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Langmuir isotherm example

Adsorption - Langmuir Isotherm Example If the plot is not linear, then the Langmuir model can not fit the adsorption process. 9.3.3 The Freundlich Adsorption Isotherm. V = KP. 1/a (9.25) V: volume of adsorbed gas . K, a : constant (a is usually >1) Freundlich can be derived theoretically with the assumption that ΔH. ad. varies exponentially with the extent of surface coverage A combination of a Langmuir and Nernst isotherm, for example, can be used to express the characteristics of acid dyeings on wool, on silk and on nylon (Aspland, 1997, p. 252). None of the models discussed so far explicitly takes into account ionic interactions between dye and fibre

3: The Langmuir Isotherm. A continuous monolayer of adsorbate molecules surrounding a homogeneous solid surface is the conceptual basis for this adsorption model. The Langmuir isotherm is formally equivalent to the Hill equation in biochemistry. Whenever a gas is in contact with a solid there will be an equilibrium established between the. Langmuir adsorption isotherm - definition. Langmuir proposed his theory by making the following assumptions. 1. Fixed number of vacant or adsorption sites are available on the surface of solid. 2. All the vacant sites are of equal size and shape on the surface of the adsorbent. 3 Langmuir Isotherm (2) Langmuir adsorption isotherm is restricted to a monomolecular layer = 1 qKq pm +Kp At low pressures (Kp≪ 1), q=Kqmp(linear isotherm) Although originally Langmuir adsorption isotherm is devised for chemisorption, it is widely applied to physical-adsorption data. •Fitting of experimental data to the Langmuir equatio Let say we are using linear langmuir isotherm. The formula is : 1 q e = 1 q m + 1 q m K L find the value of q e. Using the formula q e = (C i − C f) V mass of adsorbent, and then plot the graph 1 q e versus 1 C f

Adsorption - Langmuir Isotherm Example - YouTub

This graph can be easily explained using Langmuir Adsorption Isotherm. If BET equation, when P/P 0 <<1 and c>>1, then it leads to monolayer formation and Type I Adsorption Isotherm is obtained. The reversible Type I isotherm is concave to the relative pressure, p/p° axis and a approaches a limiting value as p/p° ~ 1 About Press Copyright Contact us Creators Advertise Developers Terms Privacy Policy & Safety How YouTube works Test new features Press Copyright Contact us Creators. 3.3. Langmuir Isotherm. Langmuir adsorption which was primarily designed to describe gas-solid phase adsorption is also used to quantify and contrast the adsorptive capacity of various adsorbents . Langmuir isotherm accounts for the surface coverage by balancing the relative rates of adsorption and desorption (dynamic equilibrium)

The Langmuir adsorption model explains adsorption by assuming an adsorbate behaves as an ideal gas at isothermal conditions. According to the model, adsorption and desorption are reversible processes. This model even explains the effect of pressure i.e at these conditions the adsorbate's partial pressure, , is related to the volume of it, V, adsorbed onto a solid adsorbent In 1916, Irving Langmuir published a new model isotherm for gases adsorbed to solids, which retained his name. It is a semi-empirical isotherm derived from a proposed kinetic mechanism. This isotherm was based on different assumptions one of which is that dynamic equilibrium exists between adsorbed gaseous molecules and the free gaseous molecules

Determination of freundlich adsorption isotherm constant

The Freundlich adsorption isotherm is followed by another two isotherms, Langmuir adsorption isotherms and BET theory. The Langmuir adsorption isotherms predict linear adsorption at low adsorption densities and a maximum surface coverage at higher solute metal concentrations. The Langmuir adsorption isotherm has the form: θ= Kp/ (1+Kp The Langmuir adsorption isotherm is used to describe the equilibrium between adsorbate and adsorbent system, where the adsorbate adsorption is limited to one molecular layer at or before a relative pressure of unity is reached. Although the isotherm initially proposed by Langmuir in 1918 is generally suitable for describing the chemisorption process when ionic or covalent chemical bonds are. The release of adsorbed gas is commonly described by a pressure relationship called the Langmuir Isotherm. The Langmuir adsorption isotherm assumes that the gas attaches to the surface of the coal or shale, and covers the surface as a single layer of gas (a monolayer) Example 19-- Modeling Cd +2 Sorption With Linear, Freundlich, and Langmuir Isotherms, and With a Deterministic Distribution of Sorption Sites for Organic Matter, Clay Minerals, and Iron Oxyhydroxides Sorption of heavy metals and organic pollutants on natural materials can be described by linear, Freundlich, or Langmuir isotherms Example - sulfate and chromate Isotherm Models. Freundlich. Langmuir, multiple site. Langmuir, multiple adsorbates. The Langmuir isotherm is the simplest representation of adsorption equilibrium. Vm is usually estimated using the BET isotherm | PowerPoint PPT presentation.

