Reaction Scheme and Rate Expressions

The first step in constructing a micro-kinetic model is to identify all the elementary reaction steps that may be involved in the catalytic process we want to describe, in this case the synthesis of ammonia. The overall reaction is 

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. 

The elementary steps in the kinetic model for ammonia synthesis are  

All coverages of adsorbed species (which, of course, can not necessarily be measured experimentally) can now be expressed as equilibrium constants and partial pressures. The reader may verify that this leads to 

The fraction of free sites follows from the condition that the sum of all the coverages is unity, and hence 

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A more quantitative analysis of the batch reactor is obtained by means of mathematical modeling. The mathematical model of the ideal batch reactor consists of mass and energy balances, which provide a set of ordinary differential equations that, in most cases, have to be solved numerically. Analytical integration is, however, still possible in isothermal systems and with reference to simple reaction schemes and rate expressions, so that some general assessments of the reactor behavior can be formulated when basic kinetic schemes are considered. This is the case of the discussion in the coming Sect. 2.3.1, whereas nonisothermal operations and energy balances are addressed in Sect. 2.3.2. 

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