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Fundamentals of Chemical Reaction Kinetics

In homogeneous reacting systems, all the reactants and products are in the same phase. If the reaction involves a catalyst, it is also in the same phase. To determine the rates of reaction, experimental information is needed, which is generated by using properly designed small-scale reactors and experiments. These reaction rates cannot be directly measured, but they are obtained by means of experimental data such as the variation of time with respect to concentration of reactants or products, partial pressures and total pressure, among others.

To obtain the kinetic expression that represents the studied reaction, there are various approaches that correlate the experimental data with the variables that affect them.

When a reaction proceeds, one or more reactants can take part. It can be carried out in either liquid or gas phase, the reaction extent is measured by means of variations of reactants or product properties, or simply the reaction mechanisms are unknown. In any case, it is necessary before starting with the mathematical treatment of the experimental data to know the fundamentals of stoichiometry, thermodynamics and kinetics that will be further used for elucidating the specific mathematical expression for each type of reaction. This chapter is then devoted to introducing the readers to these topics.

1.1 Concepts of Stoichiometry

1.1.1 Stoichiometric Number and Coefficient

A chemical reaction can be represented as follows:

where A, B, R and S are the chemical species, and a, b, r and s are their corresponding stoichiometric coefficients, which are the positive numbers before the chemical formula that balance the reaction.

Eq. (1.1) can be transformed as follows (Chopey, 1994):

or with positive values:

which can be generalized as:

where Ai is the chemical formula and ?i is the corresponding stoichiometric numbers.

Stoichiometric numbers (?i) are numerically equal to stoichiometric coefficients (a, b, r and s), but they have a negative sign for reactants and positive sign for products.

Example 1.1

Determine the stoichiometric coefficients and numbers for the following reaction for synthesis of ammonia:

Solution

According to stoichiometry, the stoichiometric coefficients and numbers are:

1.1.2 Molecularity

Molecularity is defined as the number of molecules of reactants that take part in a chemical reaction. Most of the reactions exhibit a molecularity of one or two, and in rare cases it reaches the value of three (Hill, 1977).

Molecularity is an appropriate concept for a process in which a simple or elemental step is occurring. Reactions in which one or several reactants produce one or several products in a simple path are scarce. For complex reactions, it is necessary to know the molecularity of each individual step of the reaction.

Based on this concept, the chemical reactions can be classified mainly as mono-molecular, bi-molecular and tri-molecular. A mono-molecular reaction involves one molecule of reactant. In a bi-molecular reaction, two molecules of reactants (either the same or different) are combined to form one or more products. Tri-molecular reactions are rare since they need the simultaneous collision of three molecules to produce one or several products. Examples of the different types or reactions according to their molecularity are shown in Table 1.1.

Table 1.1 Chemical reactions with different molecularity.

1.1.3 Reaction Extent

To follow the performance of a chemical reaction, it is necessary to define a parameter which properly represents the conversion of the reactants. In 1920, De Donder (1920) introduced the concept of reaction extent (?), by considering that the change in the number of moles of the chemical species is directly related to the stoichiometric number as follows:

or, in differential form:

For all chemical species, these equations can be generalized in the following manner:

Defining the parameter ?, as the reaction extent:

The integration of Eq. (1.6) gives:

It is then observed that if a moles of A1 react with b moles of A2 to produce r moles of An-1 and s moles of An, the reaction extent ? is equal to 1. Therefore, in general, it can be stated that ?a moles of A1 react with ?b moles of A2 to produce ?r moles of An-1 and ?s moles of An.

1.1.4 Molar Conversion

The molar fractional conversion (xi) is an intensive normalized parameter referred preferably to the limiting reactant; it is defined as the fraction of such a reactant that is transformed into products (Froment et al., 2010):

where .

Subindex "o" refers to the number of moles at zero time (i.e. the beginning of the reaction). Conversion can be correlated with reaction extent by means of Eqs. (1.7) and (1.8):

where:

The maximum reaction extent (?imax) can be calculated from Eq. (1.11) for the maximum conversion value :

which implies that the minimum and maximum values of ?i are in the following range:

1.1.5 Types of Feed Composition in a Chemical Reaction

When a chemical reaction involves more than one reactant, the feed composition is different depending on the relative initial concentrations of the chemical species:

• Stoichiometric feed composition: This occurs when the ratio between the stoichiometric coefficients of the reactants is equal to the ratio between the amount of moles or the molar initial concentrations of reactants.
• Non-stoichiometric feed composition: This is when the ratio between the stoichiometric coefficients of the reactants is different from the ratio between the amount of moles or the molar initial concentrations of reactants.
• Equimolar feed composition: This is when the same amount of reactants are used at the beginning of the reaction to keep the ratio between the amount of moles or the molar initial concentration equal to unity no matter the stoichiometric coefficients of the reaction.
• Reactant in excess: This is when the ratio between the amount of moles or the molar initial concentrations of the reactants with respect to the limiting reactant is much higher than the ratio between the stoichiometric coefficients.

Some feed compositions can be considered close to the stoichiometric feed composition, and this happens when the ratio between the amount of moles or the molar initial concentrations of reactants is more or less the same as the ratio between the stoichiometric coefficients.

If at the beginning of the reaction there are inert components, although they are not reacting, they must be considered to define the type of feed composition.

Example 1.2

Define the different feed compositions for the following reaction of formation of nitrogen dioxide:

Solution

If a feed consists of 4 moles of NO and 2 moles of O2, the ratio of moles...