Rate constants adsorption-desorption

These studies concern 1) activity/selectivity measurements 2) the determination of kinetic rate constants (adsorption, desorption, surface bonding) and 3) investigation of the surface topography. Important questions answered in the last study are 1) What amount of CO molecules is adsorbed on the catalyst surface 2) Where are the molecules on the siuface (e.g., Au particles or support) 3) What is the nature of the siuface chemical bonds ... 

Here, k. and kc are rate constants for desorption (evaporation) and condensation respectively. The sites on die solid at which adsorption takes place were denoted as active sites by Langmuir. 

The rate constants in table 4 for Ru/AlaOs should be considered as initial rate constants since it was not possible to achieve a higher coverage of N— than 0.25. Furthennorc, it was not possible to detect TPA peaks for Ru/AlaOs within the experimental detection limit of about 20 ppm. Ru/MgO is a heterogeneous system with respect to the adsorption and desorption of Na due to the presence of promoted active sites which dominate under NH3 synthesis conditions. The rate constant of desorption given in table 4 for Ru/MgO refers to the unpromoted sites [19]. The Na TPD, Na TPA and lER results thus demonstrate the enhancing influence of the alkali promoter on the rate of N3 dissociation and recombination as expected based on the principle of microscopic reversibility. Adding alkali renders the Ru metal surfaces more uniform towards the interaction with Na. 

The origin of the relationship between Kp and temperature in Eq. (YY) can be seen by reexamining equations (RR) and (SS), which show that Kp is directly proportional to bL, i.e., to the ratio of the rate constants for adsorption and desorption, k, k, . The rate constant for desorption from the surface, k, can be expressed as a function of the heat of desorption, A7/d (Adamson, 1982) ... 

Consequently, they are distributed on the surface randomly even if there is no surface migration. Therefore, in contrast to the discussion of adsorption and desorption processes in Section X, the mechanism (188) needs no assumed rapid surface migration (it is evident, of course, that if the migration occurs, it does not affect the results). The analysis of adsorption and desorption rates given in Section X needs only minor alterations to its application to stage 1 namely, products kbPb> would be substituted for rate constants of desorption on separate surface sites, k, and the fugacity of adsorbed particles I, px for p. Therefore, in analogy to (148) and (157), we obtain... 

Using the dynamic approach for extraction is generally advantageous, especially with respect to partitioning the solvent into the extraction media. This can be highly efficient when fresh solvent is continuously introduced into the extraction cell, that is, the rate constant for desorption need not be large compared with the rate constant for adsorption in order for the target solute to be removed efficiently. 

The obtained expression for cAads can now be used to obtain the reaction rate for B, as shown in Equation (13). If the rate constant of desorption (k i) is much higher than the rate of conversion to the product (k2), cAads can be expressed from the adsorption constant K by cAais - K x cA. ... 

F force G surface activity h Plank s constant k Boltzmann constant ka adsorption rate constant kd desorption rate constant M, Mr molecular weight... 

As we will see below, it may be easier to obtain the desired kinetic results by measuring equilibrium constants first. Then, using the equilibrium constants, one is able to obtain a set of the net rates of adsorption/desorption at various temperatures from the same run, and hence calculate the rate constants with their temperature dependencies. 

The pressure is always very low and re-adsorption can be neglected for this reason. Increasing T causes the rate constant for desorption to increase smoothly but rapidly following the Arrhenius exponential dependence... 

V, is the volume of the solid phase in the catalyst bed, and k are the rate constants of desorption and of adsorption of the sample, 6 is the surface coverage, is the amount of the sample adsorbed per unit volume of the solid phase when 6 = 1, and F is the carrier gas flow rate. 

As a prelude to the development of kinetic rate expressions for heterogeneous chemical reactions, if A reacts with B, for example, then the next step in the mechanism is ha + Ba, forming an activated complex on the snrface. Each reversible step in the seqnence above is characterized by a forward rate constant adsoiption for adsoiption, with units of mol/area time atm, and a backward rate constant A ,desoiption for desorption, with units of mol/area time. The ratio of these rate constants adsorption/ h, desoiption defines the adsorption/desorption equi-... 

AdesHA = heat of desorption AjdHA = heat of adsorption fe A = rate constant of desorption... 

It suggests a reaction rate, where adsorption-desorption and reaction occur, and the reaction is the limiting step. Try to estimate the constants with the following data, assuming that the adsorption-desorption constants of the products are approximately similar [Hill]. 

Comparing this equation with eq.(3.3-19), we see that the parameter g is simply the pre-exponential factor in the Clausius-Clapeyron vapor pressure equation. It is reminded that the parameter g is the ratio of the rate constant for desorption to that for adsorption of the second and subsequent layers, suggesting that these layers condense and evaporate similar to the bulk liquid phase. 

Dobmskin [57] proposed a model for the adsorption equilibria of multicomponent vapor mixtures based on the concept of TVFM and an adsorbed phase model in which the adsorbate-adsorbent interactions predominate over the lateral interaction between adsorbed molecules. The proportions of the component in the adsorbed phase are determined by a statistical distribution based on Frenkel s [70] mechanism and kinetic gas theory [71,72]. In Dobruskin s study, the equilibrium is viewed as a dynamic process in which the average molecular residence time T is the reciprocal of the rate constant for desorption, k. For adsorption of a binary mixture in an elementary volume dW, the ratio of the average times between two components is... 

AS, is die oitropy of adsorption h.ds is the rate constant for adsorption kdR is the rate constant for desorption. 

The parameter a is the sticking probability or accommodation coefficient for adsorption (upon a collision on the surface), and P is the rate constant for desorption. The constant B is called Langmuir constant. At low pressures, the Langmuir isotherm reduces to a linear form, or Henry s law form ... 

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