Adsorption intrinsic rate

The material balance was calculated for EtPy, ethyl lactates (EtLa) and CD by solving the set of differential equation derived form the reaction scheme Adam s method was used for the solution of the set of differential equations. The rate constants for the hydrogenation reactions are of pseudo first order. Their value depends on the intrinsic rate constant of the catalytic reaction, the hydrogen pressure, and the adsorption equilibrium constants of all components involved in the hydrogenation. It was assumed that the hydrogen pressure is constant during... 

Formation of products in paraffin cracking reactions over acidic zeolites can proceed via both unimolecular and bimolecular pathways [4], Based on the analysis of the kinetic rate equations it was suggested that the intrinsic acidity shows better correlation with the intrinsic rate constant (kinl) of the unimolecular hexane cracking than with the apparent rate constant (kapp= k K, where K is the constant of adsorption equilibrium). In... 

Figure 8 shows how the intrapellet concentration profiles vary with time during the course of CO desorption. Both the gas-phase (solid lines) and surface (dotted lines) CO concentration profiles exhibit relatively mild gradients inside the pellet, in contrast to the steep profiles established during the adsorption process. This can be attributed to the fact that the intrinsic rate of desorption is slower than that of adsorption. 

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)... 

What remains is to relate the surface potential to activation potentials for the adsorption/desorption reaction steps. Defining the activation potentials as iji, ijjf for the activation required to overcome the EDL potential for the adsorption, desorption steps, respectively, allows the intrinsic rate constants to be directly related to the rate constants k, k (4), i.e.,... 

Here kgr is the surface reaction rate constant, Rr is the adsorption equilibrium constant for product R, Pr is the partial pressure of R and Kp is the reaction equilibrium constant. At low loading the reaction rate simply becomes proportional to the product of the intrinsic rate constant and the Henry coefficient. 

The intrinsic rate of the reaction is controlled by the rate of adsorption of oxygen on the carbon and is independent of the S02 concentration. 

Prediction of the breakthrough performance of molecular sieve adsorption columns requires solution of the appropriate mass-transfer rate equation with boundary conditions imposed by the differential fluid phase mass balance. For systems which obey a Langmuir isotherm and for which the controlling resistance to mass transfer is macropore or zeolitic diffusion, the set of nonlinear equations must be solved numerically. Solutions have been obtained for saturation and regeneration of molecular sieve adsorption columns. Predicted breakthrough curves are compared with experimental data for sorption of ethane and ethylene on type A zeolite, and the model satisfactorily describes column performance. Under comparable conditions, column regeneration is slower than saturation. This is a consequence of non-linearities of the system and does not imply any difference in intrinsic rate constants. 

Physical adsorption at a surface is extremely rapid, and the kinetics of physical adsorption are invariably controlled by mass or heat transfer rather than by the intrinsic rate of the surface process. Biporous adsorbents such as pelleted zeolites or carbon molecular sieves offer three distinct resistances to mass transfer the external resistance of the... 

The interest in the properties of the chars derived from cellulosic or biomass solid.s extends beyond those associated with thermal transport in the char. Insofar as the char residue from a pyrolysis process must typically be burned, gasified, or put to use as an activated carbon product, there is also a need to examine the porous nature of the char, bi acbvated carbons, the pore structure is key to adsorption performance. In combustion or gasification, the porosity can play a role in determining conversion kinetics in the intrinsic rate controlled or pore diffusion controlled regimes. 

I able 3-3. Intrinsic rate and equilibrium constants for SO4 adsorption on goethite as determined from kinetic and equilibrium measurements (Zhang and Sparks, l990).t... 

In Step 1, the hydrated metal ions lose one H2O molecule and form an intermediate complex with a surface site. The fast relaxation associated with Step 1 was ascribed to simultaneous adsorption/desorption of the metal ions on a major portion of the 7-AI2O3 surface sites. In the second step a metal ion-surface complex is formed that results in the release of a proton. This slow relaxation was attributed to the adsorption/desorption of metal ions on the remaining, multiple type sites of the 7-AI2O3 surface that comprise a small fraction of the total surface sites. Yasunaga and Ikeda (1986) characterized the first type of surface sites as strong sites and the multiple type sites as weak sites. Linearized rate equations relating reciprocal relaxation times to the intrinsic rate constants were developed and validated for the two-step reaction mechani.sm. A plot of the linearized equation for Step 2 (the faster... 

