Anal. Chem. 1888, $5, 1897-1902
1897
Micellar Catalysis in Kinetic Multicomponent Analysis: Simultaneous Determination of Binary Mixtures of Cyanide, Sulfide, and Sulfite Ions Victoria GonzQlez?Bernard0 Moreno? Dolores Sicilia, Soledad Rubio, and Dolores Pbrez-Bendito’ Department of Analytical Chemistry, Faculty of Sciences, University of C6rdoba, Cbrdoba, Spain
A simultaneous kinetic resolution of binary mixtures of cyanide, sulfide, and sulfite by reaction with 5,5‘-dithiobis(2-nitrobenzoicacid) (DTNB) in aqueous cetyltrimethylammonium bromide (CTAB) micelles was developed. The use of micelles increased the rate constants of the three reactions involved to a different extent and this differential behavior permitted the simultaneous kinetic analysis of mixtures of the anions by using appropriate surfactant concentrations. The determinationof binary mixturesof cyanide, sulfide, and sulfite over the concentrationranges (0.5-1.5) X lo4, (0.2-1) X and (0.2-1.5) X lo4 M yrespectively, was accomplished with relative errors less than 5%. The role of micellar media in differential reaction rate methods is discussed. INTRODUCTION The influence of micelles on chemical reactions is of considerablecurrent interest. Incorporation of reactants into micellar aggregates dramatically affects their apparent reactivity compared to that observed in water.172 Rate enhancements have been rationalized in terms of favorable reagent distribution and/or changes in the apparent dissociation constants of ionizable functional groups.34 Special rate enhancements by micelles, which would imply that the intrinsic rate constant is affected by the organization of the medium, play at most a minor role.6 Few reports on analytical applications of micellar catalysis have so far been published despite their proven assets for some analytical procedures.6J Lately, micellar catalysis is being used in conventionaldeterminations,where it has shown a great analytical potential for determining catalysts”13 and substrates.14J6
* Author to whom correspondence should be addressed.
t From Departamenta de QuImica Analltica,Nutrici6n y Bromatologia, Facultad de Qufmica, Univereidad de Salamanca, S h a n c a , Spain. (1) Fendler, J. H.; Fendler, E. J. Catalysis in Micellar and Macromolecular Systems; Academic Press: New York, 1975. (2) Fendler, J. H. Membrane Mimetic Chemistry; J. Wiley & Sons: New York, 1982. (3) Bunton, C. A. Pure Appl. Chem. 1977,49,969-979. (4) Bunton, C. A,;Romsted, L. S.;Sepdveda, L. J. Phys. Chem. 1980, 84,2611-2618. (5) Bunton, C. A.; Hamed, F.;Romsten, L. S. Tetrahedron Lett. 1980, 21,1217-1218. (6) Hinze, W. L. In Colloid and Interface Science; Kerker, M., Ed.; Academic Press: New York, 1976; Vol. V, p 425. (7) Spurlin, S.; Hinze, W. L.; Armstrong, D. W. Anal. Lett. 1977,10, 997-1008. (8) Rubio, S.; Pdrez Bendito, D. Anal. Chim. Acta 1989,224,185-198. (9) Lunar,M. L.; Rubio, 5.;PBrez Bendito, D. Anal. Chim. Acta 1990, 237,207-214. (10) Sicilia, D.; Rubio, S.; PBrez Bendito, D. Talanta 1991,38,1147-
11.53.
