Adsorption/desorption equilibrium constant

Recall that the equilibrium constant for desorption of species B is the reciprocal of the equilibrium constant for the adsorption of species B ... 

If the range of temperatures is adequate, and measurement errors are small enough to establish the temperature coefficients of the equilibrium constant, then this single ramping can be used to calculate all of the equilibrium constant, the desorption, and the adsorption rate constants for the system. In practice the best operating conditions for this type of run are at high values of transit time, i.e. under conditions where Wfc is large but there is a premium on accurate data to avoid the instabilities that result from the form of the equations used. 

Note that in the final desorption step the equilibrium constant for adsorption of AB equals 1 /K4 whereas for the other adsorption steps it is defined as... 

Having estimated the sticking coefficient of nitrogen on the Fe(lll) surface above, we now consider the desorption of nitrogen, for which the kinetic parameters are readily derived from a TPD experiment. Combining adsorption and desorption enables us to calculate the equilibrium constant of dissociative nitrogen adsorption from... 

Suppose we successfully measured the sticking coefficient and the activation energy for adsorption of a certain molecule, as well as the rate of desorption. Is it then possible to estimate the equilibrium constant for adsorp-tion/desorption ... 

If the supply of surfactant to and from the interface is very fast compared to surface convection, then adsorption equilibrium is attained along the entire bubble. In this case the bubble achieves a constant surface tension, and the formal results of Bretherton apply, only now for a bubble with an equilibrium surface excess concentration of surfactant. The net mass-transfer rate of surfactant to the interface is controlled by the slower of the adsorption-desorption kinetics and the diffusion of surfactant from the bulk solution. The characteris-... 

There are three approaches that may be used in deriving mathematical expressions for an adsorption isotherm. The first utilizes kinetic expressions for the rates of adsorption and desorption. At equilibrium these two rates must be equal. A second approach involves the use of statistical thermodynamics to obtain a pseudo equilibrium constant for the process in terms of the partition functions of vacant sites, adsorbed molecules, and gas phase molecules. A third approach using classical thermodynamics is also possible. Because it provides a useful physical picture of the molecular processes involved, we will adopt the kinetic approach in our derivations. 

If one takes the ratio of the pseudo rate constant for adsorption to that for desorption as an equilibrium constant for adsorption (K), equation 6.2.4 can be written as... 

Kinetic Term The designation kinetic term is something of a misnomer in that it contains both rate constants and adsorption equilibrium constants. For thfe cases where surface reaction controls the overall conversion rate it is the product of the surface reaction rate constant for the forward reaction and the adsorption equilibrium constants for the reactant surface species participating in the reaction. When adsorption or desorption of a reactant or product species is the rate limiting step, it will involve other factors. 

It is interesting to note that, although the intrinsic rate of desorption is slower than that of adsorption, both rates were found to be sufficiently fast under our experimental conditions so that the adsorption-desorption process on the Pt surface can be assumed to rapidly equilibrate at all times that is, even a ten-fold increase in both the adsorption and desorption rate constants (while keeping their ratio constant) did not significantly change the predicted step responses. With the assumption of chemisorption equilibrium, Equations (1) and (4) can be combined into the form (35)... 

The vacancy coverage, 9V, which is initially equal to 0.075, rapidly decreases during the initial period of NO exposure but then very slowly increases. This behavior can be attributed to the following factors. The first is that 0V in equilibrium with 0.10 atm of H2 is larger than 0V in equilibrium with 0.0028 atm of NO. Calculating the equilibrium constants for H2 and NO adsorption and desorption of these gases, given in Table I, one... 

Here FMON and - mon represent the available vacant sites and surface sites occupied by B, respectively, of the first monolayer on a solid absorbate. The equilibrium constant KB for the reaction is given by the ratio of the rate constant for k.d for adsorption and k for desorption... 

The rate expression is based on adsorption-desorption equilibrium at the substrate surface with an additional term (k2pH2) representing H2 gas inhibition. The rate constants can be estimated by regression of R with the two partial pressures using experimental data (Roenigk and Jensen, 1985). 

The principle we have applied here is called microscopic reversibility or principle of detailed balancing. It shows that there is a link between kinetic rate constants and thermodynamic equilibrium constants. Obviously, equilibrium is not characterized by the cessation of processes at equilibrium the rates of forward and reverse microscopic processes are equal for every elementary reaction step. The microscopic reversibility (which is routinely used in homogeneous solution kinetics) applies also to heterogeneous reactions (adsorption, desorption dissolution, precipitation). 

