Kinetic data, interpretation

Narasimhan, B., Mallapragada, S. K., and Peppas Nicholas, A., Release Kinetics Data Interpretation, in Encyclopedia of Controlled Drug Delivery (E. Mathiowitz Ed.), pp. 921-935. Wiley, New York (1999). 

Kinetic data, interpretation, 40, 44, 78 Kinetic isotope effects, 46 carbon, 47 chlorine, 47... 

Thermogravimetry is an attractive experimental technique for investigations of the thermal reactions of a wide range of initially solid or liquid substances, under controlled conditions of temperature and atmosphere. TG measurements probably provide more accurate kinetic (m, t, T) values than most other alternative laboratory methods available for the wide range of rate processes that involve a mass loss. The popularity of the method is due to the versatility and reliability of the apparatus, which provides results rapidly and is capable of automation. However, there have been relatively few critical studies of the accuracy, reproducibility, reliability, etc. of TG data based on quantitative comparisons with measurements made for the same reaction by alternative techniques, such as DTA, DSC, and EGA. One such comparison is by Brown et al. (69,70). This study of kinetic results obtained by different experimental methods contrasts with the often-reported use of multiple mathematical methods to calculate, from the same data, the kinetic model, rate equation g(a) = kt (29), the Arrhenius parameters, etc. In practice, the use of complementary kinetic observations, based on different measurable parameters of the chemical change occurring, provides a more secure foundation for kinetic data interpretation and formulation of a mechanism than multiple kinetic analyses based on a single set of experimental data. 

Flere, we shall concentrate on basic approaches which lie at the foundations of the most widely used models. Simplified collision theories for bimolecular reactions are frequently used for the interpretation of experimental gas-phase kinetic data. The general transition state theory of elementary reactions fomis the starting point of many more elaborate versions of quasi-equilibrium theories of chemical reaction kinetics [27, M, 37 and 38]. 

A. S. Michaels Simplified Method of Interpreting Kinetic Data in Fixed-Bed Ion Exchange, Industrial and Engineering Chemistry, 44(8) 1922 (1952). 

The interpretation of kinetic data is largely based on an empirical finding called the Law of Mass Action In dilute solution the rate of an elementary reaction is... 

The values of A and E provide a full description of the kinetic data, but it may be desirable, for mechanistic interpretation, to express the results in terms of the activation parameters A// and A5. We developed equations in Section 5.2 for this purpose for convenience these are repeated here ... 

That is, ipKa = pH at the point where Eq. (6-66) holds. Because the larger of the two constants is usually much greater than the smaller one, this often may be interpreted that pA o = pH when k = k J2 (see Fig. 6-10). Graphical methods for estimating K by using all of the kinetic data are considered later. 

Interpretations may be ephemeral, but experimental data are permanent. To conserve space, the collection of kinetic data presented here is confined to studies which include the determination of at least one activation parameter. For kinetic studies reporting rate constants at a single temperature the following references should be consulted 21, 23, 27, 29(b), 30, 31, 33-39, 44, 46, 48, 52, 81, 86, 92, 96, 99, 141, and 142, as well as some of the tables in this review. Among the excluded studies, those involving catalytic phenomena are especially worthy of mention. 

Unfortunately, direct experimental proof of this mechanism is not available. Kinetic data (see below) offer none since the interpretation need not be unique—more than one mechanism can serve equally well. In addition, the physical properties of the catalyst are obviously contributing, and, in the extreme, diffusion can be rate-controlling, completely obscuring chemical mechanisms. 

The development of methods for the kinetic measurement of heterogeneous catalytic reactions has enabled workers to obtain rate data of a great number of reactions [for a review, see (1, )]. The use of a statistical treatment of kinetic data and of computers [cf. (3-7) ] renders it possible to estimate objectively the suitability of kinetic models as well as to determine relatively accurate values of the constants of rate equations. Nevertheless, even these improvements allow the interpretation of kinetic results from the point of view of reaction mechanisms only within certain limits ... 

Methods for measurement of kp have been reviewed by Stickler,340 41 van Herk Vl and more recently by Beuermann and Buback.343 A largely non critical summary of values of kp and k, obtained by various methods appears in the Polymer Handbook.344 Literature values of kp for a given monomer may span two or more orders of magnitude. The data and methods of measurement have heen critically assessed by IUPAC working parties"45"01 and reliable values for most common monomers are now available. 43 The wide variation in values of kp (and k,) obtained from various studies docs not reflect experimental error but differences in data interpretation and the dependence of kinetic parameters on chain length and polymerization conditions. 

