# 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, Herbert Freundlich gave an expression representing the isothermal variation of adsorption of a quantity of gas adsorbed by unit mass of solid adsorbent with pressure.[1] 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

Freundlich's original data for adsorption of acetic acid (page 392 in [2]) and a fit according to Freundlich's exponential law

The Freundlich adsorption isotherm is mathematically expressed as

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

It is also written as

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

or

${\displaystyle {\frac {x}{m}}=Kc^{1/n}}$

It is also written as

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

where

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

Experimentally it was determined that extent of gas adsorption varies directly with pressure and then it directly varies with pressure raised to the power 1/n until saturation pressure Ps is reached. Beyond that point, the rate of adsorption saturates even after applying higher pressure. Thus, the Freundlich adsorption isotherm fails at higher pressure.

## References

1. ^ Freundlich, Herbert. Kapillarchemie, eine Darstellung der Chemie der Kolloide und verwandter Gebiete. Akademische Verlagsgesellschaft, 1909.
2. ^ Freundlich, Herbert. " Über die Adsorption in Lösungen." Zeitschrift für Physikalische Chemie - Stöchiometrie und Verwandschaftslehre (1907): Volume 57, Issue 4, pages 385-470.

## Further reading

• Jaroniec, M. (1975). "Adsorption on heterogeneous surfaces: The exponential equation for the overall adsorption isotherm". Surface Science. 50 (2): 553–564. Bibcode:1975SurSc..50..553J. doi:10.1016/0039-6028(75)90044-8.
• Levan, M. Douglas; Vermeulen, Theodore (1981). "LeVan, M. Douglas, and Theodore Vermeulen. "Binary Langmuir and Freundlich isotherms for ideal adsorbed solutions." The Journal of Physical Chemistry 85.22 (1981): 3247-3250". The Journal of Physical Chemistry. 85 (22): 3247–3250. doi:10.1021/j150622a009.
• "Freundlich Equation". Archived from the original on 3 March 2016.