Adsorption isotherms are quantitative measurements of the equilibrium established during the adsorption process, providing valuable information about the uptake capacity of adsorbents and the adsorption equilibrium data. They are essential for designing adsorption systems and calculating the equilibrium concentration of solute in the solid and liquid phases. Various theoretical adsorption isotherms, such as Langmuir, Freundlich, Temkin, and DubininRadushkevich isotherms, can be used to describe the adsorption process, each with its unique set of isotherm constants and applicability.
Understanding Adsorption Isotherms
Adsorption is a surface phenomenon where molecules or atoms from a gas or liquid phase accumulate on the surface of a solid or liquid adsorbent. The adsorption isotherm is a graphical representation of the relationship between the amount of adsorbate (the substance being adsorbed) and the equilibrium concentration of the adsorbate in the bulk phase at a constant temperature.
The adsorption isotherm can be classified into five main types, as described by the BrunauerEmmettTeller (BET) classification:
 Type I: Characteristic of microporous adsorbents, where adsorption occurs in a monolayer.
 Type II: Characteristic of nonporous or macroporous adsorbents, where adsorption occurs in multilayers.
 Type III: Characteristic of nonporous or macroporous adsorbents, where adsorbateadsorbate interactions are stronger than adsorbateadsorbent interactions.
 Type IV: Characteristic of mesoporous adsorbents, where adsorption occurs in multilayers, and capillary condensation takes place.
 Type V: Characteristic of mesoporous adsorbents, where adsorbateadsorbate interactions are stronger than adsorbateadsorbent interactions.
Theoretical Adsorption Isotherms
Various theoretical adsorption isotherms have been developed to describe the adsorption process, each with its own set of assumptions and applicability. Here are some of the most commonly used adsorption isotherms:
Langmuir Isotherm
The Langmuir isotherm is based on the following assumptions:
 Adsorption occurs on a homogeneous surface with a finite number of identical adsorption sites.
 Each adsorption site can hold only one adsorbate molecule (monolayer adsorption).
 There are no interactions between adsorbed molecules.
The Langmuir isotherm equation is given by:
$q_e = \frac{q_m b C_e}{1 + b C_e}$
where:
– $q_e$ is the amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium (mg/g)
– $q_m$ is the maximum adsorption capacity (mg/g)
– $b$ is the Langmuir adsorption constant (L/mg)
– $C_e$ is the equilibrium concentration of the adsorbate in the solution (mg/L)
Freundlich Isotherm
The Freundlich isotherm is an empirical model that describes adsorption on heterogeneous surfaces with a nonuniform distribution of adsorption sites. The Freundlich isotherm equation is given by:
$q_e = K_f C_e^{1/n}$
where:
– $q_e$ is the amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium (mg/g)
– $K_f$ is the Freundlich adsorption constant (mg/g)(L/mg)^(1/n)
– $n$ is the Freundlich exponent, which indicates the intensity of adsorption
Temkin Isotherm
The Temkin isotherm considers the effects of indirect adsorbateadsorbate interactions on the adsorption process. The Temkin isotherm equation is given by:
$q_e = \frac{RT}{b_T} \ln(A_T C_e)$
where:
– $q_e$ is the amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium (mg/g)
– $R$ is the universal gas constant (8.314 J/mol·K)
– $T$ is the absolute temperature (K)
– $b_T$ is the Temkin isotherm constant related to the heat of adsorption (J/mol)
– $A_T$ is the Temkin isotherm equilibrium binding constant (L/g)
DubininRadushkevich (DR) Isotherm
The DubininRadushkevich (DR) isotherm is used for estimating the adsorption energy in the micropore volume. The DR isotherm equation is given by:
$q_e = q_s \exp(\beta \varepsilon^2)$
where:
– $q_e$ is the amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium (mg/g)
– $q_s$ is the maximum adsorption capacity (mg/g)
– $\beta$ is the DR isotherm constant related to the adsorption energy (mol^2/J^2)
– $\varepsilon$ is the Polanyi potential, defined as $\varepsilon = RT \ln(1 + 1/C_e)$
Experimental Determination of Adsorption Isotherms
The adsorption isotherm can be determined experimentally using various techniques, such as:
Batch Adsorption Experiments
In batch adsorption experiments, the adsorbent is equilibrated with the adsorbate solution at a constant temperature, and the equilibrium concentration is measured. The amount of adsorbate adsorbed per unit mass of adsorbent is calculated using the following equation:
$q_e = \frac{(C_0 – C_e)V}{m}$
where:
– $q_e$ is the amount of adsorbate adsorbed per unit mass of adsorbent at equilibrium (mg/g)
– $C_0$ is the initial concentration of the adsorbate in the solution (mg/L)
– $C_e$ is the equilibrium concentration of the adsorbate in the solution (mg/L)
– $V$ is the volume of the solution (L)
– $m$ is the mass of the adsorbent (g)
Colorimetric Methods
Colorimetric methods can also be used to determine the adsorption isotherm, where the adsorption process is quantified by measuring the change in solution color. This method is particularly useful for adsorbates that exhibit a color change during the adsorption process.
Adsorption Isotherm Applications
Adsorption isotherms are widely used in various fields, including:

