How does the magnitude of critical micellization concentration(cmc) of anionic detergent, (sodium dodecyl sulfate) depends on temperature, determined using conductometric analysis?

Studying something out of the IB syllabus has always fascinated me. The topic of surfactant and CMC values was something, I immediately got interested into.This is a undergraduate chemistry topic and beyond the IB curriculum to indicate my exploration in the subject and reflect my keen interest.The research provides an opportunity to understand in depth surface chemistry and their applications for the benefit of mankind.

There are various compounds present in this universe, with varying chemical and physical components, Surfactants are one of them. These compounds decrease the surface tension of liquids, these compounds also reduce the surface tension between various liquids and in some cases even between a solid and a liquid. These compounds are used worldwide in the form of various detergents, foaming agents and emulsifiers. Surfactant can be considered as an amphiphilic molecule because the molecule contains both hydrophobic hydrocarbon tail and hydrophilic head, these are the two major parts present in a surfactant molecule. A surfactant molecule contains a water soluble part and a water insoluble part which basically means oil soluble part.

There are various types of surfactants.

• Anionic Surfactants - These compounds contain negatively charged ions also called as anions and therefore are insoluble at very low temperatures, these contain hydrophobic anion which comes in effect when it is dissolved in warm or hot water. These surfactants are commonly used as soaps, silicones and it can also be used as alkyl sulfonates. These surfactants are very commonly used in industries for manufacturing of detergents and cleaning agents and are also used for corrosion prevention.
• Non-Ionic Surfactants - These compounds do not show the presence of ionization when dissolved in a liquid and therefore these surfactants are considered to be highly stable and they have very limited reaction with acids or concentrated electrolytes. These compounds constitute about 50% of the total surfactant production because they are highly stable and therefore these surfactants have better emulsifying capability and therefore it can easily remove any oily or organic dirt.
• Cationic Surfactants - These are positively charged compounds and therefore these compounds do not showcase the presence of effective cleansing agents and therefore these compounds are least used as detergents or as emulsifiers. These surfactants can be used as cleansing agents only after mixing it with fabric softeners which helps the surfactant to break down stain particles.
• Amphoteric Surfactants - These surfactants constitute the chemical properties of both Anionic and Cationic surfactants, therefore these compounds are becoming beneficial. These surfactants possess various qualities such as; these compounds are biodegradable in nature and therefore it reduces the risk of affecting the environment, they are also resistant to hard water and therefore can be used to form lather even in hard water and they are excellent emulsifiers. These surfactants are still new to the market and therefore developments is still going on to improve the quality and strength of the surfactant.

In chemistry we describe Critical Micellization Concentration as the surfactant efficiency. Lower value of CMC indicates the lack of surfactant, and which conveys that more surfactant is required in order to saturate the mixture. CMC is a point of concentration of surfactants at which the formation of micelle takes place.

The determination of the CMC value depends on the breaking point of the graph that is plotted; concentration of the SDS solution against the conductivity shown by that solution. Calculating the CMC value using the standard method is a time consuming process and therefore it is been found out that the conductivity of a solution is directly proportional to the to the concentration of the ions present in it, the point on the graph where micelles are formed is shown by the breaking point. It can also be interpreted as the CMC value is the intercept of two linear points but with varying slopes. The evaluation of breaking point in a graph is very logical, the point where the curve in the graph show a sudden change and then becomes constant is called the breaking point. It is usually marked with the help of two linear lines and the intersection is taken as the breaking point.

Temperature has varying effects on the CMC of ionic surfactants, it has been noticed that when the temperature is increased the value of CMC decreases until it reaches its minimum value and then starts to increase, this pattern in the CMC value is observed by various other scientists. The above phenomenon of varying CMC value is observed because two opposite effects are acting against each other.This ups and down varieties dependably happens when two inverse impacts are contending. On one hand, an expansion in temperature can acquire a decrease the hydration of the surfactant hydrophilic gathering; this is the outstanding desolvation impact which is in charge of the cloud point wonder of non-ionic surfactant arrangements. This impact will in general drive the surfactant out of the watery arrangement and hence it supports the development of micelles, i.e., it diminishes the CMC. Then again, an expansion in temperature results in an expanding issue in the structure of water stage, specifically the particles which are situated alongside the surfactant hydrophobe. The higher in confusion, the less characterized the course of the horrible polar/a-polar contact, and as a result it turns into the more fragile. Along these lines, the hydrophobic impact which drives the surfactant atom "tail" out of the water stage is additionally decreased when temperature is increased.

