Rate expressions ammonia synthesis

The term 6 in the previous expression is not determined by direct experiment. It is calculated from the rates of ammonia synthesis, assuming that / nhj = /( n2 H2> NH3> inert K pois), where Pi represents partial pressures, t designates... 

The calculations show that there are few free sites and that the surface may be viewed as a surface nitride with a few vacancies. As the rate of ammonia synthesis may be expressed as a turnover frequency multiplied by the coverage... 

For the synthesis of ammonia, Nj -i- 3H2 —> 2NH3, over an iron catalyst, develop the rate expression for the following mechanism... 

We will list the elementary steps and decide which is rate-limiting and which are in quasi-equilibrium. For ammonia synthesis a consensus exists that the dissociation of N2 is the rate-limiting step, and we shall make this assumption here. With quasi-equilibrium steps the differential equation, together with equilibrium condition, leads to an expression for the coverage of species involved in terms of the partial pressures of reactants, equilibrium constants and the coverage of other intermediates. 

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. 

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. 

Aparicio LM, Dumesic, JA. Ammonia synthesis kinetics surface chemistry, rate expressions, and kinetic analysis. Top Catal. 1994 1 (3—4) 233—52. 

The basic equation most widely accepted to express the kinetics of ammonia synthesis is that of Teml and Pyzbev (1940). It expresses the reaction rate as a function of the partial pressures of the reactants and products ... 

These simplifying assumptions must be adapted to some extent to explain the nature of some reactions on catalyst surfaces. The case of ammonia synthesis on supported ruthenium described in Example 5.3.1 presents a situation that is similar to rule 1, except the rate-determining step does not involve the mari. Nevertheless, the solution of the problem was possible. Example 5.3.2 involves a similar scenario. If a mari cannot be assumed, then a rate expression can be derived through repeated use of the steady-state approximation to eliminate the concentrations of reactive intermediates. 

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. 

Similarly to the concept of the biographical nonuniform surfaces mechanism (7.97) can be used to derive a rate expression in supposition of lateral interactions. Assuming that surface species other than chemisorbed nitrogen are present on the surface in inferior quantities, which is backed by experimental evidences showing that nitrogen adsorption on iron catalysts proceeds at a rate approximately equal to that of ammonia synthesis, the equilibrium constant of step 2 in eq. (7.97) can be expressed, following the general treatment, as... 

V is the rate of nitrogen adsorption and W is the rate of desorption. By assuming that the slow step in the decomposition of ammonia is the rate of nitrogen desorption and that the slow step in the synthesis is the rate of adsorption of nitrogen, one then has a basis for predicting the kinetic expressions for synthesis and decomposition of ammonia over the iron catalysts. 

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. 

As previously mentioned, two types of ammonia synthesis loops exist. For the inert- containing loop, the inert level in the synthesis loop (most often measured at converter inlet) depends on the inert level in the make-up gas, the production of ammonia per unit make-up gas (the loop efficiency), and the purge rate. The inert level in the make-up gas is solely determined by the conditions in the synthesis gas preparation unit. The ammonia production is determined by conditions around the converter, the gas flow (which may be expressed by the recycle ratio), the inlet temperature and pressure, catalyst volume and activity, and converter configuration. 

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

Table 2.5 Reaction mechanism and rate expression for ammonia synthesis...

But this proposal is not so strict scientifically due to the lack of clear definition of activity. The catalytic activity of ammonia synthesis catalyst can be expressed by outlet ammonia concentration of converter, conversion ratio of ammonia, reaction rate and rate constant of kinetics and turnover frequency of ammonia (TOF). 

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 kinetics of the ammonia synthesis have been studied extensively by Haldor Tops0e and others. The kinetic expression used by Tops0e in desiw calculations has been published by Nielsen, Kjaer and Hansen [l . The reaction rate depends on the gas... 

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... 

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. 

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