Water and Wastewater Treatment: Adsorption isotherms are used to design and optimize adsorptionbased water and wastewater treatment processes, such as the removal of organic pollutants, heavy metals, and dyes.

Air Purification: Adsorption isotherms are used to design and optimize adsorptionbased air purification systems, such as the removal of volatile organic compounds (VOCs) and odors.

Catalysis: Adsorption isotherms are used to understand the adsorption behavior of reactants and products on catalyst surfaces, which is crucial for the design and optimization of catalytic processes.

Chromatography: Adsorption isotherms are used to understand the adsorption behavior of analytes on the stationary phase in chromatographic techniques, such as highperformance liquid chromatography (HPLC) and gas chromatography (GC).

Energy Storage: Adsorption isotherms are used to design and optimize adsorptionbased energy storage systems, such as hydrogen storage and natural gas storage.

Pharmaceutical and Biomedical Applications: Adsorption isotherms are used to understand the adsorption behavior of drugs, proteins, and other biomolecules on various adsorbents, which is crucial for the development of drug delivery systems and bioseparation processes.
Conclusion
Adsorption isotherms are a fundamental tool for understanding and designing adsorptionbased systems. By determining the adsorption isotherm, researchers and engineers can gain valuable insights into the adsorption process, the uptake capacity of adsorbents, and the equilibrium concentration of the adsorbate in the solid and liquid phases. The various theoretical adsorption isotherms, along with experimental techniques such as batch adsorption experiments and colorimetric methods, provide a comprehensive framework for the analysis and optimization of adsorptionbased applications across a wide range of scientific and engineering disciplines.
References
 Adsorption Isotherm – an overview  ScienceDirect Topics, https://www.sciencedirect.com/topics/chemicalengineering/adsorptionisotherm
 A Review on the Adsorption Isotherms and Design Calculations for Adsorption Systems  ACS Omega, https://pubs.acs.org/doi/10.1021/acsomega.2c08155
 Adsorption Isotherm Using a Colorimetric Method – CliffsNotes, https://www.cliffsnotes.com/studynotes/5884570/adsorptionisothermusingacolorimetricmethod
 Brunauer, S., Emmett, P. H., & Teller, E. (1938). Adsorption of Gases in Multimolecular Layers. Journal of the American Chemical Society, 60(2), 309319.
 Langmuir, I. (1918). The Adsorption of Gases on Plane Surfaces of Glass, Mica and Platinum. Journal of the American Chemical Society, 40(9), 13611403.
 Freundlich, H. (1906). Über die Adsorption in Lösungen. Zeitschrift für Physikalische Chemie, 57(1), 385470.
 Temkin, M. I. (1941). Adsorption Equilibrium and the Kinetics of Processes on Nonhomogeneous Surfaces and in the Interaction between Adsorbed Molecules. Zhurnal Fizicheskoi Khimii, 15(3), 296332.
 Dubinin, M. M., & Radushkevich, L. V. (1947). Equation of the Characteristic Curve of Activated Charcoal. Proceedings of the Academy of Sciences of the USSR, Physical Chemistry Section, 55, 331337.
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