(11) Sicilia,D.;Rubio, S.; PBrez Bendito, D. Fresenius. J. Anal. Chem. 1992,342, 327-332. (12) Lunar,M. L.;Rubio,S.; PdrezBendito,D. Talanta 1992,39,11631173. 0003-2700/93/0365-1897$04.00/0
One interesting aspect of micelles is their ability to modify the apparent rate constant ratio of two or more species which interact with a common reagent. Thus, micelles can stereoselectively catalyze some enantiomeric reaction processes such as hydrolyses, eliminations, and deacylations and thus distinguish between enantiomeric reactants.2 Chiral resolution exists when there is a substantial difference in either the binding constants for the enantiomers with the micelle or the specific formation rate constants of the respective products, which may or may not be associated with the micellar assembly themselves. According to literature reports, strong, specific solutemicelle binding interactions are mandatory for such chiral discrimination to exist.2J6 In some instances, the specific rate constant for the reaction of one enantiomer is sufficiently different from that of the other and partial racemate resolution occurs as a result of the preferential reaction in the micelle. Therefore, if micelles can modify the apparent rate constant ratio of two or more species which interact with a common reagent, micellar system can be exploited for the simultaneous determination of such species. Thus, the use of micellar catalysis in differential reaction rate methods is of great analytical potential for resolvingsome mixtures of specieswith inadequate differences between their rate constants, by employing conventional differential reaction rate methods or in those cases where a given component takes too long to react so it precludes analytical measurements. In this work we studied the influence of the cationic surfactant cetyltrimethylammoniumbromide (CTAB)on the apparent rate constants of the reactions between 5,5’dithiobis(2-nitrobenzoicacid) (DTNB) and cyanide, sulfide, and sulfite in order to assay the simultaneous resolution of these anions in a micellar medium. These reactions were selected for several reasons: first, the reaction between DTNB and cyanidetakes about 100min to be complete in an aqueous medium,” whereas those of DTNB with sulfide and sulfite are quite fast and appear to be virtually complete within 5 min;lEJg second, the reactivity of sulfide and sulfite is very similar; third, CTAB influencesthe rate of reaction of DTNB with these anions;7 and fourth, CTAB micelles can shift the pK of these anions, similarly to CPC.20 The apparent rate constant ratios for the DTNB-anion reactions in the CTAB micellar medium may depend on three parameters, namely, the binding constant for the anions with the micelle, the (13) Sicilia, D.; Rubio, S.; Pdrez Bendito, D. Anal. Chem. 1992, 64, 1490-1495. (14) Hernhdez Torres, M. A.; Khaledi, M. G.; Dorsey, J. G. Anal. Chim. Acta 1987,201,67-76. (15) Athanaeiou-Malaki,E.;Koupparis, M. A. Anal. Chim. Acta 1989, 219,296-307. (16) Hinze, W. L. Ann. Chim. 1987, 77, 167-207. (17) Humphrey, R. E.; Hinze, W. Talanta 1971, 18, 491-497. (18) Humphrey, R. E.; Hinze, W.; Jenkines, W. M., I11 Anal. Chem. 1971,43,140-142. (19) Humphrey, R. E.; Ward, M. H.; Hinze, W. Anal. Chem. 1970,42, 698-702. (20) Abdel-Latif, M. 5.;Guilbault, G. G. Anal. Lett. 1989,22, 13551368. 0 1993 Amerlcan Chemlcal Society
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ANALYTICAL CHEMISTRY, VOL. 85, NO. 14, JULY 15, 1993
specific formation rate constant of the product from each reaction, and the apparent ionization constant of the anion in the micellar medium.21322 The analytical usefulness and implications of this research work are discussed below. EXPERIMENTAL SECTION Apparatus. Kinetic measurements were made on a Philips PU 8625 UV/vis spectrophotometer fitted with a stopped-flow module23 (Quimi-Sur Instrumentation, Seville, Spain). The module, furnished with an observation cell of 0.3-cm path length, was controlled by its associated electronics via a 640 K Mitac computer for acquisition and processing of kinetic data. The solutions in the stopped-flow module and the cell compartment were kept at a constant temperature by circulating water from a thermostated tank. A classical stalagmometer was used for surface tension measurements in order to determine the critical micelle concentration (cmc) of CTAB under different reaction conditions. Reagents. Commerciallyavailablehighest grade reagents were used, without