Consider the effect of surface diffusion on the effectiveness factor for a first-order, irreversible, gaseous reaction on a porous catalyst. Assume that the intrinsic rates of adsorption and desorption of reactant on the Surface are rapid with respect to the rate of surface diffusion. Hence equilibrium is established between reactant iii the gas in the pore and reactant adsorbed on the surface. Assume further that the equilibrium expression for the concentration is a linear one. Derive an equation for the effectiveness factor for each of the following two cases ... 

The reaction is reversible and believed to be first order. Also, strong adsorption of hydrogen reduces the rate. The concepts of Chap. 9 suggest that a logical assumption for the form of the rate equation at a catalyst site (an intrinsic rate equation) would be... 

Chap. 8 begins with a discussion of catalysis, particularly on solid surfaces, and this leads directly into adsorption and the physical properties of porous solids. The latter is treated in reasonable detail because of the importance of solid-catalyzed reactions and because of its significance with respect to intrapellet transport theory (considered in Chap. 11). With this background, the formulation of intrinsic rate equations at a catalyst site is taken up in Chap. 9. 

Adsorption processes at natural phase boundaries occur from the aqueous phase containing complex mixtures of different organic and inorganic compounds and they are not in equilibrium. Adsorption behavior of organic molecules can be described by competitive adsorption of the mixture, in which very often less adsorbable materials are present at higher concentrations and strongly adsorbable substances are present at lower concentrations. Since the adsorption process depends on both the adsorption constant and the adsorption kinetics, which include the mass transfer of adsorbable molecules from the bulk phase toward the surface as well as the intrinsic rate of attachment to the surface, the adsorption layer formed is influenced by qualitative and quantitative composition of the complex mixture of adsorbable solutes. 

Kinetic performances of Rh/AljOj and Pt/AljO, catalysts have been examined using the competitive adsorption model. The intrinsic rate constant of NO dissociation k, and the equilibrium adsorption constant of NO X-nq, are considerably higher on RI1/AI2O3 than on Pt/Al203. This result corroborates earlier observations on the adsorption of NO on Rh (111) and Pt (111) surfaces showing that NO dissociates easier on Rh than on Pt [3-5]. 

The intrinsic rate of physical adsorption is very rapid so the overall sorption rate is generally controlled by the diffusional resistances associated with mass transfer to the adsorption site. Commercial zeoUte-based catalysts and adsorbents consist of small (micron-sized) zeolite crystals formed into macro-porous (milUmeter-sized) particles, generally with the aid of a clay binder. Such materials offer at least three and in some cases four distinct mass transfer resistances (see Fig. 10) [35] ... 

Any intrinsic property that influences the conductivity of an electrodematerials system, or an external stimulus, can be studied by IS. The parameters derived from an IS spectrum fall generally into two categories (a) those pertinent only to the material itself, such as conductivity, dielectric constant, mobilities of charges, equilibrium concentrations of the charged species, and bulk generation-recombination rates and (b) those pertinent to an electrode-material interface, such as adsorption-reaction rate constants, capacitance of the interface region, and diffusion coefficient of neutral species in the electrode itself. 

Cumene is cracked in a recycle reactor over commercial H-ZSM5 extrudates. A Thiele modulus approach is used to determine the diffusion coefficient and the intrinsic rate constant. The results are compared to those obtained from pulse experiments. A linear model for diffusion, adsorption and reaction rate is applied for reactants and products. In contrast to literature it is argued that if the Thiele modulus is greater than five, the system becomes over parameterised. If additionally adsorption dynamics are negligible, only one lumped parameter can be extracted, which is the apparent reaction constant found from steady state experiments. The pulse experiment of cumene is strongly diffusion limited showing no adsorption dynamics of cumene. However, benzene adsorbed strongly on the zeolite and could be used to extract transient model parameters which are compared to steady state parameters. 

Table 1 summarises the steady state experiments over the zeolite crystals and pellets. The activation energy for the intrinsic rate constant kmtr was 34.4 kJ/mol. The low value indicates that the adsorption enthalpy is of the same order as the reaction enthalpy, i.e. (ERx ,obs = Ekr + EAds). The diffusion coefficient under steady state conditions was found to be an order of magnitude higher than that calculated from Knudsen diffusion (2x10 cmVs) using an average pore size of 3.8x10 cm measured by BET and a tortuosity factor of 4. The estimated... 

Intrinsic rate = (Kinetic term) x (Driving force term)/(Adsorption term)... 

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