Rideal rate law

Problem 9.5 Considering reaction between A and B catalyzed by a solid there are two possible mechanisms by which this reaction could occur. The first is that one of them, say A gets adsorbed on the solid surface and the adsorbed A then reacts chemically with the other component B which is in the gas phase or in solution and is not adsorbed on the surface. The second mechanism is that both A and B are adsorbed, and the adsorbed species undergo chemical reaction on the surface. The reaction rate expression derived for the former mechanism is the Rideal rate law and that for the second mechanism is the Langmuir-Hinshelwood rate law. Obtain simple derivations of these two rate laws. 

Equations (9.25) and (9.27) are the Rideal rate laws for the Ziegler-Natta polymerization. 

Table 9.5 Experimental Values of Adsorption Constants in Langmuir-Hinshelwood and Rideal Rate Laws...

Ziegler-Natta catalyst systems being mostly heterogeneous in nature, adsorption reactions are most likely to occur in such polymerizations and feature in their kinetic schemes (Erich and Mark, 1956). A number of kinetic schemes have thus been proposed based on the assumption that the polymerization centers are formed by the adsorption of metal alkyl species on to the surface of a crystalline transition metal halide and that chain propagation occurs between the adsorbed metal alkyl and monomer. In this regard the Rideal rate law and the Langmuir-Hinshelwood rate law for adsorption and reaction on solids assume importance see Problem 9.4). 

It is worth noticing that equation 27 formally reduces to equation 16 in the limit of low ammonia coverages (0nh3 0). In other words, the dual-site modified-redox SCR rate law predicts ammonia kinetic order less than one and o gen kinetic effects at low temperatures, but becomes equivalent to the well-established Eley-Rideal rate law at T > 250°C, where such effects are indeed negligible. It is also worth stressing that a modified red-ox rate law is more consistent with the mechanism of the standard SCR reaction 1. 

Fig. 11. Step feed and shutoff of ammonia in He + O2 2% vN + H2O 1% v/v + NO 1000 ppm over a V205-W0s/Ti02 catalyst at 175°C. Dashed lines feed NH3 concentration solid thick lines model fitted with the modified redox rate law (MR, equation 27) solid thin lines model fitted with the modified Ealy-Rideal rate law (ER, equation 26) (adapted from Ref. 101).

Derive the probable rate law for the reaction CO + j02 = CO2 as catalyzed by a metal surface assuming (a) an Eley-Rideal mechanism and (b) a Langmuir-Hinshelwood mechanism. 

This mechanism, known as the Eley-Rideal mechanism, has the following rate law ... 

A global multiresponse non-linear regression was performed to fit Eq. (57) to all the runs with both 2% and 6% v/v 02 feed content to obtain the estimates of the kinetic parameters (Nova et al., 2006a). Figure 37 (solid lines) illustrates the adequacy of the global fit of the TRM runs with 2 and 6% 02 the MR rate law can evidently capture the complex maxima-minima NO and N2 traces (symbols) at low T at both NH3 startup, that a simple Eley-Rideal (ER), approach based on the equation... 

The kinetics of the esterification of 1-octanol with hexanoic acid on zeolite BE A was studied by Nijhuis et al. [29], For the acid, a first-order behavior was found, whereas the alcohol showed a negative reaction order of -1. From the data, an Eley-Rideal mechanism was concluded. The acid adsorbs onto the surface of the catalyst and reacts with an alcohol. The adsorption of water, alcohol, ester or ether inhibits the reaction. Hoek [30] found that the adsorption constant of water is more than one order of magnitude higher than those of the other compounds. The rate law given by Nijhuis et al. [29] also includes the equilibrium limitation ... 

Weigert discovered that water is formed if a mixture of CI2, O2, and is irradiated. Sometime later, Norrish and Rideal did experiments at 700 torr total pressure with [H2 ]/ [O2 ] between 0.25 and 4 and found that water formation obeyed the rate law... 

Alkylation reactions, on solid ion exchange resins as heterogeneous Bronsted acids, obey Rideal kinetics (25), as shown in Equation 6 at low pressure (F olefin < 2 atm), where K 01 << 1, the rate law simplifies to Equation 7. 

