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Solubilization Processes in Autocatalytic Biphasic Reactions C. Roque, V. Pimienta, D. Lavabre, and J. C. Micheau* Laboratoire des IMRCP, UMR au CNRS Nο. 5623, Universite´ Paul Sabatier, 118 route de Narbonne, F-31062 Toulouse Cedex, France Received March 31, 2000. In Final Form: May 22, 2000 The kinetics of solubilization of ethyl hexanoate into an aqueous phase was investigated in the presence of various additives (NaCl, ethanol, and sodium hexanoate). The salting-out effect of NaCl and the solvent effect observed in the presence of ethanol were quantified. Solubilization by sodium hexanoate shows a dramatic enhancement when the critical micellar concentration is exceeded. This effect was interpreted by the formation of mixed oil/surfactant aggregates. The kinetic rate constants of solubilization of ethyl hexanoate into the water phase were determined in the presence of sodium hexanoate using a model including salting-in, salting-out, and aggregation effects. When NaCl was replaced by NaOH, ethyl hexanoate was hydrolyzed to sodium hexanoate and ethanol. The kinetics of this reaction was recorded in the same geometrical setup as for previous solubilization experiments. The solubilization kinetic model was able to describe the hydrolysis reaction by just adding a rapid bulk hydrolysis step. The model quite accurately predicts the autocatalytic effect of sodium hexanoate formation and the overall reaction time. This result clearly shows the crucial role of solubilization processes on this biphasic hydrolysis reaction.
I. Introduction The autocatalytic biphasic alkaline hydrolysis of ethyl octanoate was first described by Bachmann et al.1 In the original paper, the reaction was performed under slow stirring of the water phase so that the two phases remained clearly separate. The kinetics shows a very long induction period followed by a pronounced acceleration that results in a monophasic aqueous solution of sodium octanoate and ethanol. Since then, several interpretations for this phenomenon have been published.2-5 To get further insight into the mechanism, we have reproduced the reaction, using an emulsified system6,7 and also shorter alkyl chains, from C-4 to C-8.8 All of the reactions show an autocatalytic evolution, although the acceleration effect is greater with increasing chain length. For C-4 and C-5 the autocatalytic behavior is attributed to enhanced dissolution of ester caused by solvent and salting-in effects, respectively due to the formation of ethanol and alkanoate ions. For the three other compounds (C-6, C-7, and C-8), aggregation occurs during the course of the reaction when the critical concentration of the amphiphile alkanoate ions is reached.9,10 These aggregates allow extensive additional solubilization of ester in the water bulk, leading to the rapid acceleration effect.11 Previously, the models we proposed were based on these solubilization processes, * To whom correspondence should be addressed. E-mail:
[email protected]. (1) Bachmann, P. A.; Luisi, P. L.; Lang, J. Nature 1992, 357, 57-9. (2) Chizmadzhew, Y. A.; Maestro, M.; Mavelli, F. Chem. Phys. Lett. 1994, 226, 56. (3) Billingham, J.; Coveney, P. V. J. Chem. Soc. 1994, 90, 1953. (4) Coveney, P. V.; Wattis, A. D. Proc. R. Soc. London A 1996, 452, 2079. (5) Maestro, M. Mol. Eng. 1996, 6, 391. (6) Buhse, T.; Nagarajan, R.; Lavabre, D.; Micheau, J. C. J. Phys. Chem. A 1997, 101, 3910. (7) Tixier, J.; Pimienta, V.; Buhse, T.; Lavabre, D.; Nagarajan, R.; Micheau, J. C. Colloids Surf. A 2000, 167 (1-2), 131. (8) Buhse, T.; Lavabre, D.; Nagarajan, R.; Micheau, J. C. J. Phys. Chem. A 1998, 102, 10552. (9) Danielson, I.; Stenius, P. J. Colloid Interface Sci. 1971, 37, 264. (10) Rosenholm, J. B.; Stenius, P.; Danilelsson, I. J. Colloid Interface Sci. 1976, 57, 551. (11) Kust, P. R.; Rathman, J. Langmuir 1995, 11, 3007.
