Compensation isokinetic relationship

Comparisons of reactivity at different temperatures may be misleading if the Compensation Law or isokinetic relationship applies. i 152c... 

It is also a point of change in control of the reaction rate by the energy of activation below it to control by the entropy of activation above it. The effect of changes in structure, solvent, etc., will depend on the relation of the experimental temperature to the isokinetic temperature. A practical consequence of knowing the isokinetic temperature is the possibility of cleaning up a reaction by adjusting the experimental temperature. Reactions are cleaner at lower temperatures (as often observed) if the decrease in the experimental temperature makes it farther from the isokinetic temperature. The isokinetic relationship or Compensation Law does not seem to apply widely to the data herein, and, in any case, comparisons are realistic if made far enough from the isokinetic temperature. 

The problem of relationship between the activation parameters-the so called isokinetic relationship or compensation law—is of fundamental importance in structural chemistry, organic or inorganic. However, there are few topics in which so many misunderstandings and controversies have arisen as in connection with this problem. A critical review thus seems appropriate at present, in order to help in clarifying ideas and to draw attention to this treatment of kinetic or equilibrium data. The subject has already been reviewed (1-6), but sufficient attention has not been given to the statistical treatment which represents the heaviest problems. In this review, the statistical problems are given the first place. Theoretical corollaries are also dealt with, but no attempt was made to collect all examples from the literature. It is hoped that most of the important... 

Instead of its reciprocal value, denoted 7, is used sometimes (3, 124, 156) in eqs. (10) and (11) however, the symbol 7 can also stand for 1/(2.303 Rj3) (154, 155). For this reason, it will not be used in this paper. Alternatively, these equations can be modified by taking TAS as a variable, and the proportionality constant is then j3/T and is called the compensation factor (173). As an example of the graphical representation of the isokinetic relationship in the coordinates AH and AS, see Figure 1, ionization of meta- and para-substituted anilinium ions in water. This example is based on recent exact measurements (69, 71) and clearly shows deviations that exceed experimental error, but the overall linear correlation cannot be doubted. 

Figure 18. Schematic representation of the isokinetic relationship, a, in an isoentropic series, b, in an isoenthalpic series, c, with compensation Texp d, with compensation < Tgxp.

Another simple approach assumes temperature-dependent AH and AS and a nonlinear dependence of log k on T (123, 124, 130). When this dependence is assumed in a particular form, a linear relation between AH and AS can arise for a given temperature interval. This condition is met, for example, when ACp = aT" (124, 213). Further theoretical derivatives of general validity have also been attempted besides the early work (20, 29-32), particularly the treatment of Riietschi (96) in the framework of statistical mechanics and of Thorn (125) in thermodynamics are to be mentioned. All of the too general derivations in their utmost consequences predict isokinetic behavior for any reaction series, and this prediction is clearly at variance with the facts. Only Riietschi s theory makes allowance for nonisokinetic behavior (96), and Thorn first attempted to define the reaction series in terms of monotonicity of AS and AH (125, 209). It follows further from pure thermodynamics that a qualitative compensation effect (not exactly a linear dependence) is to be expected either for constant volume or for constant pressure parameters in all cases, when the free energy changes only slightly (214). The reaction series would thus be defined by small differences in reactivity. However, any more definite prediction, whether the isokinetic relationship will hold or not, seems not to be feasible at present. 

FIGURE 1. Isokinetic relationship derived from an enthalpy/entropy plot compensation effect... 

This paper focuses on the influence of the support on the H/D exchange of CP over supported Pt catalysts. It will be shown that kinetics and selectivities are largely affected by the support material. Particle size effects are separated from support effects. The activity shows a compensation effect, and the apparent activation energy and pre-exponential factor show an isokinetic relationship . This can be explained by different adsorption modes of the CP on the metallic Pt surface. The change in adsorption modes is attributed to a change in the electronic structure of the Pt particles, which in turn is induced by changes in the acid/base properties of the support. 

Liu L (2001) Q.-X Guo, Isokinetic relationship, isoequilibiium relationship, and enthalpy-entropy compensation. Chem Rev 101 673... 

