Order of an elementary reaction

The order of an elementary reaction is defined by the number of individual atoms or molecules involved in the reaction. The concept of overall reaction order can only be applied to single-term, simple, product rate equations such as... 

With certain exceptions, discussed below, we can legitimately assume that the order of an elementary reaction indicates the number of molecules which enter into reaction, i.e.,.that the order and the molecularity are the same. For example, if an elementary reaction is of the first order with respect to a reactant A and of the first order with respect to another substance B, the conclusion is that the reaction... 

The most commonly used method of identifying a composite reaction is via an examination of the experimental rate equation. As discussed in Section 7.1, the experimental overall order of an elementary reaction is the same as its moleculaiity. 

The order of a reaction with respect to a component is the exponent to which the concentration of the components influencing the rate of the reaction are to be raised in order to get the rate expression. The order of the reaction is the sum of the orders with respect to all the components. The basic assumption of mass action kinetics is that the orders of an elementary reaction with respect to the components are given by the stoichiometric coefficients or molecularities as in (1.2). 

In contrast with the rate expressions for stoichiometric reactions, which must be obtained empirically, the rate expressions for elementary reactions can be written down by inspection. The kinetic order of an elementary reaction is equal to its molecularity, and is thus limited to the positive integral values 1, 2, and 3. For example, the order of a bimo-lecular reaction is 2 because for the reaction to occur both reactants must interact via a collision. The maximum possible bimolecular reaction rate is the collision rate, which is proportional to the product of the concentration of each species, making the reaction first order with respect to each species, and second order overall. The rate of the elementary reaction between the hydroxyl radical and molecular hydrogen, to form water and atomic hydrogen. 

The Arrhenius equation relates the rate constant k of an elementary reaction to the absolute temperature T R is the gas constant. The parameter is the activation energy, with dimensions of energy per mole, and A is the preexponential factor, which has the units of k. If A is a first-order rate constant, A has the units seconds, so it is sometimes called the frequency factor. 

Molecularity must be integral, but order need not be there is no necessary connection between molecularity and order, except for an elementary reaction the numbers describing molecularity, order, and stoichiometry of an elementary reaction are all the... 

The exponents i and s in equations 15.13 and 15.14, referred to as the order of integration and overall crystal growth process, should not be confused with their more conventional use in chemical kinetics where they always refer to the power to which a concentration should be raised to give a factor proportional to the rate of an elementary reaction. As Mullin(3) points out, in crystallisation work, the exponent has no fundamental significance and cannot give any indication of the elemental species involved in the growth process. If i = 1 and s = 1, c, may be eliminated from equation 15.13 to give ... 

Under this treatment, the reaction order of an elementary unimolecular or bimolecular reaction must identify with molecularity, and K is related in Equation 9.3 to the standard molar free energy difference, AG, between reactants and transition state (a hypothetical construct comprising one mole of transition structures, see below) ... 

As seen in Table 2.1, the overall order of an elementary step and the order or orders with respect to its reactant or reactants are given by the molecularity and stoichiometry and are always integers and constant. For a multistep reaction, in contrast, the reaction order as the exponent of a concentration, or the sum of the exponents of all concentrations, in an empirical power-law rate equation may well be fractional and vary with composition. Such apparent reaction orders are useful for characterization of reactions and as a first step in the search for a mechanism (see Chapter 7). However, no mechanism produces as its rate equation a power law with fractional exponents (except orders of one half or integer multiples of one half in some specific instances, see Sections 5.6, 9.3, 10.3, and 10.4). Within a limited range of conditions in which it was fitted to available experimental results, an empirical rate equation with fractional exponents may provide a good approximation to actual kinetics, but it cannot be relied upon for any extrapolation or in scale-up. In essence, fractional reaction orders are an admission of ignorance. 

The order of a reaction is derived from an empirical reaction rate equation the molecularity refers to a molecular mechanism and hence to a theoretical model of a certain elementary step in a reaction. For example, it appears that in the reaction between iodine vapour and hydrogen there is a single elementary step involving the collision of tioo molecules (Hg and Ig) and their emergence as two molecules of HI. This is accordingly a 6 molecular reaction. The molecularity of an elementary reaction is defined as the smallest number of molecules which must coalesce prior to the formation of the products. The term does not apply to processes which consist of a succession of elementary steps, such as chemical reactions very often are. Thus, the oxidation of an iron(II) salt by a permanganate,... 