but the parameters used in these models had no real physical significance. The aim of this work is not to propose a more detailed model but to quantify the parameters of the different steps of a simpler model only taking into account spontaneous solubilization, solubilization by micelles, and hydrolysis. For this purpose we studied the kinetics of solubilization of ethyl hexanoate (C-6) in a nonreactive system. We chose this compound because its kinetics behavior is comparable to that of C-8 (formation of aggregates) and it has the great advantage of being more soluble in water, facilitating detection. During the hydrolysis reaction, different species are present: NaOH and the products of the reaction, ethanol, and hexanoate ions. In the first part of this work, we studied the influence of each species, considered one by one, on the solubilization of ethyl hexanoate; NaCl replaces NaOH to give a nonreactive system. The solubilization experiments were then fitted, and we obtained kinetic and thermodynamic parameters. These parameters were used in the second part to model the hydrolysis reaction. II. Experimental Section Reagents. All of the reagents purchased from commercial sources were of the highest purity available and were used without further purification: ethyl hexanoate (Fluka), cyclohexane (SDS), n-octane (Merck), ethanol (Prolabo), sodium hydroxide (SDS), sodium chloride (SDS), and sodium hexanoate (Fluka). Water was double distilled. Experimental conditions. Experiments were performed in a thermostated (T ) 25 °C) round-bottom, twonecked flask (cross-sectional area 20 cm2). The water phase (38.5 mL) was first introduced into the flask, and then the organic phase (11.5 mL) was poured carefully along the inner wall. The aqueous phase was gently stirred (70 rpm) so it could be considered that it was homogeneous although the two phases remained clearly separate. The parameters obtained from the solubilization experiments are strongly dependent on the geometrical (area of the interface) and hydrodynamic conditions. To use the same parameters for the hydrolysis reaction model, the water and oil phase volumes, stirring rate, and temperature were maintained
10.1021/la0004911 CCC: $19.00 © 2000 American Chemical Society Published on Web 07/08/2000
Processes in Autocatalytic Biphasic Reactions
Figure 1. Concentration of solubilized ester in water versus time: (o) experimental points; (s) simulation using [Eaq] ) (k1/k-1)(1 - exp(-k-1t)). Optimized parameters: k1 ) 5.30 × 10-5 mol-1‚L‚min-1 and k-1 ) 1.64 × 10-2 min-1.
strictly identical in solubilization experiments and in the hydrolysis reaction. Solubilization of Ethyl Hexanoate. Before the introduction of the organic phase, a long sampling needle was placed in the water phase to avoid any contact with the organic phase during sampling. Aqueous phase samples of 0.5 mL, taken at regular intervals, were analyzed by gas chromatography (GC) after extraction by cyclohexane. n-Octane was used as an internal standard. Hydrolysis Reaction. In our experiment, the temporal dependence of the reaction was followed by measurement of the decrease of the organic phase volume. Moreover, we checked that no significant amounts of hexanoate ions or ethanol passed into the organic phase. III. Solubilization of Ethyl Hexanoate (1) Solubilization in Water. In our first experiment we followed the dissolution of the ester in water without further additives. The evolution of the concentration of ester in the water phase is represented in Figure 1. The solubilization kinetics are first order, and saturation is obtained at 3.23 × 10-3 mol‚L-1. Moreover, we verified that the kinetics did not depend on the volume of the supernatant organic phase. According to our observations and the literature,12 the model proposed for this process is represented by
Eorg a Eaq
r1 ) k 1 r-1 ) k-1[Eaq]
The rate law r1 is zero order with respect to ester in the organic phase (Eorg), while the reverse step is first order with respect to the dissolved ester (Eaq). At equilibrium, the saturation concentration is given by
k1/k-1 ) [Eaq]sat,H2O ) 3.23 × 10-3 mol‚L-1 Fitting of the experimental curves by the model (Figure 1) allows the determination of k1 and k-1. (2) Solubilization in the Presence of NaCl. Dissolved electrolytes such as NaOH decrease the solubility of noncharged solutes. This effect, known as salting-out,13 is caused by electrostriction of the solvent. This contraction of the total volume, due to polarization and attraction of solvent molecules around the ions, makes cavity creation harder. To mimic the effect of NaOH on the solubilization of ethyl hexanoate, several experiments were run in the presence of NaCl. The effect of chloride ions has been neglected because only sodium ions have smaller partial (12) Noyes, A. A.; Withney, W. R. J. Am. Chem. Soc. 1897, 19, 930. (13) Dack, M. R. J. Chem. Soc. Rev. 1975, 4, 211.