further purification. Bidistilled water was used throughout. Stock solutions of DTNB (Aldrich),approximately 5 X 10-3M, were made in 95 % ethanol. Buffer solutions consisted of 0.1 M KHzP04 (pH 8) and 0.04 M NazB40,-10HzO(pH 10). A sodium hydroxide solution (0.01 M) was also prepared. A cetyltrimethylammonium bromide (CTAB) solution (le2 M) (Serva) was prepared by dissolving the surfactant in bidistilled water. A sodium sulfite solution (10-2 M) in EDTA (le2 M) was made from the anhydrous compound. Working solutions were made by dilution with bidistilled water. These solutionsremained stable for as long as 2 weeks." Stock solutions of sulfide ion, ca. M, were prepared from NazS.9H20 in bidistilled water. Potassium cyanide stock solutions (le3 M) were also prepared in bidistilled water. Procedure for the Simultaneous Resolution of Binary Mixtures of Cyanide, Sulfite, and Sulfide. Two solutions (A and B) were used to fill the two 10-mL reservoir syringes of the stopped-flow module. Solution A contained 0.8 mL of 0.01 M sodium hydroxide, 2 mL of 5 X M DTNB, an appropriate volume of 10-3 M CTAB solution (1 mL for the sulfide-sulfite and sulfide-cyanide mixtures and 0.75 mL for the sulfite-cyanide mixture), and bidistilled water. Solution B contained the following reactants, which were added in this order: buffer, analytes, EDTA, and bidistilled water t o a final volume of 10 mL. The reactant concentrations in solution B are for each mixture. (1)Sulfite-cyanide mixture: [phosphate buffer] = 5 X lO-'M (pH 8); [CN-I = (0.5-1.5) X 10-4 M; [ F J O ~=~(0.2-1.5) I X 10-4M and [EDTAIba = 3 X 10-4 M (since the sulfite solution was made in EDTA, an appropriate volume of 1 x lo3 M EDTA solution was added to give a final concentration of 3 X 10-4 M). (2) Sulfide-sulfite mixture: [phosphate buffer] = 5 X 10-2 M (pH 8); [S2-]= (0.1-0.9) X lo4 M; [S03%]= (0.2-1.5) X 10-4 M; [ E D T A l b ~= 3 X 10-4 M. (3) Sulfide-cyanide mixture: [NazB40,] = 2 X 1k2M (pH 10); [CN-] = (0.2 - 1.0) X 10-4 M; [S2-] = (0.2 - 1) X lo4 M. After the two 2-mL drive syringes had been filled with the corresponding solutions from the reservoir syringes, 0.15 mL of each solution was mixed in each run. At least three runs were recorded for each sample. The reaction was monitored at 440 nm by recording the variation of absorbance as a function of time while the system was kept at 20 f 0.1 "C. Absorbance data were acquired and subsequently processed by the microcomputer running a laboratory-developed linear-regression program for application of the initial rate method. Absorbance values at 300, 30, and 180 s for the sulfite-cyanide, sulfide-sulfite, and sulfidecyanide mixtures, respectively, were obtained. The overall reaction developedto 80-9070 over such periods. Blank solutions were prepared like the samples but contained no analytes; their signals were subtracted from those obtained for the samples. (21) Berenzin, I. V.; Martinek, K.; Yatsimirskii, A. K. Russ. Chern. Rev. 1973, 42,787-802. (22) Quina, F. H.; Chaimovich, H. J.Phys. Chern. 1979,83,1844-1850. (23) Loriguillo, A,; Silva, M.; PBrez Bendito, D. Anal. Chirn. Acta 1987, 299, 29-40.
The analyte concentrations in each mixture were calculated by measuring both the initial rate ( u ) and the absorbance ( A )at the above-stated times, in each run. The dependence of u and A on the concentration of the analytes in the binary mixtures was found to conform to the following equations: LJ =
Po + PlX, + P2X2
A = Po+ P1X1+ P2X2
(1) (2)
where X1 and Xz are the concentrationsof the analytesexpressed as moles per liter. Parameter u was expressed as absorbance units per second. The coefficientsPO,@1,@2, PO,PI,and P2 were estimated by multiple linear regression (MLR) from 20 binary mixtures containing cyanide, sulfide,and sulfite at concentrations in the above established ranges for each mixture, by using a laboratory-developed FORTRAN 77 program. The expression of MLR for eqs 1 and 2 in matrix notation is y=XXp+e where y is the measurement vector ( A or u ) , e the residual vector, p the parameter vector, and X the independent variable matrix. The least-squares estimate of 8, b , was obtained from b = (X'X)-JX' y where X' is the transpose of X and (X'X)-l the inverse of X'X. Once the estimates of coefficients were obtained, unknown samples were analyzed by substituting the measured parameters u and A into eq 1and 2 and calculating the analyte concentrations by using a laboratory-developed FORTRAN 77 program.
