Adsorption Isotherm: Freundlich, Langmuir Model, Types

Adsorption Isotherm: Adsorption happens 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 on the surface. We will go through the many forms of Adsorption Isotherms and how they are used in this post.

What is an Adsorption Isotherm?

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

Freundlich Adsorption Isotherm

Freundlich showed empirically that at any given temperature, the amount of gas adsorbed \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) by unit mass of the adsorbent is related 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 relation is generally represented in a curve where the mass of the gas adsorbed per gram of the adsorbent is plotted against pressure. These curves indicate a decrease in physical adsorption at a fixed pressure with an increase in temperature. These curves always seem to approach saturation at high pressure.

Since the relation holds good only at a constant temperature, the relation is referred to as adsorption isotherm. A graph of the type shown below is obtained when \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\)  is plotted against ‘P’, the equilibrium pressure of the gas. Where ‘n’ is a positive integer and n and k are constants depending upon the nature of adsorbate and adsorbent at a particular temperature. The factor \(\frac{{\rm{1}}}{{\rm{n}}}\) has values between \(0\) and \(1\). 

This relationship was put forwarded by Freundlich in \(1909\). So, it is known as Freundlich adsorption isotherm.

The Freundlich equation can be written in the form of the logarithm 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 gives a linear graph. The graph is shown in the figure below.

\(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) generally, increases with an increase in the surface area of the adsorbent (solid) exposed to the gas. At any given temperature, the greater the surface area, the greater is the amount of the gas adsorbed. For this reason, solids with a large surface area are used in the adsorption process or heterogeneous catalysis based on adsorption phenomena. Finely divided metals will have larger surface areas than coarsely divided metals. Hence, finely divided metals are generally used. The process to increase the adsorbent’s surface area is done by activating by heating them in a vacuum or the presence of inert gas to high temperatures (\({\rm{573K}}\) to \({\rm{1273K}}\)).

Effect of Temperature on Adsorption

The amount of gas adsorbed by unit mass of adsorbent \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) changes with temperature. Adsorption is an exothermic process, and the magnitude of adsorption (physical especially) decreases with the increase of temperature as per Le Chatelier’s principle. In the case of physical adsorption, the above principle holds, but in chemical adsorption, where the chemical forces are involved in holding the adsorbate molecules to the surface of the adsorbent, the variation with the temperature is complex. The magnitude of adsorption first increases and reaches a maximum and subsequently decreases with a further rise in temperature. The variation of magnitude \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) of adsorption with the temperature (t) for both the physical adsorption and chemical adsorption is shown below.

• (a) Physical adsorption
• (b) Chemical adsorption

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

Langmuir Adsorption Isotherm

Langmuir later investigated the phenomenon of adsorption of gases by solids theoretically and derived the relationship between the magnitude of 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 Langmuir adsorption isotherm. The equation explains the variation of the magnitude of adsorption \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) with pressure in all the types of adsorption processes. 

Adsorption from Solutions

Porous and finely divided solid substances adsorb dissolved substances from their solutions when the solutions are shaken thoroughly with these solid substances. Activated charcoal is used extensively to remove coloured impurities from impure coloured organic substances. The charcoal adsorbs many dyestuffs, and hence the dyestuffs present as impurities in solutions of industrial preparation are removed using the activated charcoal.

For example, aqueous coloured solutions of raw sugar formed initially in sugar factories are decolourised by pouring them through the beds of animal charcoal. Similarly, charcoal adsorbs acetic acid from aqueous solutions of acetic acid. Freshly precipitated inorganic residues (for example, metal hydroxides) act as good adsorbent for the dyestuffs.

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

• (i) An increase in the surface area increases the extent of adsorption.
• (ii) An increase in 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 effectively than the others (selectively).

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

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

Or \({\rm{log}}_{\rm{m}}^{\rm{x}}{\rm{ = logk + }}\frac{{\rm{1}}}{{\rm{n}}}{\rm{logC}}\)

The precise mechanism of adsorption from solutions is not clear. But it is observed that there is a limit to the adsorption by a given mass of the adsorbent.

Applications of Adsorption Phenomena 

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

2. Chromatographic Separations: Organic substances or inorganic ions are separated from their mixtures, making use of adsorption phenomena by column chromatography. Aluminium oxide is used generally as an adsorbent.

3. Softening of Hard Water: Hard water contains salts of calcium and magnesium. It is softened by removing these salts by the process of adsorption by adsorbents.

4. Washing Process: Surface active detergents function as an adsorbent in this process.

5. Production of High Vacuum: Partially evacuated vessels are connected to the activated charcoal containers cooled in liquid air. The charcoal adsorbs all the residual gases in the vessel and helps to attain a high vacuum.