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Figure 2. Saturation concentrations of ethyl hexanoate versus [Na+]: (o) experimental points; (s) simulation using [Eaq]sat,Na+ ) [Eaq]sat,H2O exp(RNa+[Na+]) with RNa+ ) -0.64.
molal volumes than water and have a significant electrostrictive effect on the water structure.14 The evolution of the concentration of dissolved ester in these conditions was still first order, like in pure water, but as expected the equilibrium concentrations were lower. The saturation values plotted against Na+ concentration can be fitted using an exponential relationship (Figure 2), which is in agreement with the thermodynamic approach proposed by Nagarajan in ref 6. The equilibrium values were calculated using
[Eaq]sat,Na+ ) [Eaq]sat,H2O exp(RNa+[Na+]) ) k1/k-1 exp(RNa+[Na+]) where k1 and k-1 were provided by the previous experiments (section III-1); the value obtained for RNa+ was -0.64. (3) Solubilization in the Presence of Ethanol. During hydrolysis, ethanol is formed and its concentration in the water phase varied from 0 to 1.4 mol‚L-1. Solubilization of ethyl alkanoates was enhanced by the presence of this cosolvent because ethanol molecules are able to enter the solvation sphere and act as bridges between the solute and water, thus reducing the energy of the solutemedium solvation interactions.15 Experiments performed in the presence of increasing ethanol concentrations showed first-order kinetics and an increase of the saturation concentration of ethyl hexanoate of 23% in the presence of 1 mol‚L-1 ethanol. Like for NaCl and according to the thermodynamic approach,6 an exponential dependence of the saturation concentration was observed. Treatment similar to that in section III-2 led to the experimental evaluation of REtOH at 0.25. (4) Solubilization in the Presence of Sodium Hexanoate. Besides producing ethanol, the hydrolysis of ethyl hexanoate produces hexanoate ions. This shortchain carboxylate is referred to in the literature as a hydrotrope.16,17 Like surfactant molecules, hydrotropes have the ability to form aggregates, leading to a pronounced enhancement of the capacity to solubilize lipophilic compounds. The distinction, made in the literature, between surfactants and hydrotropes (octanoate is considered as the borderline compound for alkanoate ions) lies mainly in the aggregate size, size distribution, and shape of the aggregates.18,19 For the sake of simplicity, (14) Leberman, R.; Soper, A. K. Nature 1995, 378, 364. (15) Breslow, R.; Guo, T. Proc. Natl. Acad. Sci. U.S.A. 1990, 87, 167. (16) Srinivas, V.; Balasubramanian, D. Langmuir 1998, 14, 6658. (17) Balasubramanian, D.; Friberg, S. E. Surface and Colloid Science; Plenum Press: New York, 1993; Vol. 15, p 197. (18) Balasubramanian, D.; Sharma, M. M. J. Phys. Chem. 1989, 93, 3865. (19) Srinivas, V.; Rodley, G. A.; Ravikumar, K.; Robinson, W. T.; Turnbull, M. M.; Balasubramanian, D. Langmuir 1997, 13, 3235.
