Reaction orders definition

Elementary reactions are characterized by their moiecuiarity, to be clearly distinguished from the reaction order. We distinguish uni- (or mono-), hi-, and trimoiecuiar reactions depending on the number of particles involved in the essential step of the reaction. There is some looseness in what is to be considered essential but in gas kinetics the definitions usually are clearcut through the number of particles involved in a reactive collision plus, perhaps, an additional convention as is customary in iinimolecular reactions. 

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. 

A formal definition of the reaction order with respect to the concentration of substance i, C,, is... 

To summarize the analysis of pH profiles, even complex ones, is not an arcane or difficult art. Systematic analysis in terms of ionic equilibria, predominant species, and the reaction orders with respect to [H+] provides the solution. Kinetically indistinguishable alternatives can never, by definition, be distinguished from the kinetic data contained in the pH profile. Other measurements, including some alluded to earlier and others given in Chapter 10, may, however, allow these distinctions. 

Reaction mechanism, definition, 4, 12 Reaction order apparent, 7 defined, 5... 

This definition for reaction order is directly meaningful only for irreversible or forward reactions that have rate expressions in the form of Equation (1.20). Components A, B,... are consumed by the reaction and have negative stoichiometric coefficients so that m = —va, n = —vb,. .. are positive. For elementary reactions, m and n must be integers of 2 or less and must sum to 2 or less. 

Parsons, R., Electrode reaction orders, charge transfer coefficients and rate constants. Extension of definitions and recommendations for publication of parameters. Pure Appl. Chem., 52, 233 (1979). 

The second observable is the reaction order, which has two eommonly used definitions. The simplest definition to use, though not necessarily to measure,... 

Since all of the above-mentioned interconversion reactions are reversible, any kinetic analysis is difficult. In particular, this holds for the reaction Sg - Sy since the backward reaction Sy -+ Sg is much faster and, therefore, cannot be neglected even in the early stages of the forward reaction. The observation that the equilibrium is reached by first order kinetics (the half-life is independent of the initial Sg concentration) does not necessarily indicate that the single steps Sg Sy and Sg Sg are first order reactions. In fact, no definite conclusions about the reaction order of these elementary steps are possible at the present time. The reaction order of 1.5 of the Sy decomposition supports this view. Furthermore, the measured overall activation energy of 95 kJ/mol, obtained with the assumption of first order kinetics, must be a function of the true activation energies of the forward and backward reactions. The value found should therefore be interpreted with caution. 

There are some common characteristics for gas-phase reaction systems that form the basis for understanding and describing the chemical behavior. In this section we will discuss some basic definitions and terms that are useful in kinetics, such as reaction order, molec-ularity, chain carriers, rate-limiting steps, steady-state and partial equilibrium approximations, and coupled/competitive reactions. 

We adopt this kinetic definition of reaction order without reference to the actual number of molecules involved in each act of chemical transformation. In homogeneous reactions the kinetically determined order is equal to the number of molecules participating in the actual change of which the rate is being measured. In heterogeneous reactions this equality is not necessarily preserved. It will be convenient to call the order inferred from the effect of pressure on the time of half-change the apparent order, and to refer to the number of molecules involved as the true order of the reaction. We have now to consider the relation of the true and the apparent order in various cases. ... 

Effective Over-all Chemical Reaction Orders. Values of the effective over-all reaction order a have been obtained by many investigators. The published data are not comprehensive enough to permit any definite correlations to be made between reaction orders, pressure, temperature, and mixture ratios (26). One or more of the three basic types of flame measurements are used in determining reaction orders, these being flame thickness, burning velocity, and quenching distance. Reaction order data are available in the more recent literature for the following mixtures, obtained by the indicated method for various pressures, temperatures, and mixture ratios. 

This has been studied much less frequently and appears to be a rather more complex reaction. The first results obtained, for the butyl-lithium, styrene reaction in benzene have already been described. In a similar way the addition of butyllithium to 1,1-diphenylethylene shows identical kinetic behaviour in benzene (26). Even the proton extraction reaction with fluorene shows the typical one-sixth order in butyllithium (27). It appears therefore that in benzene solution at least, lithium alkyls react via a small equilibrium concentration of unassociated alkyl. This will of course not be true for reactions with polar molecules for reasons which will be apparent later. No definite information can be obtained on the dissociation process. It is possible that the hexamer dissociates completely on removal of one molecule or that a whole series of penta-mers, tetramers etc. exist in equilibrium. As long as equilibrium is maintained, the hexamer is the major species present and only monomeric butyllithium is reactive, the reaction order will be one-sixth. A plausible... 