6. Decolourisation of Industrial Impure Coloured Solutions: Animal charcoal removes coloured impurities from impure synthetic organic compounds. Example- coloured impure raw sugar solution in sugar factories.

7. Gas Masks: Masks containing the adsorbent are used to prevent inhaling poisonous gases by the workers. For example, masks used in the chlorine industry use animal charcoal as the adsorbent in preparing these masks.

8. Control Humidity: Silica gel and alumina gel are used as adsorbents for removing moisture and controlling the humidity of air in rooms.

BET Adsorption Isotherm

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

Postulates:

1. The adsorption occurs only on well-defined adsorption active sides.
2. Adsorption is multilayer.
3. Adsorption is physical. 
4. The uppermost layer is in equilibrium with its adsorbate molecules. 

Summary

In this article, we learnt about Freundlich and Langmuir adsorption isotherms. Effect of temperature on adsorption, adsorption from solutions, and some applications of adsorption. The following are some examples of adsorption applications:

• When coal workers wear gas masks, poisonous gases are adsorbed to the mask’s surface, preventing them from coming into contact with them.
• Vacuum is created by adsorbing traces of air on charcoal and removing them from devices that are being evacuated.
• Moisture removal: Silica gel pellets are used to manage humidity in pharmaceuticals and new plastic bottles by adsorbing moisture.
• Removal of colour: To get a clear liquid solution, the juice collected from cane is treated with animal charcoal to remove the colouring ingredient.
• As Catalysts: Appropriate materials are employed as catalysts so that reactants attach to their surface, allowing the reaction to occur more quickly and increasing the rate of reaction.

Frequently Asked Questions on Adsorption Isotherm

Q.1. What are the limitations of Freundlich adsorption isotherm?
Ans: The limitations of Freundlich adsorption isotherm are the experimental values; when plotted, however, show some deviations from linearity, especially at high pressures. Hence the relation is considered as an approximate one and holds good over a limited range of pressure. Moreover, the concept of Freundlich adsorption isotherm is purely empirical, and it assumes the adsorption to be multimolecular. Hence it applies only to physical adsorption. 

Q.2. What is the difference between Freundlich and Langmuir isotherm?
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. Langmuir adsorption isotherm is a mathematical expression by equation.

Q.3. What is the purpose of adsorption?
Ans: The molecules in a gas/ liquid/solution, on coming into intimate contact with the surfaces of solids or liquids for a long time, tend to adhere or accumulate on these surfaces. This phenomenon is referred to as adsorption. 

Q.4. What is Temkin adsorption isotherm
Ans: The Temkin adsorption isotherm model assumes that the adsorption heat of all molecules decreases linearly with the increase in coverage of the adsorbent surface and that adsorption is characterised by a uniform distribution of binding energies up to maximum binding energy.  

Q.5. What are the different types of adsorption isotherm?
Ans: There are five main types of isotherm. In this case, we are discussing Type I and Type II. Type I isotherm is monolayer adsorption of chemically active gases on microporous metal surfaces and non-polar gases (for example, methane and nitrogen) on zeolites. It implies to be typical of chemisorption. Water vapour adsorption on non-porous aluminium oxide will lead to the Langmuir Type II isotherm with condensation. The potential fields from neighbouring walls tend to overlap, and interaction forces solid.

The gas molecule is correspondingly enhanced, so the interaction might be strong enough to fill the pores at low relative pressure or concentration. Type II shows significant deviation from the Langmuir model of adsorption; it is a multilayer physical adsorption of a gas on a non-porous solid. It is often referred to as sigmoid isotherms. This type of isotherm can be a result of physical adsorption on microporous solid. Examples of Type-II adsorption are Nitrogen (g) adsorbed at \(-1950\) degree Celsius on Iron \(\left( {{\rm{Fe}}} \right)\) catalyst and Nitrogen (g) adsorbed at \(-1950\) degree Celsius on silica gel.

Q.6. What is the effect of temperature in adsorption isotherm?
Ans: The amount of gas adsorbed by unit mass of adsorbent \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) changes with temperature. Since adsorption is an exothermic process, generally, the magnitude of adsorption (physical especially) decreases with the increase of temperature per Le Chatelier’s principle. It is true in the case of physical adsorption.

But in chemical adsorption, where the chemical forces are involved in holding the adsorbate molecules to the surface of the adsorbent, the variation with the temperature is complex. The magnitude of adsorption first increases and reaches a maximum and subsequently decreases with a further rise in temperature. The variation of magnitude \(\left( {\frac{{\rm{x}}}{{\rm{m}}}} \right)\) of adsorption with the temperature (t) for both the physical adsorption and chemical adsorption is shown below.

(a) Physical adsorption 

(b) Chemical adsorption

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

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