Activation Energy and Reaction Orders

Important observable parameters such as the apparent activation energy and the reaction order can be derived using our knowledge gained in Chapter 2  

Note that we are interested only in the forward rate. In kinetics studies we prefer to carry out measurements far from equilibrium. Performing the necessary differentiations we obtain the orders  

We see again that, through the coverages in Eqs. (54)-(57), the overall kinetic parameters are very much dependent on the actual experimental conditions. 

The rate of the ammonia production can now be predicted if we can estimate all of the participating equilibrium constants and k. Where possible, one should take experimental values for the different constants. For instance, it is possible to measure the uptake of atomic nitrogen on the Fe or Ru surface and thereby determine 

the properties of the molecularly adsorbed N2 cancel as soon as we take kj Ki together, which is the relevant term in the formation of atomic nitrogen. Similarly, but on a much larger scale, partition functions cancel in the term hi Eqs. (51) and (52). Returning to Eq. (59), the factor of two arises because the rate describes the number of nitrogen atoms, whereas the transition state refers to the molecule, which dissociates into two atoms. 

---

Equal activation energies of about 17 kcal mol 1 are found for the three butenes. The authors further report that, besides combustion products, furan is the major by-product (in yields of 2—7% depending on the conditions). Minor products (<0.5%) are acrolein, n-butyraldehyde and acetaldehyde. A rather complex network of isomerization, butadiene formation and a number of side reactions was analyzed and, based on simple power rate equations, over 100 kinetic parameters (rate coefficients, activation energies and reaction orders) were estimated. 

The many preexponential factors, activation energies and reaction order parameters required to describe the kinetics of chemical reactors must be determined, usually from laboratory, pilot plant, or plant experimental data. Ideally, the chemist or biologist has made extensive experiments in the laboratory at different temperatures, residence times and reactant concentrations. From these data, parameters can be estimated using a variety of mathematical methods. Some of these methods are quite simple. Others involve elegant statistical methods to attack this nonlinear optimization problem. A discussion of these methods is beyond the scope of this book. The reader is referred to the textbooks previously mentioned. 

Figure 6.6 Plot to determine the activation energy and reaction order of a decomposition reaction. The slope indicates a second order reaction and the intercept, being Ea4>/R ( = 10°C/min), indicates that the activation energy is 111 kj/mol. The noise at the end of the trace is a result of double precision round-off error.

Two important restrictions must be introduced to allow a general representation of the temperature and concentration dependence of the effective reaction rate in the diffusion controlled regime. The first concerns the restriction to simple reactions, i.e. which can be described by only one stoichiometric equation. Whenever several reactions occur simultaneously, it is obvious that the individual activation energies and reaction orders may be influenced quite differently by transport effects. Thus, how the coupled system in such a case finally will respond to a change of temperature or concentration cannot be specified in a generally valid form. 

For pore diffusion resistances in reactions having moderate heat evolution, the following phenomena characteristically hold true in industrial ammonia synthesis [212] in the temperature range in which transport limitation is operative, the apparent energy of activation falls to about half its value at low temperatures the apparent activation energy and reaction order, as well as the ammonia production per unit volume of catalyst, decrease with increasing catalyst particle size [211], [213]-[215]. For example at the gas inlet to a TVA converter, the effective rate of formation of ammonia on 5.7-mm particles is only about a quarter of the rate measured on very much smaller grains (Fig. 13) [157]. 

The mechanism and kinetics of the NO + CO reaction on Rh(lll) have been discussed in detail by Zhdanov and Kasemo (108). They showed that simulations based on surface science data obtained at low pressures reproduce the scale of the reaction rate at the pressure regime of interest for the TWC but fail to predict accurately the apparent activation energy and reaction orders. 

The method to select a representative reactivity value from one experiment has more influence on the frequency factor than on the activation energy and reaction order. The accuracy of the calculation might also be affected. 