Langmuir Isotherm - an overview ScienceDirect Topic

If we get a region of Langmuir behavior, we have saturated the stationary phase or overloaded the capacity of the column. Figure 12. Plot of the Langmuir isotherm. We might also ask whether you could ever get the following plot, which is called anti-Langmuir behavior. Figure 13. Plot of the anti-Langmuir isotherm The langmuir isotherm adsorption equation: The monolayer approach. Patiha 1, E Heraldy 1, Y Hidayat 1 and M Firdaus 1. Published under licence by IOP Publishing Ltd IOP Conference Series: Materials Science and Engineering, Volume 107, 10th Joint Conference on Chemistry 8-9 September 2015, Solo, Indonesia Citation Patiha et al 2016 IOP Conf. Ser.: Mater. Sci Ans: The Freundlich isotherm is empirical, and Langmuir 's model was a theoretical construct. Langmuir adsorption isotherm is based on the kinetic theory of gases. Freundlich adsorption isotherm is based on the assumption that every adsorption site is equivalent. Freundlich isotherm is a graphical representation energy of adsorption. Additional, the important characteristics of the Langmuir isotherm can be separation factor RL which is calculated by the equation 4.24 RL = 1/ (1+bQo) ----- (5) The RL value assumes the nature and the feasibility of adsorption process are specified in Table 1. Table 1 Nature of adsorption isotherm

3: The Langmuir Isotherm - Chemistry LibreText

  1. The Langmuir equation or Langmuir isotherm or Langmuir adsorption equation relates the coverage or adsorption of molecules on a solid surface to gas pressure or concentration of a medium above the solid surface at a fixed temperature. The equation was developed by Irving Langmuir in 1916. The equation is stated as
  2. In PUPAIM: A Collection of Physical and Chemical Adsorption Isotherm Models. Description Usage Arguments Value Author(s) References Examples. Description. The Langmuir Linear Equation I adsorption isotherm is used to describe the equilibrium between adsorbate and adsorbent system, where the adsorbate adsorption is limited to one molecular layer at or before a relative pressure of unity is reached
  3. Transcribed image text: At 25°C, ethyl chloride (C2H5C1) can chemisorb onto charcoal according to the Langmuir isotherm when equilibrium is reached. Batch adsorption experiments on the adsorption of pure C2HCl gas on a particular charcoal sample has shown that 0.1 g of C2H5C1 has adsorbed per g of charcoal when equilibrium is reached at a pressure of 120 torr
  4. Langmuir and Freundlich adsorption constants and correlation coefficients are presented in Table 2. To find the most appropriate model for the metal ions adsorption; data were fitted to Langmuir and Freundlich isotherm models. Results revealed that Langmuir adsorption isotherm was the best model for the metal ions adsorption onto ATS with o
  5. e the values of the constants. Example 1
  6. Reactions on surfaces are reactions in which at least one of the steps of the reaction mechanism is the adsorption of one or more reactants. The mechanisms for these reactions, and the rate equations are of extreme importance for heterogeneous catalysis.Via scanning tunneling microscopy, it is possible to observe reactions at the solid|gas interface in real space, if the time scale of the.
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the surface of polymer particles). The Langmuir isotherm is a famous example for 1:1 matching of adsorbate and active site: G G m ¼ KC 1 þ KC ðone-parametered KÞ G is the adsorbed amount per unit surface area, G m is its maximum value (full coverage of surface, or saturated adsorption), and C is the concentration of protein. K is th basis. Examples are the distribution coefficient, the Freundlich adsorption isotherm, and the Langmuir adsorption isotherm. Chemical models provide a molecular description of adsorption using an equilibrium approach. Surfac e com-plexation models are chemical models designed to calculate values of thermody-namic properties mathematically Get e-Alerts. This virtual issue celebrates the remarkable creativity of Irving Langmuir, in particular, the isotherm that bears his name. Two of Langmuir's papers are included in this issue: a work on monolayers at the air/water interface and the publication, 100 years ago, in which the isotherm is reported mentioned, at low concentration a Langmuir isotherm may appear to be nearly linear. The non-linear form can be evaluated by transforming to the linear equation: eq 1 LL c n qKbK =+ (7) Other linear forms are also used (for example): LL eq q KbKq c =− (8) Figure 7.5 Example of a Langmuir Isotherm and the linear form of the data. Equilibrium. For chemisorption too, Langmuir's equation works very well but fails for the cases where multilayer formation takes place. 36.2 Adsorption Isotherms 36.2.3 Langmuir Adsorption Isotherm (contd..) Example 36.2: the volume of CH4 (corrected to STP) adsorbed per gram of charcoal at 240 K various pressures of CH4 is: P/(Torr) 38 55 78 104 133 173 21

