Notes on Adsorption Isotherm

Adsorption is a process where the adsorbate molecular species get trapped in the adsorbent surface. In other words, Adsorption is the accumulation of the adsorbate particles on the surface of the adsorbent. It is a surface phenomenon. Certain graphs were employed to study adsorption, known as adsorption isotherms. 

The relationship between the adsorbate in the liquid phase and the adsorbate adsorbed on the surface of the adsorbent at equilibrium at constant temperature is known as the adsorption isotherm. The adsorption isotherm is a plot where the x-axis is the x/m, x is the number of adsorbate species, m is the amount of the adsorbent molecules, and the y axis is the pressure. A curve termed an adsorption isotherm depicts the fluctuation in the amount of gas adsorbed at a fixed temperature, the adsorbent with a change in pressure.

When a solid is sprayed with a surfactant solution at a given temperature and reaches the equilibrium concentration, the adsorption isotherm is a graph that illustrates the surfactant concentration against the amount of surfactants adsorbed onto unit mass solid.

Types of Adsorption isotherms

Isotherms, or the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (for liquid phase solutes) at a constant temperature, are commonly used to describe the adsorption of gases and solutes. To allow the comparison of different materials, the quantity adsorbed is almost typically standardised by the mass of the adsorbent.

The different types of Adsorption Isotherms are:

• Freundlich Adsorption Isotherm

• Langmuir Adsorption Isotherm 

• BET Adsorption Isotherm

Freundlich Adsorption Isotherm

Freundlich developed an empirical equation in 1909 to represent the isothermal variation of adsorption of an amount of gas adsorbed by the unit mass of solid adsorbent as a function of pressure. Freundlich Adsorption Isotherm, Freundlich Adsorption Equation, or simply Freundlich Isotherm is the name given to this equation.

                                                           xm = kP1n

Where x/m  is the adsorption per gram of adsorbent, calculated by dividing the amount of adsorbate (x) by the adsorbent’s weight (m), P stands for pressure, whereas k and n are constants whose values are determined by the adsorbent and gas at a given temperature.

Limitation 

The Freundlich Isotherm accurately established the link between adsorption and pressure at lower pressures, but it failed to anticipate the value of adsorption at higher pressures. The Freundlich adsorption isotherm is the name given to this relationship. The value of x/m increases as p increases, but it does not increase abruptly as n>1.

Langmuir Adsorption Isotherm

Irving Langmuir, in 1916, published a new model isotherm for gases adsorbed on solids, and it was named Langmuir adsorption isotherm. It’s a semi-empirical isotherm developed from a kinetic mechanism that’s been postulated. This Isotherm is based on several assumptions: there is a dynamic equilibrium between adsorbed and free gaseous molecules.

This Isotherm was based on the following four assumptions:

• The adsorbent’s surface is uniform, meaning that all adsorption sites are equal.
• There is zero interaction between the adsorbed molecules.
• The mechanism of adsorption is the same in all cases.
• Only a monolayer forms at maximum adsorption: adsorbate molecules do not deposit on other, already adsorbed, adsorbate molecules, but only on the free surface of the adsorbent.

The mechanism, according to Langmuir, that is responsible for adsorption is

                                                  A(g) + B(s) ⇌ AB

A is the unadsorbed gas molecules, B is the unoccupied metal surface, and AB is the adsorbed gaseous molecules.

Based on his theory, Langmuir developed an equation to explain the relationship between the number of active sites on a surface undergoing adsorption and pressure. Langmuir Equation is the name of this equation.

                                                          ϴ= kP1+kP

Where,

 ϴ = the number of surface sites that are covered by a gaseous molecule,

 P = Pressure,

 K =  is the adsorbate distribution equilibrium constant between the surface and the gas phase.

The Langmuir adsorption equation, which was first developed to describe gas-solid phase adsorption, is now used to compare and measure the adsorptive capacity of various adsorbents. The Langmuir isotherm balances the relative adsorption and desorption rates to account for surface coverage (dynamic equilibrium). Adsorption is proportional to the available fraction of the adsorbent surface, while desorption is proportional to the covered fraction of the adsorbent surface.

Limitations of Langmuir Adsorption Isotherm

The Langmuir adsorption model deviates dramatically in many circumstances, owing to its failure to account for the adsorbent’s surface roughness. Rough inhomogeneous surfaces have a variety of adsorption site types, with some parameters, such as the heat of adsorption, varied from site to site. Furthermore, the specific surface area is a scale-dependent quantity for which no one genuine value exists. As a result, using different probe molecules can often result in different numerical results for surface area, making comparison difficult.

BET Adsorption Isotherm

• The Brunauer–Emmett–Teller (BET) theory tries to explain the physical adsorption of gas molecules on a solid surface and serves as the foundation for a critical analysis technique for calculating the specific surface area of materials.
• BET theory is used to determine the specific surface area in multilayer adsorption systems that use a probing gas (called the adsorbate) that does not react chemically with the adsorptive (the material on which the gas clings and the gas phase is termed the adsorptive). The most often used gaseous adsorbate for probing surfaces is nitrogen. Hence,the routine BET analysis is usually performed at N2 boiling temperature (77 K).
• The theory’s concept is a multilayer extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, with the following hypotheses:

• Gas molecules adsorb in layers indefinitely on a solid; gas molecules only interact with nearby layers, and the Langmuir theory may be applied to each layer.
• The first layer’s enthalpy of adsorption is constant and higher than the second (and higher).
• For the second (and higher) layers, the enthalpy of adsorption is the same as the enthalpy of liquefaction.

The BET equation is

                                                         ϴ= cP(1-P/Po)(Po+p(c-1))

Where, c is the BET constant, P0 is the vapour pressure of the adsorptive bulk liquid phase at the adsorbate’s temperature, and ϴ is the “surface coverage.”

Applications of Adsorption Isotherms

• Adsorption isotherms are often employed in the adsorptive separation of gases to select the adsorbent or even the adsorption process as a unit operation.
• Although isotherms provide information about an adsorbent’s efficiency in removing a specific adsorbate, they do not provide any data that can be used in the calculation of the contact time or the amount of adsorbent needed to drop the solute concentration below stipulated limits.

Conclusion

The adhesion of atoms, ions, or molecules from a gas, liquid, or dissolved solid to a surface is adsorption. To study the process of adsorption, adsorption isotherms were employed. The adsorption isotherm is a graph that gives the change in the amount of the adsorbate that is adsorbed on the surface of the adsorbent. The adsorption isotherm shows the extent of adsorption. The x/m is plotted against the pressure. The main two types of adsorption isotherm are Freundlich and Langmuir isotherm. Adsorption isotherms have played a critical role in studies of environmental protection and adsorption strategies.