In the LaboratoryAn Undergraduate Physical Chemistry Experiment on Surfactants: Electrochemical Study of a Commercial Soap Pablo C. Schulz* Departamento de Química, Universidad Nacional del Sur, Bahía Blanca, Argentina; *
[email protected] Danièle Clausse Département du Génie Chimique, Université de Technologie de Compiègne, Compiègne, France W Undergraduate students frequently ask for laboratories having some relation to industry and practical applications, whereas professors want to introduce the students to fundamental theory by laboratories carried out with common, inexpensive apparatus and inexpensive, innocuous chemicals. At the Department of Chemical Engineering at the Compiègne Technology University in France we developed the experiment described here. We used conductivity and pH measurements on a commercial soap to determine some of its properties and to relate the properties to surfactant theory. The experiment was used after lectures on the nature, properties, and technical applications of surfactants. This laboratory may be included in an undergraduate chemistry curriculum in physical chemistry or instrumentation. This laboratory gives information of practical interest on commercial soaps and insight on the theoretical treatment of conductivity and pH data to determine several surfactant properties: • • • • • • • • • • Number average molar weight, Mn Number of carbon atoms in the soap chain, nC Critical micelle concentration, CMC Micelle ionization degree, α Aggregation number, n Molar conductivity of micelles, ΛM Electrophoretic mobility of micelles, umic Equivalent conductivity of surfactant ions, λanion Existence of a critical concentration range, CCR Influence of the CCR on the CMC value obtained by different techniques or different treatment of the same data Mixed fatty acid ionization constant Mixed fatty acid solubility in water, SHA Constant of formation of the mixed “acid soap” complex, KNaHA2 Degree of hydrolysis of the soap mixture, β Concentration at which the first aggregates form, CF Constant of distribution of mixed fatty acid between micelles and aqueous solvent, KF Differences between pure soap and mixed soap aqueous solutions behaviors • • • • pH meter with glass electrode Commercial soap (may be a hand-washing bar) Conductivity calibration solution (KCl) Buffer (pH 7.00 or 8.00) for pH-meter calibration Theory The concepts of surfactant, self-aggregation, micelles, micelle structure, and micellar solubilization must be explained to the students before this laboratory. Information on the interpretation of the electrochemical data is available in the Supplemental Material.W Sample Preparation Commercial soaps contain a large quantity of water that must be eliminated before the preparation of soap solutions of known concentration. A commercial soap sample was cut into small pieces and dehydrated in a laboratory oven at 110 C overnight. The dehydrated material was pulverized in a mortar and placed again into the oven at 110 C until constant weight was attained. A portion of the anhydrous soap was weighed using an analytical balance and then dissolved in double-distilled water to obtain 500 mL of a solution of about 1% (w/v). Because dried soaps are difficult to dissolve, some heating may be necessary. The working temperature was 30 C to ensure solubility of the majority of commercial soaps. A soap bar obtained from a hotel room was used. Solutions with a decreasing soap concentrations of between 1% and 0.001% were prepared by dilution with double-distilled water. Thirteen samples having concentrations of about 0.0010, 0.0025, 0.0050, 0.0075, 0.010, 0.025, 0.050, 0.075, 0.10, 0.25, 0.50, 0.75, and 1.0% w/v would be sufficient. Specific Conductivity Measurements and Results After calibrating the conductimeter with a KCl solution of known specific conductivity (κ, S cm 1), the conductivities of all samples were measured, starting with the most dilute. This method avoids the necessity of washing the conductivity cell between measurements. A κ versus concentration (% w v) plot was made and the CMC value was obtained from the breakpoint (Figure 1). A CMC value of 0.105 ± 0.003% was found from the data of 12 students. The confidence level of the error was 0.90. A plot of nC versus log CMC was made (not shown) using literature data (1) and was used to obtain the average nC and molar weight values, Mn. The commercial soap had a nC of 13.5 ± 0.4 and Mn of 257 ± 7 g. The CMC in molar concentration units was 0.0041 ± 0.0001 mol dm 3. 