ADSORPTION Theory, Modeling, and Analysis docx

[...]... , Y ¼ vs and vg, and Z ¼ As ; we can now discuss the problems of the adsorption mechanism as in Ref 5 The molecules in the gas phase have two types of energy: potential and kinetic During the adsorption process, these energies change and these changes appear in the differential heat of adsorption The potential energy of a molecule of adsorptive can be characterized by a comparison: A ball standing on... between the differential heat of adsorption and the energy of lateral interactions; that is, diff U0 ¼ qdiff À Uls ð71Þ As will be demonstrated in the next section, the thermodynamic parameter functions, As and diff U0 are the bases of a uniform interpretation of S=G adsorption However, before this interpretation, a great and old problem of S=G adsorption should be discussed and solved II THERMODYNAMIC... electrolytes, and (3) lateral and vertical interaction do not take place between the components In Fig 1 can be seen the five types of isotherm, nnðsÞ 1 versus x1 , classified for the first time by Schay and Nagy [4] In Fig 2 are shown the corresponding composite isotherms calculated by Eqs (37) and (38) It should be emphasized that the fundamental thermodynamics of S=L adsorption is exactly defined by (35) and. .. (J=mol), P is the pressure ðJ=m3 Þ, and n is the amount of the component (mol) Interpretation of Adsorption Isotherms nðsÞ FIG 1 The five types of excess isotherm n1 versus x1 classified by Schay and Nagy [4] 7 8 ´ Toth FIG 2 The composite monolayer isotherms corresponding to the five types of excess isotherm and calculated by Eqs (37) and (38) Interpretation of Adsorption Isotherms 9 Let us apply Eq... the adsorbent structure during the adsorption processes, and interactions of composite molecules in the bulk and Gibbs phases are problems open for further investigation More of them are successfully discussed in Chapter 10 D Derivation of the Gibbs Equation for Adsorption on Gas=Solid Interfaces This derivation essentially differs from that applied for the free and S=L interfaces, because, in most... P þ 45 ð76Þ (Fig 3, top) and V s ðPÞ ¼ À0:2 Â 10À6 P þ 45 ð77Þ (Fig 3, bottom), where P is expressed in MPa Equations (76) and (77) mean that a smaller and greater decreasing of V s ðPÞ have been taken into account In the right-hand side of Fig 3, the functions ns ðPÞ can be seen These functions have been calculated using Eq (73), assuming different values of vs ð30 cm3 =mol and 20 cm3 =molÞ Evidently,... calculated by Eqs (115) and (120) are attributed the values of As ðYÞ, so we r obtain the functions As ðPr;m Þ These two types of function in the bottom of Fig 6 characterize r thermodynamically the adsorption process and thus seem to complete the uniform interpretation of the mL and other isotherm equations The thermodynamic consistency is best reflected by the functions As ðYÞ and As ðPr;m Þ because... cðYÞ > 1 and cðYÞ < 1 and the point where the proportional line drawn from the origin is a tangent can be seen Evidently, cðYÞ ¼ 1 is also valid when the initial domain of an isotherm is a proportional line (i.e., the isotherm begins with a Henry section) The above analysis is also represented in Fig 8 The first figure ðwF ¼ 1Þ relates to the original FG equation, which can describe Types I and V and condensation... Adsorptive Potential The Gibbs equations derived for free, S=L, and S=G interfaces provide a uniform picture of physical adsorption; however, they cannot give information on the structure of energy [i.e., we do not know how many and what kind of physical parameters or quantities influence the energy (heat) processes connected with the adsorption] As it is well known these heat processes can be exactly... is equal to that in the bulk liquid in the real system Equations (28) and (29) were derived for first time by Bartell and Ostwald and de Izaguirre [2, 3] The importance of Eq (29) is in the fact that it permits the measurement of the nnðsÞ versus x1 excess 1 isotherms directly However, the exact thermodynamical interpretation of S=L adsorption requires that the measured value of nnðsÞ in Eq (29) be compared . section of the recent theoretical and practical results achieved in gas–solid and liquid–solid adsorption, and it can be proved that the methods of discussion (modeling, analysis) have the same root 375 Alexander A. Shapiro and Erling H. Stenby 7. Rare-Gas Adsorption 433 Angel Mulero and Francisco Cuadros 8. Ab Fine Problems in Physical Chemistry and the Analysis of Adsorption Desorption. giving new results and aspects for a better and deeper understanding of the problem in question. The same statements are valid for Chapters 4–7. In Chapters 8 and 9, the problems of adsorption kinetics,