Substrate Partitioning and Chemical Equilibrium in a Micellar Solution Elsa B. Abuin and Eduardo A. Lissi Departamento de Quimica, Facultad de Ciencia, Universidad de Santiago de Chile, Casilla 307, Correo 2, Santiago, Chile
Micellar solutions can be considered microheterogeneous svstems. The ex~erimentwe describe in this article is desighed to study one very important aspect of these solutions that is due to their microhetero~eneouscharacter: As a solute is dissolved, it is inhomoge&ously distributed throughout the entire volume of the resulting solution. The experiment is used to determine the distribution of iodine between a micellar pseudophase, formed by sodium dodecylsulfate micelles, and the intermicellar aqueous phase. This is achieved by measuring the effect of adding surfactant on the following reversible reaction.
Introduction Micellar solutions are formed by dissolving certain types of surfactants in water. The surfactants that form micelles are amphiphilic molecules whose structures simultaneously bear one (rarely more) hydrophobic chain (typically an alkyl chain with at least 6-8 methylene groups) and a polar head group (typically a n ion or very hydrophilic group). The unique structure of this type of molecule, with its hydrophobic and hydrophilic character, is required to form micelles. Dissolved surfactants in water display different behavior depending on the range of concentration considered. At low concentrations they dissolve as isolated molecules. At high concentration, dissolution occurs with self-association of the surfactant molecules into aggregates of colloidal dimensions (radii of about 1.5-2 nm), called "micelles". The self-association of the surfactant molecules is strongly cooperative. The onset of micelle formation, which marks the change from dissolution as monomers to dissolution as aggregates, occurs in a very narrow concentration range-virtually a t a single concentration. There are two fundamental models used to interpret the associr~tionof surfactant into micelles. One is theequilibrium model in which micelle formation is treated as being analogous to a chemical equilibrium. The other is the phase separation model in which micelle formation is considered to be analogous to a phase separation. According to the phase separation model (psm), the concentration that corresponds to the onset of micelle formation is considered to be the saturation concentration of the surfactant in the monomeric form. It is called the critical . micelles are condidered micelle concentration ~ C M C IThc to constitute a separated pseudophase. The psm will be operationally convenient for our study. Regardless of the model used to explain the formation of the micellar aggregates, a micellar solution can be described as a system of hydrophobic domains of colloidal dimensions. These domains are represented by the micelles (the micellar pseudophase in the psm) immersed in a dispersion medium or intermicellar phase, which is the aqueous phase containing surfactant at a concentration equal
Correspondence should be addressed to E. 6. Abuin. 340
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to the CMC in the psm. Certainly, such a system will behave as microheterogeneous. When a solute is added to a solution of this type, a solute-containing micellar solution is formed in which the solute is inhomogeneously distributed. There will be a t least three zones (1-5)available to the solute as solubilization loci: The "bulk" of the micellar pseudophase, which is the micelle core and represents something like a hydrocarbon solvent
The aqueous phase The interface between the micellar pseudophase and the aqueous phase I t is sometimes convenient to make no distinction between the bulk of the micelles and the interface. In other words, consider that the assembly of all micelles is the only distinct phase existing in the solution besides the aqueous phase. Then we can treat the solute distribution as a partitioning between just two phases: t h e micellar pseudophase and the aqueous phase. This will be the approach used in this experiment in which we interpret the partitioning of iodine in sodium dodecyl sulfate (SDS) micellar solutions. Reaction in Water Without Surfactant Adding iodide to an aqueous iodine solution will increase the absorbance a t 353 nm, which corresponds to the presence of triiodide ion (6).The equilibrium constant for the reaction of eq 1 can be obtained by measuring absorbance a t 353 n m as a function of the amount of iodide added to an aqueous iodine solution. Assuming dilute solution behavior, we get
where x is the concentration of triiodide formed; a is the total concentrations of iodine, and b is the total concentration of iodide. Substituting y = x/a and z = bla, eq 2 can be rearranged.
