Secondary kinetic data

The observed or primary kinetic data are described as those kinetic data determined directly by experiment, and the treatment of such data with an empirical or theoretical kinetic equation involves either a linear (Equation 7.74) or a nonlinear equation (Equation 7.75), which shows the variation of dependent variable Y with independent variable X. The dependent variable may be the concentration or equivalent of any physical property such as absorbance, A bs, of either reactant or product that has been monitored as a function of an independent variable such as reaction time, t. In kinetic studies, the rate constants, under specific reaction conditions, are obtained from primary kinetic data and, therefore, such experimentally determined rate constants may be considered secondary kinetic data. Dependent variables may be experimentally determined rate constants (also called observed rate constants or secondary kinetic data), which have been determined as functions of independent variables such as the concentrations of reaction components (reactants and catalysts), temperature, and reaction medium. The reliability of the calculated kinetic parameters from a kinetic equation using primary and secondary kinetic data may be described as follows. 

Kinetic Equations Involving Secondary Kinetic Data (Y vs. X)... 

The only kinetic data reported are in a Ph.D. thesis (41). Integral order kinetics were usually not obtained for the reaction of a number of ketones with piperidine and a number of secondary amines with cyclohexanone. A few of the combinations studied (cyclopentanone plus piperidine, pyrrolidine, and 4-methylpiperidine, and N-methylpiperazine plus cyclohexanone) gave reactions which were close to first-order in each reactant. Relative rates were based on the time at which a 50% yield of water was evolved. For the cyclohexanone-piperidine system the half-time (txn) for the 3 1 ratio was 124 min and for the 1 3 ratio 121 min. It appears that an... 

Pyrolyses of formates, oxalates and mellitates yield CO and C02 (H2, H20 etc.) as the predominant volatile products and metal or oxide as residue. It is sometimes possible to predict the initial compositions from thermodynamic considerations [94], though secondary reactions, perhaps catalyzed by the solids present, may result in a final product mixture that is very different. The complex mixtures of products (hydrocarbons, aldehydes, ketones, acids and acid anhydrides) given [1109] by reactants containing larger organic groupings makes the collection of meaningful kinetic data more difficult, and this is one reason why there are relatively few rate studies available for the decompositions of these substances. 

Kinetic data may be collected in which the final instrument reading is unreliable or unavailable. Perhaps excessive time would be needed, or a slow secondary reaction sets in, or the instrument baseline slowly drifts. Nowadays, with readily available nonlinear least-squares programs, one may simply treat as a floated variable, along with k. 

Table 1 shows the kinetic data available for the (TMSjsSiH, which was chosen because the majority of radical reactions using silanes in organic synthesis deal with this particular silane (see Sections III and IV). Furthermore, the monohydride terminal surface of H-Si(lll) resembles (TMSjsSiH and shows similar reactivity for the organic modification of silicon surfaces (see Section V). Rate constants for the reaction of primary, secondary, and tertiary alkyl radicals with (TMSIsSiH are very similar in the range of temperatures that are useful for chemical transformations in the liquid phase. This is due to compensation of entropic and enthalpic effects through this series of alkyl radicals. Phenyl and fluorinated alkyl radicals show rate constants two to three orders of magnitude... 

TABLE III. Kinetic Data for Nitrosation of Secondary Amino Acids at pH 2.5... 

The dynamics of interstrand hole transport have also been investigated for several hairpins possessing GACC hole transport sequences in which a GG secondary donor is located in the complementary strand [41]. Kinetic data for 4GACC are reported in Fig. 9 and the resulting equilibrium data in Table 1. Comparison of the values of kt for 4GACC and 4GAGG shows that there is a kinetic penalty of 1/6 for inter- vs intrastrand hole transport. A... 

The bromination products of a-methylstilbenes, XC6H4C Me= C HC6H4Y, have been extensively studied in methanol as a function of X and Y (Ruasse and Argile, 1983). In agreement with kinetic data, which establish that the intermediates are exclusively tertiary and/or secondary bromocarbocations, the bromination of these olefins is completely regio-selective but hardly stereoselective at all. The two diastereoisomeric di-bromides and methoxy-... 

It should be noted at this point that primary and secondary reaction products can be distinguished not only by kinetic data (13) but also by suppression of the secondary reactions. E.g substitution of 2,2,2-trifluoroethanol for p-dioxane as solvent for HCoCCO) suppresses homologation and methane formation addition of a phosphine to give the less acidic catalyst HCo(CO)3PR3 has the same effect, as has the substitution of the less acidic catalyst HMn(CO)5. 

Fig- PoIat angle distributions for various azimuthal angles for fixed secondary kinetic energy of the Rh atoms. In each frame the data are normalized to the — 30° peak... 