The water-gas shift reaction (CO -I- H20- C02 + H2) has been studied in detail over a Cu(l 11) surface at pressures up to 15 torr CO and 200 torr H20 by Campbell and co-workers (26). The specific activity, activation energy, and reaction orders are very similar to those extrapolated from kinetics at somewhat higher pressures over Cu/ZnO and Cu/ZnO/A1202 catalysts. Similarly, doping of the Cu(lll) surface with ZnO had no distinct effect on the observed activity. These results suggested that there is no specific Cu-ZnO interaction necessary for an active water-gas shift catalyst, the essential ingredient of which is metallic Cu surface. Kinetic analysis using kinetic parameters obtained from both UHV and medium-... 

The rate data are reported at the temperature, pressure, and gas composition used by the authors. However, some authors have themselves converted their results to a given set of conditions, by means of activation energies and reaction orders that they consider appropriate. However, these parameters themselves may be structure sensitive, so that the results at the conditions actually used are of the most fundamental interest. 

Theoretical treatment of this polymerization is difficult because of the presence of both primary and secondary amine reactions as well as tertiary amine catalyzed epoxy homopolymerization. To obtain kinetic and viscosity correlations, empirical methods were utilized. Various techniques that fully or partially characterize such a system by experimental means are described in the literature ( - ). These methods Include measuring cure by differential scanning calorimetry, infra-red spectrometry, vlsco-metry, and by monitoring electrical properties. The presence of multiple reaction mechanisms with different activation energies and reaction orders (10) makes accurate characterizations difficult, but such complexities should be quantified. A dual Arrhenius expression was adopted here for that purpose. 

Rosner DE. The apparent chemical kinetics of surface reactions in external flow systems Diffusional falsification of activation energy and reaction order. AIChE Journal 1963 9 321-331. 

Table 3.112. Activation energy and reaction order of polyurethane elastomer thermal decomposition [969]...

The effect of the heating rate and the degree of transformation on such kineti c parameters as the activation energy and reaction order in the thermal degradation of phenyl- or pyridyl-carbamoylmethyl cellulose, indicated that the degradation reaction was very complex. Amidation of carboxymethyl-cellulose decreased the heat resistance and favoured the breaking of macro-molecular chains so that the supramolecular structure affected the heat stability of the derivative and the mechanism of thermal degradation. 

To minimize diffusion effects, established kinetic practice requires that samples should be as small as possible (thin layers spread on multistory crucible [574,689]). However, the smaller the sample, the greater is the ratio of its surface to its bulk and this may overemphasize surface reactions and make correlation with large-scale processes poorer. Experience shows, however, that even very small samples (less than 1 mg) are far from being small enough to be free of diffusion inhibition. To justify the obvious errors, the adjectives "apparent", "formal" and "procedural" are used in conjunction with the otherwise strictly-defined terms of activation energy and reaction order as established in homogeneous chemical kinetics. 

As shown by Eq. (8), the kineties governing a thermal decomposition event depend on time, temperature, and rate of decomposition. TG experiments performed at a constant heating rate allow temperature and time to be interehanged in the ease of first order kinetics and one-step decompositions. ] Hi-Res TGA allows the determination of kinetic parameters such as activation energy and reaction order for each step in multiple component materials using four different TG approaches I constant heating rate, constant reaction rate, dynamic heating rate, and stepwise isothermal. 

The activation energies and reaction order for the decomposition reaction RCrO - RCrOj + jO2 have been determined by Doyle and Pryde (1976) and Roy et al. (1978). As these calculations are strongly dependent on the experimental and calculation methods, the significantly different activation energies obtained by the two groups cannot be directly compared. Nevertheless, it may be noted that both isothermal measurements (Doyle and Pryde, 1976) and nonisothermal measurements combined with another computational procedure (Roy et al., 1978) support a first-order reaction mechanism for LaCrO. ... 

Chen et alf" investigated the thermal decomposition kinetics and mechanism of MH at high temperature (973-1123 K). They found that the apparent activation energy and reaction order of the thermal decomposed reaction are 50.9kJmol and 0.55, respectively. 

---