isotherme de langmuir




Introduction

Surface adsorption to a solid falls into two broad categories; physisorption and chemisorption. Physisorption is a non-specific loose binding of the adsorbate to the solid via van der Waals type interactions. Multilayered adsorption is possible and it is easily disrupted by increasing
temperatures. Chemisorption involves a more specific binding of the absorbate to the solid. It is a process that is more akin to a chemical reaction and hence, only monolayer adsorption is possible. “The difference between physical and chemisorption is typified by the behavior of nitrogen on iron. At the temperature of liquid nitrogen, -190oC, nitrogen is adsorbed physically on iron as nitrogen molecules, N2. The amount of N2 adsorbed decreases rapidly as the temperature rises. At room temperature iron does not adsorb nitrogen at all. At high
temperatures, ~500oC, nitrogen is chemisorbed on the iron surface as nitrogen atoms.” (Castellan 1983) The Langmuir Isotherm best describes chemisorption processes.


  
The Langmuir Adsorption Isotherm:

          In this laboratory exercise, we will generate a Langmuir Isotherm for the adsorption of Acetic Acid on the surface of Norit A Activated Charcoal. The surface area of the Activated Charcoal available for adsorption of Acetic Acid will be determined from the Isotherm data and other assumptions. Activated Charcoal is particularly useful in purification processes involving impurity adsorption because of its high porosity, giving
an very high surface to mass ratio. It has      
 been noted: Adsorption by a solid is not a very important process unless the solid has a very large surface area compared to its mass. Consequently, charcoal made from bone, blood, or coconut shells is
 especially effective because it has a highly porous structure. Charcoal is activated by being heated to quite high temperatures in a vacuum or in a stream of dry air. This treatment probably desorbs the hydrocarbons that are adsorbed when the charcoal is first produced.   

1- Langmuir life:
Irving Langmuir was awarded the Nobel Prize in 1932 for his investigations concerning surface chemistry. Langmuir’s isotherm describing the Adsorption of Adsorbate (A) onto the surface of the Adsorbant (S) requires three assumptions:
• The surface of the adsorbant is in contact with a solution containing an
adsorbate which is strongly attracted to the surface.
• The surface has a specific number of sites where the solute molecules
can be adsorbed.
• The adsorption involves the attachment of only one layer of molecules
to the surface, i. e. monolayer adsorption. The chemical reaction for monolayer adsorption can be represented as follows:
                                                                           
where AS represents a solute molecule bound to a surface site on S. The equilibrium constant Kads for this reaction is given by:


denotes the concentration of A, while the other two terms [S] and [AS] are two-dimensional analogs of concentration and are expressed in units such as mol/cm2. The principle of chemical equilibrium holds with these terms. The complete form of the Langmuir isotherm considers (Eq. 1) in terms of surface coverage q which is defined as the fraction of the adsorption sites to which a solute molecule has become attached. An expression for the fraction of the surface with unattached sites is therefore (1 - q). Given these definitions, we can rewrite the term [AS]/[S]
Now we express [A] as C and rewrite (Eq. 1) as:

Rearranging, we obtain the final form of the Langmuir adsorption isotherm:



If we define Y as the amount of adsorption in units of moles adsorbate per mass adsorbant, andYmax and the maximal adsorption, then:
                                             
and the isotherm can be expressed as:



This is the form of the isotherm we will use for our Charcoal-Acetic Acid system. At lower concentrations, an alternate isotherm developed by Herbert F. Freundlich frequently describes the data better. The Freundlich Isotherm is:

where the Freundlich parameters k and n are empirically determined. A plot of log Y vs. log C allows for a determination of these parameters.
We will prepare our Acetic Acid-Charcoal isotherm by allowing Acetic Acid solutions of various concentrations to equilibrate for about a week with a given mass of Norit A. The amount of Acetic Acid (HAc) not adsorbed to the Norit A will be determined by titration with Sodium Hydroxide (NaOH).

This will allow us to easily determine the amount of Acetic Acid that has adsorbed to a given mass of the Charcoal.
3-Procedure:
Week 1
Prepare about 1L of 0.1M NaOH from a 6M stock solution and store it in a tightly stoppered plastic bottle. Standardize the NaOH against Potassium Hydrogen Phthalate (KHP).
Weigh about 1.5g Charcoal into 6 stopper 250 mL Erlenmeyer flasks. This should be recorded to +/- 1 mg. Prepare a series of Acetic Acid solutions according to:




For each sample above, add 100 mL of the solution to a charcoal sample. Swirl the flasks vigorously and then place them into the shaker bath at 25oC. Let them agitate until next week.
Pre-Lab Preparation
1. Determine how to prepare the stock 0.4M Acetic Acid solution.
2. Determine the dilution factor for the preparation of the 0.1M NaOH solution.
3. Determine the amount of KHP needed for the standardization.

Week 2
Filter your charcoal solutions (discard the first 10 ml of filtrate to clean the filter flask of any contaminants and to saturate with acid any adsorption sites which might be on the filter paper) and titrate a suitable aliquot with the standardized NaOH. Perform your titrations in triplicate. Be sure to also titrate your original 0.4M Acetic Acid solution to confirm its  concentration exactly.
Data Analysis:

All results must be accompanied by an appropriate error estimate.
1. Determine the concentration of the NaOH solution from your standardization data.
2. Using your titration data, for each sample:
Calculate the number of moles of acetic acid in the solution before adsorption.
Calculate the number of moles of acetic acid in the solution after adsorption.
3. Determine Y for each sample. Include appropriate error estimates for each Y value.
4. Plot your isotherm; Y vs. C. Include appropriate error bars for Y.
5. Plot the isotherm in the form of (Eq. 6) and determine the Langmuir parameters Ymax and Kads. Include appropriate error estimates for each parameter.
6. Make the suggested plot to determine the Freundlich parameters k and n. Again, include appropriate error estimates for each parameter.
7. Re-plot your isotherm; Y vs. C. Include the Langmuir and Freundlich isotherms, in each case generated using the parameters determined above. Comment on the quality of the Langmuir and Freundlich isotherms.
8. Assume the surface area occupied by one acetic acid molecule on the surface of the charcoal is 21Å2. Determine the surface area of 1 g of charcoal. Express your result in m2/g. Is your number reasonable? Compare your result with that of the literature.



conclusion

The Langmuir isotherm was developed by Irving Langmuir in 1916 to describe the dependence of the surface coverage of an adsorbed gas on the pressure of the gas above the surface at a fixed temperature. There are many other types of isotherm (Temkin, Freundlich ...) which differ in one or more of the assumptions made in deriving the expression for the surface coverage; in particular, on how they treat the surface coverage dependence of the enthalpy of adsorption. Whilst the Langmuir isotherm is one of the simplest, it still provides a useful insight into the pressure dependence of the extent of surface adsorption.

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