Order follows from the stoichiometry of the reactants in an elementaiy reaction. Note that products do not appear in the rate law of an elementary reaction. See Table 13.3 in the text. 

The reaction orders are the same as the stocheiometric coefficient in the case of an elementary reaction only in most cases they must be determined experimentally and are valid in the window of experimental conditions. 

Consider acUiorbates which cover one tenth of their 10 cm phj i-cally identical sites on a catalyst, as one would say of moderate coverage. The thickness of the surface phase ought to be of the order of magnitude of 10 cm in consistence with the number 10 cm of sites. The three-dimensional concentration of the adsorbates in the surface phase is now 10 X 0.1/10 = 10 cm , which is comparable to that of liquid molecules. The system of an elementary reaction consisting of an adsorbed species could hardly be statistically independent of surrounding adsorbates any more than a liquid molecule is from the surrounding ones. 

Equation (9) is valid if, as in the case of reaction (3), the partial orders of the reagents in the forward and reverse reactions equal their molecularities (i.e., the number of species involved in the process). This is true for all elementary reactions and, depending on the mechanism, for some composite reactions also. According to the thermodynamic formulation of conventional transition-state theory, the rate constant of an elementary reaction is given by ... 

The reaction is first order in H, first order in HBr, and second order overall. This elementary reaction involves two molecules and is known as a bimolecular reaction. This is the most common type of an elementary reaction. The other two are unimolecular reactions and trimolecular (or termolecular) reactions the latter are rare. 

An elementary reaction step is a reaction that converts reactants directly to products through a single transition state (see Chapter 5). The reaction order for an elementary reaction step usually reflects the molecularity of the reaction. The molecularity of an elementary reaction step is the number of species that come together to form the activated complex. 

It is important to distinguish clearly between the molecularity and the order. The latter is a purely experimental quantity, which is concerned with how the rate depends on reactant concentrations the concept of order applies to some composite reactions. The molecularity of an elementary reaction, on the other hand, is arrived at by inference from all of the evidence available about the reaction. One such piece of evidence is the order. If a reaction in the gas phase appears to be elementary and has an order of one, it is reasonable to conclude that it is unimolecular. However, as will be seen in Section VI, unimolecular gas reactions become second order at low pressures, and it is therefore unsafe to conclude that a second-order gas reaction is bimolecular it may be a unimolecular reaction in its second-order region. 

The molecularity of an elementary reaction is the number of molecules that are to collide in order that the elementary reaction take place. In a bimolecular reaction the transformation is the result of the collision of two molecules. The collision of three or more molecules is highly improbable, a seemingly trimolecular reaction usually is the resultant of mono- and bimolecular elementary steps. In our example the molecularities of the chemical species A, B, C and D are a, b, c and d. 

A reaction is not necessarily elementary if only one of the limitations mentioned above is true. Eor example, many reactions in which one, two, or three molecules are participating are not elementary. Eurthermore, in some cases the kinetic law of a complex reaction may be approximated by the kinetic mass-action law of an elementary reaction. Kinetic orders of single reactions, apparent or trae, can be found based on patterns presented by Eqs. (3.68), (3.70), (3.72). 

Expression (4.2) illustrates an important kinetic feature the order of a catalytic reaction depends strongly on the reaction concentration. At low pressure, the rate is first order in reactant and at high pressure the rate is zero order in reactant. Second, the overall rate depends on the intrinsic rate constant of an elementary reaction step, fcact, and also on the adsorption constants. Expression (4.2) is valid only under the ideal conditions that all catalytic centers are similar and there are no interactions between reactant and (or) product molecules. These conditions are rarely satisfied and, for this reason, practical rate-expressions are often more complicated than Elq. (4.2). Ekpression (4.2) illustrates, however, that the interplay between surface coverage and elementary rate constants is very important, so that for an overall prediction of the reaction rate one needs to integrate intrinsic reaction rate predictions with surface state predictions. As mentioned earlier, the equilibrium constants for adsorption can be calculated using either statistical or dynamical Monte Carlo methodsl 46]... 

Although the order of a chemical reaction cannot be predicted from the overall reaction, the order of an elementary process is predictable. For example, for the general unimolecular process... 

We can write down the rate law of an elementary reaction from its chemical equation. First, consider a unimolecular reaction. In a given interval, 10 times as many A molecules decay when there are initially 1000 A molecules as when there are only 100 A molecules present. Therefore the rate of decomposition of A is proportional to its concentration and we can conclude that a unimolecular reaction is first order ... 

