# Adsorption isotherm: Freundlich, Langmuir model, types (2023)

• Written byShalini Kaveripakam Adsorptionsisotherme:Adsorption occurs when a liquid or gas particle adheres to the surface of an adsorbent, resulting in the formation of an atomic layer on the adsorbate. This is not the same as absorption when the solute diffuses into the solid rather than onto the surface. We will go through the many forms of adsorption isotherms and their uses in this post.

## What is an adsorption isotherm?

A diagram between the amount of gas adsorbed per gram of adsorbent $$\left( {\frac{{\rm{x}}}{{\rm{m}}}}} \right)$$ and the equilibrium pressure of the adsorbate at constant temperature is shown called the adsorption isotherm.

Freundlich showed empirically that at any given temperature the amount of gas adsorbed $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ per unit mass The adsorbent is stationary in relation to the adsorption equilibrium pressure (p) of the gas by the mathematical equation.

$$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right){\rm{ = k}}{{\rm{P}}}^{\frac {{\rm{1}}}{{\rm{n}}}}}$$ where x is the mass of the adsorbate gas and 'm' is the mass of the adsorbent (solid) and k and n are the constants. The relationship is generally represented in a graph of mass of gas adsorbed per gram of adsorbent versus pressure. These curves show a decrease in physical adsorption at a fixed pressure with increasing temperature. These curves always seem to approach saturation at high pressure.

Since the relationship is only valid at constant temperature, the relationship is called the adsorption isotherm. A diagram of the type shown below is obtained if $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ is plotted against 'P', that equilibrium pressure of the gas. Where "n" is a positive integer and n and k are constants that depend on the type of adsorbate and adsorbent at a given temperature. The factor $$\frac{{\rm{1}}}{{\rm{n}}}$$ has values ​​between $$0$$ and $$1$$.

Freundlich presented this relationship in $$1909$$. It is therefore known as the Freundlich adsorption isotherm.

(Video) Lecture 7: Adsorption and the Langmuir and Freundlich Models

The Freundlich equation can be written in logarithmic form as;

$${\rm{log}}\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right){\rm{ = logk + }}\frac{{ \rm{1}}}{{\rm{n}}}{\rm{logP}}$$

A plot of log $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ against log P results in a linear graph. The graph is shown in the figure below.

$$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ generally increases with increasing surface area of ​​the adsorbent (solid) the gas. The greater the surface area, the greater the amount of gas adsorbed at any given temperature. For this reason, solids with a large surface area are used in the adsorption process or in heterogeneous catalysis based on adsorption phenomena. Finely divided metals have larger surface areas than coarsely divided metals. Therefore, finely divided metals are generally used. The process of increasing the surface area of ​​the adsorbent is activated by heating it in a vacuum or in the presence of inert gas to high temperatures ($${\rm{573K}}$$ to $${\rm{1273K}}\ )). ### Effect of temperature on adsorption The amount of gas adsorbed by the unit mass of the adsorbent \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ changes with temperature. Adsorption is an exothermic process and the extent of adsorption (particularly physical) decreases with increasing temperature according to Le Chatelier's principle. In the case of physical adsorption, the above principle applies, but in chemical adsorption, where the chemical forces are involved in keeping the adsorbate molecules on the surface of the adsorbent, the variation with temperature is complex. The magnitude of the adsorption first increases and reaches a maximum and then decreases with a further increase in temperature. The variation of the size $$\left( {\frac{{\rm{x}}}}{{\rm{m}}}} \right)$$ of the adsorption with the temperature (t) both for the physical adsorption as well as chemical adsorption is shown below.

The isobar diagrams of $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ vs t are drawn at constant pressure. The difference in the shapes of the graphs is used to distinguish physical adsorption from chemical adsorption (chemisorption).

Langmuir later investigated the phenomenon of adsorption of gases on solids theoretically and derived the relationship between the size of the adsorption $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right )$$ and P the equilibrium pressure. It is represented mathematically as:

$$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right){\rm{ = }}\left( {\frac{{{\rm{bp }}}}{{{\rm{1 + ap}}}}} \right)$$

Where a, b are constants. It is known as the Langmuir adsorption isotherm. The equation explains the variation of the adsorption size $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ with the pressure for all types of adsorption processes.