RESULTS AND DISCUSSION The organic disulfide DTNB has been used as a chromogenic reagent for the spectrophotometric determination of cyanide," sulfide,l8 and ~u1fite.l~ Methods for the determination of these analytes using DTNB involve measuring the absorbance of the thiol anion formed as reaction product. Their chief drawbacks are severe mutual interferences of the analytes and the slowness of the reaction between cyanide and DTNB. Cationic micelle systems are known to catalyze these nucleophilic reactions.7~~~ Thus, the time required for the spectrophotometric determination of cyanide ion is decreased from 100 to 1-3 min in an aqueous CTAB micellar reaction mediuma7 Also, cationic surfactants increase the absorbance and rate of the reaction between sulfite and DTNB, which was exploited for adapting the former manual method to flow injection analysis.20 No attempts at the simultaneous analysis for cyanide, sulfide, and sulfite using DTNB as a reagent have so far been made. We found than the simultaneousresolution of these analytes by using DTNB in an aqueous medium and conventional kinetic differential methods was either impossible or inadvisable, as inferred from the various calculated constants of the cyanide-DTNB, sulfite-DTNB, and sulfide-DTNB systems at various pH values. Because a slightly basic medium must be used for the reaction between cyanide and DTNB to develop a t a resonably rapid rate,17 the rate constant of this reaction was only significant above pH 8. On the other hand, at high pH values, DTNB undergoes alkaline hydrolysis, which detracts from its analytical use. Table I lists the observed rate constants and their ratios for the three analytes tested a t two significant pH values. As can be inferred from the constant ratios, the similar reactivity of sulfite and sulfide makes it impossible to resolve them by using a conventional kinetic differential method. On the other hand, the slowness of the cyanide reaction makes using the procedure for the simultaneous resolution of sulfide-cyanide and sulfitecyanide mixtures inadvisable with routine analyses. Study of theReaction of DTNB withcyanide, Sulfide, and Sulfite in a CTAB Micellar Medium. Berezin,21
ANALYTICAL CHEMISTRY, VOL. 65, NO. 14, JULY 15, 1993
Table 1. Observed First-Order Rate Constants for the Reactions of DTNB with Sulfite, Sulfide, and Cyanide in an Aqueous Medium (k f SD) (8-9 reaction PH 8 pH 10 sulfite-DTNB sflide-DTNB cyanide-DTNB sulfide-DTNB/ Sulfite-DTNB sulfide-DTNB/ cyanide-DTNB aulFits-DTNB/ cyanide-DTNB
(9.04 f 0.07)X le2 (10.31 0.06)X le2 (3.01& 0.01) X lo-‘ 1.14
(10.1f 0.1)X le2 (10.7f 0.2)X le2 (3.42f 0.01)X l e 1.06
342.5
312.8
300.3
295.3
*
8
f-’
to/
& I
,
0
Romsted-Cordes,24t6 and Chaimovich-Quina22have put forward severalcomprehensive kinetic theories in order to explain and analyze the catalytic action of micelles on chemical reactions. These general quantitative treatments of kinetic data provide an appropriate description of the alkaline hydrolysis of DTNB in micellar CTAB.26 DTNB and hydroxide ion bind to CTAB micelles [binding constants KDTM and KOHwere found to be -104 M-1 and between (1-2) X 102 M-1, respectively], and the observed rate enhancements are a result of these efficient bindings to the micellar pseudophase, which effectively reduces their volume element (the “true” second-orderrate constant, k,, in CTAB micelles is slower by a factor of 5-18 than that in water alone). The basic hydrolysisof DTNB can be used as a model for the DTNB-cyanide, DTNB-sulfide, and DTNB-sulfite disulfide cleavage reactions. Thus, according to the ion-exchange treatment,22 a common relationship can be used to describe the micellar effects on these bimolecular reactions taking into account that the anions are weakly acidic [pK2(H2SO3)= 7.0; pKl(H2S)= 7.05; pKa(HCN) = 9.11; the partitioning of DTNB and HA (where HA is HS03-, H2S, or HCN) between the CTAB micellar and aqueous phases; the ion exchange of A (where A is SO+-,HS-, or CN-) with the micellar counterion, B r ; and assuming that the reactions occur preferentially in the micellar phase and A is the reactive species. Under pseudo-first-order conditions, the general expression for the observed second-order rate constant (k,) according to the treatment developed by Quina and Chaimovich22 is
1899
41
3 20
40
60
T I M E (s) Figure 1. Kinetic curves, obtained at pH 8, for the sulfide-DTNB (I), sulfite-DTNB (21, and cyanide-DTNB (3) systems In the absence (A) and presence of 1 X 1O4 MCTAB (B), expressed as inltiai concentration In the syringe. Solutionswere prepared as descrlbed under Experimental . .
