Langmuir equation

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Langmuir isotherm. Value of constant increases from blue, red, green and brown
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. The Langmuir equation (as a relationship between the concentration of a compound adsorbing to binding sites and the fractional occupancy of the binding sites) is equivalent to the Hill equation.

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[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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