Temkin equations development

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 ... 

We have already pointed out (see Section I) the similarity of the multiplet theory and the theory of catalysis by Polanyi. The equations of the multiplet theory [(1I.9)-(1I.11)] were given by the author as early as in 1929 Polanyi suggested similar equations in 1934 (35), how ever, for one reaction only—the para-ortho-conversion of hydrogen. In 1957 Temkin (366) developed the Polanyi theory and also obtained Eqs. (II.9) and (II.10), the same as in the multiplet theory. 

It was demonstrated in the early days that nitrogen adsorption is the rate-determining step in ammonia synthesis, and this was the basic assumption used in the development of the Temkin equation. It was also assumed that hydrogen and ammonia have no significant influence on nitrogen adsorption, and that the kinetics of nitrogen adsorption and desorption can be described adequately by Elovich-type expressions, namely. 

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. 

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

Introduction of stoichiometric number concept and linear transformation of the "conventional" QSSA equations (16) to the equivalent system (20) was essentially the major (and, possibly, only) result of theory of steady reactions developed independently by J. Horiuti in 1950s and M. I. Temkin in 1960s. 

It is important to notice that when the concentration of ammonia approaches zero, equation (3.156) cannot apply since r will then approach infinity. For this case Temkin ei at. (1963) have developed equation (3.157) that can be applied under conditions of dilute ammonia concentration. 

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

The derivation above considered a two-step sequence on biographically nonuniform surfaces and followed the treatment first developed by Temkin. For induced nonuniform surfaces the reaction rates of elementary reactions are described by eq. 3.103-3.105. These general equations which take into account all the possible lateral interactions between all the surface adsorbed species on the surface can be applied to treat the same two-step sequence. 

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). 

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. 

The potential energy diagram was therefore modified following suggestions by Ertl, on the basis that, under the conditions of temperature and pressure required for industrial ammonia synthesis, the dissociative adsorption of nitrogen becomes an activated process. The potential energy diagram is reported in Fig. 4.13. While there is no direct experimental evidence for this postulate, it is noteworthy that the same basic assumption was taken by Temkin for the development of his kinetic equation. ... 

Brunauer et al. [29] extended the range of the Eqs. (12), (13), (14), which are the basis for the Temkin-Pyzhev equation. In order to develop an adsorption isotherm, Brunauer et al. subdivided the surface into elements each following (the original) Langmuir isotherm, so that... 

Ozaki et al. also extended the Temkin-Pyzhev equation by using the isotherm developed by Brunauer et al. [27]. 

In a later communication [62], Temkin et al. developed a rate equation covering the complete range of operating conditions including the transition... 

In summary, it is noteworthy that the first workable rate equation for ammonia synthesis was proposed before the second world war by people with very limited experimental resources. The Temkin-Pyzhev equation still is the rate equation of choice for engineering purposes. Further progress in better understanding of the fundamental rate-determining process(es) is still, however, needed in order to develop better catalysts. 

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