The value of y is obtained experimentally. It is the ratio between the absorbances a t 353 nm measured for two different solutions: a solution with a given concentration of iodine and iodide, and a solution in which the iodine is converted completely to triiodide ion by addition of excess iodide. Plotting the left hand side of eq 3 against (z -y) yields a straight line whose slope is the value of K. Reaction With Surfactant In the uresence of surfactant. iodine will be ~artitioned between ihe micellar pseudophase and the aqueous phase, whlle iod~deand triiodide will be solubilized exclusivelv in the aqueous phase. Since these hydrophilic ions a r e charged, their interaction with the micellar pseudophase is prevented by wulombic repulsion. Thus, in the presence
of surfactant, the reaction scheme can he represented as below.
Equations 4 and 5 show that adding SDS to a given Iflsolution in water will decrease the production of triiodide as compared to the amount formed in the same Ifl- solution without surfactant. Extraction of part of the iodine to the micellar pseudophase will diminish the amount of iodine available in the aqueous phase to react with the iodide. The concentration of (I&, which affects the reaction in the aqueous phase, will be subjected to the partition equilibrium condition given in eq 4. To obtain the partition constant, the amount of iodine in the micellar ~ s e u d o ~ h amust s e be emressed in terms of its intramicellar concentration. Asuitableconcentration scale can be defined cat low incorporation values, as below.
=meiated is the analytical concentration of iowhere [Izlrnieelle dine associated with the micelles (mol iodine& of solution); and [SDSIMis the concentration of micellized surfactant. I t is given by - CMC [SDSIM= [SDSllbtsll (7)
The partition constant Kp for the phase equilibrium of eq 4 is then given by
in water (0.1 M) was prepared, titrated following standard methods, and used throughout the experiments. Absorption spectra and absorhances were recorded ona Shimadzu W-160 spectmphotometer that was equipped with a thermoregulated cell compartment. The experiments were done a t 21 T. (This was also the temperature of the mom.) For each iodine concentration considered the experiments were performed as follows. Without Surfactant
Iodine solution (3 mL) was delivered into the cuvette of the spectrophotometer (rectangular; pathlength: 1 em), and the spectrum was recorded at 300-650 nm. This spectrum had a bmad hand a t 460 nm, corresponding to the absorption of iodine in water, and a very weak absorption a t 353 nm. The absorbance at 353 nm for this starting solution is recorded and used as a background signal to be subtracted from the readings taken in the presence of iodide. Aliquots of2 pLof the potassium iodide stock solution were added to the starting solution in the cuvette in succesive steps to a total addition of 20 pL. ARer each addition, the mixture is homogeneized by manual shaking, and the absorbance a t 353 nm is recorded. With Surfactant
Four solutions were prepared in which the solvents used were the same iodine solutions used in the experiments done without surfactant. 0.05 M and 0.1 M SDS in which the 0.183m M iodine solu-
tion was used as the solvent
0.05 M and 0.1 M SDS in which the 0.366mM iodine solu-
tion was used as the solvent. Each of these solutions were used following the same pmcedure described for the experiments without surfactant.
Next we combine eqs 2,4,5, and 8, taking into account the mass balance condition of eq 9. We neglect the volume occupied by the micellar pseudophase.
Equation 10 can be derived.
where y' has the same meaning as y in eq 2, but here it applies to the results obtained in the presence of surfactant. A straight line is obtained from plotting the left hand side of eq 10 against l/(z -y'), using results obtained from experiments in which the concentrations of iodine and SDS were kept constant, while the concentration of iodide was varied. K, is obtained fmm the slope of the line.
K
P
slope - 1 -- [SDSI.
