Rate expression and reaction mechanism

In kinetic studies of the hydrogenation of aromatic hydrocarbons, the dependence of rate upon reactant pressures has usually been expressed in Power Rate Law formulations, that is, by orders of reaction that are simple exponents of the pressures. These as we have seen (Section 5.2) are at best approximations to more fundamental expressions based on concentrations of adsorbed species, although they may well represent results over the limited range in which measurements were made. The Langmuir-Hinshelwood formalism has however sometimes been used, and heats of adsorption of the reactants in their reactive states derived from the temperature-dependence of their adsorption coefflcients.  

The next step is to develop a quantitative framework based on an assumed mechanism, and to test this against the experimental results. A particular feature is the dependence of the orders, especially those of hydrogen, upon temperature (Table 10.1). Aspects of the perceived mechanisms, which will now be briefly reviewed, usually ignore any precise description of the reactant hydrocarbon or derived species these matters will be covered in the section dealing with the exchange reaction. 

A further vexed question is whether the reaction proceeds through hydrogen molecules arriving from the gas phase or through chemisorbed hydrogen atoms. Most workers opt for the latter, and, when the temperature-variation of their 

It seems somewhat odd that two sets of results similar in respect of kinetic parameters, including their temperature-dependence, should be described by mechanisms that differ so considerably. It is of course possible for the mechanistic framework demanded by every catalyst to be unique, however improbable this appears. This seemingly straightforward class of reactions is in fact very complex, and none of the mechanistic proposals embraces all the potentially available information. If each group produces a scheme that satisfies ifs resulfs wifhin fhe 

It is interesting to compare the mechanisms proposed for the hydrogenations of ethyne and benzene. With the former, there is no suggestion of a role for spillover catalysis with the latter there is no role for carbonaceous deposits in creating active centres or in acting as vehicles for hydrogen atom transfer. 

---

Illustration 9.5 indicates one type of rate expression and reaction mechanism that may be associated with an autocatalytic reaction. 

An experimental test for autocatalysis involves addition of the suspected autocatalytic species to the reaction mixture. If the material added is the responsible agent, one may generally expect behavior like that shown in Figure 9.15. Illustration 9.6 indicates one type of rate expression and reaction mechanism that may be associated with an autocatalytic reaction. 

From Stoichiometry and Rate Expression to Reaction Mechanism... 

Although reaction rate expressions and reaction stoichiometry are the experimental data most often used as a basis for the postulation of reaction mechanisms, there are many other experimental techniques that can contribute to the elucidation of these molecular processes. The conscientious investigator of reaction mechanisms will draw on a wide variety of experimental and theoretical methods in his or her research program in an attempt to obtain information about the elementary reactions taking... 

The rate expressions and values, mechanisms, and the activation energies for the condensation reactions forming polymers are similar to those of small molecule reactions. Reaction rate increases with temperature in accordance with the Arrhenius equation. Average DP also increases as the reaction temperature increases to the ceiling temperature where polymer degradation occurs. Long chains are only formed at the conclusion of classical polycondensation processes. 

In general, the nature of the rate expression and hence the reaction order depend on the mechanism by which the reaction takes place. 

As we have seen, rate expressions for reactions must be determined experimentally. Once this has been done, it is possible to derive a plausible mechanism compatible with the observed rate expression. This, however, is a rather complex process and we will not attempt it here. Instead, we will consider the reverse process, which is much more straightforward. Given a mechanism for a several-step reaction, how can you deduce the rate expression corresponding to that mechanism ... 

This chapter treats the descriptions of the molecular events that lead to the kinetic phenomena that one observes in the laboratory. These events are referred to as the mechanism of the reaction. The chapter begins with definitions of the various terms that are basic to the concept of reaction mechanisms, indicates how elementary events may be combined to yield a description that is consistent with observed macroscopic phenomena, and discusses some of the techniques that may be used to elucidate the mechanism of a reaction. Finally, two basic molecular theories of chemical kinetics are discussed—the kinetic theory of gases and the transition state theory. The determination of a reaction mechanism is a much more complex problem than that of obtaining an accurate rate expression, and the well-educated chemical engineer should have a knowledge of and an appreciation for some of the techniques used in such studies. 

Preliminary Criteria for Testing a Proposed Reaction Mechanism— Stoichiometry and Derivation of a Rate Expression for the Mechanism... 

Show that both of these mechanisms are consistent with the observed rate expression and the stoichiometry of the reaction. 

With this general sequence of reactions as our proposed mechanism, we are now prepared to use the corresponding rate expressions and our standard assumptions to show that rate expressions with reaction orders of 1/2, 1, and 3/2 can be derived. The form of the rate expression that results is an indication of the nature of the chain breaking process. 