Table I. Rate Constants of the Adsorption/Desorption and Equilibrium Acidity Constants...

The dependences of pH and C-potential on the adsorbed amount of M(H20)2+ at the total metal ion concentrations of 3 x10-3 mol dm-3 are shown in Figures 7 and 8, respectively. The amount adsorbed for each M2+ increases with the pH, and the inflection points are shifted toward the lower pH region in the order of Co2+, Zn2+, Pb2+, Cu2+, which corresponds to the order of the hydrolysis constant of metal ions. To explain the M2+-adsorption/desorption, Hachiya et al. (16,17) modified the treatment of the computer simulation developed by Davis et al. (4). In this model, M2+ binds coordina-tively to amphoteric surface hydroxyl groups. The equilibrium constants are expressed as... 

We consider dehydration-adsorption of hydrated protons (cathodic proton transfer) and desorption-hydration of adsorbed protons (anodic proton transfer) on the interface of semiconductor electrodes. Since these adsorption and desorption of protons are ion transfer processes across the compact layer at the interface of semiconductor electrodes, the adsorption-desorption equilibrium is expressed as a function of the potential of the compact layer in the same way as Eqns. 9-60 and 9-61. In contrast to metal electrodes where changes with the electrode potential, semiconductor electrodes in the state of band edge level pinning maintain the potential d(hi of the compact layer constant and independent of the electrode potential. The concentration of adsorbed protons, Ch , is then determined not by the electrode potential but by the concentration of h3 ated protons in aqueous solutions. 

This is called a Langmuir adsorption isotherm for a species A, and the function 9a( Pa) isi shown in Figure 7-23. The KjS are the adsorption-desorption equilibrium constants for species A and B. By historical convention we call these the adsorption isotherms. Before i we proceed let us note that this is a true thermodynamic equilibrium relation so that... 

The relation (Pa) is called the adsorption isotherm. It is used to detennine surface areas of solids and catalysts as well as to determine the adsorption-desorption equilibrium constant Ka- This is measured by determining the amount of a gas that can be adsorbed by a known weight of solid, as shown in Figure 7-24. 

The products of the surface reaction adsorbed are subsequently desorbed into the gas phase. The rate of desorption of C is exactly the opposite in sign to the rate of adsorption of C and the desorption equilibrium constant Ktx. is the reciprocal of the adsorption equilibrium constant Kc. For the desorption of C, according to... 

For enzyme reactions K is the traditional Michaelis constant. For a heterogeneous surface on which adsorption and desorption but no reaction occurs (k2 = 0) K is simply an equilibrium constant for adsorption. (Actually we are not being as economical as we could be in this non-dimensionalization of the equations. We could have divided throughout by K instead of introducing the pressure scale p°, and eqn (12.9) would then have read... 

The constant K characterizes the equilibrium adsorption/desorption between a bare surface site and an adsorbate-covered one (i.e., reaction 11.39). In the higher-adsorption / desorption processes (e.g., reaction 11.41) the adsorption (left-hand side) and desorption (right-hand side) sites are already adsorbate covered such reactions are physically very similar no matter what the particular number of adsorbed layers i is involved. Therefore the approximation is made that... 

Physically, this is essentially the same process as the adsorption/desorption in reaction 11.41 when i becomes large. Assuming that the governing equilibrium constant is thus the same as in Eq. 11.47, the steady-state expression result is... 

In the following discussion we will concentrate on the surface reaction, adsorption, and desorption. The complications induced by the transport phenomena will be ignored. In order to develop an expression for the overall rate, the surface concentrations, AL, BL, etc., are related to the concentrations of the reactants in the bulk phase by an "Equilibrium constant". For example ... 

If the adsorption of A is the rate determining step in the sequence of adsorption, surface reaction and desorption processes, then equation 3.71 will be the appropriate equation to use for expressing the overall chemical rate. To be of use, however, it is first necessary to express CA, Cv and Cs in terms of the partial pressures of reactants and products. To do this an approximation is made it is assumed that all processes except the adsorption of A are at equilibrium. Thus the processes involving B and P are in a state of pseudo-equilibrium. The surface concentration of B can therefore be expressed in terms of an equilibrium constant KB for the adsorption-desorption equilibrium of B ... 

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