Temkin kinetic equation

Annable, D., Application of the Temkin kinetic equation to ammonia synthesis in large-scale reactors, Chem. Eng. Sci. 1(4), 145-153 (1952). 

D. Annable, Application of the Temkin Kinetic Equation to Ammonia... 

In the Temkin kinetic equation a can usually be assumed to be 0.5, although values as high as 0.67 have been reported for magnetite, while for metals such as nickel and cobalt it may drop to as low as 0.1. 

On inhomogeneous surfaces where adsorption obeys the Temkin isotherm, an exponential factor will appear in the kinetic equation ... 

Figure 13.6 Step feed and shut-off of 700 ppm NH3 in He -I- 700 ppm NO -I- l%v/v Oj over VjO., WO,/liO, model catalyst at 220 C. Dashed lines, inlet NH, concentration solid lines, model fit with Temkin-type coverage dependence and modified Langmuir kinetics, Equation (13.10). (Adapted from ref. [52]).

As to when to use Frumkin s approach or that of Temkin, as long as one is willing to accept the approximation leading to Eq. (7.156), it does not matter as far as the resulting kinetic equations (see below) are concerned. However, the thought process behind Frumkin s equation is to take account of the interaction between the adsorbed entities and that behind Temkin s is to allow for the difference in adsorption energies in different sites on the surface equation. 

This equation is independent of the order in which the steps are numbered. Temkin suggested an algorithm on the basis of eqn. (30) to obtain an explicit form of the steady-state kinetic equations. For linear mechanisms in this algorithm it is essential to apply a complex reaction graph. In some cases the derivation of a steady-state equation for non-linear mechanisms on the basis of eqn. (30) is also less difficult. 

It is almost surprising that in spite of this a simple kinetic equation has been formulated which gives a good approximation to experimental data under widely different conditions of temperature, pressure, gas composition, and space velocity and for different types of catalysts. An equation has been suggested by Temkin and Pyzhev (62,63) and the simple form in which it was originally presented is given in Equation (1)... 

When reactants or intermediates are adsorbed, the rate of the reaction may no longer be related to the concentration by a simple law. This situation is best understood where a reactant is nonspecifically adsorbed in the outer -> Helmholtz plane. The effect of such adsorption on the electrode kinetics is usually termed the -> Frumkin effect. Physical and chemical adsorption on the electrode surface is usually described by means of an -> adsorption isotherm and kinetic equations compatible with various isotherms such as the - Langmuir, -> Temkin, -> Frumkin isotherms are known. 

Tims, we reach the (happy) conclusion that the kinetic equations are independent of the shape of the variation of AGq with 0, making the treatment of electrode kinetics in terms of the Temkin isotherm much more general. In fact, we could have used any unspecified function f(0) in Eq. 291. The result is the same, as long as the function chosen... 

We saw earlier (cf. Section 19) that the potential dependence of adsorption of intermediates formed by charge transfer affects the kinetics of electrode reactions. We have worked out the kinetic parameters for a few mechanisms under so-called Langmuir and Temkin conditions (i.e., when the Langmuir and the Temkin isotherms are applicable, respectively). Here we shall derive the appropriate kinetic equations for the combined adsorption isotherm. 

The use of cyclic graphs proved to be very fruitful for the deduction of kinetic equations and in the analysis of kinetic data for linear mechanisms. It should also be mentioned that Temkin s kinetic graphs provide a unique approach to both catalytic and non-catalytic reactions. In the latter case, one of the graph vertices contains a zero intermediate of concentration 1 not included in the kinetic equations. Thus, the use of kinetic graphs for non-catalytic reactions is justified only for mechanisms with at least one intermediate. 

Catalyst systems in general can contain several reaction routes as discussed in chapter 4. The same is valid also for reaction with organometallic complexes. An example is the hydrofonnylation reaction (Figure 5.23). A general form of the kinetic equation was derived by Temkin in the following way... 

Nothing more will be said about the synthesis data except to point out that one numerical change has to be made in the kinetic equation according to a much later paper by Anderson and Tour ( 32). This has yet to be applied to the FNRL data. The Temkin-Pyzhev equations without this added refinement represent the data for 3 1, 1 1, and 1 3 H N fairly well. ... 

