Temkin rate equation

The Temkin rate equation for NH3 synthesis is based on the 2-step sequence provided in Illustration 8.1 and it is given by equation 2 in that Illustration. With the information given there, i.e., m = 1/2, verify that equation 3 ean be derived and that the listed values of k and k are obtained. 

The assumption that nitrogen adsorption was the rate-limiting step of ammonia synthesis had already been applied in the derivation of the Temkin rate equations, which have proved to be quite successful in describing the kinetics of industrial ammonia synthesis provided that the empirical parameters included were properly selected. This formalism also includes the nonuniformity of the surface, viz. the variation of the adsorption parameters with coverage. As was pointed out by Boudart, integration of the rates over this (assumed) distribution yields an expression for the overall turnover rate that is interestingly rather similar to the equation which results for a uniform surface (modeled by Langmuir kinetics) with... 

Smirnov et conducted experiments at ambient pressure and suggested a modification of the conventional Temkin rate equation of ammonia synthesis (see Chapter 7). This equation was later generalized by Smimov to cover higher pressures. The expression was... 

The Temkin-Pyzhev equation deseribes the net rate of synthesis over promoted iron eatalyst as ... 

Develop the rate equation of Temkin Pyzhev for the rate of the reaction, N2 (A) + 3H2(B) > 2NH3(C), on these assumptions ... 

Information on the steps in a reaction mechanism can be extended significantly by isotopic tracer measurements, especially by transient tracing [see Happel et al. (54,55)]. Studies by Temkin and Horiuti previously referenced here have been confined to steady-state isotopic transfer techniques. Modeling with transient isotope data is often more useful since it enables direct determination of concentrations of intermediates as well as elementary step velocities. When kinetic rate equations alone are used for modeling, determination of these parameters is more indirect. 

Changes with time in the isotopic exchange reaction rate between H2 and HDO(v) over a hydrophobic Pt-catalyst induced by the addition of HN03 were studied experimentally The HN03 poisoning was found to be reversible and was well explained in terms of the competitive adsorption of HNO, with H2 or HDO onto the catalytic active sites. The adsorption equilibrium for HN03 could be expressed by the Frumkin-Temkin equation and the time evolution of the activity was well expressed by the Zeldovich rate equation. 

This is the Frumkin-Temkin adsorption equation considering adsorption heat,7). Substituting Eq.(l I) and Eq,(l6) into Eq.(19), we get a normalized reaction rate at a poisoned steady state as follows. 

The principal application of yield ratio equations is in network elucidation, to be discussed in Section 7.3.2. An additional example will be given in that context. Further examples for establishment of yield ratio equations and their application in network elucidation can be found in Temkin s book on reaction networks [24], although not under that name. Also, in mathematical modeling, simple algebraic yield ratio equations can sometimes be substituted for rate equations, which may be differential (see Section 11.2). 

The numerical values of the Tafel slope and reaction order will depend on the value of p (just as they both depend on the value of P), but the form of the rate equations is not changed. The same is true for any mechanism, and the use of the same symmetry factor in Eq. 5D and Eq. 171 does not restrict the validity or generality of the rate equations derived under Temkin conditions. 

Ivanovskii et al. (1964) found that this expression adequately describes experimental rate data for the shift reaction from 10 to 30 atm and 350°C. The activation energy for the reaction was found to be 36 kcal/mol indicating no diffusional limitations. Sen et al. (1964) used the rate equation of Kul kova and Temkin (eq. 3.125) to correlate kinetic data. Their activation energies of 25.1 to 46.0 kJ/mol (6 to 11 kcal/mol) appear to indicate diffusion control in the shift reaction. 

Kinetic model (2) This was developed by Dyson and Simon (1968) in which the rate equation is slightly modified from that of the Temkin equation and which is based on activities instead of partial pressures ... 

Temkin et al. (1963) developed another rate equation where the intrinsic rate is given by ... 

Adopting the mechanism involving steps (VII.2)-(VII.7) and introducing special assumptions in order to account for the heterogeneity of the surface, Temkin and Pyzhev (73) have deduced the rate equation... 

Based on the experimental data which covered the pressure range from below 1 atm up to 500 atm, it was proposed that near equilibrium, the reaction rate is described by the following equation, which is often referred to in the literature as the Temkin-Pyzhev equation... 

In the design of synthesis facilities, the rate at which the ammonia is formed has to be considered The most widely used equation for the intrinsic rate of reaction is the Temkin-Pyzher equation (11) ... 

The rate equations used in these simulations is that proposed by Temkin and Pyzhev [118] ... 

Consider the scheme given above [equations (64)-(66)] for formic acid oxidation. The rate-determining step (65) may be regarded as an adsorption step, since it results in an increase in the number of sites occupied on the surface. The corresponding rate equation, under Temkin conditions will be... 

Assuming that step (88) is rate-determining, and following the treatment used previously with 0qh negligible but 0[hcoohi+ in the Temkin region, the rate equation is of the form... 

For Temkin conditions, the rate equation for (92) rate-determining... 

Under Temkin conditions the rate equation may be written as... 

Under the assumption that dissociative nitrogen chemisorption is the ratedetermining step and that the heat of adsorption varies linearly with coverage, Temkin and Pyzhev (18) derived their famous and widely used rate equation for the kinetics of ammonia synthesis ... 

A logarithmic value of the reaction-rate constant taken from Temkin-Pyzhev equation as a function of reciprocal temperature for the catalysts pressed at different pressures is presented in figure 1. This function is nonlinear, the reason for this being an increase of the diffusion effects together with increasing temperature. 

One of the first rate equation for engineering purposes was published by Temkin and Pyzhev (1940) ... 

Temkin-Pyzhev equations mentioned above was in agreement with a number of kinetic measurement made on various catalysts such as Mo, W, Tc, Ru, Os and promoted Fe. One characteristic feature of ammonia synthesis rate is the retardation by the product ammonia, and reasonably explained by the Temkin theory. The assumption of rate determining step is also supported by the chemisorption of nitrogen. 

The rate equation derived from Temkin equation can also be written in a similar... 

The third assumption of Temkin. Prom the preceding relations, we can now relate the four rate constants in the rate equation (2.120) to the standard affinity of adsorption. So, the third assumption proposed by Temkin is that Bornsted transfer coefficient is the same for the two chemically similar steps (e.g., adsorption and desorption) ... 

The first application of Temkin theory in history was on cataljdic reaction for ammonia synthesis on iron catalyst. The famous reation rate equation of Temkin-Pyzhev was obtained, corresponding to the overall reaction ... 

An attempt was made by Ozaki et al to verify the mechanism, on which the Temkin-Pyzhev equation was derived, by comparing the rate of the following two reactions obtained on the same catalyst ... 

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