1053 • • • • • • • Required Apparatus and Chemicals • • Laboratory oven Conductimeter with immersion cell JChemEd.chem.wisc.edu • Vol. 80 No. 9 September 2003 • Journal of Chemical Education From the differential conductivity of the soap monomers.wisc.0 1. Differential Conductivity Measurements and Results The differential conductivity. The micelle ionization degree. v = 26. as a function of the square root of the concentration (a). we estimated the average equivalent conductivity of soap anion.0001 300 0. 19.04 C / (mol dm 3 ) Figure 1. This decrease was not sudden.02 0. Λd. which is seen at C ≈ 0. the formation of micelles is indicated by a reduction of the slope.5 1. The equivalent differential conductivity of the soap monomers was 65 S cm2 eq 1 and of the micelles was 21 S cm2 eq 1. Λ.001 3 ) 0. The sodium ion conductivity.9 = 14.1 1 a) Λ / (S cm2 eq b a 100 CMC CMC 100 0 0.01 0. related to micelle electrical mobility. was plotted as a function of the average concentration square root. l.00 0. (See the circled section in Figure 1.05 and thus CMC ≈ 0. but the √CMC seemed to be about 0. Equivalent conductivity of commercial soap aqueous solutions. According to Zimmels and Lin (1). The CMC zone is circled.In the Laboratory The concentrations in weight volume percent of all solutions were translated to molar concentrations and the κ versus molar concentration plot was made (Figure 1. plot a) was not very clear because of the wide CMC zone. λNa+.) Equivalent Conductivity Measurements and Results The CMC zone was also assessed by plotting the equivalent conductivity.4 cm2 eq 1 for tretradecylsulphonate (5). This value is comparable to the values for other surfactant ions of similar chain length: 13. The usual representation of Λ versus √C (Figure 2.07.0 0.0049 mol dm 3.0070 mol dm 3. the molar conductivity of micelles (6). umic. upper concentration scale).0035 mol dm 3. The equations of the straight lines before and after the CMC were calculated by the least-squares method. This situation could be due to the fact that the commercial soap is a rather complex mixture and to the hydrolysis of the different components. √Cav (Figure 3).mon.6 × 10 4 cm2 V 1 s 1 at the CMC.0 1000 dκ dC = n 3 α 2 1000 2 − λX 1 + αλX (1) 1 2 dκ dC ) CMC 0. The aggregation number was obtained from the value of nC and the relationships relating this number to the length of the soap chain. The micelle electrical mobility was umic = 2. versus log C (Figure 2. but it may be situated at √CMC ≈ 0. the infinite dilution equivalent conductivity. κ / (S cm C (% w/v) 0. λanion: λanion = Λd. α was found to be 0.9 S cm2 eq 1 was obtained from the literature (3).chem.1 S cm2 eq 1 1054 0.86 nm.95 nm3.0025 mol dm 3. and n is the aggregation number of the micelle. It was difficult to determine exactly where the inflection point is. It was impossible to determine by extrapolation the value of Λ0.1. plot b).0 0. Λd. 80 No.0 0. and the concentration logarithm (b).0026 to about 0. 9 September 2003 • JChemEd. as a function of the concentration in grams per 100 cm3 and in mol dm-3. α. At about the same concentration of Journal of Chemical Education • Vol.2 a) C / (mol dm 3 ) Figure 2. again reflecting the wide critical concentration range. b) C / (mol dm 0. and to the volume of the micellized soap chain. an additional series of about five samples in this zone should be prepared and measured. giving a CMC ≈ 0. was obtained from Evans’ equation (2). by ΛM = α(Fumic + λX) where α is the micelle ionization degree and F is the Faraday constant. Then using eq 1. Λ. κ. λX is the equivalent conductivity of the counterion. There was a very pronounced decrease of Λd at the CMC zone.W From calculations we obtained l = 1.0 0. and n = 69. (If the experimental data do not show points in the CMC zone.edu b) Λ / (S cm2 eq 200 1 200 ) ) .5 cm2 eq 1 for tetradecyltrimethylammonium (4).1 0.mon − λNa+ = 65 − 50.01 0. Each point is an average of the data from 12 students. Experimental specific conductivity data of commercial soap aqueous solutions.03 0. v.) The CMC zone in our experiment ranged from about 0. The Λ d value at the minimum of the post-CMC curve is taken as ΛM. of 50. because the values of Λ at very low concentration were too high.5 where (dκ dC )1 and (dκ dC )2 are the slopes of the κ versus C straight lines before and after the CMC.278. Closer examination of the CMC zone of Figure 1 shows that the CMC was not a unique concentration but a concentration range. as a function of the square root of the average concentration. pH of commercial soap aqueous solutions as a function of the concentration logarithm. the straight zone of the graph. This theory also