Fluid-Solid Equilibria The Langmuir Isotherm

One of the earliest attempts to derive a theoretical expression for these isotherms, and to date also the most successful one, is that due to Langmuir. In this derivation, Langmuir postulated that the adsorption equilibrimn was the result of two rate processes, equal in magnitude but opposite in direction The rate of adsorption, which was taken to be proportional to solute pressure or concentration and the available free surface area, and a desorption rate, which varied directly with the fractional surface coverage. The result of equating these two rate expressions can be expressed, after some manipulation, in the following form  

Here and are semiempirical constants, p and C are gas partial pressure and solute concentration, respectively, and X represents the amoimt adsorbed. For general engineering purposes, it is often more convenient to replace p and C by a single fluid-phase concentration Y, expressed in units of kg solute/kg inert gas, or kg solute/kg solvent. Equation 6.5a and Equation 6.5b can then be coalesced into a single expression of the form 

Let us now examine the asymptotic behavior of the Langmuir isotherm At low values of the fluid-phase concentration Y, the term bY becomes small compared to 1, and the Langmuir isotherm approaches the limiting linear form 

The slope of this line is often referred to as Henry s constant, and Expression 6.5d as Henry s law for adsorption, in analogy to the corresponding case of gas-liquid equilibrium (see Equation 6.2). 

At the other extreme of high values of Y, bY becomes the dominant factor and the Langmuir isotherm converges to the form 

Mass Transfer and Separation Processes Principles and Applications 

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