Correlations isokinetic plot

Thus the rate of uptake does not depend on the nature of the metal, but depends on the nucleophilic-ity of the bound hydroxide ion, which correlates well with the strength of the O—H bond in the conjugate acid. Isokinetic plots (AH vj. AS ) show parallel lines for C02 uptake and decarboxylation, confirming that these complexes share a common mechanism which does not involve cleavage of a metal-ligand bond.641... 

It is also widely appreciated that extrathermodynamic linear correlations between enthalpy and entropy changes are widespread in nature. The interrelations of G°, AJI° and AS° were probably first discussed at length by Evans and Polanyi (1936, 1937). They were explored in much greater detail twenty-seven years later by Leffler and Grunwald (1963). Particular discussion has revolved around the value (or lack thereof) of so-called isokinetic correlations between enthalpy and entropy changes for various processes. Two questions in particular have prevented the development of widespread interest in isokinetic plots. 

The first of these is, can I believe that there really is a genuine correlation between AIJ° and AS° for a set of kinetic or thermodynamic data, or is a linear isokinetic plot just an artifact produced by common errors in deriving both AII° and AS° from the same set of data through the van t Hoff, Arrhenius, or Eyring equations Thanks to the rapidly expanding use of solution calorimetry, enthalpy changes ( H°) for many thermodynamic processes are now often measured directly and quite independently of AG°. This allows realistic separation of errors in AH° and AG° and hence a realistic assignment of errors in AS°. 

A 2 indicative of an 8 2 mechanism common to all the reactions. However, there are notable exceptions to this graph, such as Li2[PtMeJ, which does not lie on the line despite strong indications of its nucleophilicity. Further corroboration of a common mechanism for all these complexes is the observed isokinetic plot. However the closeness of the isokinetic temperature to room temperature (T = 282 + 22 K) and the variety of solvents used in these studies make any such conclusions from these correlations highly dubious. Indeed [ColCN) ] " also lies on this isokinetic plot, but is known to react with Mel by halogen-atom abstraction (Chock and Halpern, 1969). 

Earlier analyses making use of AH vs. AS plots generated many p values in the experimentally accessible range, and at least some of these are probably artifacts resulting from the error correlation in this type of plot. Exner s treatment yields p values that may be positive or negative and that are often experimentally inaccessible. Some authors have associated isokinetic relationships and p values with specific chemical phenomena, particularly solvation effects and solvent structure, but skepticism seems justified in view of the treatments of Exner and Krug et al. At the present time an isokinetic relationship should not be claimed solely on the basis of a plot of AH vs. A5, but should be examined by the Exner or Krug methods. 

In the graph of AH versus AS, large deviations in the direction of T are thus admissible, while much smaller ones in the perpendicular direction are not. Hence, sequences of points with the slope T can easily result from experimental errors only this is why the value of T is called error slope (1-3,115, 116, 118, 119). Isokinetic relationships with slopes close to T should be viewed with suspicion, but they have been reported frequently. However, we shall see later that even correlations with other slopes are only apparent, or at least the isokinetic temperature is determined erroneously from the plot of AH versus AS. 

The method outlined is quick and useful for testing isokinetic relationships described in the literature and for finding approximate values of j3 (149). It should replace the incorrect plotting of E versus log A, which gives fallacious results for the value of (3 and which usually simulates better correlations than in fact apply. Particularly, the values of correlation coefficients (1) in the E versus log A plane are meaningless. As shown objectively in Figures 9-12, the failure of this plotting is not caused by experimental errors only (3, 143, 153), nor is it confined to values of j5 near the error slope or within the interval of experimental temperatures (151). 

The natural and correct form of the isokinetic relationship is eq. (13) or (13a). The plot, AH versus AG , has slope Pf(P - T), from which j3 is easily obtained. If a statistical treatment is needed, the common regression analysis can usually be recommended, with AG (or logK) as the independent and AH as the dependent variable, since errors in the former can be neglected. Then the overall fit is estimated by means of the correlation coefficient, and the standard deviation from the regression line reveals whether the correlation is fulfilled within the experimental errors. 

A large value for the activation energy is correlated with a large prefactor and all lines in the Arrhenius plot intersect in a single point, the isokinetic point. 

The observed substituent effect on the reaction rate in the oxidation of substituted aliphatic ketoximes by /V-bromosaccharin has been rationalized in terms of a mechanism.126 The oxidation of acetophenones with N-bromophthalimidc exhibited a linear correlation with Brown s a+ with reaction constant p = —0.52. An Exner plot gave an isokinetic temperature p = 263 K. A mechanism consistent with the kinetic data has been proposed.127... 

R= Me, Et, Pr , or Pr ) mixtures, and the stability constants (Xml) decreased with increasing alcohol concentration. Xml values were found to correlate with the protonation constants of the various anilines. The formation rate constants decrease with increasing concentrations of MeOH or EtOH, and the lowest rates were observed in propan-2-ol. In aqueous solution (7=0.25 mol dm [NaC104]), a plot of ATT versus SS is linear with an isokinetic temperature of 437 K. ... 

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