Desorption rate constant

Derive Eq. XI-IS, assuming a Langmuir adsorption process described in Eq. XI-2, where ka and kd are the adsorption and desorption rate constants. Treat the solution... 

Now, if (kd) is the desorption rate constant, then the mean desorption time (td) for... 

They varied only the values of the adsorption and desorption rate constants of the reaction intermediate B, and by using the simplest Langmuir kinetics, they calculated time-concentration curves of compounds A, B, and C shown in Fig. 5. Also from this example, which does not consider any step as clearly rate determining, it is evident how very different concentration versus time plots can be obtained for the same sequence of surface reactions if adsorption and desorption of the intermediate B proceed by different rates, which are, however, comparable with the rate of surface reactions. In particular, the curves in the first and second columns of Fig. 5 simulate the parallel formation of substances B and C, at least... 

A reaction with a high activation energy tends to have a weaker interaction with the surface and hence will have enhanced mobihty that is reflected in a larger activation entropy. For this reason, the pre-exponents of surface desorption rate constants are lO — lO larger than the pre-exponents of surface reaction rates. 

In order to extract adsorption and desorption rate constants from these data. It Is necessary to adopt a model. The normal... 

B.) In steady state, the mobile pool of nuclides is constant. For a long-lived nuclide (solid circles), the adsorbed abundances are determined by exchange with the groundwater. For a short-lived isotope that has a decay constant that is comparable to the desorption rate constant k i, decay of sorbed atoms is a significant flux, and so the steady state sorbed abundance is lower (see Eqn. 3). 

Krishnaswami S, Graustein WC, Turekian KK, Dowd F (1982) Radium, thorium, and radioactive lead isotopes in groundwaters application to the in-situ determination of adsorption-desorption rate constants and retardation factors. Water Resour Res 6 1663-1675 Krishnaswami S, Bhushan R, Baskaran M (1991) Radium isotopes and Rn in shallow brines, Kharaghoda (India). Chem Geol (Isot Geosci) 87 125-136 Kronfeld J, Vogel JC, Talma AS (1994) A new explanation for extreme " U/ U disequilibria in a dolomitic aquifer. Earth Planet Sci Lett 123 81-93... 

It occurs via two adjacent adsorbed NO molecules, leading to an adsorbed dinitrosyl species. These last two co-adsorbed NO species made the two N-O bonds weaker, and the successive two N-O bond scissions led to N2. According to a general kinetic model [12], the NzO intermediate can desorb before dissociating to N2, if the desorption rate constant, kdes, is higher than the reaction (dissociation) rate constant, k, as presented in the following set of rate constants (Figure 5.2) ... 

Sorption (k -Desorption (k2) Rate constants desorption rate constant of 0.018 d 1 with t,/2 = 38.5 d from sediment under conditions mimicking marine disposal (Zhang et al. 2000). 

Cycled Feed. The qualitative interpretation of responses to steps and pulses is often possible, but the quantitative exploitation of the data requires the numerical integration of nonlinear differential equations incorporated into a program for the search for the best parameters. A sinusoidal variation of a feed component concentration around a steady state value can be analyzed by the well developed methods of linear analysis if the relative amplitudes of the responses are under about 0.1. The application of these ideas to a modulated molecular beam was developed by Jones et al. ( 7) in 1972. A number of simple sequences of linear steps produces frequency responses shown in Fig. 7 (7). Here e is the ratio of product to reactant amplitude, n is the sticking probability, w is the forcing frequency, and k is the desorption rate constant for the product. For the series process k- is the rate constant of the surface reaction, and for the branched process P is the fraction reacting through path 1 and desorbing with a rate constant k. This method has recently been applied to the decomposition of hydrazine on Ir(lll) by Merrill and Sawin (35). 

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 expected areas of future expansion of EFLC are in the separation of highly polar solutes. Mixtures of 61.7/27.7/10.6 and 55.7/25/1/19.2 mol ratio methanol/H20/C02 were predicted to have dielectric constants of 38 and 34 [28], respectively. Ion-exchange EFLC should be viable in these and other higher polar EFL mixtures, such as acetontrile/H20/C02 and THF/H2O/CO2 mixtures. Ultra high-speed gradient separations may be possible in EFLC as a result of the fast desorption rate constants for solutes under EFLC conditions. 