Hydrogen abstraction from propan-2-ol and propan-2-ol- /7 by hydrogen and deuterium atoms has been studied by pulsed radiolysis FT-ESR. A secondary kinetic isotope effect was observed for H (D ) abstraction from the C—H (C—D) bonds. The results were compared with ab initio data. In similar work, the kinetic isotope effects in H and D abstraction from a variety of other alcohols in aqueous solvents have been measured. It was found that, compared with the gas phase, the reactions exhibit higher activation energies in agreement with the ability of solvation to decrease the dipole moment from the reactant alcohol to the transition state. 

Secondary plots of kinetic data are used to obtain various rate constants and other kinetic parameters such as and Vmax- To simply the analysis, one choses a algebraic transform of the rate equation that allows the observed data to be graphed in a hnear format. 

Literature has revealed limited kinetic data on secondary nucleation of alumina trihydrate in the precipitator of the Bayer Process for alumina production. A batch agitated, isothermal, three litre crystallizer was used in the study. A Coulter-Counter was utilized as the particle sizing equipment. The effects of seed density, supersaturation and temperature on secondary nucleation were investigated. Maximum nucleation rates were found to occur at about 70 C and for any crystallization temperature, the nucleation rate passed through a maximum. The correlated equation for the effective secondary nucleation rate of alumina trihydrate is... 

Sixteen years later Baldwin and co-workers published the results of even more elegant experiments in which the stereomutation of optically active 7-l- C-l,2,3-was studied. Because a deuterium atom is attached to each of the carbons in this compound, it was unnecessary for Baldwin to assume the size of a secondary deuterium isotope effect on which bond cleaves, in interpreting his kinetic data. The results of his experiments led him to conclude, the double rotation mechanism does not predominate by a substantial factor. ... 

The use of chemical modelling to predict the formation of secondary phases and the mobility of trace elements in the CCB disposal environment requires detailed knowledge of the primary and secondary phases present in CCBs, thermodynamic and kinetic data for these phases, and the incorporation of possible adsorp-tion/desorption reactions into the model. As noted above, secondary minerals are typically difficult to identify due to their low abundance in weathered CCB materials. In many cases, appropriate thermochemical, adsorption/desorp-tion and kinetic data are lacking to quantitatively describe the processes that potentially affect the leaching behaviour of CCBs. This is particularly tme for the trace elements. Laboratory leaching studies vary in the experimental conditions used (e.g., the type and concentration of the extractant solution, the L/S ratio, and other parameters such as temperature and duration/ intensity of agitation), and therefore may not adequately simulate the weathering environment (Rai et al. 1988 Eary et al. 1990 Spears Lee, 2004). 

Secondary phases predicted by thermochemical models may not form in weathered ash materials due to kinetic constraints or non-equilibrium conditions. It is therefore incorrect to assume that equilibrium concentrations of elements predicted by geochemical models always represent maximum leachate concentrations that will be generated from the wastes, as stated by Rai et al. (1987a, b 1988) and often repeated by other authors. In weathering systems, kinetic constraints commonly prevent the precipitation of the most stable solid phase for many elements, leading to increasing concentrations of these elements in natural solutions and precipitation of metastable amorphous phases. Over time, the metastable phases convert to thermodynamically stable phases by a process explained by the Guy-Lussac-Ostwald (GLO) step rule, also known as Ostwald ripening (Steefel Van Cappellen 1990). The importance of time (i.e., kinetics) is often overlooked due to a lack of kinetic data for mineral dissolution/... 

Organonickel(II) species are believed to be formed during the reaction between [Ni(TMC)] and primary alkyl halides, and subsequently undergo hydrolysis with cleavage of the Ni—C bond. Kinetic data measured in the presence of excess alkyl halide indicate a rate law -dlNi1 (TMC)+]/cft = MNi (TMCr][RX]. The rate constants increase for R and X in the order methyl < primary < secondary < allyl < benzyl halides and Cl < Br < I (133, 140). This suggests that the rate-determining step is electron transfer from the Ni(I) complex to R—X via an inner-sphere atom-transfer mechanism (143). 

The published data5 14,16,17 29,30,50,54-641 on the relation between the constants of the addition of primary and secondary amines are most discrepant. On one hand, such a situation is due to the different experimental conditions, and on the other hand, to the dissimilar methods of calculating the kinetic constants. Most researchers used the kinetic data for reactions in excess alcohol to estimate the quasibimolecular rate constants of the primary and secondary additions. The constants were estimated assuming the validity of a simple scheme of the successive bimolecular reaction [Scheme (1)]. 

In Chapter 2 the DSC technique is discussed in terms of instruments, experimental methods, and ways of analysing the kinetic data. Chapter 3 provides a brief summary of epoxy resin curing reactions. Results of studies on the application of DSC to the cure of epoxy resins are reviewed and discussed in Chapter 4. These results are concerned with the use of carboxylic acid anhydrides, primary and secondary amines, dicyanodiamide, and imidazoles as curing agents. 

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