As we have mentioned, the Elovich equation for adsorption kinetics is associated mainly with the systems in which the equilibrium adsorption isotherm is described by Temkin s equation [3],... 

Thus. Eq. (94) looks something like the Elovich equation and was developed here as the kinetic equation corresponding to a Temkin isotherm for adsorption equilibria. This agrees with common experimental observations. We see that the Elovich equation should apply at conditions where the desorption rate can be neglected, since we developed it by generalizing the adsorption rate term in Eq. (77) and neglecting the desorption rate term in Eq. (78). 

Let us address now the issue of identifying the kinetic significance of individual steps. It is easy to see that according to equation (2.7) the rate of each reverse reaction may be estimated from experimentally measured data on the rates of reaction paths. Hence, the role of (y -s) steps is revealed. It should be mentioned that in the framework of pathway theory, M.I. Temkin [18] offers a method to derive the kinetic equations. This is when the rate on reaction path, and further according to (2.6) the rate of multistep reaction, is expressed through the rate constants of individual steps and characteristics, and more often concentrations of the initial substances, determined in kinetic experiments. In the final kinetic model the dependency on the rate constants of steps specifies their kinetic participation in the total chemical process [17]. 

Whatever is the mechanism of OHad and Oad formation, the principal point of this adsorption theory is that Pt surface atoms are stable in their positions in the lattice and the integrity of the Pt lattice is retained after an adsorption-desorption cycle in the voltammetry studies. The formation of adsorbed layer is described quantitatively by adsorption isotherms at equilibrium, e.g., Temkin or Frumkin adsorption isotherms and corresponding kinetic equations such as the Elovich equation. Intrinsic to the adsorption theory is the concept of the maximum surface concentration corresponding to monolayer coverage by the ad-particles on all available adsorption sites. " ... 

This uncertainty makes the kinetic analysis in terms of Frumkin and Temkin adsorption isotherms also uncertain. As long as there is no clear evidence to the contrary, it may be safer to rely on a simple form of a kinetic equation consistent with the Langmuir adsorption isotherm. Therefore, it is usually accepted that in not too concentrated acids the OER occurs on Pt according to... 

The kinetic behavior corresponding to this equation is often referred to as Temkin kinetics in relation to the Temkin isotherm [M. I. Temkin, Zh. Fiz. Khim. 15, 296 (1941) see also A. N. Frumkin, Z. Phys. Chem. 116, 466 (1925)], but the latter refers to heterogeneity rather than interaction effects with regard to the origin of the exp - rdj) term. 

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. 

For an overall reaction involving multi-elementary steps, Temkin formula can be used for the calculation of kinetics although it is very complicated. If a rate determining step is existed, the kinetic equations could be derived simply by a two-step mechanism. Two-step sequence is a simple method and can be used to obtain a better kinetic expression even though the understanding for reaction mechanism is not complete. 

It can be seen from the above-mentioned discussion that the Temkin s theory of catalytic reaction kinetics on heterogeneous surfaces is confirmed not only by overall reaction kinetic data of ammonia synthesis, isotherms and adsorptive rates of nitrogen on iron catalysts, more importantly, perhaps, but also some very useful generalization results derived from this theory. For instance, Temkin s equation is obtained based on two steps or simplified two steps mechanism. So, it can apply to any kind of catalytic reactions. The problem is Are some simplifications required by reasonable formation of two step mechanism, and can the assumption of rate determining step be made for non-uniform surface The answer of Temkin s theory is positive, and especially Temkin s theory of catalytic reaction kinetics on non-uniform plays an important role in solving the selection and improvement of catalysts. 

The rate constant ki or in Temkin-Pyzhev kinetics equation, r = klfN2fkANHs - k2fNHjHA-... 

On iron catalyst, the classical ammonia synthesis reaction kinetics equation of Temkin-Pyzhev is expressed as (with fugacity express when a = 0.5) ... 

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... 

Ammonia synthesis is a relatively simple reaction without the complication of any secondary reaction product, and is especially suitable for a theoretical approach to its kinetics. In fact, the most used kinetic equation for ammonia synthesis was developed by Temkin on the basis of theoretical assumptions about 50 years ago and is still used successfully by chemists and engineers. 

While the Temkin equation has found wide application during the last fifty years, many other kinetic equations have also been developed using both theoretical and practical approaches. 

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