Here /jr is the desorption rate constant for R. Another rate expression that is often appHcable is when kinetics are controlled by impact of gas phase A on adsorbed B for the A -i- B R reaction. For this case ... 

In a sediment system, the hydrolysis rate constant of an organic contaminant is affected by its retention and release with the sohd phase. Wolfe (1989) proposed the hydrolysis mechanism shown in Fig. 13.4, where P is the organic compound, S is the sediment, P S is the compound in the sorbed phase, k and k" are the sorption and desorption rate constants, respectively, and k and k are the hydrolysis rate constants. In this proposed model, sorption of the compound to the sediment organic carbon is by a hydrophobic mechanism, described by a partition coefficient. The organic matrix can be a reactive or nonreactive sink, as a function of the hydrolytic process. Laboratory studies of kinetics (e.g., Macalady and Wolfe 1983, 1985 Burkhard and Guth 1981), using different organic compounds, show that hydrolysis is retarded in the sohd-associated phase, while alkaline and neutral hydrolysis is unaffected and acid hydrolysis is accelerated. 

Wolfe (1989) suggested a model to describe abiotic reduction in sediments, where a nonreactive sorptive site and an independent reactive sorptive site are considered. The nonreactive sorptive sink is consistent with partitioning of the contaminant to the organic carbon matrix of the solids. The model is described by Fig. 13.5 where P S is the compound at the reactive sorbed site P is the compound in the aqueous phase S and S are the sediments, P S is the compound in the nonreactive sink k, k , k , and k are the sorption-desorption rate constants, and k, k, and k are the respective reaction rate constants. If the reaction constants k and k are neglected, two rate-limiting situations are observed transport to the reactive site and reduction at the reactive site. The available kinetic data, however, do not allow one to distinguish between the two mechanisms. 

Adsorption and desorption reactions of protons on iron oxides have been measured by the pressure jump relaxation method using conductimetric titration and found to be fast (Tab. 10.3). The desorption rate constant appears to be related to the acidity of the surface hydroxyl groups (Astumian et al., 1981). Proton adsorption on iron oxides is exothermic potentiometric calorimetric titration measurements indicated that the enthalpy of proton adsorption is -25 to -38 kj mol (Tab. 10.3). For hematite, the enthalpy of proton adsorption is -36.6 kJ mol and the free energy of adsorption, -48.8 kJ mol (Lyklema, 1987). 

The homogeneity of the surface should be such that the free-energy changes and the adsorption-desorption rate constants associated with the chromatographic process on the molecular level fall within a narrow range. 

If the desorption rate constant K is less than the value given in eqn (12.37), the stationary-state locus (whether for extent of conversion or for reaction rate as functions of the reactant partial pressure p) displays multiplicity, as shown in Fig. 12.3. As the desorption rate increases, the range of multiple solutions decreases and vanishes when (12.37) is satisfied. For larger desorption rates, the reaction rate and extent of coverage increase monotonically with partial pressure. 

Although this set of equations has four parameters, it will be enough to demonstrate that multiple stationary states and sustained oscillatory responses are possible to consider variations in the dimensionless reactant partial pressures p and r, with fixed values for the desorption rate constants k1 = 0.001 and k2 = 0.002. 

With the values of the dimensionless desorption rate constants used above, k1 = 0.001 and k2 = 0.002, condition (12.64) describes two curves in the p-r parameter plane. These are shown in Fig. 12.6, which also gives their relative location with respect to the loci of turning points (i.e. where det(J) = 0) which mark the boundaries of the region of multiplicity. 

We now have a total of six parameters four from the autonomous system (p, r0, and the desorption rate constants k, and k2) and two from the forcing (rf and co). The main point of interest here is the influence of the imposed forcing on the natural oscillations. Thus, we will take just one set of the autonomous parameters and then vary rf and co. Specifically, we take p = 0.019, r0 = 0.028, fq = 0.001, and k2 = 0.002. For these values the unforced model has a unique unstable stationary state surrounded by a stable limit cycle. The natural oscillation of the system has a period t0 = 911.98, corresponding to a natural frequency of co0 = 0.006 889 6. 

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