Porous and finely divided solids adsorb solutes from their solutions when the solutions are thoroughly shaken with these solids. Activated carbon is used extensively to remove colored contaminants from impure colored organic matter. The activated carbon adsorbs many dyes, and therefore the dyes present as impurities in industrial manufacturing solutions are removed with the activated carbon.

For example, aqueous, colored solutions of raw sugar originally produced in sugar mills are decolorized by pouring them through beds of animal charcoal. Similarly, charcoal adsorbs acetic acid from aqueous solutions of acetic acid. Freshly precipitated inorganic residues (eg metal hydroxides) act as good adsorbents for the dyes.

The concentration of low-sulfur ores by the froth flotation process is an example of adsorption from solution, in which the froth adsorbs the ore particles. Column chromatography, used to separate organic substances and inorganic ions from their mixture, is another example of adsorption from solution. In this technique, alumina is generally used as the adsorbent. Adsorption from solutions follows the same principle as adsorption of gases on metals. These are:

• (i) Increasing the surface area increases the extent of adsorption.
• (ii) Increasing the temperature generally decreases the extent of adsorption.
• (iii) The extent of adsorption depends on the concentration of the solute in the solution.
• (iv) Some adsorbents selectively adsorb some solutes more efficiently than the others (selectively).

The Freundlich isotherm equation, which uses a concentration term (C) of the solution instead of the pressure (P) of gases, obeys the case of adsorption from solutions. The quantitative relationship is therefore written mathematically as

$$\left( {\frac{{\rm{x}}}{{\rm{m}}} \right){\rm{ = k \times }}{{\rm{C}}^{ \frac{{\rm{1}}}{{\rm{n}}}}}$$

Oder $${\rm{log}}_{\rm{m}}^{\rm{x}}{\rm{ = logk + }}\frac{{\rm{1}}}{{\rm {n}}}{\rm{logC}}$$

The exact mechanism of adsorption from solutions is not clear. However, it is observed that adsorption is limited by a given mass of adsorbent.

1.Heterogeneous Catalysis:Many industrial synthetic chemical reactions use metal or metal oxides as a catalyst. The catalysts act as adsorbents. For example, the mixture $$({\rm{Fe}} + {\rm{Mo}})$$ is used to produce ammonia using the Haber process. Platinized asbestos is used as a catalyst in the production of sulfuric acid by the contact process. Platinum is used in the production of nitric acid after the Ostwald oxidation process by $${\rm{N}}{{\rm{H}}_3}.$$. Nickel is used as a catalyst to produce solid fats from liquid oils (Vanaspathi) through hydrogenation.

2.Chromatographic Separations:Organic substances or inorganic ions are separated from their mixtures by column chromatography utilizing adsorption phenomena. Alumina is generally used as the adsorbent.

3.Hard water softening:Hard water contains calcium and magnesium salts. It is softened by removing these salts by adsorption by adsorbents.

4.washing process:Detergent surfactants act as an adsorbent in this process.

(Video) Langmuir Isotherm Introduction

5.Generation of high vacuum:Partially evacuated vessels are connected to the activated carbon canisters cooled in liquid air. The activated carbon adsorbs any residual gases in the vessel and helps achieve high vacuum.

6.Decolorization of industrial impure color solutions:Animal charcoal removes colored impurities from impure synthetic organic compounds. Example of colored impure raw sugar solution in sugar factories.

7.Gas masks:Masks containing the adsorbent are used to prevent workers from inhaling toxic gases. For example, masks used in the chlorine industry use animal charcoal as an adsorbent in the manufacture of these masks.

8.Control humidity:Silica gel and alumina gel are used as adsorbents to remove moisture and control indoor humidity.

This theory aims to explain the physical adsorption of gas molecules on a solid surface and serves as a basis for an important analysis of measuring the specific surface area of ​​the material.