Experimental Sodium dodecylsulfate (BDH, specially pure) was used as received. Iodine (Merck) was purified by sublimation. Potassium iodide (Merck)was used without treatment. Two solutions of iodine in water were prepared, titrated following standard methods, and used thmughout the experiments. The concentrations of these solutions were 0.183 and 0.366 mM. A stock solution of potassium iodide
Results And Discussion Iodine concentrations considered were 0.183 mM and 0.366 mM. The production of IB-was followed by measuring the absorbance of the solutions a t 353 nm a h r addition of increasing amounts of iodide. The range of iodide concentrations considered was 0.066-0.66 mM. Figure 1 shows the results obtained for the reaction in water without SDS, plotted according to eq 3. The linearity of the plot indicates that, under the experimental conditions used, the assumption of diluted behavior is reasonable. The slope of the line shown in Figure 1 gives K = 783 f 19 M-'. Experiments carried out with surfactant used two different concentrations: 0.05 and 0.1 M. For each SDS concentration, the iodine concentrations considered were the same as those used for the reaction in water without surfactant. Figure 2 shows the results obtained, plotted according to eq 10. In the figure, the results obtained using both iodine concentrations lie on the same line for each surfactant concentration, and the slope of the line is larger for the highest surfactant concentration. These are the expected behaviors because iodine partitioning between the micellar pseudophase and the aqueous phase must be independent of the iodine concentration and because the slope of the line is a direct function of SDS concentration (see eq 10). From the slopes of lines A and B of Figure 2, K, is calculated as slope - 1 Kp = -[SDSI, using [SDSIMfrom eq 7 with CMC = 0.008 M (7).Both sets of experiments give very similar values for K,.The values for Kp obtained from the experiments are Volume 69 Number 4 April 1992
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Kp = 17 i 0.5 M-' when the concentration SDS is 0.1 M Kp = 17.2 f 0.8 M-l when the concentration of SDS is 0.05 M of
Figure 1. Results obtained for the reaction in water without surfactant, plotted according to eq 3. Temperature: 21'C. Iodine mncentrations: 0.183 mM (0)and 0.366 mM (+).
This is consistent with the definition of Kp (see eq 8) in which it is considered to be independent of the surfadant concentration. The value ofKp obtained implies that 50% of the iodine is associated with the micelles (with no added iodide) when the SDS concentration is 0.067 M. Also. the value ofK, implies that, at SDS = 0.067 M, the concentration of iodine in the micellar pseudophase (81, defined in moles of solute per liter of micellar pseudophase, is nearly 25 times the analytical iodine concentration. This higher concentration of the solute in the micellar pseudophase is one of the most relevant characteristics of the solutions of surfadants. I t explains their main ~ r o ~ e r t iboth e s as solvents and as reaction to increase the rate of bimolecular processes ( 9 , I O ) .
Acknowledgment Thanks a r e given to FONDECYT (Grant#775/90) for financial support.
Literature Cited 1. McBain. M. L.E.;HutEbbsonE.SdubiiL~Liolo ond&lotd P & n o m m : Academic Press:NewYmL. 1955.
3. Cardinal J. R.: Mukerjee P. J Phya C k m . 1818,82,161& 1620
4. Mukerjee P PunondAppl. C k m . lW,62,1317-1321. 5. sepvlveda L.; ~ l s sEl.;%haF.A Inforfrf Science lS88,25,1-57
~ U M ~inS colloid
6. Awtrey A. 0.: Connick E. J. Amp?
Figure 2. Resunsobtained forthe reaction in the presence of SDS micelies plotted according to eq 10. (Solid line):[SDSITmI= 0.1 M. (Dashed line): [SDSJTml = 0.05 M. Iodine concentrations: 0.183 mM (0); 0.366 mM (+); 0.366 mM (x), in which both the ordinate and the abscisa are multiplied by a factorof 0.5.
342
Journal of Chemical Education
Cham. Soe. 1961, 73. 1842-1845. 7. Mukdelee, P; Mysels, K. J. Cllticol Micelk Concpntmtions olAguwus S u r f a e t ~ Systems; t National Bureauof Standards. U S . Go*. Printing Omee: Washingtan, DC,1970. 6. The hbamicellar molar concentration is ~alcvlatedassumb e a densitv of0.8ermL for the micellar . laeudo~hase. . 9. Cbimo