Section.
1201
P
u
60
W I-
0
w
>
20
0
0.0
a:
z
w, 0.0
1 .o
2.0 [CTAB] ( M I x 10‘
Figure 2. Observed rate constants for the sulfide-DTNB (I), suifiteDTNB (2), and cyanide-DTNB (3, 4) systems as a function of CTAB concentration: curves 1,2, and 4 pH 8, curve 3 pH 10; [S2-] = [SO3*-] = [CN-] = 1 X lo4 M; [DTNB] = 5 X lo4 M. These concentrations
are initial concentrations in the syringes. where [AHTI denotes the total concentration of cyanide, sulfide, or sulfite ion; K, the ionization constant of these ions in water; k2, and k2O the second-order rate constants in micelles and water, respectively; V the partial molar volume of the surfactant; K m and KHAthe binding constants of DTNB and HA, respectively, to CTAB;KA/B,the ion exchange constant for the surfactant counterion (Br)-A ion (SO3”, HS-, CN-) equilibrium; C the difference between the total surfactant concentration and the cmc value; and Kappthe apparent ionization constant of the analytes in the presence of CTAB. Subscripts m and w are used to denote the micellar and water phases, respectively. Some considerations can be drawn from eq 3 in relation to the use of micelles in the differential kinetic analysis of cyanide, sulfide and sulfite by reaction with DTNB. Under the selected reaction conditions, such parameters as C, K m , V, and EH,+l are constant and independent of the analyte considered. The likelihoodof variations in the observed rate (24)Cordes, E.H.Pure Appl. Chem. 1978,50,617. (25)Romstad, L.5.Ph.D. Thesis, Indiana University, 1975. (26)Fendler, J. H.;Hinze, W. L.J. Am. Chem. SOC.1981,103,54395447.
constant ratios for two analytes and hence for their resolution willessentially depend on such parameters as k h , KA/Br,K,pp, and Km. If the reactant concentrations in the micellar phase are responsible for the efficiency of micellar catalysis, then the k t value for each reaction will be largely determined by that of K A and, ~ in some instances, by that of KaPp In order to check the use of CTAB micelles for resolving cyanide, sulfide, and sulfite mixtures, k r values were calculated for each reaction as a function of both the CTAB concentration and pH. Typical kinetic curves obtained at pH 8 for the three reactions in the absence (A) and presence (B) of CTAB micelles are shown in Figure 1. The use of this cationic surfactant altered the reaction rates of cyanide, sulfide, and sulfite to different extents, thereby enablingtheir simultaneous determination. Figure 2 shows the most representative dependences obtained by plotting the observed rate constants as a function of the CTAB concentration. Because of the rapidity of the reactions in the presence of this surfactant, the stopped-flow technique was used to measure the rate constants. Some considerations can be made from the data obtained: (1)The DTNB-sulfide system (curve 1)reacts too rapidly at CTAB
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 14, JULY 15, 1993
concentrations above ca 1.5 X 10-4 M to be monitored in a reproducible manner by the stopped-flowtechnique used here. For this reason, the effect of higher CTAB concentrations in this reaction could not be investigated. ( 2 ) The rate constant of the DTNB-sulfite system (curve 2) was hardly modified by the presence of CTAB. (3) The dependence of the rates of the DTNB-sulfide and DTNB-sulfite systems on the CTAB concentration changed only slightly with pH above pH 8. The rate constant of the DTNB-cyanide system was a function of both pH and the CTAB concentration (curves 3 and 4). (4) The rate constant for the DTNB-cyanide system was increased to a much greater extent than those of the DTNB-sulfide (curve 1)and DTNB-sulfite (curve2) systems (catalytic factors expressed as the ratios of the maximum rate observed in the presence of the surfactant compared to that in water were ca. 50, 6, and 2 for cyanide, sulfide, and sulfite, respectively). (5) The reaction between DTNB and cyanide was rapid enough to allow the analytical resolution of the sulfide-cyanide and sulfite-cyanide mixtures in a practical time. (6) The rate constant ratio for the sulfidesulfite mixture was increased to the extent required (compare curves 1 and 2 ) to permit simultaneous resolution by using a conventional differential kinetic method. (7) The sulfidecyanide mixture was resolved at pH 10, where the most favorable sulfide-cyanide constant ratios were obtained. Therefore, if characteristic parameters for each analyte in the micelle phase (e.g., kzm, K A , B ~ITapp, , etc.) are different enough from each other, then a plot of k * as a function of surfactant concentration will provide different observed rate constant ratios for