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phase. The concentration of Eaq corresponds to solubilization in a water phase containing the cmc of free hexanoate ions in the presence of 3 mol‚L-1 Na+. The model proposed to describe the overall set of experiments and thus the aggregate-mediated transfer is summarized by the following four steps.
r1 ) k1(exp(RNa+[Na+]) + (RS[S])) (1)
Eorg a Eaq
r-1 ) k-1[Eaq] Figure 3. Saturation concentration of ethyl hexanoate versus surfactant concentration. In each experiment the concentration of sodium ions was adjusted to 3 mol‚L-1 by addition of the corresponding amounts of NaCl.
sodium hexanoate will be referred to as “surfactant” and aggregation as “micellization”. The critical micellar concentration (cmc), which must be reached for aggregation to occur, was evaluated using a surface tension technique. To recreate the microenvironment20 of the reactive mixture (3 mol‚L-1 NaOH), the concentration of sodium was adjusted to 3 mol‚L-1 by addition of NaCl. It is important to maintain the concentration of Na+ at that of the NaOH used in the hydrolysis reaction because it plays the role of counterion for the negatively charged hexanoate aggregates and therefore has an influence on the aggregation number and the cmc. The value measured for the cmc in these conditions was 0.46 mol‚L-1. Then, ethyl hexanoate was added to each solution used for the cmc determination, and the saturation concentrations of solubilized ester in the water bulk were measured. These values plotted versus surfactant (S) concentration (Figure 3) present a slight increase in the first part of the curve followed by a sharp enhancement of solubilization after 0.5 mol‚L-1, i.e., slightly after the cmc. The experiments, performed in the range of the hexanoate concentrations met during the hydrolysis reaction, give a good image of the solubilization enhancement caused by the formation of aggregates by this surfactant. To model this effect, two phenomena were examined: we first considered the slight effect of free surfactants using experiments where concentrations were smaller than the cmc; then we considered the whole set of experiments to add up all of the processes together accounting for solubilization in the aggregates. a. Below the cmc. The slight increase in solubilization for the lowest hexanoate concentrations has already been attributed to a salting-in effect.7 Indeed, these short-chain surface-active ions disrupt the structure of water, decreasing the energy required for cavitation of the solute.21 Like for ethanol and NaCl, an exponential dependence accounts for the increase in the ester concentration at saturation as a function of the amount of hexanoate. Because both sodium hexanoate and NaCl are present in the medium, the model used to reproduce the data was
[Eaq]sat,S ) [Eaq]sat,H2O exp(RNa+[Na+] + RS[S]) Fitting of the equilibrium data gives RS ) 0.44. b. Above the cmc. Above the cmc, the dissolved ester partly came from direct solubilization in water (Eaq) and partly from the ester contained in the “pseudomicellar” (20) Kuhn, H.; Rehage, H. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1485. (21) Breslow, R. Acc. Chem. Res. 1991, 24, 159.
r2 ) k2Sn
nS a Sn
(2)
r-2 ) k-2[Sn] Sn + pEorg f SnEp r3 ) k3[Sn]
(3)
SnEp a Sn + pEaq
(4)
r4 ) k4[SnEp] r-4 ) k-4[Sn][Eaq]
Step (1) accounts for solubilization in the presence of NaCl and hexanoate below the cmc, the values of k1 and k-1 were obtained in section III-1, and RNa+ was determined in section III-2 and RS in section III-4-a. Step (2) represents the fast aggregation process: n molecules of surfactant (S) are involved in a cooperative association and form pure amphiphile aggregates (Sn). For the sake of simplicity, we consider only one size of aggregate: the average aggregation number (n) has been estimated by thermodynamical calculations at 24.6 The high-order rate law r2 generates a threshold concentration that can be adjusted to the cmc by fixing the ratio k2/k-2 using Benjamin’s22 calculations: k2/k-2 ) cmc(1-n)/2n2. This step being very fast compared to the time scale of solubilization, the values for k2 and k-2, although not known, just need to be high enough to not interfere with slower processes (we used k2 ) 1015 mol1-n‚Ln-1‚min-1 and so k-2 )1010 min-1). Step (3) accounts for solubilization by the aggregates at the surface of the organic phase (Eorg):23,24 p molecules of ester are trapped by the aggregates to form mixed aggregates (SnEp). The capacity of these aggregates to dissolve ester molecules is given by the following ratio: ester solubilized in the aggregates/aggregated surfactants. The numerator was obtained by subtracting, from the measured saturation values, the concentration of ester dissolved by the nonaggregative process (Eaq in step (1)). The concentration of hexanoate ions that participate in aggregation is found by subtracting the cmc from the total hexanoate concentration, i.e.