Problem 3: Using the Langmuir isotherm, plot c/ Γ vs. c. Also using the Freundlich isotherm plot log(Γ) vs. log(c). It is obvious from the plots that the data fits the Langmuir isotherm (R 2 =0.9991) better than the Freundlich isotherm (R 2 =0.899). From the slope of the curve: Γ mono = 0.14 g solute g alumina-1 From the intercept B= 60.5 cm. K.Y. Foo, B.H. Hameed / Chemical Engineering Journal 156 (2010) 2-10 3 Nomenclature aK Khan isotherm model exponent aR Redlich-Peterson isotherm constant (1/mg) aRP Radke-Prausnitz isotherm model constant aS Sips isotherm model constant (L/mg) aT Toth isotherm constant (L/mg) A Koble-Corrigan isotherm constant (L nmg1− /g) AT Tempkin isotherm equilibrium binding constan On the Use of Linearized Langmuir Equations. Soil Science Society of America Journal 71:1796-1806 see also the erratum). Because the use of linearized Langmuir equations is largely due to the ease of using linear regression, we make available an easy-to-use Microsoft Excel spreadsheet capable of fitting nonlinear sorption equations to isotherm. The Langmuir isotherm is accurate under conditions of low coverage and high adsorption enthalpy (such that interactions between neighboring adsorbed molecules can safely be neglected.) For this reason it is widely used in studies of chemisorption and analysis of heterogeneous catalysis kinetics ii. Langmuir iii. Freundlich iv. Brunauer, Emmet, and Teller (BET) The most commonly used isotherms for the application of activated carbon in water and wastewater treatment are the Freundlich and Langmuir isotherms. Freundlich isotherm is an empirical equation. Langmuir isotherm has a rational basis

The classical Langmuir adsorption isotherm equation is derived from reaction kinetics (Sohn and Kim 2005 ). Suppose there is an adsorption and desorption reaction of pure gas A: A_ {\left ( g \right)} + S \leftrightarrow AS. (3) where S stands for the vacant sites and AS the occupied sites with gas A. When this reaction reaches chemical. a) Use the associative and dissociative versions of the Langmuir isotherm to find the types of adsorption occurring. Plot on graph paper or spreadsheet/printer. Calculate V m and b (10 pts) Solution : The associative Langmuir isotherm can be written as : m 1 V b P V b P or 1 1 = mm P V b V V P Langmuir assoc isotherm CO/charcoa The Langmuir equation is. Figure 1 Plot of Langmuir isotherm. Note: The non-adsorbable value should be a bit lower than 0.8. If you choose 0.8, the graph will move horizontally between the two first (left) two points

Langmuir Isotherms Definition, Examples, Diagram

single-component isotherm properties (Langmuir constants) based upon coal characterization data alone. Six individual models were constructed (one for each Langmuir constant for each gas), each with seven input variables. The variables used for each model, their relative impact, and the predictive accuracy of each model are presented in Table 3 Isotherm modelling ¶ In this notebook we'll attempt to model isotherms using the included models. For example, trying to model the MCM-41 sample with a Langmuir model does not throw any errors but it is obvious that the model is not representative of the mesoporous condensation in the pores. [8]: isotherm = next. Abstract: Langmuir monolayers can be assembled from molecules that change from a low-energy orientation occupying a large cross-sectional area to a high-energy orientation of small cross-sectional area as the lateral pressure grows. Examples include cyclosporin A, amphotericin B, nystatin, certai Abstract The extended Langmuir (EL) model is a popular multicomponent adsorption equilibria model, which can be based on single component Langmuir isotherms fitted on pure component data. Such explicit models are preferred over their implicit counterparts due to a lower computational requirement. An important shortcoming of the EL model is its inability to capture the adsorbate size effect.

