What is the Difference Between Freundlich and Langmuir Adsorption Isotherms?

The Freundlich and Langmuir adsorption isotherms are two models used to describe the adsorption of molecules onto a surface. They differ in terms of their underlying assumptions, mathematical representation, and applicability to different adsorption scenarios.

Freundlich Adsorption Isotherm:

Empirical model: It is based on experimental data and observations.
Applicability: It suits multilayer adsorption on heterogeneous sites.
Mathematical representation: The Freundlich isotherm can be represented by the following equation: $$\log x = \log K + \frac{1}{n} \log C$$ where x is the mass of the gas adsorbed, m is the mass of the adsorbent, K is the Freundlich adsorption coefficient, n is a constant related to the degree of adsorption, and C is the equilibrium concentration of the adsorbate.

Langmuir Adsorption Isotherm:

Theoretical model: It is based on theoretical principles and is applicable for monolayer adsorption on homogeneous sites.
Applicability: It is used to predict linear adsorption at low adsorption densities and a maximum surface coverage.
Mathematical representation: The Langmuir isotherm can be represented by the following equation: $$\frac{x}{m} = \frac{abc(1 + ac)}{1 + bc + ac^2}$$ where x is the weight of solute sorbed, m is the mass of the adsorbent, c is the equilibrium concentration of the solute, and a and b are constants.

In summary, the Freundlich adsorption isotherm is an empirical model suitable for multilayer adsorption on heterogeneous sites, while the Langmuir adsorption isotherm is a theoretical model applicable for monolayer adsorption on homogeneous sites. The two models have different mathematical representations and are used to predict adsorption capacity under different conditions.

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What is the Difference Between Freundlich and Langmuir Adsorption Isotherms?

Comparative Table: Freundlich vs Langmuir Adsorption Isotherms

The main difference between Freundlich and Langmuir adsorption isotherms lies in their empirical and theoretical nature, as well as their graphical representation and mathematical expression. Here is a comparison table outlining the key differences between the two isotherms:

Parameter	Freundlich Adsorption Isotherm	Langmuir Adsorption Isotherm
Nature	Empirical	Theoretical
Graphical Representation	Measures variation in the quantity of gas adsorbed by a unit mass of solid adsorbent	Predicts linear adsorption at low adsorption densities and a maximum surface coverage
Mathematical Expression	$$x/m = kP^{1/n}$$	$$qe = aCe + bCe^2$$
Assumptions	- Gas and adsorbent are in equilibrium	- Adsorption occurs on homogeneous sites
- There is no interaction between adsorbed species	- Adsorption does not result in multilayer formation
Constant	$$k$$: Adsorption coefficient (dependent on the nature of the adsorbent and adsorbate)	$$a$$: Adsorption coefficient, related to the energy of adsorption ($$\frac{l}{mg}$$)
- $$n$$: Constants depends on the nature of the adsorbent and the gas	$$b$$: Adsorption coefficient ($$l^2/mg^2$$), related to the equilibrium concentration at which half of the sites are occupied
Applications	Suitable for multilayer adsorption onto heterogeneous surfaces	Applicable to monolayer adsorption on homogeneous surfaces

In summary, Freundlich adsorption isotherm is an empirical model that measures the variation in the quantity of gas adsorbed by a unit mass of solid adsorbent, while Langmuir adsorption isotherm is a theoretical model that predicts linear adsorption at low adsorption densities and a maximum surface coverage.

Guilherme Mazui

Guilherme Mazui is graduated in journalism from the Federal University of Minas Gerais (UFMG) and a master's degree in Communication from the University of São Paulo (USP). In addition, he has experience in advertising writing and has worked as a content editor in several companies.