the reactions, allowing one to select the optimal ratio according to specific requirements. This aspect of micellar systems is relevant to the use of these organized media in differential kinetic analysis. Effect of Variables. The cyanide, sulfite, and sulfide systems were optimized by changing each experimental variable in turn while keeping all others constant. Two parameters were measured in order to solve binary mixtures of the analytes: the initial rate and absorbance at a fixed time. Both parameters were found to be additive for binary mixtures of the studied systems throughout the tested analyte concentration ranges. Because of the rapidity of the reactions, use of the stopped-flow technique was mandatory for determining their initial rates. All concentrations expressed below are initial concentrations in the syringes (twice the actual concentrations in the reaction mixture a t time zero after mixing). Each kinetic result was the average of three measurements. The reactants involved in each reaction were mixed in various sequences to determine their optimum distribution in each syringe of the stopped-flow module. Mixing DTNB and CTAB in the same syringe at concentrations above 5 X 104 and 5 X 10-5 M, respectively, resulted in precipitation. Adjusting the pH of this solution to 4 with sodium hydroxide increased its solubility enough to permit the determination, yet turbidity gradually developed 0.5 h after DTNB and CTAB were mixed under these conditions. Even though it was more practical to place one reactant in each of the two syringes, the resolution of sulfide and sulfite with this reactant distribution was impossible because the observed rate constant ratio for the two reactions was between 1 and 2 in the CTAB interval tested. No problems arising from viscosity differences in the mixing chamber were encountered on mixing the two solutions. Because of the instability of sulfite solutions, addition of a stabilizing agent was necessary, so its effect on both the initial rate and the absorbance value a t a fixed time was investigated for the three studied systems. Three stabilizing agents were tested: glycerine, CTAB, and EDTA. Sulfite
4
12
8 PH
Flgure 3. Effect of pH on the observed rate constants for the suifideDTNB (A), sulfite-DTNB (B), and cyanide-DTNB (C) systems in the absence (1) and presence of 1.O X lo-' M (2) CTAB: [S2-] = [SO3*-] = [CN-] = 1 X lO-'M. These concentrationsare initial concentrations
in the syringes.
solutions were not stabilized by addition of the surfactant. Glycerine was a good stabilizing agent for sulfite solutions, but the consecutive kinetic curves recorded for cyanide in the presence of a glycerine concentration between 0.2 and 0.6 % showed a gradual decrease in both measured parameters (initial rate and absorbance a t a fixed time). The aproximate percent decrease was about 6 and 8% for initial rate and absorbance, respectively, for two consecutive injections. EDTA stabilized sulfite solution and had no effect on the measured parameters for any of the three analytes at the EDTA concentration used (3 X lo4 M). Increasing DTNB concentrations resulted in increasing rates of reaction and absorbances at a fixed time for the three systems. DTNB concentrations higher than about 8 X 10-4 M gave rise to pseudo-zero-order conditions. Above this concentration, the absorbance values obtained remained constant. Since the background absorbance increased as the dye concentration was raised, a 1 X 10-3 M DTNB concentration was chosen as optimal in terms of precision and sensitivity. The effect of pH was tested over a wide interval in order to determine whether the attack on the disulfide bond in the studied analytes occurred a t lower pH values in the presence of CTAB micelles. Figure 3 shows the results obtained for the sulfide-DTNB (A), sulfite-DTNB (B), and cyanideDTNB (C) reactions in the absence (1)and presence (2) of CTAB micelles. No further reaction between DTNB and the analytes occurred a t lower pH values when the surfactant was added to the reaction medium compared with the aqueous medium. Thus, the accelerating effect of the surfactant was only observed when the reaction in the aqueous medium occurred to some extent and catalytic factors, expressed as the ratios of maximum observed rates at a given pH in the presence of the surfactant, compared to that in water, increased to a greater extent with increasing pH. Thus, for cyanide this catalytic factor was ca. 2,12, and 50 at pH 6,8, and 10, respectively. Therefore, if micelles modified the pK, of these analytes, the effect was not important on the acceleration observed in the presence of CTAB.