R)
[total ester solubilized] - [Eaq]sat,S [total surfactant] - cmc
This ratio increases with the surfactant concentration; it appears that the aggregates formed in more concentrated solutions have a greater solubilization capacity. This can be attributed to variations in the size and maybe the geometry of the aggregates. In our model, because only one size of aggregate is considered (n ) 24), the increasing ability of the aggregates to trap oil molecules appears in the value of p (p ) 24R). The values of p varied from 0.3 to 1.4; for the calculations this value was fixed at 1. The (22) Benjamin, L. J. Phys. Chem. 1964, 68, 3575. (23) Karaborni, S.; Van Os, N. M.; Esselink, K.; Hilbers, P. A. J. Langmuir 1993, 9, 1175. (24) Plucinski, P.; Nitsch, W. J. Phys. Chem. 1993, 97, 8983.
Processes in Autocatalytic Biphasic Reactions
Figure 4. Kinetics of solubilization of ester in 1 mol‚L-1 sodium hexanoate with 2 mol‚L-1 NaCl: (o) experimental points; (s) simulation [Eaq] + p[SnEp] versus time. Optimized parameter: k3 ) 7.84 × 10-3 min-1. Fixed parameters: k4 ) 104 min-1; k-4 ) 109 mol-1‚L‚min-1.
rate law for this interface process (r3) is first order with respect to the aggregate concentration and zero order with respect to Eorg because the rate for filling the aggregates cannot depend on the organic phase available. Moreover, because we assume that all of the aggregates are filled at saturation, no reverse step is taken into account. Step (3) is rate determining, and the value of k3 was determined by fitting experimental solubilization kinetics (Figure 4). Step (4) represents the dynamical equilibrium accounting for fast molecular exchange that results in the transient release of ester molecules in the aqueous phase. Relaxation studies,25 devoted to micellar dynamics, show that the relaxation time for micelle dissolution in water, i.e., the destruction of the aggregate into free surfactants, is less than 1 ms. We can assume that this is the time scale representative of ester release. Therefore, step (4) is very fast and, like in step (2), the values for k4 and k-4 simply need to be high. The ratio k4/k-4 is fixed so that, at equilibrium, the saturation concentration in the water bulk is limited to [Eaq]sat,S ) 5.7 × 10-4 mol‚L-1. This value corresponds to the saturation concentration obtained in a 0.46 mol‚L-1 solution of free hexanoate, i.e., the cmc in the presence of 3 mol‚L-1 Na+. The values for these rate constants were fixed at k4 ) 104 min-1 and k-4 ) 109 mol-1‚L‚min-1. The experiment performed to determine the value of k3 used a 1 mol‚L-1 surfactant solution (containing 2 mol‚L-1 NaCl). The curve recorded shows, as before, a pattern that is correctly reproduced by our model. Fitting gave k3 ) 7.84 10-3 min-1. To test if the main solubilization processes, liable to occur during hydrolysis, have been correctly identified and evaluated, the above results were integrated into the model of the reactive system.