Postulate:

4. The top layer is in equilibrium with its adsorbate molecules.

### Summary

• When coal workers wear gas masks, toxic gases are adsorbed on the surface of the mask, preventing them from coming into contact with them.
• Vacuum is created by adsorbing traces of air onto charcoal and removing it from equipment to be evacuated.
• Moisture Removal: Silica gel pellets are used to regulate moisture in medicines and new plastic bottles by adsorbing moisture.
• Color Removal: To obtain a clear liquid solution, the juice collected from the sugar cane is treated with animal charcoal to remove the colorant.
• As Catalysts: Appropriate materials are used as catalysts to allow reactants to adhere to their surface, allowing the reaction to proceed faster and increasing the reaction rate.

Q.1. What are the limits of the Freundlich adsorption isotherm?
The limits of the Freundlich adsorption isotherm are the experimental values; however, when plotted they show some deviations from linearity, particularly at high pressures. Therefore, the relationship is considered approximate and applies over a limited range of pressures. Furthermore, the Freundlich adsorption isotherm concept is purely empirical and assumes that the adsorption is multimolecular. Therefore, it only applies to physical adsorption.

F.2. What is the difference between Freundlich and Langmuir isotherms?
TheFreundlichisotherm is empirical, and Langmuir'SModel was a theoretical construct. The Langmuir adsorption isotherm is based on the kinetic theory of gases. The Freundlich adsorption isotherm is based on the assumption that each adsorption site is equivalent. The Freundlich isotherm is a graphical representation. The Langmuir adsorption isotherm is a mathematical expression by equation.

F.3. What is the purpose of adsorption?
The molecules in a gas/liquid/solution tend to stick or collect on the surfaces of solids or liquids when they are in close contact for a long time. This phenomenon is called adsorption.

F.4. What is the Temkin adsorption isotherm?
The Temkin adsorption isotherm model assumes that the heat of adsorption of all molecules decreases linearly with increasing occupancy of the adsorbent surface and that adsorption is characterized by a uniform distribution of binding energies up to the maximum binding energy.

(Video) Types of adsorption isotherm model

F.5. What are the Different Types of Adsorption Isotherms?
There are five main types of isotherms. In this case we speak of Type I and Type II. Type I isotherm is a monolayer adsorption of chemically active gases on microporous metal surfaces and non-polar gases (e.g. methane and nitrogen) on zeolites. It implies that it is typical of chemisorption. Adsorption of water vapor on non-porous alumina results in the Langmuir Type II isotherm with condensation. The potential fields of adjacent walls tend to overlap and interaction forces are fixed.

The gas molecule is amplified accordingly, so the interaction may be strong enough to fill the pores at low relative pressure or low concentration. Type II shows a significant deviation from the Langmuir adsorption model; it is a multilayered physical adsorption of a gas on a non-porous solid. It is often called the sigmoid isotherm. This type of isotherm can be a result of physical adsorption onto microporous solids. Examples of type II adsorption are nitrogen (g) adsorbed at $$-1950$$ degrees Celsius on iron $$\left( {{\rm{Fe}}} \right)$$ catalyst and nitrogen (g) adsorbed at $$-1950$$ degrees Celsius on silica gel.

F.6. How does temperature affect the adsorption isotherm?
The amount of gas adsorbed by the unit mass of the adsorbent $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ changes with temperature. In general, since adsorption is an exothermic process, the magnitude of adsorption (particularly physical) decreases with increasing temperature according to Le Chatelier's principle. This applies in the case of physical adsorption.

But in chemical adsorption, where the chemical forces involved in keeping the adsorbate molecules on the surface of the adsorbent, the variation with temperature is complex. The magnitude of the adsorption first increases and reaches a maximum and then decreases with a further increase in temperature. The variation of the size $$\left( {\frac{{\rm{x}}}}{{\rm{m}}}} \right)$$ of the adsorption with the temperature (t) both for the physical adsorption as well as chemical adsorption is shown below.

These graphs of $$\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)$$ vs t are known as adsorption isobars. These are used to distinguish physical adsorption from chemical adsorption (chemisorption) based on the shape of graphene.

## Videos

1. Different forms of Langmuir isotherm model
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3. Difference between Langmuir and Freundlich Adsorption Isotherm
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5. Example 12.1-1 Adsorption isotherm for phenol in wastewater (Freundlich and Langmuir Isotherm)
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