From this expression, it is obvious that the rate is proportional to the concentration of A, and k is the proportionality constant, or rate constant, k has the units of (time) usually sec is a function of [A] to the first power, or, in the terminology of kinetics, v is first-order with respect to A. For an elementary reaction, the order for any reactant is given by its exponent in the rate equation. The number of molecules that must simultaneously interact is defined as the molecularity of the reaction. Thus, the simple elementary reaction of A P is a first-order reaction. Figure 14.4 portrays the course of a first-order reaction as a function of time. The rate of decay of a radioactive isotope, like or is a first-order reaction, as is an intramolecular rearrangement, such as A P. Both are unimolecular reactions (the molecularity equals 1). 

According to the definition given, this is a second-order reaction. Clearly, however, it is not bimolecular, illustrating that there is distinction between the order of a reaction and its molecularity. The former refers to exponents in the rate equation the latter, to the number of solute species in an elementary reaction. The order of a reaction is determined by kinetic experiments, which will be detailed in the chapters that follow. The term molecularity refers to a chemical reaction step, and it does not follow simply and unambiguously from the reaction order. In fact, the methods by which the mechanism (one feature of which is the molecularity of the participating reaction steps) is determined will be presented in Chapter 6 these steps are not always either simple or unambiguous. It is not very useful to try to define a molecularity for reaction (1-13), although the molecularity of the several individual steps of which it is comprised can be defined. 

More will be said about jump experiments in Chapter 11, which deals with fast reaction techniques. Very fast equilibration reactions are especially amenable to this method. As developed there, a first-order equation describes the approach to equilibrium irrespective of the actual rate law. The most general case is represented by an elementary reaction of the form... 

The overall reaction between CO2 and GMA was assumed to consist of two elementary reactions such as a reversible reaction of GMA and catalyst to form an intermediate and an irreversible reaction of this intermediate and carbon dioxide to form five-membered cyclic carbonate. Absorption data for CO2 in the solution at 101.3 N/m were interpreted to obtain pseudo-first-order reaction rate constant, which was used to obtain the elementary reaction rate constants. The effects of the solubility parameter of solvent on lc2/k and IC3 were explained using the solvent polarity. 

Since an elementary reaction occurs on a molecular level exactly as it is written, its rate expression can be determined by inspection. A unimolecular reaction is first-order process, bimolecular reactions are second-order, and termolecular processes are third-order. However, the converse statement is not true. Second-order rate expressions are not necessarily the result of an elementary bimolecular reaction. While a... 

The molecularity of an elementary process is the number of reactant molecules in that process. This molecularity is equal to the order of the overall reaction only if the elementary process in question is the slowest and, thus, the rate-determining step of the overall reaction. In addition, the elementary process in question should be the only elementary step that influences the rate of the reaction. 

Molecularity of a reaction the number of reacting partners in an elementary reaction uni-molecular (one), bimolecular (two), or termolecular (three) in the mechanism above, the first and third steps are unimolecular as written, and the remainder are bimolecular. Molecularity (a mechanistic concept) is to be distinguished from order (algebraic). 

The solid lines in the figure are model fits of the experimental data. For fitting the experimental data, numerous research groups have proposed more or less complex models [45,47,53,54], Here we apply a simple rate expression derived by Wheeler et al. [45], and approximating the WGS process as a single reversible surface reaction assuming an elementary reaction with first-order kinetics with respect to all species in the WGS reaction ... 

Table 7.5 WGS Reaction Kinetics, Apparent Activation Energies, Eaf (Forward), and Modeled Values for the Backward Activation Energy Eab and Pre-Exponential Factors /r0f, kob, Assuming an Elementary Reaction with First-Order Kinetics of the WGS Reaction...

Again, the molecularity of a reaction is always an integer and only applies to elementary reactions. Such is not always the case for the order of a reaction. The distinction between molecularity and order can also be stated as follows molecularity is the theoretical description of an elementary process reaction order refers to the entire empirically derived rate expression (which is a set of elementary reactions) for the complete reaction. Usually a bimolecular reaction is second order however, the converse need not always be true. Thus, unimolecular, bimolecular, and termolecular reactions refer to elementary reactions involving one, two, or three entities that combine to form an activated complex. 

---