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Figure 5. Volume of the organic phase versus time in the biphasic hydrolysis reaction of ethyl hexanoate with 3 mol‚L-1 NaOH: (o) experimental points; (s) simulation using the complete model presented in the appendix.
involved in a bimolecular process with OH-:
Eaq + OH- f S + EtOH
r5 ) k5[Eaq][OH-]
(5)
(1) The Reaction. The kinetics of the biphasic hydrolysis was monitored by measuring the volume of the residual organic phase. The experiment, performed at 25 °C, lasted for 45 days. The curve, presented in Figure 5, shows a long induction period followed by a sharp acceleration of the consumption of the organic volume, leading to a monophasic solution. Owing to the solubilization model, ethyl hexanoate is present in the water bulk as free molecules (Eaq) or solubilized in the aggregates (SnEp). Because the electrostatic repulsive interactions between the anionic aggregates and the hydroxyl ions are unfavorable to surface reactions, we considered Eaq as the reactive species,
Because of its low solubility in water, the available kinetics studies concerning the hydrolysis of ethyl hexanoate were all performed in solvent mixtures.26 To evaluate the hydrolysis rate constant in pure water, sodium hydroxide was added to ester-saturated water solutions and the reaction followed, as before, by GC. The first results led to the puzzling observation that the kinetics cannot be reproduced by a second-order rate law. Nevertheless, before further investigations are performed on this system and as far as the present study is concerned, one result that is to be pointed out is the rapidity of the process. The half-time observed for a quasi-stoichiometric mixture of both reactants (4.8 × 10-4 mol‚L-1) was about 80 min, leading, if we approximate the kinetics to a second-order law, to k5 ) 35 mol-1‚L min-1. The time needed to consume the same quantity of ester in a 3 mol‚L-1 NaOH solution can then be estimated at about 3 s. If we compare this to the time scale of the biphasic reaction (45 days), we can assume that a detailed mechanism is not relevant for the present study and the hydrolysis process will be represented by step (5) and k5 ) 35 mol-1L‚min-1. (2) Results and Discussion. The complete model, steps (1)-(5), presented in the appendix and the corresponding parameters provided by the various studies were used to simulate the biphasic reaction. Step (1) has to take into account for the salting-out effect due to sodium ions and increasing ethanol and free hexanoate effects. The calculated curve, represented by the solid line in Figure 5, reveals that the induction period, the sharp acceleration, and the global reaction time are reproduced with satisfactory precision. It should be pointed out that slow processes (spontaneous solubilization, salting-in, or solvent effects) occurring before aggregation have crucial consequences on the induction period and thus on the reaction duration. The time-dependent concentration curves, calculated by the model, show that step (1) is rate determining during the induction period. The ester dissolved (Eaq) is instantaneously hydrolyzed, and the surfactant concentration slowly increases. When the hexanoate threshold concentration is reached, step (3), which is representative of solubilization in the aggregates, governs the rapid reaction period. During this stage, mixed aggregates accumulate slightly in the medium. Transient release of ester in water (step(4)) leads to faster hydrolysis and formation, at the end of the reaction, of pure aggregates (Sn). However, the relatively simple model
(25) Lang, J.; Tondre, C.; Zana, R.; Bauer, R.; Hoffmann, H.; Ulbricht, W. J. Phys. Chem. 1975, 79, 276.
(26) Evans, D. P.; Gordon, J. J.; Watson, H. B. J. Chem. Soc. 1938, 1439-44.
IV. Biphasic Alkaline Hydrolysis
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proposed here does not perfectly reproduce the shape of the curve at the beginning of the reaction. The first difference to notice is the smaller initial slope of the experimental kinetics. This can be attributed to the use of NaCl instead of NaOH to measure direct solubilization. As a matter of fact, it is known that NaOH has a greater salting-out effect than NaCl27 and moreover the NaOH solution is more viscous than NaCl, leading to slower transfer. The second difference between the predicted and experimental curves concerns the extent of the reaction when acceleration occurs. In the real system the acceleration starts before the value of the cmc (0.46 mol‚L-1), measured in sodium chloride solutions, is reached. Although the nature of the anion may have an influence on the critical concentration, we must also consider that the model relies on the assumption that the medium is totally homogeneous. We do not take into account the concentration gradients at the interface,28,29 which can lead to earlier formation of aggregates and subsequent solubilization. Nevertheless, the macroscopic model proposed seems to account correctly for the main processes, because the quite precise prediction of the reaction time cannot be casual. V. Conclusion This study clearly points out the essential part played by solubilization processes on the autocatalytic kinetics of the biphasic reaction. This simple system accounts for many aspects of the solubilization properties of water. Each phenomenon has been isolated and quantified in the preliminary experiments performed with the nonreactive system. Salting-out, salting-in, and solvent effects are determinant during the induction period before aggregate-mediated transfer takes place. The rate of the biphasic reaction depends only on the ester available in the water phase, and no further hypothesis needs to be invoked concerning any possible catalysis of the hydrolysis step.
