Constant rate correlation

The test is conducted in a bath of oil, with the temperature increased at a constant rate of 2°C per minute. The DTUL is the temperature at which the sample attains a deflection of 0.0254 cm (0.010 in.). This test is only a guide. It represents a method that could be correlated to product designs, but as with most other tests conducted on test specimens and not on a finished product, it is just a guide (Fig. 5-7). 

Abbreviations k = pseudo-first order rate constant R2 = correlation coefficient r° = initial reaction rate in mmole/gcataiystxh r0Pi and r°Re = reaction rate related to the amount of Pt and Re, respectively C = conversion of AcOBu at t=24 h selectivity to BuOH was above 90 % a2 g catalyst was used. 

The kinetic experiments were not performed under true catalytic conditions, i.e. the pre-prepared [FeL(DTBC)] complexes were introduced into the reaction mixtures as reactants and excess substrate was not used. Nevertheless, the results are important in exploring the intimate details of the activation mechanisms of the metal ion catalyzed autoxida-tion reactions of catechols. In excess oxygen the reaction was first-order in the complex concentration and the first-order dependence in dioxygen concentration was also confirmed with the BPG complex. As shown in Table II, the rate constants clearly correlate with the Lewis character of the complex, i.e. the rate of the oxidation reaction increases by increasing the Lewis acidity of the metal center. 

Table 22.2 Rate constants and correlation coefficients obtained from treatment of adsorption data according to the two kinetic models...

In higher acidity, the rate constant may correlate better with (the Hammet-Deyrup acidity scale) than with the stoichiometric concentration of H+. Since nearly all the studies involve hydrolysis reactions, the depletion of the reagent water may be an important consideration also. 

One of the surprising features of Ritchie s studies was a constant selectivity. While the absolute rate constants differed considerably over the series of cations, the selectivities toward pairs of nucleophiles were constant and independent of the reactivities of R" ". Rate constants were correlated by a simple two parameter equation... 

Using these data, some of the related parameters, i.e. rate constant ( ), correlation coefficient (r) and the values for the Y intercepts, were calculated (Table 7). Comparing these data... 

A similar picture holds for other nucleophiles. As a consequence, there might seem little hope for a nucleophile-based reactivity relationship. Indeed this has been implicitly recognized in the popularity of Pearson s concept of hard and soft acids and bases, which provides a qualitative rationalization of, for example, the similar orders of reactivities of halide ions as both nucleophiles and leaving groups in (Sn2) substitution reactions, without attempting a quantitative analysis. Surprisingly, however, despite the failure of rate-equilibrium relationships, correlations between reactivities of nucleophiles, that is, comparisons of rates of reactions for one carbocation with those of another, are strikingly successful. In other words, correlations exist between rate constants and rate constants where correlations between rate and equilibrium constants fail. 

The apparent first-order degradation rate constants of six dichlorophenols and three trichlorophenols were studied by D Oliviera et al. (1993). ft was determined that the first-order rate constant, k, correlated with the Hammett s constant o and the octanol/water partition coefficient. The Hammett correlation for the cholorophenols was developed as follows ... 

The oxidation of glutamic acid to cyanopropionic acid with CAB in acid solution showed an inverse fractional dependence on acidity. Similarly in alkaline medium, the order in alkali is fractional inverse.143 Kinetics of ruthenium(III)-catalysed oxidation of diols with CAB have been obtained. The products arise due to a fission of the glycol bond.144 The oxidation of isatins with CAB, in alkaline solutions, showed a first-order dependence on CAB and isatin and fractional order in alkali. The rates correlate with the Hammett relationship, the reaction constant p being —0.31. The observed results have been explained by a plausible mechanism and the related rate law has been deduced.145 The oxidation of cysteine with CAB in sulfuric acid medium is first order in CAB and cysteine and the rate is decreased with an increase in the hydrogen ion concentration.146... 

Haag and Mill (1987) reported rate constants and correlation equations for oxidation of a series of phenylazonaphthol dyes, where oxidation of the naphthol and naphtholate ion are accounted for mainly by reaction with singlet oxygen, with some contribution from R02. Naphtholate anion is about ten times more reactive than naphthol toward oxidants. The correlation equations for these compounds are similar to those used for phenol oxidations (Tratnyek and Hoigne, 1991) ... 

For redox reactions of a series of closely related compounds, redox potentials and rate constants often correlate to descriptor variables that reflect the electron donor or electron acceptor properties of P. Such correlations can be used to derive quantitative structure-activity relationships (QSARs), and these QSARs provide the basis for predicting properties of environmental contaminants that have not previously been measured (173). 

Chien and Clayton (1980) compared several equations for describing P04 release from soils and found that the Elovich equation [Eq. (2.49)] was best based on the highest values of the simple correlation coefficient (r2) and the lowest SE. The two-constant rate equation also described the data satisfactorily. The parabolic diffusion equation was judged unsatisfactory due to low r2 and high SE values. 

The amounts of mRNA and amylase that are formed in vivo in the first 12 hr of incubation with GA correlate well (65). However, questions were not answered in this study. Levels of cA-amylase mRNA s were measured during the first 15 hr of incubation with GA, when only 10 to 15% of the total < -amylase molecules are formed. Correlation of the level of mRNA and the level of < -amylase produced during a particular period of incubation implies that for every molecule of template, a constant amount of peptide is formed. The template is either recycled at a constant rate or destroyed after the formation of the first molecule of peptide. 

Newtonian and non-Newtonian calibration fluids were used to determine the necessary calibration constants for the impeller method. It has been previously determined that the impeller method is only valid for a Reynolds number (Re) <10. Impeller rotational speed and torque data from Newtonian calibration fluids of known viscosity were employed to determine the Newtonian calibration constant, c. Cone-and plate-viscometer data from non-Newtonian calibration fluids were used to determine a viscosity vs shear rate relationship. Impeller rotational speed and torque data of the non-Newtonian calibration fluids combined with a determined viscosity vs shear rate correlation were utilized to calculate the shear rate constant, k. The impeller method calibration constants allow the calculation of viscosity, shear rate, and shear stress data of non-Newtonian suspensions. Metz et al. (2) have thoroughly discussed the equations utilized in the impeller method. 

Ortho-adduct formation is an unlikely complication in transfer of hydride to substituted 9-phenylfluoren-9-yl cations from triphenylmethane, or 4,4 -dimethoxydiphenylmethane (Bethell et al., 1981). The log of the rates correlated with a+ constants, giving p-values of 2.44 when triphenylmethane is the donor and 3.02 when the diphenylmethane was the" donor. They also correlate with the difference in pA R+ between the product and acceptor carbocation. There does not seem to be a simple pattern of reactivity in the... 

Figure 7.17 Estimated accretion rates of intertidal salt marshes on the coast of Rhode Island (USA). Despite having well-developed exponential decay curves of excess 210Pb in most marsh sediment cores, indicating a relatively a constant rate of sediment accretion, some variations in the log excess 210Pb indicate that accretion may not have been constant through time. R = correlation coefficient, I = inventories of excess 210Pb (dpm cm-2) (Benninger, 1979 Olsen et al., 1985). (Modified from Bricker-Urso et al., 1989.)...

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