Null hypotheses: No correlation between temperature and CMC

Alternate hypotheses: Positive correlation between temperature and CMC

• Independent variable

Temperature – room temperature (27°C), 37°C and 47°C.

• Dependent variable – Value of CMC of SDS in moldm-³
• Controlled variable

Volume of solution used – 2 cm³

Surface area-same test tube was used.

Apparatus used to measure conductivity – conductivity probe.

Method of determining CMC – conductivity method.

Hazards of using SDS

• Impurities and stabilizing agents present in SDS solution can have an adverse effect on the skin.
• It can cause eye irritation if not handled properly.
• If consumed orally it can cause stomach infections and can lead to severe condition.
• It is very toxic in nature, and therefore can cause damaging impact on human body.
• The solution is flammable and if brought near fire can lead to excessive burns and bruises. 

Safety precautions

• Non-sparking tools should be used during the experiment.
• The container containing SDS solution should be kept away from heat.
• Wear protective gloves and eye wear before conducting the experiment.
• Keep the solution away from water, to avoid violent reaction and possible flash fire.
• Wear respiratory protection in case of an inadequate ventilation.
• Avoid eye and skin contact.

Ethical consideration

Minimum amount of chemicals were used in the experiment and there was no such wastage of any chemicals during the experiment, I tried to conserve fuel by not using Bunsen burner and rather used hot water bath.

Environmental concerns

• No toxic gases were emitted during my experiment by which the environment can be affected.
• Waste chemicals were not thrown directly, rather they were diluted and were disposed in a disposing area.

Preparation of SDS solutions

Seven different solutions of SDS were prepared of varying concentration. The required mass of solid SDS was weighed on a watch glass using a spatula and an electronic mass balance. The weighed solid was transferred to a 10cm³ volumetric flask using a funnel. 10 ± 0.05 cm³ of distilled water was added to it using a 10cm³ graduated pipette. The solid was allowed to dissolve and the lid of the flask was closed and kept aside.

Sample calculation

Mass (m) = moles (n) 𝒙 Molar mass (M)

C = concentration in moldm^-3 , V = volume in dm³

m = C𝒙 V X M = 2.00 𝒙 10^-2 𝒙 \(\frac{10}{1000}\) 𝒙 288.30 = 0.05

A test tube was taken and 2.00 ± 0.05 cm³ of  2.00 X 10^-2 moldm^-3 of SDS solution with was added to it using a 10 cm³ graduated pipette. The temperature of the solution was recorded using a laboratory thermometer and noted down. The conductivity probe was inserted into the test tube and the reading displayed in the Lab Quest was noted down. [The conductivity probe was calibrated using the standard solution supplied along with the kit before use].The conductivity reading was taken in triplicates. The same process was applied for other solutions of SDS.

The conductivity reading of the same set of solutions was recorded at 37.0 ±0.5°C and 47.0 ± 0.5°C. The test tube containing the solution of SDS was inserted in a water bath and heated to reach the desired temperature. The temperature of the solution inside the test tube was checked using a laboratory thermometer. The conductivity of the solution was recorded as soon as it reached the desired temperature.

A 250cm³ glass beaker filled with tap water placed over a wire gauge on a tripod stand with a Bunsen burner below it was used as a water bath.

Sample calculation

Average value of conductance =\(\frac{Trial-1+Trial-2+Trial-3}{3}\)

=\(\frac{1.35+1.34+1.35}{3}\) = 1.35

The average value of conductance was plotted along the y axes and the value of molar concentration of SDS solution along x axes. Two best fit lines- AB and CD are drawn which intersects each other at the point X. This point X is considered as the breaking point. A perpendicular is drawn from the point X to both x and y axes. The perpendicular intersects the x axes at the point 6.6 and the y axes at the point 4.1.