k-1 ) 1.64 × 10-2 min-1
r-1 ) k-1Eaq
k2 ) 1015 mol1-n‚Ln-1‚min-1
r2 ) k2Sn/(Vaq)n-1
k-2 ) 1010 min-1
r-2 ) k-2Sn r3 ) k3Sn
k3 ) 7.84 × 10-3 min-1
r4 ) k4SnEp
k4 ) 104 min-1
r-4 ) k-4SnEaq/Vaq
k-4 ) 109 mol‚L-1‚min-1
r5 ) k5OH-Eaq/Vaq
k5 ) 35 mol‚L-1‚min-1
with Vaq ) Vtot - Vorg (assuming Vtot constant ) 50 mL). Differential Equations. A semi-implicit RungeKutta method was used for the numerical integration and a nonlinear minimization algorithm for fitting the experimental data.
dEorg/dt ) -r1 + r-1 - pr3 dEaq/dt ) r1 - r-1 + pr4 - pr-4 - r5 dS/dt ) -nr2 + nr-2 + r5 dSn/dt ) r2 - r-2 - r3 + r4 - r-4 dSnEp/dt ) r3 - r4 + r-4 dOH-/dt ) -r5
Appendix: Equations for the Biphasic Hydrolysis Model
dEtOH/dt ) r5
Reaction Scheme
Eorg a Eaq
(1)
The experimental data Vorg is calculated by multiplying Eorg by its molar volume: Vorg ) VmEorg.
nS a Sn
(2)
List of Variables
Sn + pEorg f SnEp
(3)
SnEp a Sn + pEaq
(4)
Eaq + OH- f S + EtOH
(5)
Rate Equations in mol‚min-1. Because of the nonhomogeneous (biphasic) character of the reactive system, the total quantities of each species are expressed in numbers of moles instead of concentrations (indicated by square brackets). The rate constants are expressed in the usual units.
r1 ) k1Vaq exp[(RNa+Na+ + RSS + REtOHEtOH)/Vaq] k1 ) 5.3 × 10-5 mol‚L-1‚min-1 (27) McDewit, W. F.; Long, F. A. J. Am. Chem. Soc. 1952, 74, 1773. (28) Otsuki, J.; Seno, M. J. Phys. Chem. 1991, 95, 5234. (29) Kabalnov, A.; Weers, J. Langmuir 1996, 12, 3442.
Eorg ) ethyl hexanoate in the organic phase Eaq ) ethyl hexanoate in the aqueous phase OH- ) hydroxide ion EtOH ) ethanol S ) free surfactants (hexanoate ion) Sn ) aggregates formed by n molecules of surfactant SnEp ) mixed aggregates formed by n molecules of hexanoate and p molecules of ester Vorg ) volume of the organic phase Vaq ) volume of the aqueous phase Vtot ) total volume Vm ) molar volume of ethyl hexanoate: 0.166 L‚mol-1 RNa+ ) correction factor related to the salting-out effect due to sodium RS ) correction factor related to the salting-in effect due to free surfactants REtOH ) correction factor related to the solvent effect due to ethanol n ) average aggregation number p ) average number of molecules of ester in mixed aggregates LA0004911
