Temkin-Pyzhev rate expression

As an example, the Temkin-Pyzhev rate expression for ammonia synthesis reproduces the experimentally observed kinetics quite well. However, this rate expression was originally derived from a proposed mechanism which had both the wrong key intermediates and the wrong rate-limiting step. 

Table 8.1. Comparison of experimental and theoretical rate parameters in the Temkin-Pyzhev rate expression for NH3 synthesis (Equation 2 with m = 1 /2).

The Temkin and Pyzhev rate expression (Annable, 1952) is used, given by... 

This agrees with the experimentally found equation for n = 0.5. These rate laws were formerly derived on the assumption of surface heterogeneity according to the scheme first put forward by Temkin and Pyzhev (39) for the ammonia synthesis. As shown by one of us (40) the assumption of heterogeneity is unnecessary for the derivation of the rate expression even in that case. 

Numerous studies of the kinetics of ammonia synthesis and decomposition have been made. With a few exceptions, work has tended to show that the slow step in the synthesis of ammonia is the chemisorption of nitrogen and the slow step for the decomposition is the desorption of nitrogen. Furthermore, it turns out that the decomposition and synthesis of ammonia usually involve in the rate expression a term where y/x is close to 1.5. In 1940, Temkin and Pyzhev derived an equation consistent with both of these observations [M. I. Temkin and V. Pyzhev, Acta Physiochim. U.R.S.S. 12, 327 (1940)]. It has formed the basis for most of the kinetic treatments of ammonia synthesis and decomposition in recent years. 

In its simplified form (Temkin and Pyzhev), the expression of the conversion rate can be represented by the network of cnrves in Fig. 1.17. An examination of this graph shows that, to obtain a maximum reaction rate, irrespective of the conversion, the reactor must be designed to achieve the temperature gradient which, at any point, serves to reach these optimal values. 

It was early recognised that the rate limiting step in the ammonia synthesis is the dissociative adsorption of nitrogen (23) and that hydrogenation proceeds at a much faster rate (24). Temkin and Pyzhev (25) proposed a rate expression. 

The most widely known rate expression for ammonia synthesis was provided by Temkin in the early 1940s (Temkin and Pyzhev, 1940) ... 

Based on Temkin-Pyzhev mechanisms (steps 1- 3), the rates for ammonia decomposition can be expressed by Eq. (2.27), and its kinetic parameters calculated from equation V = fc (PnH3) /(Eh2) are given in Table 2.7. The value of parameter n/m in Table 2.7 is about 3/2, demonstrating that the Temkin Pjrahev mechanisms can be used for most metal catalysts, such as Re, Fe, Co, Ni, Ru and Rh, at the common conditions of ammonia decomposition. 

The well-known experimental rate expression for ammonia synthesis on a doubly promoted iron catalyst was obtained by Temkin and Pyzhev in 1940 [15], i.e.. 

The Temkin and Pyzhev equation expressed above was in agreement with a number of kinetic measurement made on various catalysts as summarized in Table 3.8 for the synthesis and in Table 3.9 for the decomposition. One characteristic feature of the ammonia synthesis rate is the retardation by the product ammonia, and this is reasonably explained by the Temkin theory. The basic assumption of the rate-determining step, N2 chemisorption was also supported. 

The rate equation of ammonia decomposition was expressed in Eq. (7) according to the Temkin-Pyzhev mechanism (Eq. 1-3). The observed parameters in Table 3.9 show that n/m values are mostly 3/2, which indicates that the Temkin-Pyzhev mechanism is applicable on most catalysts (Re, Fe, Co, Ni, Ru and Rh) under normal ammonia decomposition conditions. 

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