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Difference between revisions of "Adsorption"

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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.
 
"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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109201.png" /> and on the pressure <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109202.png" />, 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 <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109203.png" /> of the adsorbent and the relative concentration <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109204.png" />, where the index <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109205.png" /> stands for the limit value at a constant temperature, is known as the adsorption isotherm.
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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
 
Langmuir's equation of mono-molecular adsorption has the form
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109206.png" /></td> </tr></table>
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$$\phi=\frac{\theta}{k(1-\theta)},$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109207.png" /> is the equilibrium constant which roughly describes the interaction between the adsorbent and the adsorbate.
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where $k$ is the equilibrium constant which roughly describes the interaction between the adsorbent and the adsorbate.
  
 
Brunauer's equation [[#References|[1]]] is commonly used in the case of a homogeneous surface of the adsorbent and poly-molecular adsorption.
 
Brunauer's equation [[#References|[1]]] is commonly used in the case of a homogeneous surface of the adsorbent and poly-molecular adsorption.
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Posnov's formula [[#References|[2]]], which is empirical, is widely employed for capillary bodies:
 
Posnov's formula [[#References|[2]]], which is empirical, is widely employed for capillary bodies:
  
<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109208.png" /></td> </tr></table>
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$$\frac1\theta=A\ln\phi+1,$$
  
where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/a/a010/a010920/a0109209.png" /> is a coefficient which varies with the temperature and with the structure of the adsorbent.
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where $A$ is a coefficient which varies with the temperature and with the structure of the adsorbent.
  
 
====References====
 
====References====

Latest revision as of 15:48, 4 November 2014

"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

$$\phi=\frac{\theta}{k(1-\theta)},$$

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:

$$\frac1\theta=A\ln\phi+1,$$

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

References

[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)


Comments

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].

References

[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: http://encyclopediaofmath.org/index.php?title=Adsorption&oldid=17661
This article was adapted from an original article by A.V. Lykov (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article