Both the Rideal and Langmuir-Hinshelwood rate laws are based upon the Langmuir adsorption equation, which is applicable for gas-solid as well as liquid-solid systems where diffusion of the sorbate to the solid surface is not rate limiting (generally true). The basic assumption of the Langmuir adsorption is that adsorption occurs at adsorption sites and all these sites are equivalent. For gas-solid systems, the rate of adsorption, fo, of the gas A is proportional to the gas pressure, pa, and the number of vacant sites, i.e.. 

The rate V of the reaction is now expressed by the current treatment, in terms of the mass action law, as proportional to 0(H2)0(CO2) for the Langmuir-Hinshelwood mechanism and similarly to (7 0(CO2) or C ° 0(H2) for the Rideal-Eley mechanism, depending on the premised adsorption state of the initial system. The rate law is thus obtained according to Eqs. (11.24) as... 

The Hougen-Watson kinetic model that is consistent with the Langmuir-Rideal mechanism can be obtained from the rate law in equations (14-63) and (14-64) via the following modification of each generic term ... 

The kinetic rate law for the Langmuir-Rideal single-site mechanism is... 

In the Eley-Rideal mechanism (ER mechanism) of a surface-catalyzed reaction, a gas-phase molecule collides with another molecule already adsorbed on the surface. The rate of formation of product is expected to be proportional to the partial pressure, p% of the non-adsorbed gas B and the extent of surface coverage, 6a, of the adsorbed gas A. It follows that the rate law should be... 

Figure 2 I. Langmuir s view about the mechanism of the catalytic oxidation of carbon monoxide on platinum, taking place within the monolayer of chemisorbed species. The observed rate law led him to the (erroneous) conclusion of the operation of the Eley-Rideal mechanism.

Eley-Rideal Kinetics (ER)—In line with several literature indications [18, 19], we started from an Eley-Rideal (ER) rate law [1, 3, 5, 12, 19, 22] assuming that the SCR reaction occurs between adsorbed ammonia and gaseous (or weakly adsorbed) NO ... 

Rate law for Eley-Rideal surface-reaction-limited mcchanUm... 

The rate of thiosulfate oxidation on polymer-attached Cu(II)-bipyridine complex was examined in terms of the Langmuir-Hinshelwood model, which is derived from considering the reaction of two different absorbants on the surface, and the Rideal model, which is applicable for the surface reaction of an absorbed molecule with the other substrate species in solution. Assuming that (1) the equilibrium concentration of S,0 and O , represented by A and B, respectively, are established on the catalyst surface (2) the reaction between the two absorbed species is rate-controlling and (3) the reaction is first-order relative to both A and B, a Langmuir-Hinshelwood type of rate law can be derived as ... 

The value of (Ca), calculated from Eq. (65) at 93.0 kPa using the foregoing values of K, and AT, is 0.098 M, which is in good agreement with the experimental data. The kinetics of oxidation of thiosulfate by molecular oxygen in the presence of Cu(II) complex of this polymer-bound ligand can be explained by a Langmuir-Hinshelwood-type rate law, whereas a Rideal-type rate applies only at low concentrations of thiosulfate (< 0.05 M). 

The speed of a reaction between molecules in a film and those in the underlying solution depends on the rate of approach of the latter to the interface. There are two ways of exactly evaluating the latter, one depending, as we have seen in Section II, on the use of the gas laws and the other using the diffusion coefficient of the molecules in solution. The former method w as suggested by Fosbinder and Rideal (16), who used the Hertz expression,... 

To be able to quantitatively describe and predict the aforementioned phenomena and to be able to relate catalyst properties to unit operation performance, a more detailed description of the species involved as well as a better representation of the fundamental processes that are occurring between the bulk fluid and the catalyst surface than that which is currently employed in pseudo-component, lumped parameter, power law models is required. This more fundamental approach to kinetic modelling has been achieved in many other systems where there are only a few components and reactions by using Langmuir-Hinshelwood and/or Eley-Rideal type rate expressions such expressions are usually developed by considering the... 

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