ANALYTICAL CHEMISTRY, VOL. 65, NO. 14, JULY 15, 1993
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Table 11. Quantitative Performance of the Proposed Method for the Determination of Binary Mixtures of Sulfide, Sulfite, and Cyanide Using DTNB as Reagent mixture mead coeff of eqs 1 and 2 x1 Paam Bo OF bo f SD or f SD SZor 6’2 f SD IQ SEE*
xz
sulfide
cyanide
v
A sulfide
sulfite
v
A sulfite
cyanide
U
A a
(1.0f 0.5) X (4f 1) X -(2.2 f 0.6) X 103 (1.9f 0.6) X 1&2 -(2.4 f 0.6)X 103 (4f 2) X le2
1971 f 52 4761 f 126 2435 f 10 6587 f 93 306 f 6 2995 f 198
310 f 58 3713 f 140 693 f 6 3811 f 62 30f4 3302 f 134
0.999 0.999 0.9999 0.999 0.999 0.99
4.1 X 9.9 x 7.3 x 8.7 X 4.5x 1.4 X
10-9 10-9
lo-‘ 10-9 lo-‘
Correlation coefficient n = 20. Standard error of the estimate.
We could not determine changes in the acidity constants of the SHz/SH- and HCN/CN- equilibria in the micellar medium owing to the high volatility of the species HzS and HCN. The equilibrium constant of the HS03-/S03” system in the micellar medium was determined spectrophotometrically and was found not to differ significantly from that in the aqueous medium (pK, N 7.0). This is quite logical since the two forms of the species involved in the equilibrium are of opposite sign to the micelles and both can be attracted to their surface through electrostatic interactions. The reaction of DTNB with sulfite was not pH-dependent in the range 8-10, so neither measured parameter (initial rate or absorbance a t a fixed time) was altered in the interval. The reaction of DTNB with sulfite and cyanide was pHdependent over the tested range (Figure 3B,C). Although the cyanide rate at pH 10was higher, pH 8 was used whenever possible because of the high blank signals obtained, presumably arising from reaction of DTNB with hydroxide ionz7at higher pH values. The initial rates and absorbances of the three studied systems at a fixed time were not affected by the buffer solutions (phosphate and borate) used to adjust pH. Since ethanol was used to dissolve DTNB, the influence of this solvent on the studied reactions was investigated. No effect was observed at least up to an ethanol content of 10% in the reaction medium. Higher concentrations gave rise a gradual decrease in the rate that was proportional to the surfactant concentration used. The selected working temperature was ca. 20 “C. Temperatures above 25 “Cwere avoided since they increased the rate of alkaline decomposition of DTNB. Absorbance values for each binary mixture were acquired at times ensuring additivity and maximal sensitivity. Longer reaction times resulted in a slight negative synergistic effect on the measured absorbance values. Since the CTAB concentrations used in the reaction medium (5 X 103 M for sulfide-sulfite and sulfide-cyanide mixtures and 3.75 X 10-5 M for the sulfite-cyanide mixture) were well below the CTAB critical micelle concentration calculated in water at 25 “C (ca. 9.2 X lo-‘ M),we calculated the cmc for the three studied mixtures under the reaction conditions described in the Experimental Section. cmc values were calculated from surface tension measurements of solutions containing all the ingredients of the corresponding reaction and variable amounts of surfactant and were 2.1 X 10-5,1.5X 10-5,and 3.6 X 10-5M for the sulfite-sulfide, sulfidecyanide, and sulfite-cyanide mixtures, respectively. Therefore, the reaction medium was found to contain micelles. Features of Proposed Methods. The calibration graphs for cyanide, sulfide, and sulfite were constructed by plotting the initial rates and absorbances a t a fixed time obtained from the absorbance-time curvesfor each analyte as a function of the analyte concentration. The calibration graphs for the individual determinations were linear over the concentration ranges stated under Procedure (Experimental Section). The (27)Parker, A. J.; Kharaech, N.Chem. Rev. 1959,59,608.
