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**Lecture 20. Adsorption Phenomena**

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Adsorption is the accumulation of atoms or molecules on the surface of a material. This process creates a film of the adsorbate (the molecules or atoms being accumulated) on the adsorbent's surface. It is different from absorption, in which a substance diffuses into a liquid or solid to form a solution. The term sorption encompasses both processes, while desorption is the reverse process of "adsorption".

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Isotherms Adsorption is usually described through isotherms, that is, the amount of adsorbate on the adsorbent as a function of its pressure (if gas) or concentration (if liquid) at constant temperature. some of these isotherms are: Langmuir BET

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Langmuir Langmuir derived a relationship for q; weight adsorbed per unit wt of adsorbent and C; concentration in fluid based on some quite reasonable assumptions. These are: a uniform surface, a single layer of adsorbed material, and constant temperature. The rate of attachment to the surface should be proportional to a driving force times an area. The driving force is the concentration in the fluid, and the area is the amount of bare surface. If the fraction of covered surface is F , the rate per unit of surface is:

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Langmuir rate going on = k1 C ( 1 - ϕ ) The evaporation from the surface is proportional to the amount of surface covered: rate leaving = k2 ϕ where k1 and k2 are rate coefficients C = concentration in the fluid ϕ = fraction of the surface covered

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Langmuir At equilibrium, the two rates are equal, and we find that: A plot of versus should indicate a straight line of slope and an intercept of . The graph shows data points and lines fitted to both Freundlich and Langmuir equations.

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Langmuir Isotherm

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BET Theory BET theory is a rule for the physical adsorption of gas molecules on a solid surface and serves as the basis for an important analysis technique for the measurement of the specific surface area of a material. The concept of the theory is an extension of the Langmuir theory, which is a theory for monolayer molecular adsorption, to multilayer adsorption with the following hypotheses:

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BET Theory gas molecules physically adsorb on a solid in layers infinitely; (b) there is no interaction between each adsorption layer; and (c) the Langmuir theory can be applied to each layer.

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BET Theory The resulting BET equation is expressed by: P and P0 are the equilibrium and the saturation pressure of adsorbates at the temperature of adsorption, v is the adsorbed gas quantity (for example, in volume units), and

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BET Theory vm is the monolayer adsorbed gas quantity. c is the BET constant. The BET method is widely used in surface science for the calculation of surface areas of solids by physical adsorption of gas molecules.

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BET Isotherm

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