How to determine Langmuir adsorption isotherm constants

Langmuir's model was a theoretical construct, while the Freundlich isotherm is empirical. In the Langmuir model, it is assumed that at maximum coverage, there is only a monomolecular layer on the surface. This means that there is no stacking of adsorbed molecules. What is adsorption example Langmuir isotherm:mx = 1+bpap where x is the mass of the adsorbate and m is the mass of the adsorbent at pressure p. a,b are the Langmuir parametersAt high pressure , bp >>1, thus 1+bp≈ bpand mx = bpap mx = ba option D is correct Because isotherm data from protein adsorption studies often appear to be fit well by the Langmuir isotherm model, estimates of protein binding affinity have often been made from its use despite that fact that none of the conditions required for a Langmuir adsorption process may be satisfied for this type of application Many adsorption isotherm equations have been derived including the Langmuir, the Freundlich, the Brunauer-Emmett-Teller (BET) and the Dubinin equations. These are some of the most widely used isotherms but for the purposes of this project we will be using the Langmuir isotherm equations to represent the equilibrium state of our systems

Langmuir Example - YouTub

Modelling and Interpretation of Adsorption Isotherm

Isotherm parameters obtained from the four Langmuir linear equations differed. Though Langmuir type 1 is the most popular form, but the type 2 had the highest coefficient of determination (R 2 = 0.931-0.984) compared with the other Langmuir linea The Langmuir isotherm has the form: The BET isotherm has the form: Both the Laugmuir equation and the BET equation were developed basing on similar assumptions. However, t'he Langmuir equation assumed a monolayer adsorp- tion and the BET equation extended Langmuir's idea to multiple layer adsorption. Since in most realistic cases, adsorption is. Isotherm studies are quite important in analyzing the mechanism of undertaken adsorption data (Kamau and Kamau, 2017). In the present study, three adsorption isotherms; Langmuir, Freundlich, and D-R models are employed and evaluated at three different temperatures viz., 298, 308, and 318 K with varying concentrations between 100 - 400 ppm restrict the equation of an isotherm to a certain class of equations, of which Langmuir's is the simplest example. Some thermodynamic consequences of the equation of state for mobile adsorbed fihns have been developed by VolmerO), who considered a cycle in which the temperature remained constant. Bein Langmuir monolayers can be assembled from molecules that change from a low-energy orientation occupying a large cross-sectional area to a high-energy orientation of small cross-sectional area as the lateral pressure grows. Examples include cyclosporin A, amphotericin B, nystatin, certain alpha-helical peptides, cholesterol oxydation products, dumbbell-shaped amphiphiles, organic-inorganic.

BET Adsorption Isotherm example - YouTube

Langmuir adsorption model - Wikipedi

Adsorption Isotherm (Theory) : Physical Chemistry Virtual

Adsorption Isotherms - Freundlich Adsorption Isotherms

  1. a at different pH values using the Langmuir iso-therm. Hsia et al. (1992) used a modified Langmuir isotherm to model arsenic adsorption on amorphous iron.
  2. The Langmuir Model (Adamson, 1990) Often the amount adsorbed is measured as a function of the partial pressure or concentration at a given temperature and the result expressed as an adsorption isotherm. There are many empirical adsorption models, but the most common is the Langmuir adsorption isotherm model. This model assumes tha
  3. Langmuir's theory of unimolecular layer can be extended in an exactly analogous manner to adsorption from solutions. The workable form is at once obtained by putting C in place of and x/m in place of V, a quite justifiable procedure. The linear equation ( Gas-Solid Systems: Langmuir Isotherm ) then becomes. [C / (x/m)] = C/k 1 + 1/k 2