The cases discussed above represent only a small fraction of the surface reaction mechanisms which might be considered. Yang and Hougen (12) have considered several additional surface reaction mechanisms and have developed tables from which rate expressions for these mechanisms may be determined. They approached this problem by writing the rate expression in the following form. 

When translational diffusion and chemical reactions are coupled, information can be obtained on the kinetic rate constants. Expressions for the autocorrelation function in the case of unimolecular and bimolecular reactions between states of different quantum yields have been obtained. In a general form, these expressions contain a large number of terms that reflect different combinations of diffusion and reaction mechanisms. 

Since the discovery of the deuterium isotope in 1931 [44], chemists have long recognized that kinetic deuterium isotope effects could be employed as an indicator for reaction mechanism. However, the development of a mechanism is predicated upon analysis of the kinetic isotope effect within the context of a theoretical model. Thus, it was in 1946 that Bigeleisen advanced a theory for the relative reaction velocities of isotopic molecules that was based on the theory of absolute rate —that is, transition state theory as formulated by Eyring as well as Evans and Polanyi in 1935 [44,45]. The rate expression for reaction is given by... 

There are three areas of investigation of a reaction, the stoichiometry the kineticSy and the mechanism. In general, the stoichiometry is studied first, and when this is far enough along, the kinetics is then investigated. With empirical rate expressions available, the mechanism is then looked into. In any investigative... 

Although complex reactions can be classified as non-chain and chain, the type of experimental data collected and the manner in which it is analysed is common to both. The ultimate aim is to produce a mechanism, to determine the rate expression and to find the rate constants, activation energies and A-factors for all of the individual steps. 

It is important to realize that a steady state treatment on a mechanism does not necessarily generate a rate expression in which all the individual rate constants appear. If, as in the H2/Br2 reaction above, all the rate constants do appear in the rate expression, then it may be possible to determine the magnitudes of all the rate constants from a steady state analysis. But if they do not all appear, then the steady state treatment can only allow determination of those rate constants which do appear in the rate expression, and alternative ways will have to be found to give an independent determination of the remaining rate constants. 

Chemical reactors are the most important features of a chemical process. A reactor is a piece of equipment in which the feedstock is converted to the desired product. Various factors are considered in selecting chemical reactors for specific tasks. In addition to economic costs, the chemical engineer is required to choose the right reactor that will give the highest yields and purity, minimize pollution, and maximize profit. Generally, reactors are chosen that will meet the requirements imposed by the reaction mechanisms, rate expressions, and the required production capacity. Other pertinent parameters that must be determined to choose the correct type of reactor are reaction heat, reaction rate constant, heat transfer coefficient, and reactor size. Reaction conditions must also be determined including temperature of the heat transfer medium, temperature of the inlet reaction mixture, inlet composition, and instantaneous temperature of the reaction mixture. 

To date, numerous model compounds simulating the pollutants in common waste streams have been studied under laboratory-scale conditions by many researchers to determine their reactivities and to understand the reaction mechanisms under supercritical water oxidation conditions. Among them, hydrogen, carbon monoxide, methanol, methylene chloride, phenol, and chlorophenol have been extensively studied, including global rate expressions with reaction orders and activation energies [58-70] (SF Rice, personal communication, 1998). 

Empirical Rate Expression and Search for a Reaction Mechanism. Based on the steady state results, the initial rate expression can be represented as ... 

Development of rate expressions and evaluation of kinetic parameters require rate measurements free from artifacts attributable to transport phenomena. Assuming that experimental conditions are adjusted to meet the above-mentioned criteria for the lack of transport influences on reaction rates, rate data can be used to postulate a kinetic mechanism for a particular catalytic reaction. 

There is significant support for this mechanism, both from kinetic and spectroscopic data. For example, the oxidation of CO adsorbed on a precious metal by oxygen from the ceria has been observed to occur below 400 K in temperature programmed-desorption (TPD) measurements [27]. Indeed, recent spectroscopic data has shown that Pd particles are oxidized by their ceria zirconia support, beginning at -470 K [28]. Evidence for the other important step in the reaction, the oxidation of reduced ceria by steam, has also been presented [29]. Finally, the kinetic rate expression for the WGS reaction over ceria-supported precious metals, in which the reaction is zeroth order in CO, agrees with expected rate expression for the mechanism shown above [29]. 

These four expressions for the reaction rate have one feature in common, namely that the influence of the concentrations of reactants and products on the reaction rate is separated from the influence of the other reaction parameters. The reason for proceeding in this way is that these rate expressions suggest possible mechanisms for the reaction in question, a feature which will be dealt with later on, in Volume 2. 

If the rate expression and/or the Arrhenius parameters vary with a, i.e. the reaction mechanism changes, the kinetic analysis becomes very much more complicated and the results of such analyses become less reliable and less useful. 

---