Supposed isokinetic relationships as established by direct correlation of Awith A S are often spurious, and the calculated value of P is meaningless, because errors in Alead to compensating errors in A S. Satisfactory methods of establishing such relationships have been devised. 

L. Liu and Q-X. Guo, Isokinetic Relationship, Isoequilibrium Relationship, and Enthalpy-Entropy Compensation, Chem. Rev., 2001,101, 673. R.A. Marcus, Skiing the Reaction Rate Slopes, Science, 1992, 256, 1523. 

Liu L, Guo OX (2001) Isokinetic relationship isoequilibrium relationship, and enthalpy - entropy compensation. Chem Rev 101 673-695... 

The stereoselectivity in the electron transfer reactions between reduced spinach [2Fe-2S]-ferredoxin and optical isomers of [Co(alamp)py], [Co(promp)H20] and [Co(promp)py] (alamp = iV,W -[(pyridine-2,6-diyl)bis(methylene)]bis[(5)- or (iJ)-alaninate] and promp = iV,W -[(pyridine-2,6-diyl)bis(methylene)]bis[(S )- or (R)-proline]) have been investigated. The stereoselectivities are observed to be temperature dependent, with the large differences in the enthalpies of activation compensated by the entropies in an isokinetic relationship. 

Figure 9 demonstrates this compensation effect by the linear relationship between AS and AH. This indicates that both activation parameters depend equally on a and that the isokinetic temperature, i.e. the slope of the line, amounts to 256°K. Thus, at -17°C the rate would become independent of a, whereas it increases with a at higher temperatures. 

From the data listed in Tables I-V, we conclude that most authors would probably accept that there is evidence for the existence of a compensation relation when ae < O.le in measurements extending over AE 100 and when isokinetic temperature / , would appear to be the most useful criterion for assessing the excellence of fit of Arrhenius values to Eq. (2). The value of oL, a measure of the scatter of data about the line, must always be considered with reference to the distribution of data about that line and the range AE. As the scatter of results is reduced and the range AE is extended, the values of a dimin i, and for the most satisfactory examples of compensation behavior that we have found ae < 0.03e. There remains, however, the basic requirement for the advancement of the subject that a more rigorous method of statistical analysis must be developed for treatment of kinetic data. In addition, uniform and accepted criteria are required to judge quantitatively the accuracy of obedience of results to Eq. (2) or, indeed, any other relationship. 

The dependences, such as Eq. 2.47, are known as compensation effect, and coefficient (3C is denoted as isokinetic temperature at which all reactions of given series have the same rate constant. An example of compensation effect for for catalytic rate constant of the Sulfolobus solfataricus p-glycosidase reaction with different substrates is shown in Fig. 2.19. Similar relationships were reported for many other prosesses, involving the binding ligands to hemoglobin, the oxidation of alcohols by catalase, the hydroxylation of substrates by cytochrome c, etc. 

However, even Cremer (d), who reviewed this subject more than 10 years ago, expressed the suspicion that some cases of observed compensation might be caused by experimental error. Later NoUer and Schwab (7) were able to show how the diffusion of reactants into the pores of the solid catalysts may result in a frequency factor-activation energy relationship. Recently, Exner (5) demonstrated that published isokinetic relations are often fictitious because of the peculiar character of error distribution in the calculation of the frequency factor and activation energy from rate constants measured at different temperatures. 

Figure 5.7. Enthalpy/entropy plot (AH /AS ) according to Equ. 5.11 exhibiting a linear relationship ( linear enthalpy/entropy compensation law ). From the slope of the line the isokinetic temperature Tp can be estimated.

The slope of this straight line is referred to as the isokinetic temperature, Tp (Barnes, Vogel, and Gordon, 1969 Leffler, 1966). This relationship with a linear thermodynamic compensation of rates is called enthalpy/entropy compensation it is important for the physiological stability of proteins (Lumry and Eyring, 1954). The value Tp is generally between 270°K and 320°K for the thermal destruction of cells Tp is between 320°K and 350°K. The importance of this fact is the possible implication of a uniform mechanism for cell death through protein denaturation. 

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