. The concentration range of anhydrous LiCl, CaCl2‚2H2O, and AlCl3‚6H2O was 8.50-85.0, 25.0-120.0, and 24.0-241 g/L, respectively. Sensors BCG, BCP, and NR were tested in several salt-HCl solutions (salt ) LiCl, CaCl2, or AlCl3). If corrections are made, (29) The Merck Index of Chemicals and Drugs; Merck & Co., Inc.: Rahway, NJ, 1960; pp 613 (LiCl), 192 (CaCl2), and 42 (AlCl3). (30) BET data were confirmed by running a sample of Davisil-635 silica standard purchased from Aldrich.
error (%) in CHCl before correction CHCl (M)
(BCP1)
(BCG1)
(NR1)
5.00 8.00 9.00
1.5-19.1 4.1-16.8 1.4-12.5
12.1-21.6 6.0-14.9 4.7-14.8
1.6-23.4 2.8-10.2 1.0-9.2
error (%) in accuracy (%) in CLiCl after CHCl after correction correction 0.2-2.7b 0.4-0.7c 0.5-1.7d
61.0-94.9b 95.5-98.0c 89.3-99.5d
a Standard deviations in C HCl and CLiCl were 0.05-0.13 M and 1.182.84 g/L, respectively. b Combination of sensors BCP1 and NR1. c Combination of sensors BCG1 and NR1. d Combination of sensors BCG1 and BCP1.
Table 3. Comparisons for the CaCl2-HCl Solutions22,a,b error (%) in CHCl before correction CHCl (M)
(BCP2)
(NR2)
1.92 3.00 3.95 5.87
10.8-38.9 8.4-27.4 6.2-22.5 5.4-20.8
20.5-48.3 13.7-34.4 7.9-27.7 10.2-41.8
error (%) in accuracy (%) CHCl after in CCaCl2 after correction correction 0.5-8.9 3.6-7.0 0.4-6.4 3.1-4.4
55.0-98.9 80.8-98.4 53.8-99.5 66.2-94.9
a Sensors BCP2 and NR2. b Standard deviations in C HCl and CCaCl2 were 0.02-0.19 M and 4.48-6.15 g/L, respectively.
Table 4. Comparisons for the AlCl3-HCl Solutions22,a,b error (%) in CHCl before correction CHCl (M)
(BCP3)
(NR3)
2.99 3.96 5.94 6.96 7.92
7.4-38.7 6.1-40.0 3.4-22.3 4.5-32.7 3.2-24.5
2.3-28.1 5.9-26.9 1.6-20.5 2.1-17.6 2.2-11.7
error (%) in accuracy (%) CHCl after in CAlCl3 after correction correction 3.5-6.5 3.1-5.5 2.9-5.1 0.2-3.7 0.5-3.1
65.5-91.0 60.0-96.2 61.0-77.7 83.4-98.4 67.8-97.5
a Sensors BCP3 and NR3. b Standard deviations in C HCl and CAlCl3 were 0.05-0.11 M and 9.78-14.92 g/L, respectively.
as shown in Tables 2-4, there are substantial increases in the Cacid accuracy. In the range of solutions tested (∼2-9 M HCl, 0-2 M salt), errors in Cacid were reduced from as much as 48.3% to
