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Langmuir equation

From Wikipedia, the free encyclopedia

Langmuir isotherm. Value of constant increases from blue, red, green and brown
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Langmuir isotherm. Value of constant increases from blue, red, green and brown

The Langmuir equation or Langmuir isotherm or Langmuir adsorption equation relates the coverage or adsorption of molecules on a solid surface to gas pressure or concentration of a medium above the solid surface at a fixed temperature. The equation was developed by Irving Langmuir in 1916. The equation is stated as:

\theta  =\frac{\alpha \cdot P}{1+\alpha \cdot P}

θ or theta is the percentage coverage of the surface, P is the gas pressure or concentration, α alpha is a constant.

The constant α is the Langmuir adsorption constant and increases with an increase in the strength of adsorption and with a decrease in temperature. The equation is derived starting from the equilibrium between empty surface sites, particles and filled particle sites

S^* + P  \leftrightarrow S-P

equilibrium between empty surface sites S* and particles P and filled surface sites S-P

K  =\frac{[S-P]}{[S^*][P]}

Because the fraction of filled surface sites is equal to θ and the fraction of unfilled sites equal to 1-θ and because P is proportional to the gas pressure or concentration the equation can be rewritten to

K  =\frac{\theta}{(1-\theta)P}

Other equations relating to adsorption exist such as the Temkin equation or the Freundlich equation.

[edit] External links

[edit] References

  • The constitution and fundamental properties of solids and liquids. part i. solids. Irving Langmuir; J. Am. Chem. Soc. 38, 2221-95 1916 First Page
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