Freundlich equation

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The Freundlich equation or Freundlich adsorption isotherm, an adsorption isotherm, is an empirical relation between the concentration of a solute on the surface of an adsorbent to the concentration of the solute in the liquid with which it is in contact. In 1909, Freundlich gave an expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with pressure. This equation is known as Freundlich Adsorption Isotherm or Freundlich Adsorption equation. As this relationship is entirely empirical, in the case where adsorption behavior can be properly fit by isotherms with a theoretical basis, it is usually appropriate to use such isotherms instead (see for example the Langmuir and BET adsorption theories).

Freundlich adsorption isotherm[edit]

Example of the Freundlich isotherm, showing the amount adsorbed, q (e.g., in mol/kg), as a function of equilibrium concentration in the solution, c (e.g., in mol/L). The graph is for the values of the constants of K=4 and 1/n=0.6.

The Freundlich Adsorption Isotherm is mathematically expressed as

\frac{x}{m} = Kp^{1/n}

It is also written as

 \log\frac{x}{m}  = \log K + \frac{1}{n} \log p


\frac{x}{m} = K c^{1/n}

It is also written as

\log \frac{x}{m}  = \log K + \frac{1}{n} \log c


x = mass of adsorbate
m = mass of adsorbent
p = Equilibrium pressure of adsorbate
c = Equilibrium concentration of adsorbate in solution.

K and n are constants for a given adsorbate and adsorbent at a particular temperature.

At high pressure 1/n = 0, hence extent of adsorption becomes independent of pressure.

It is used in cases where the actual identity of the solute is not known, such as adsorption of colored material from sugar, vegetable oil etc.

Limitation of Freundlich adsorption isotherm[edit]

Experimentally it was determined that extent of adsorption varies directly with pressure until saturation pressure Ps is reached. Beyond that point rate of adsorption saturates even after applying higher pressure. Thus Freundlich adsorption isotherm failed at higher pressure.


Freundlich HMF. Über die Adsorption in Lösungen. Z Phys Chem. 1906;57(A):385–470

Adsorption on heterogeneous surfaces: the exponential equation for the overall adsorption isothermM Jaroniec - Surface Science, 1975 Elsevier

Binary Langmuir and Freundlich isotherms for ideal adsorbed solutionsMD LeVan… - The Journal of Physical Chemistry, 1981 - ACS Publications

See also[edit]

Langmuir adsorption isotherm

External links[edit]