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dpf = RTd In yi P Make Denso QR Bar Code In None Using Barcode printer for Software Control to generate, create QR Code image in Software applications. Decode QR Code ISO/IEC18004 In None Using Barcode decoder for Software Control to read, scan read, scan image in Software applications. Combining the last two equations with the Gibbs adsorption isotherm gives: Encoding QR In Visual C#.NET Using Barcode generation for .NET framework Control to generate, create QR Code JIS X 0510 image in VS .NET applications. QR Generation In .NET Using Barcode generation for ASP.NET Control to generate, create QR Code JIS X 0510 image in ASP.NET applications. where x and yi represent adsorbate and gasphase mole fractions respectively i
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European Article Number 13 Generation In None Using Barcode generator for Software Control to generate, create EAN / UCC  13 image in Software applications. Print GS1  12 In None Using Barcode printer for Software Control to generate, create UCC  12 image in Software applications. Basic to the experimental study of puregas adsorption are measurements at constant temperature of n , the moles of gas adsorbed, as a function of P, the pressure in the gas phase Each set of data represents an adsorption isotherm for the pure gas on a particular solid adsorbent Available data are summarized by Valenzuela and ~ y e r s " The correlation of such data ECC200 Printer In None Using Barcode drawer for Software Control to generate, create DataMatrix image in Software applications. Bar Code Maker In None Using Barcode drawer for Software Control to generate, create barcode image in Software applications. 2 0 ~ P Valenzuela and
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Barcode Creation In Visual Studio .NET Using Barcode maker for Visual Studio .NET Control to generate, create barcode image in VS .NET applications. Print Barcode In Java Using Barcode drawer for BIRT Control to generate, create bar code image in BIRT applications. requires an analytical relation between n and P , and such a relation should be consistent with Eq (14102) Written for a pure chemical species, this equation becomes: Creating Code 128A In None Using Barcode encoder for Excel Control to generate, create Code 128 image in Microsoft Excel applications. Barcode Encoder In .NET Framework Using Barcode maker for ASP.NET Control to generate, create bar code image in ASP.NET applications. The compressibilityfactor analog for an adsorbate is defined by the equation: Scan EAN13 In Visual Basic .NET Using Barcode recognizer for VS .NET Control to read, scan read, scan image in VS .NET applications. UPC A Creation In C#.NET Using Barcode creator for Visual Studio .NET Control to generate, create UPC Symbol image in VS .NET applications. Differentiation at constant T yields: Replace the last term by Eq (14103) and eliminate n / R T in favor of z / a in accord with Eq (14104) to yield: Substituting a = A / n and da =  A d n / n 2 gives: dlnP =
z  d z
dn n
Adding d n l n to both sides of this equation and rearranging, Integration from P = 0 (where n = 0 and z = 1) to P = P and n = n yields: The limiting value of n / P as n + 0 and P + 0 must be found by extrapolation of experimental data Applying l'H6pital's rule to this limit gives: Thus k is defined as the limiting slope of an isotherm as P + 0, and is known as Henry's constant for adsorption It is a function of temperature only for a given adsorbent and adsorbate, and is characteristic of the specific interaction between a particular adsorbent and a particular adsorbate The preceding equation may therefore be written: 148 Equilibrium Adsorption of Gases on Solids
This general relation between n, the moles adsorbed, and P, the gasphase pressure, includes z, the adsorbate compressibility factor, which may be represented by an equation of state for the adsorbate The simplest such equation is the idealgas analog, z = 1, and in this case Eq (14105) yields n = k P , which is Henry's law for adsorption An equation of state known as the ideallatticegas equation2' has been developed specifically for an adsorbate: where rn is a constant This equation is based on the presumptions that the surface of the adsorbate is a twodimensional lattice of energetically equivalent sites, each of which may bind an adsorbate molecule, and that the bound molecules do not interact with each other The validity of this model is therefore limited to no more than monolayer coverage Substitution of this equation into Eq (14105) and integration leads to the Langmuir Solution for n yields: Alternatively, where b = m/ k , and k is Henry's constant Note that when P + 0, n / P properly approaches k At the other extreme, where P + oo, n approaches m , the saturation value of the specific amount absorbed, representing full monolayer coverage Based on the same assumptions as for the ideallatticegas equation, Langmuir in 1918 derived Eq (14106) by noting that at equilibrium the rate of adsorption and the rate of desorption of gas molecules must be the same23For monolayer adsorption, the number of sites may be divided into the fraction occupied 0 and the fraction vacant 1  0 By definition, n rn n and 10=rn rn where m is the value of n for full monolayer coverage For the assumed conditions, the rate of adsorption is proportional to the rate at which molecules strike the surface, which in turn is proportional to both the pressure and the fraction 1  0 of unoccupied surface sites The rate of desorption is proportional to the occupied fraction 0 of sites Equating the two rates gives: 1 3 