Langmuir Adsorption - an overview ScienceDirect Topic

b) Test the validity of Freundlich and Langmuir Adsorption Isotherm. c) Values of constants , , and Figure 2.8: Langmuir Isotherm Illustrating the Relationship between Equilibrium Gas Content and Pressure. Figure 3.1: Dimensionless Rate Versus Dimensionless Time of Langmuir constants in Different Basins. Figure 4.1: Type curve at a constant Langmuir Volume and varying Langmuir Pressure Some examples of experimental adsorption isotherms. Thermodynamics of adsorption: The concept of the adsorption isotherm (cont'd) Langmuir isotherms (type I) are usually observed during adsorption of chemically active gases on metal surfaces, but also with non-polar gases (methane, nitrogen N. 2 , ethane) on zeolites, wherea For situations where the Langmuir assumptions do not hold, numerous other models have been proposed. Most, like the Langmuir isotherm, contain first- and zero-order regions over certain ranges of partial pressure or concentration. One common model is the Freundlich isotherm: where n is the weight adsorbed per unit weight of adsorbent From the Langmuir adsorption isotherm, From equation C/(x/m) = i/k 1 k 2 + C/k 2. Hence the slope of the plot of C/ (x/m) against C is the 1/k 2, and we get 1/k 2 =0.19. Hence k 2 = 5.2. Discussion . By a few simplifying assumptions, the Langmuir Isotherm theory can be applied in finding the surface area of activated carbon adsorbent 3. The.

C. BET (Brunauer, Emmett and Teller) isotherm: This is a more general, multi-layer model. It assumes that a Langmuir isotherm applies to each layer and that no transmigration occurs between layers. It also assumes that there is equal energy of adsorption for each layer except for the first layer If the Langmuir isotherm is an adequate description process, then a plot of c/N versus c will yield a straight line with slope 1/N m. If the area σ occupied by an adsorbed molecule on the surface is known, the specific area A (in square meters per gram) is given by A = N mN0σ×10-20 (4 isotherm. The isotherm is useful in determining the interactions between the adsorbate and the adsorbent. The extent of adsorption is usually measured by coverage,θ which is given by θ = (number of surface sites occupied)/(total number of surface sites) (1) Langmuir isotherm is concerned with the monolayer (single layer) coverage of th Anti-Langmuir isotherm. The anti-Langmuir isotherm is an overloading isotherm often used to describe convex downward isotherms in gas-liquid or liquid-solid equilibria [7]. In this isotherm, the stationary phase concentration starts increasing towards infinity when in-creasing the mobile phase solute concentration (fig. 1(b))

Langmuir Isotherm - Marki

Langmuir isotherm parameters Xm which measure the monolayer capacity of the adsorbent and the Freundlich isotherm parameter Kf, which indicates the extent of adsorption, follow the same trend and were good measures of the adsorption capacity of the different activated carbon sample. Percent of MB adsorbed was also estimated As an example, to construct a ModelIsotherm using the Langmuir adsorption model for methane (see Fig. 1), we pass the DataFrame df_ch4 and the names (keys) of the columns that correspond to the loading and pressure Langmuir Systems Support Forum is a passionate group of over 5,000 CrossFire users with over 60,000 posts on over 4,000 topics. Ask a question, share your cool new project, or chat with other CrossFire customers. Join the Forum Answers to the problems on the BET isotherm. 1. The following data refer to the adsorption of dinitrogen (N 2) on a sample of carbon black at 77 K.. Use the equation for the BET isotherm to calculate V m, the volume of nitrogen adsorbed which corresponds to a monolayer.If 1 g of carbon black was used in the experiment, calculate the surface area assuming the area occupied by one nitrogen. Shape of Langmuir IsothermShape of Langmuir Isotherm 15. Shape of Freundlich Isotherm n fq k c= 16. The Freundlich (or Classical) adsorption isotherm The variation of adsorption with pressure can often be represented (especially at moderately low pressures) by the equation where k and n are constants, n usually being greater than unity

Langmuir isotherm equation. An equation, useful chiefly for gaseous systems, for the amount of material adsorbed on a surface as a function of pressure, while the temperature is held constant, assuming that a single layer of molecules is adsorbed; it is ƒ = ap / (1 + ap ), where ƒ is the fraction of surface covered, p is the pressure, and a. The bi-Langmuir isotherm calculation is carried out from sorption data for single-component systems. It is shown that good agreement of calculated and experimental data is reached only when protein-sorbent interaction weakens because of implementation of the competitive sorption mechanism

