Rate limiting step, ammonia synthesis

A classical example of promotion is the use of alkalis (K) on Fe for the ammonia synthesis reaction. Coadsorbed potassium (in the form of K20) significantly enhances the dissociative adsorption of N2 on the Fe surface, which is the crucial and rate limiting step for the ammonia synthesis5 (Fig. 2.1). 

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. 

Ammonia Synthesis. - Ammonia (NH3) synthesis is another well-known structure-sensitive reaction. The two most widely accepted mechanisms involve adsorption of nitrogen as the rate limiting step. A main question has been whether nitrogen adsorption is dissociative [37,38] or associative [38]. For NH3... 

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. 

Under many conditions the rate-limiting step in urea synthesis is the carbamoyl phosphate synthase reaction. Isolated liver mitochondria will synthesize citrulline from added ammonia under appropriate conditions. The rate of citrulline synthesis can be shown to depend on the intramitochondrial content of acetylglutamate, and both the mitochondrial acetylglutamate content and the rate of citrulline synthesis increase on adding glutamate to the mitochondria. 

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... 

To model a catalytic reaction, some knowledge of the elementary reaction steps must be assumed. For ammonia synthesis it is usually accepted that the dissociative chemisorption of nitrogen is the rate-limiting step, a process which requires two adjacent open sites on the catalyst surface. " Using Langmuir-Hinshelwood kinetics the rate of ammonia synthesis (denoted by r) can be written as... 

The effect of oxygen poisoning in their model is that the activation energy for the rate-limiting step in the synthesis of ammonia will be increased. The reason for this is that the adsorption enthalpy for oxygen is high. Stoltze and N0rskov ... 

The apparent inability to apply this approach to many ammonia synthesis systems could, at first sight, be attributed to the clear deviation of all synthesis catalysts from the main Langmuir assumption that the heat of adsorption of the reacting species is independent of coverage. However, it can also be attributed to the use of simplified LH expressions that do not take adequate account of all the intermediate species. To derive the complete rate expression it is necessary to postulate a full mechanistic pathway with one rate-limiting step. In the case of ammonia... 

The rate-limiting step in the decomposition reaction is a very sensitive function of the surface coverages of the various components and, in particular, of atomic nitrogen. Studies using both single-crystal and polycrystalline platinum and several other transition metals (tungsten, nickel, rhenium, and ruthenium ) have confirmed that the reaction follows the same pathway as the ammonia synthesis reaction on iron. All of the transition metals show broadly... 

While the models of Bowker, Parker, and Waugh and by Trivino and Dumesic do not make a priori assumptions on the nature of the rate limiting step, Stoltze and Norskov make the explicit assumption that the dissociation of N2 is rate limiting. The assumption leads to a considerable simplification in the further treatment of their model. While Bowker, Parker, and Waugh, and Trivino and Dumesic must calculate reaction rates iteratively, the model by Stoltze and Norskov allows the derivation of explicit solutions for the coverages and reaction rates. Further, a number of aspects of the kinetics of ammonia synthesis, such as the activation enthalpy and the reaction orders may be investigated analytically in the model by Stoltze and Norskov. 

One important question about the mechanism of ammonia synthesis is the nature of the rate limiting step. The question about the nature of the rate... 

One famons example of a promoter is the effect that alkali metals have on Fe-based ammonia synthesis catalysts. Figures 10.1 and 10.2 show the effect on the rate of dissociation of Nj and on the total rate. Clearly, part of the effect of adding potassium to the surface is to iuCTcase the rate of the rate-limiting step Nj dissociation. 

The heat of chemisorption is, of course, the energy difference between the chemical bonds formed and those broken. One of the strongest bonds to be broken in dissociative chemisorption on metals is the N-N bond of N2. This chemisorption is known to be rate limiting in ammonia synthesis. Brill et al. reported in 1967 field emission results indicating that N2 adsorption on Fe is strongest on the (111) face." Then-suspicion that this might be the initial step in ammonia synthesis over Fe catalysts... 

Several important conclusions can be drawn from Figure 4.38. It appears that in general a simple catalytic reaction, which includes the dissociation of a diatomic molecule, will have this dissociation as the rate-determining step, when the reaction takes place under conditions close to equilibrium. This agrees well with the ammonia synthesis being dissociation rate-determined, as this process is the prototype of an equilibrium-limited reaction [128]. When the reaction is taking place far from equilibrium, the actual approach to equilibrium becomes unimportant, and the volcano plot very closely follows the volcano defined by the minimum value among the maximal possible rates for all reaction steps. 

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