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"Consumption" of matter from a gas or from an opening of the interface between them (or from the surface of a solid body). In other words, adsorption is the "consumption" by an adsorbate from a volume of gas on the surface of the adsorbent. Adsorption is a particular case of sorption.

The molecules of the adsorbate falling on the surface of the adsorbent are retained by the surface force for a period of time, which depends on the natures of the adsorbent and adsorbate, on the temperature $T$ and on the pressure $p$, after which they leave the surface (are desorbed). Under conditions of thermodynamic and molecular equilibrium, the rates of adsorption and desorption are equal. The relation between the relative pressure $\phi=p/p_s$ of the adsorbent and the relative concentration $\theta=c/c_s$, where the index $s$ stands for the limit value at a constant temperature, is known as the adsorption isotherm.

Langmuir's equation of mono-molecular adsorption has the form


where $k$ is the equilibrium constant which roughly describes the interaction between the adsorbent and the adsorbate.

Brunauer's equation [1] is commonly used in the case of a homogeneous surface of the adsorbent and poly-molecular adsorption.

Posnov's formula [2], which is empirical, is widely employed for capillary bodies:


where $A$ is a coefficient which varies with the temperature and with the structure of the adsorbent.


[1] S. Brunauer, "Adsorption of gases and vapors" , Princeton Univ. Press (1943)
[2] V.A. Posnov, Zh. Tekhn. Fiz. : 23 (1953) pp. 865
[3] B.V. Il'in, "The nature of adsorption forces" , Moscow-Leningrad (1952) (In Russian)
[4] J.H. de Boer, "The dynamical character of adsorption" , Clarendon Press (1968)


The Brunauer–Emmett–Teller equation, or BET-equation, [a1] generalizes the Langmuir equation. It assumes multi-molecular adsorption for which each layer obeys a Langmuir equation. There are several modifications, cf. [a2].


[a1] S. Brunauer, P.H. Emmett, E. Teller, J. Amer. Chem. Soc. , 60 (1938) pp. 309
[a2] S. Brunauer, L.E. Copeland, "Surface tension, adsorption" E.U. Condon (ed.) H. Odishaw (ed.) , Handbook of physics , 2 , McGraw-Hill (1967) pp. Chapt. 7
How to Cite This Entry:
Adsorption. Encyclopedia of Mathematics. URL:
This article was adapted from an original article by A.V. Lykov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article