In the Laboratory

An Undergraduate Physical Chemistry Experiment on Surfactants: Electrochemical Study of a Commercial Soap

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 Compigne 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, Aggregation number, n Molar conductivity of micelles, M Electrophoretic mobility of micelles, umic Equivalent conductivity of surfactant ions, anion 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, 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 (, 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 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.
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Required Apparatus and Chemicals

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In the Laboratory

The concentrations in weight volume percent of all solutions were translated to molar concentrations and the versus molar concentration plot was made (Figure 1, upper concentration scale). The equations of the straight lines before and after the CMC were calculated by the least-squares method. The micelle ionization degree, , was obtained from Evans equation (2),
/ (S cm

C (% w/v)
0.0 0.5 1.0

1.0

1000

d dC

= n 3 2 1000
2

X
1

+ X (1)

d dC

CMC
0.5

where (d dC )1 and (d dC )2 are the slopes of the versus C straight lines before and after the CMC, X is the equivalent conductivity of the counterion, and n is the aggregation number of the micelle. The aggregation number was obtained from the value of nC and the relationships relating this number to the length of the soap chain, l, and to the volume of the micellized soap chain, v.W From calculations we obtained l = 1.86 nm, v = 26.95 nm3, and n = 69.1. The sodium ion conductivity, Na+, of 50.9 S cm2 eq 1 was obtained from the literature (3). Then using eq 1, was found to be 0.278. Closer examination of the CMC zone of Figure 1 shows that the CMC was not a unique concentration but a concentration range. (See the circled section in Figure 1.) The CMC zone in our experiment ranged from about 0.0026 to about 0.0070 mol dm 3. (If the experimental data do not show points in the CMC zone, an additional series of about five samples in this zone should be prepared and measured.) Equivalent Conductivity Measurements and Results The CMC zone was also assessed by plotting the equivalent conductivity, , versus log C (Figure 2, plot b). According to Zimmels and Lin (1), the formation of micelles is indicated by a reduction of the slope, which is seen at C 0.0035 mol dm 3. The usual representation of versus C (Figure 2, plot a) was not very clear because of the wide CMC zone, but the CMC seemed to be about 0.05 and thus CMC 0.0025 mol dm 3. It was impossible to determine by extrapolation the value of 0, the infinite dilution equivalent conductivity, because the values of at very low concentration were too high. 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. Differential Conductivity Measurements and Results The differential conductivity, d, was plotted as a function of the average concentration square root, Cav (Figure 3). There was a very pronounced decrease of d at the CMC zone. This decrease was not sudden, again reflecting the wide critical concentration range. It was difficult to determine exactly where the inflection point is, but it may be situated at CMC 0.07, giving a CMC 0.0049 mol dm 3. The equivalent differential conductivity of the soap monomers was 65 S cm2 eq 1 and of the micelles was 21 S cm2 eq 1. From the differential conductivity of the soap monomers, d,mon, we estimated the average equivalent conductivity of soap anion, anion: anion = d,mon Na+ = 65 50.9 = 14.1 S cm2 eq 1
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0.0 0.00 0.01 0.02 0.03 0.04

C / (mol dm

Figure 1. Experimental specific conductivity data of commercial soap aqueous solutions, , as a function of the concentration in grams per 100 cm3 and in mol dm-3. The CMC zone is circled. Each point is an average of the data from 12 students.

b) C / (mol dm
0.0001 300 0.001

)
0.01 0.1

a) / (S cm2 eq

b a
100

CMC CMC

100

0 0.0 0.0 0.1 0.2

a)

C / (mol dm

Figure 2. Equivalent conductivity of commercial soap aqueous solutions, , as a function of the square root of the concentration (a); and the concentration logarithm (b).

This value is comparable to the values for other surfactant ions of similar chain length: 13.5 cm2 eq 1 for tetradecyltrimethylammonium (4), 19.4 cm2 eq 1 for tretradecylsulphonate (5). The d value at the minimum of the post-CMC curve is taken as M, the molar conductivity of micelles (6), related to micelle electrical mobility, umic, by M = (Fumic + X) where is the micelle ionization degree and F is the Faraday constant. The micelle electrical mobility was umic = 2.6 10 4 cm2 V 1 s 1 at the CMC. At about the same concentration of

Journal of Chemical Education Vol. 80 No. 9 September 2003 JChemEd.chem.wisc.edu

b) / (S cm2 eq

200

200

In the Laboratory
70
0.04

60

CMC
0.03

0.01

d / (S cm2 eq

)
50

40

0.02
0.00

0.000

30

0.001

0.002

0.003

0.01

C / (mol dm

d,M
20 0 0.0
0.00 0.00

0.1

0.2

0.01

0.02

0.03

0.04

0.05

Cav / (mol dm

C / (mol dm

Figure 3. Differential conductivity of commercial soap aqueous solutions, , as a function of the square root of the average concentration.