After the absence of film diffusion effects has been verified and if the reaction order n is known, the expression for the rate equation r = r) kcat[E][S]buik/KM (first-order reaction assumed) can be inserted into the definition for 7j and the unknown rate constant k can be eliminated (Weisz, 1954) [Eq. (5.66)]. 

The choice of reaction path definition used as the reference for such a constrained dynamics is arbitrary any path may be used in practice. However, a natural choice in order to ensure that the simulation moves along the bottom of the potential energy valley connecting reactants/products with TS is the intrinsic reaction path (IRP) of Fukui.46,47 IRP by definition goes along the bottom of such a valley. IRP simply corresponds to a steepest descent path in a mass-weighted coordinates ... 

Figure 12 shows the effectiveness factor as a function of the Wheeler-Weisz modulus for different reaction orders, indicating that criterion (33) holds for the generalized Thiele modulus. Due to the definition of L it is fairly independent of the catalyst geometry. 

By a complex reaction system we shall mean any reaction system in which we have more than one reaction process occurring. This may include systems in which we have two or more concurrent or consecutive reactions. Unfortunately such a definition in its subtler aspects may include all reaction systems, since, as we shall see in later chapters, even simple reaction systems involve both consecutive and concurrent reactions. We can, however, attempt to distinguish simple and complex systems pragmatically by saying that complex systems will include all those reactions whose rate expressions cannot be characterized experimentally by simple reaction orders over the accessible range of experimental conditions. That is, they will show systematic deviations from any of the simple rate laws by amounts which exceed the estimated experimental errors. 

The general formula for the rate in simple pathways, derived in Section 6.3, can be used for deducing a large number of rules that relate observable kinetic behavior, such as reaction orders, to properties the network may have or definitely cannot have. (Catalytic reactions require qualifications see Section 8.6.) These rules greatly facilitate network elucidation Pathways or networks that include a feature producing behavior contrary to observation can be ruled out by whole groups rather than one at a time. 

Slight variations in the definition of reaction order may be found in the literature. For example, for some reactions there may be reason to believe that one species (for example, nitrogen) is inert, in the sense that changes in its concentration do not influence the rate of the reaction at constant pressure, and in such cases rij may be defined by considering simultaneous changes in the concentrations of species j and of the inert, with the total pressure held constant. In general, the resulting value of rij diflers from that defined above therefore it is important to ascertain the specific definition employed. An empirical formula that is often useful—for example, in the presence of an inert—is... 

From the definition of Ao.s, it follows that to.s is inversely proportional to the rate constant of the chemical reaction. The influence of substrate concentration, proton concentration pH), and temperature on the reaction rate can therefore be deduced simply from the variation in For example, the reaction order of the substrate can be determined as - logros/ logCo- Likewise, apparent activation energies, Fa, may be obtained from plots of to,5 against the inverse temperature (T ), since the slope is equal to —E /R [8], Kinetic isotope effects can also easily be... 

A reaction has an elementary rale law if the reaction order of each species is identical with the stoichiometric coefficient of that species for the reaction as written. For example, the oxidation of nitric oxide presented above has an elementary rate law under this definition, while the phosgene synthesis reaction does not. Another example of this type of reaction with an elementary rate law is the gas-phase reaction between hydrogen and iodine to form hydrogen iodide ... 

It appears to be established that, at low temperatures, the reaction order is close to i and that the experimental results can be interpreted by a simple Rice-Herzfeld mechanism. At higher temperatures, the decomposition of the C2H5 radical becomes significant and the mechanism discussed above describes the kinetic data (at small conversions). There are, however, definite indications that at higher conversions and temperatures several secondary reactions occur resulting in the formation of a number of minor products. The kinetics of the reaction is rather complex under such circumstances. If these reactions can be neglected (small conversions), the mechanism is resonably described by steps (3)-(9). The steady-state treatment leads to... 

The decomposition is homogeneous. The rate of disappearance of cyclopentanone shows an induction period and cannot be described by a definite reaction order. The shapes of the concentration-time curves indicate acceleration by the products, most probably the olefinic ones. 

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