Example 19--Modeling Cd+2 Sorption With Linear, Freundlich

  1. The commonest form of Langmuir's adsorption isotherm is. where θ is the fraction of the surface of the solid covered by adsorbed molecules, p the gas pressure in equilibrium with the adsorbed layer and A = A (T) a function of the temperature alone.This formula is usually derived by a kinetic argument which balances the rates of deposition and re-evaporation
  2. Langmuir isotherm constants for modified oil shale ash Langmuir isotherm constants Heavy metal ion Q, mg/g b [R.sup.2] [Pb.sup.2] 9.407 4.016 0.9995 [Cd.sup.2] 12.05 4.416 0.9963 Adsorption of lead and cadmium ions from aqueous solutions by modified oil shale as
  3. The Langmuir isotherm - derivation from equilibrium considerations. The basic idea behind the Langmuir model is the coverage of the surface by a monomolecularic layer. The model approach also assumes that only one gas is being adsorbed. For example Hydrogen is adsorbed on Nickel as an atom, not as a molecule

isotherms. The values of Freundlich isotherm constant (K F and n), Langmuir isotherm constant (Qo and K L), and its correlation coefficient (r 2) derived form Figure 1 and 2 were presented in Table 2. The adsorption capacities (Qo) related to Langmuir isotherm was found to be 1.296, 0.061 and 0.077 mg/g for COD, BOD and Color respectively Langmuir, Freundlich, Temkin and Dubinin-Radushkevich Isotherms Studies of Equilibrium Sorption of Zn 2+ Unto Phosphoric Acid Modified Rice Hus Which of the following statements are correct with respect to adsorption of gases on a solid ? <br> (i) The ectent of adsorption is equal to according to Freundlich isotherm. <br> (ii) The extent of adsorption is equal to according to Frendlich isotherm. <br> (iii) The extent of adsorption is equal to (1+bP)/aP according to Langmuir isotherm. <br> (iv) The extent of adsorption is equal to aP. Adsorption isotherm is a mathematical model equations used to describe the relationship between the adsorbed materials with absorbent material. Isotherm is also used to determine the required amount of absorbent material. Langmuir and Freundlich isotherm is two standard models in adsorption experiments

Adsorption isotherm

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 A major drawback of Freundlich adsorption isotherm it fails at high pressure. It could not explain the multi-layered adsorption process. Langmuir Theory. In 1916, Langmuir proposed the theory of adsorption of a gas on the surface of the solid to be made up of elementary sites each of which would adsorb one gas a. Plot the isotherm, adsorbed volume (V) as a function of the nitrogen pressure (p). We will calculate the specific surface area of the sample in two different ways, first by linearizing the Langmuir isotherm and then using the BET method. b. Show that the Langmuir isotherm (single adsorbate, non-dissociative) may b

Adsorption

Langmuir Adsorption Isotherm. In 1916, Irving Langmuir published a new model isotherm for gases adsorbed to solids, which retained his name. It is a semi-empirical isotherm derived from a proposed kinetic mechanism. This isotherm was based on different assumptions one of which is that dynamic equilibrium exists between adsorbed gaseous. Langmuir Isotherm - 5) Rate processes in adsorption and simple design methods for fixed bed 29 dyne/cm ; vL = 89 cm3/mole =0 Isotherm Models. Example - sulfate and chromate Isotherm Models. Freundlich. Langmuir, multiple site. Langmuir, multiple adsorbates. Langmuir.

CHEM355 EXPERIMENT 9 Adsorption Adsorption is the accumulation of a gas or liquid solute (the adsorbate) on a surface of a solid or a liquid (the adsorbent) forming a molecular or atomic film.It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution Langmuir monolayers and pressure/area isotherm Langmuir monolayer consists of an insoluble molecules floating on aqueous solution and has a thickness of single monolayer. Molecules consisting Langmuir monolayer are usually 'amphiphilic' (means that having both hydrophobic and hydrophilic parts); a common example is fatty acid

OSTI.GOV Journal Article: Thermodynamically derived relationships between the modified Langmuir isotherm and experimental parameter The Freundlich isotherm is appropriate to both monolayer and multilayer adsorption and is based on the assumption that the adsorbates are adsorbed onto the heterogeneous surface of an adsorbent 14. The Langmuir isotherm assumes monolayer adsorption on a uniform surface with a finite number of adsorption sites 15 The results obtained were fitted to Brunauer-Emmett-Teller (BET), Langmuir and Freundlich adsorption isotherms using least square fit method. The best fit among the isotherm models is assessed by the linear coefficient of regression ( R 2 ) and by non-linear Chi-square test

Surface chemistryAdsorption presentation