Adsorption Isotherms and its Interpretation
Adsorption isotherms are essential tools in understanding the behavior of molecules and particles in various chemical and biological processes. The adsorption isotherm describes the relationship between the adsorbate concentration and the amount of adsorbate adsorbed on a surface at a constant temperature. In this blog, we will explore the basics of adsorption isotherms, its interpretation, and its applications in various fields.
There are several types of adsorption isotherms, including Langmuir, BET, and Freundlich isotherms. The Langmuir isotherm is commonly used to describe adsorption onto a homogeneous surface with a finite number of identical sites, whereas the BET isotherm is used to describe adsorption onto a heterogeneous surface with varying site energies. The Freundlich isotherm is often used to describe adsorption onto a surface with varying site energies and/or with multiple types of adsorption sites.
Adsorption Isotherms:
Adsorption isotherms can be classified into different types based on the physical and chemical interactions between the adsorbate and adsorbent. The most commonly used adsorption isotherms are Langmuir, Freundlich, and BET isotherms.
Langmuir Isotherm:
The Langmuir isotherm assumes that the adsorption occurs on a homogeneous surface where each site has the same energy and is independent of its neighboring sites. The Langmuir isotherm is given by the following equation:
θ = (K_ads * C_ads) / (1 + K_ads * C_ads)
where θ is the fractional surface coverage, K_ads is the equilibrium constant, and C_ads is the concentration of the adsorbate in the bulk phase. The Langmuir isotherm assumes that the adsorption process is reversible and that there is a finite number of adsorption sites on the surface.
Freundlich Isotherm:
The Freundlich isotherm assumes that the adsorption occurs on a heterogeneous surface where each site has a different energy level. The Freundlich isotherm is given by the following equation:
θ = K_F * C_ads^(1/n)
where θ is the fractional surface coverage, K_F is the adsorption constant, C_ads is the concentration of the adsorbate in the bulk phase, and n is the Freundlich exponent, which reflects the surface heterogeneity.
BET Isotherm:
The BET (Brunauer, Emmett, and Teller) isotherm is used for the adsorption of gas molecules on solid surfaces. The BET isotherm is given by the following equation:
θ = (C_ads * V_m * K_ads) / (1 — C_ads * (1 — K_ads) * V_m)
where θ is the fractional surface coverage, C_ads is the concentration of the adsorbate in the bulk phase, V_m is the monolayer capacity of the surface, and K_ads is the equilibrium constant.
Temkin Isotherm:
The Temkin isotherm is an empirical adsorption model that describes the adsorption process on a heterogeneous surface. It was developed by M. J. Temkin and V. Pyzhev in 1940.
The Temkin isotherm assumes that the heat of adsorption of a molecule on a surface decreases linearly with coverage due to the interactions between the adsorbate molecules. The isotherm is given by the following equation:
q = B ln (A x + 1)
where q is the amount of adsorbate adsorbed per unit weight of adsorbent (mg/g), A is the Temkin isotherm constant related to the heat of adsorption (J/mol), x is the fraction of the surface covered by the adsorbate, and B is the constant related to the equilibrium binding constant (L/g).
Elovich Isotherm:
The Evolich isotherm assumes that the adsorption process occurs on a heterogeneous surface with a distribution of adsorption energies. It is given by the following equation:
q = qm [(Kc x)/(1 + Kc x)]^n
where q is the amount of adsorbate adsorbed per unit weight of adsorbent (mg/g), qm is the maximum adsorption capacity, x is the equilibrium concentration of the adsorbate in the gas phase (mmol/L), Kc is the equilibrium constant, and n is the Evolich exponent.
The Evolich isotherm can be linearized by plotting q/m against (Kc x)/(1 + Kc x)^n to obtain a straight line with a slope of 1/Kc and an intercept of qm. The Evolich exponent n is related to the heterogeneity of the adsorption sites, with higher values of n indicating a more heterogeneous surface.
Interpretation of Adsorption Isotherms:
The interpretation of adsorption isotherms depends on the type of isotherm and the physical and chemical properties of the adsorbent and adsorbate. The Langmuir isotherm is typically used to describe the adsorption of gases on solid surfaces, while the Freundlich isotherm is used to describe the adsorption of liquids and ions on solid surfaces.
The Langmuir isotherm can be used to calculate the maximum amount of adsorbate that can be adsorbed on a surface, which is known as the monolayer capacity. The Freundlich isotherm can be used to estimate the surface heterogeneity and the strength of the interaction between the adsorbate and adsorbent.
The BET isotherm is used to determine the specific surface area of a material. The BET isotherm can be used to calculate the amount of adsorbate adsorbed on a surface at different pressures, and the data can be used to determine the specific surface area of the material.