enabled the determination of the solubility of the fatty acid (SHA) as a function of C. was computed. According to Lucassen theory (9). which was smaller than the value obtained by conductivity. For the soap mixture.06.2 0. The line with a slope of about +3 (line B) is related to the formation of “acid soap”.03 0.0005 M. Inset: amplification of the low concentration zone.03 0. which depended on the nature of these fatty acids and their proportion in the system. of 3.00 β 0. KF. β = [OH ] C.04 0. Our data is shown in Figure 5. of the mixture of fatty acids in the commercial soap was found to be 8.0052 M. Figure 5.1 0. was extrapolated to zero concentration giving SHA = 5.1 × 10 7 M. For comparison.7 × 10 4 cm2 V 1 s 1 (7) and dodecyltrimethylammonium hydroxide micelles have umic = 3. The value obtained here was a combination of the distribution constants for every fatty acid in the mixture. the KF value for pure sodium dodecanoate at 40 C is 4. Both literature data were directly measured by electrophoresis. 1055 pH JChemEd.5Cmax = 0.edu • Vol. The intercept is equivalent to log KHNaA2.02 0.5 (line A) indicates a “normal” hydrolysis. HNaA2 where A is the soap anion. The difference could be due to the fact that the Stainsby and Alexander theory was developed for a single soap solution and not for a mixture.5292. To obtain the thermodynamic value.01 0.00 0. This gave KF = 4. 80 No. as a function of the concentration.04 60 CMC 0. β.0 0. ρ. Us- ing the intercept of 9.372.4441 nm3. From Stainsby and Alexander theory (10).9625 g cm 3.In the Laboratory 70 0. The distribution constant of fatty acid molecules between micelles and aqueous solution.5 × 105.25 × 10 16 for the commercial soap mixture.02 0. pH Measurements and Results The measured pH values were plotted against the logarithm of C (Figure 4). added salt.003. the CMC = 0.05 Cav / (mol dm 3 ) C / (mol dm 3 ) Figure 3.01 Λd / (S cm2 eq 1 ) 50 β 40 0. From the intercept of 15.44 × 10 12 M. This figure showed the typical hydrolysis curve of hydrolyzable surfactants. and for sodium tetradecanoate.001 0. 9 September 2003 • Journal of Chemical Education . the concentration at which small aggregates start to form. Hydrolysis degree of commercial soap aqueous solutions.73 × 10 6 and the pKa = 5. 1 × 106 (10).M 20 0 0.01 C / (mol dm 3 ) Λd.00001 0.94 × 10 4 cm2 V 1 s 1 (8).3 × 105.00 0. Hazards There are no significant hazards. Cmax = 0.0026 M. 10 CMC line A 9 line B 8 7 0. where βmax = 0.0113. was 0. KHNaA2 was found to be 4. Λ. βmin = 0. The agreement between the data is satisfactory. and the intercept is equivalent to 0.01 0. Differential conductivity of commercial soap aqueous solutions. sodium dodecyl sulfate micelles have umic ≈ 3.0001 0. From the same theory we obtained CF. the line with a slope ≈ +0. thus the density of micelles.chem.1 C / (mol dm 3 ) Figure 4.003 0. was also computed from Stansby and Alexander theory.001 0. Cmin = 0. log SHA versus √C (not shown). The degree of hydrolysis.wisc.002 0. vMmolec = 0.000 30 0. Ka.5log KaKw. the constant of acidity. R.. Gaillon. J. G. G. Y.. 1974. Sugihara. Pt 1. K. C. Mysels. Symons. the average composition of the soap and information of the structure and properties of micelles were obtained. Stainsby. Soc. 9 September 2003 • JChemEd. CRC Press: Boca Raton. T. J. W Literature Cited 1. 6. 1967. 63. 1949. Chem. J.. A.. Trans Faraday Soc.. Y. C. Lin. Pys. 7. 1955. J.edu . Clunie. 585.. 802. Colloid Polym.wisc. 59. 70. 9. Zimmels. J. Funatsu. F. S. Handbook of Chemistry and Physics.. S. Era... D. Phys. S. 4.. 54.. Chim. 8. 1056 Journal of Chemical Education • Vol. Chem. FL. M.. 435. 275. M. Gaboriaud. Lee. Phys. 1997. 728. Lucassen. 1997. C. Weast. 1966. 80 No. H. Morini. Colloid Polym. R. Colloid Interface Sci. 187. J. 1956. 1824. Astle. Supplemental Material Information on soaps. 1987. 45. It also shows the importance of knowing theory behind these techniques to obtain the maximum of information. 94. Trans Faraday Soc.. Alexander. P. 594. Sasaki. Stigter. 2. Chem. 579 3.chem. 56th ed. J.. Kunitake. 1975–1976. C. 754. I.. Through conductivity and pH measurements.. such as soaps. 252. Y. J.In the Laboratory Conclusions This experiment demonstrates that by using unsophisticated and inexpensive equipment it is possible to obtain information about the composition and properties of common but very useful substances used in everyday life. Sci. Evans. 10. theory on electrochemical data treatment and interpretation. Eds. J. A. E. Goodman. Schulz. 5. M. Sci. and instructions for the students are available in this issue of JCE Online. L. J. P.