Figure 5. Hydrolysis degree of commercial soap aqueous solutions, , as a function of the concentration. Inset: amplification of the low concentration zone.

10

CMC

line A

line B

7 0.00001

0.0001

0.001

0.01

0.1

C / (mol dm

Figure 4. pH of commercial soap aqueous solutions as a function of the concentration logarithm.

added salt, sodium dodecyl sulfate micelles have umic 3.7 10 4 cm2 V 1 s 1 (7) and dodecyltrimethylammonium hydroxide micelles have umic = 3.94 10 4 cm2 V 1 s 1 (8). Both literature data were directly measured by electrophoresis. The agreement between the data is satisfactory. pH Measurements and Results The measured pH values were plotted against the logarithm of C (Figure 4). According to Lucassen theory (9), the line with a slope +0.5 (line A) indicates a normal hydrolysis, and the intercept is equivalent to 0.5log KaKw. Us-

ing the intercept of 9.5292, the constant of acidity, Ka, of the mixture of fatty acids in the commercial soap was found to be 8.73 10 6 and the pKa = 5.06. The line with a slope of about +3 (line B) is related to the formation of acid soap, HNaA2 where A is the soap anion. The intercept is equivalent to log KHNaA2. From the intercept of 15.372, KHNaA2 was found to be 4.25 10 16 for the commercial soap mixture. This theory also enabled the determination of the solubility of the fatty acid (SHA) as a function of C. To obtain the thermodynamic value, the straight zone of the graph, log SHA versus C (not shown), was extrapolated to zero concentration giving SHA = 5.1 10 7 M. The degree of hydrolysis, = [OH ] C, was computed. Our data is shown in Figure 5. This figure showed the typical hydrolysis curve of hydrolyzable surfactants, where max = 0.0113; Cmax = 0.0052 M; min = 0.003, Cmin = 0.0005 M. From Stainsby and Alexander theory (10), the CMC = 0.5Cmax = 0.0026 M, which was smaller than the value obtained by conductivity. 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. From the same theory we obtained CF, the concentration at which small aggregates start to form, of 3.44 10 12 M. The distribution constant of fatty acid molecules between micelles and aqueous solution, KF, was also computed from Stansby and Alexander theory. For the soap mixture, vMmolec = 0.4441 nm3, thus the density of micelles, , was 0.9625 g cm 3. This gave KF = 4.3 105. For comparison, the KF value for pure sodium dodecanoate at 40 C is 4.5 105, and for sodium tetradecanoate, 1 106 (10). The value obtained here was a combination of the distribution constants for every fatty acid in the mixture, which depended on the nature of these fatty acids and their proportion in the system. Hazards There are no significant hazards.
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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, such as soaps. It also shows the importance of knowing theory behind these techniques to obtain the maximum of information. Through conductivity and pH measurements, the average composition of the soap and information of the structure and properties of micelles were obtained.
W

Literature Cited
1. Zimmels, Y.; Lin, I. J. Colloid Polym. Sci. 1974, 252, 594. 2. Evans, H. C. J. Chem. Soc. 1956, Pt 1, 579 3. Handbook of Chemistry and Physics, 56th ed.; Weast, R. C., Astle, M. A., Eds.; CRC Press: Boca Raton, FL, 19751976. 4. Gaillon, L.; Gaboriaud, R. J. Chim. Pys. 1997, 94, 728. 5. Clunie, J. S.; Goodman, J. F.; Symons, P. C. Trans Faraday Soc. 1967, 63, 754. 6. Sugihara, G.; Era, Y.; Funatsu, M.; Kunitake, T.; Lee, S.; Sasaki, Y. J. Colloid Interface Sci. 1987, 187, 435. 7. Stigter, D.; Mysels, K. J. J. Phys. Chem. 1955, 59, 45. 8. Morini, M. S.; Schulz, P. C. Colloid Polym. Sci. 1997, 275, 802. 9. Lucassen, J. J. Phys. Chem. 1966, 70, 1824. 10. Stainsby, G.; Alexander, A. E. Trans Faraday Soc. 1949, 54, 585.

Supplemental Material

Information on soaps, theory on electrochemical data treatment and interpretation, and instructions for the students are available in this issue of JCE Online.

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