The Langmuir equation is derived starting from the equilibrium between empty surface sites (S^*), particles (P) and filled particle sites (SP) S^* + P \rightleftharpoons SP The equilibrium constant K is thus given by the equation: K =\frac{[SP]}{[S^*][P]} Because the number of filled surface sites (SP) is proportional to θ, the number of unfilled sites (S^*) is proportional to 1-θ, and the number of particles is proportional to the gas pressure or concentration (p), the equation can be rewritten as: \alpha =\frac{\theta}{(1-\theta)p} where \alpha is a constant. Rearranging this as follows: \theta = \alpha(1-\theta)p \theta = p\alpha - p\theta\alpha \theta + p\theta\alpha = p\alpha \theta (1 + p\alpha) = p\alpha leads to Langmuir equation: \theta =\frac{\alpha \cdot p}{1+\alpha \cdot 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 (biochemistry).
Posted on: Fri, 02 Jan 2015 19:29:30 +0000
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