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

Models of this type were used successfully in the interpretation of the kinetic data of Maennig and Kolbel as well as of kinetic data obtained for the hydrogenation of a-methylstyrene and cyclohexene. 

Since the free energy of a molecule in the liquid phase is not markedly different from that of the same species volatilized, the variation in the intrinsic reactivity associated with the controlling step in a solid—liquid process is not expected to be very different from that of the solid—gas reaction. Interpretation of kinetic data for solid—liquid reactions must, however, always consider the possibility that mass transfer in the homogeneous phase of reactants to or products from, the reaction interface is rate-limiting [108,109], Kinetic aspects of solid—liquid reactions have been discussed by Taplin [110]. 

Some studies of more complicated systems have been attempted but, as the number of variables increases, the complexities of interpretation and the difficulties in obtaining meaningful kinetic data become intractable. 

Innumerable experimental rate measurements of many kinds have been shown to obey the Arrhenius equation (18) or the modified form [k = A T exp (—E/RT)] and, irrespective of any physical significance of the parameters A and E, the approach is an important, established method of reporting and comparing kinetic data. There are, however, grounds for a critical reconsideration for both the methods of application and the theoretical interpretations of observed obedience of experimental data for the reactions of solids to eqn. (18). 

Boddington and Iqbal [727] have interpreted kinetic data for the slow thermal and photochemical decompositions of Hg, Ag, Na and T1 fulminates with due regard for the physical data available. The reactions are complex some rate studies were complicated by self-heating and the kinetic behaviour of the Na and T1 salts is not described in detail. It was concluded that electron transfer was involved in the decomposition of the ionic solids (i.e. Na+ and Tl+ salts), whereas the rate-controlling process during breakdown of the more covalent compounds (Hg and Ag salts) was probably bond rupture. 

The kinetic behaviour of metal salts of oxyacids may be influenced by water of crystallization. Where complete-dehydration precedes decomposition, the anhydrous material is the product of a previous rate process and may have undergone recrystallization. If water is not effectively removed, there may at higher temperature be the transient formation of a melt prior to decomposition. The usual problems attend the identification of partial or transient liquefaction of the reactant in the mechanistic interpretation of kinetic data. 

Such systems have the experimental advantage that kinetic data may be obtained by gravimetric or evolved gas pressure measurements. However, these data must be interpreted with care, since gas release is not necessarily concurrent with the solid—solid interaction but may, in principle, be a distinct rate process under independent kinetic control and occur either before or after reaction between the solids. Possible mechanisms to be considered, therefore, include the following. 

The route from kinetic data to reaction mechanism entails several steps. The first step is to convert the concentration-time measurements to a differential rate equation that gives the rate as a function of one or more concentrations. Chapters 2 through 4 have dealt with this aspect of the problem. Once the concentration dependences are defined, one interprets the rate law to reveal the family of reactions that constitute the reaction scheme. This is the subject of this chapter. Finally, one seeks a chemical interpretation of the steps in the scheme, to understand each contributing step in as much detail as possible. The effects of the solvent and other constituents (Chapter 9) the effects of substituents, isotopic substitution, and others (Chapter 10) and the effects of pressure and temperature (Chapter 7) all aid in the resolution. 

Everyday laboratory reactions are emphasized, and the working practice of kinetics takes precedence over the theoretical. The audience remains the first-year graduate student (or advanced undergraduate) as well as research workers from other areas who seek guidance in the concepts and practice of kinetics and in the evaluation and interpretation of kinetic data. 

Both the reactors are operated in batch, and the concentrations of components involved are measured online by electro-conductivity. Data interpretation is made by the kinetic equation of second order. The results obtained in the range of 25-45"C are given in Table 3. Again, the values for the rate constant measured in SCISR, ks, are S5 tematically higher than those in STR, ksr, by about 20%, and no significant difference betvi een the values for the active energy measured in SCISR and STR has been found. 

The reaction was followed by means of the strong absorption of the Os(II) complex at 480 m/i. Unlike the Tl(riI) + Fe(II) system, there is a slight increase in rate as the hydrogen-ion concentration is increased. The kinetic data were interpreted on the basis that both Tl and TIOH react with Os(bipy)3 (with rate coefficients and respectively). At 24.5 °C and ju = 2.99 M, kj = 36.0 l.mole. see and= 14.7 l.mole sec corresponding activation energies are 6.90 and 11.5 kcal.mole" The latter values are considerably smaller than those for the T1(III) + T1(I) exchange and for the Tl(III)- -Fe(II) reaction . On the other hand, all three reactions are subject to retardation by Cl ions. 

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