At breaking point,

Molar concentration of SDS = 6.6 X 10^-2 moldm^-3

Hence, CMC value of SDS at 27°C = 6.60 X 10^-2 moldm^-3

The average value of conductance was plotted along the y axes and the value of molar concentration of SDS solution along x axes. Two best fit lines- AB and CD are drawn which intersects each other at the point X. This point X is considered as the breaking point. A perpendicular is drawn from the point X to both x and y axes. The perpendicular intersects the x axes at the point 8.4 and the y axes at the point 9.0.

At breaking point,

Molar concentration of SDS = 8.4 X 10^-2 moldm^-3

Hence, CMC value of SDS at 27°C = 8.40 X 10^-2 moldm^-3

Hence, CMC value of SDS at 27°C = 8.70 X 10^-2 moldm^-3

The CMC value (moldm^-3) of SDS is plotted along the y axes while the temperature (± 0.5°C) is plotted along the x-axes.

The data points provide a best fit straight line obeying the equation:

y = 0.105 x + 4.015

Where y = CMC value of SDS in moldm^-3

x = temperature

Hence, the equation can be re-written as,

CMC = 0.105(temperature) + 4.015

The graph was plotted using MS-Excel and the value of constant of determination(R²) was deduced using the more trendline options at MS-Excel (Version 2007). The value, thus obtained is 0.854 which indicates that there is a weak positive correlation between the value of temperature and CMC value of SDS. As the temperature of the surfactant solution increases, the surfactant molecules begins to move faster and hence, more number of particles of the surfactant are required to form the aggregate of molecules or the micelle. So, the magnitude of CMC of SDS increases as we increase the value of temperature.

As evident from the above graph, the value of conductivity in mScm^-1 increases with temperature for each and every solutions of SDS. This is quite expected as the rise of temperature increases the average kinetic energy of the molecules which in turn increases their mobility and hence the conductivity.

CMC of SDS at 25°C = 8.30 moldm^-3(literature value)

Equation obtained in the investigation

CMC = 0.105(temperature) + 4.015

At temperature = 25.0°C,

CMC = 0.105(25.00) + 4.015 = 2.625 + 4.015 = 6.64

Experimental value of  CMC at 25°C = 6.64 moldm^-3

Percentage error = \(\frac{mod\ (literature-experimental) }{literature}\)X100 = \(\frac{mod\ (8.30-6.64)}{8.30}\) X 100 = 20

The high value of percentage error (20%) indicates a major systematic error in the design of the experiment. Moreover, the systematic error is in the negative direction as the experimentally obtained value is lower than the literature value.

The basic aim of the investigation was to answer the research question-

How does the magnitude of Critical Micellization Concentration(CMC) of anionic detergent, (Sodium dodecyl sulfate ) depends on temperature, determined using conductometric analysis?

• It is clearly evident from the data processing and analysis that there is a weak positive correlation between the value of CMC of SDS and temperature. The correlation is supported by the value of constant of determination (R² = 0.854).
• The correlation between the variables may be quantitatively expressed as;
• CMC = 0.105(temperature) + 4.015
• It has also been observed as an accessory finding that the magnitude of conductivity for all solutions of SDS increases as we increase the magnitude of temperature. This indicates that, as we increase the temperature, the average kinetic energy of the molecules of SDS increases and thus the mobility of the molecules increases which increases the number of particles that must aggregate together to form the micelle and thus increases the value of CMC.
• A percentage error of 20% has been reported in the investigation which indicates a systematic error in the negative direction.
• The null hypotheses is rejected and the alternate hypotheses is accepted.

• Random errors are caused due to uncertainty of the apparatus used. To avoid this, the readings are taken in triplicates and average values are considered.
• Although it was ensured that the temperature of the solution reaches the desired value by using a laboratory thermometer, but the lag between the point where the temperature reaches the desired value and the recording of conductivity introduces a major systematic error as indicated by the value of percentage error.
• Apart from considering values of temperature above the room temperature, a few values below it must also have been considered to obtain a more comprehensive result.

• The readings obtained are precise in nature.
• Enough care towards environment and safety issues have been considered.
• Claims made are supported using logic.
• Report maintains a coherent structural layout.

Apart from temperature, the major factors that influences the CMC value of a surfactant is presence of impurity. I would like to repeat the same investigation by using a mixture of SDS and impurities like urea, ethanamide and so on to investigate how the nature of the impurity added influences the value of CMC.

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