Table 111. Multiple Linear Regression Prediction for Binary Mixtures of Cyanide, Sulfide, and Sulfite actual concn (M) relative error ( 7%) anal* ratio cyanide sulfide sulfite cyanide sulfide sulfite
CN-:S” 5:1 2:5 1:l 2:l 1:2 1:5
5.0 X 2.0 X 5.0 X 1.0 X 5.0 X 2.0x
106 1.0X 106 106 5.0X 106 I06 5.0X 106 lo-’ 5.0X 106 106 1.0 X lo-‘ 106 1.0 x lo-‘
-4.6 -0.7 2.2 -3.7 1.8 1.6
-9.4 3.1 3.1 5.3 -1.7 -0.9
S”:SOs”
1:5 1:2 5:1 1:15 2:5 9:2 CN-:S08% 5:2 5:1 2:1 1:2 3:l 15:2
1.0 X 5.0 X 5.0X 1.0 X 2.0X 9.0x
5.0X 1.0 x 1.0x 5.0X 1.5 X 1.5 X
106 lo-‘
lo-‘ 106 lo-‘ lo-‘
106 106 I06 106 10-d 106
5.0X 1.0X 1.0 X 1.5 X 5.0 X 2.0x
106 lo-‘ I06
3.8 -0.6 -1.9 2.8 -4.6 3.3
lW I06 1od
2.0 x I06 2.0 x 106 5.0 X 106 1.0X lo-‘ 5.0X 10-d 2.0 X 106
-2.2 -1.2 4.6 -2.3 0.7 -2.3
-3.0 1.4 -5.3 -0.2 3.1 -9.3 -0.4 -2.5 1.4 -0.2 1.2 -4.5
absence of synergistic effects ensured that the parameters obtained from the kinetic curve for a mixture of two analytes were the sums of the corresponding parameters obtained for each analyte separately. Since the CTAB concentration directly influences the rate constant ratios of the studied binary mixtures (Figure 21, a surfactant concentration was chosen for each mixture in order to keep the ratio between 4 and 10. In order to calculate the analyte concentration in each mixture, eqs 1and 2 (see Procedure) were solved by using a straightforward, laboratory-developed FORTRAN 77 program. Coefficients p ~j31,82, , p ’ ~p, ’ ~and , p ’ were ~ estimated for each binary mixture by linear regression from 20 observations made on the variablesu and A on 20 samplescontaining different combinations of analyte concentrations. The results obtained are shown in Table 11,which includes the statistical parameters of these equations. The precision of the proposed method, expressed as relative standard deviation (%), was 1.6% for sulfide and 4.0% for cyanide in a 1:2 mixture ([S”] = 5.0 X lk5M; [CN] = 1.0 X lo-‘ M),3.5% for sulfide and 2.4% for cyanide in a 1:2 mixture ([S032] = 5.0 X 10-5 M; [CN-] = 1.0 X lo-‘ M),and 10.0% for sulfide and 8.7% for sulfite in a 2:5 mixture ([S2-l = 2.0 X 10-5; [S03-21 = 5.0 X 1 e 5 MI.
The predictive ability of indirect calibration by MLR for the binary mixtures of cyanide, sulfide, and sulfite was tested by using six mixtures containing the analytes in different ratios as unknown samples and making measurements under the same experimental conditionsas those used for calibration. Table I11 summarizes the results obtained from the corresponding eqs 1 and 2. Relative errors less than 5 % were obtained for most of the tested mixtures, which testify to the good accuracy of the proposed method.
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ANALYTICAL CHEMISTRY, VOL. 65, NO. 14, JULY 15, 1993
CONCLUSION Accounting for and analyzing the catalytic effect of CTAB micelles on the sulfide-DTNB, sulfite-DTNB, and cyanideDTNB systems calls for a comprehensive quantitative treatment21~22~24~25 to calculate the degree of partitioning or binding of the reactants in the surfactant pseudophase and the specific rate constant for reaction in the micelles. This is beyond the scope of this paper but, whatever determines micellarcatalysis in each reaction, the reported results confirm the potential of micelles for differential kinetic analysis. The presence of micelles in the reaction medium introduces a dependence of the rate constant on several parameters (binding or partition constant, specific rate constant, etc.) which act as differential elements for the reactivity of the different analytes involved. Kinetic discrimination in a micellar medium will be possible
provided the analytes have differential affinity for the micelles. One major inference in this respect is the possibility of selecting the rate constant ratio for the analytes as a function of the surfactant concentration in order to address the resolution of mixtures of analytes in different ratios.
ACKNOWLEDGMENT We gratefully acknowledge financial support from CiCyT (Project PB91-0840, University of C6rdoba and Project PB910185, University of Salamanca).
RECEIVED for review December 7, 1992. Accepted April 5, 1993.
