Activation parameters entropy correlation

In addition to chemical reactions, the isokinetic relationship can be applied to various physical processes accompanied by enthalpy change. Correlations of this kind were found between enthalpies and entropies of solution (20, 83-92), vaporization (86, 91), sublimation (93, 94), desorption (95), and diffusion (96, 97) and between the two parameters characterizing the temperature dependence of thermochromic transitions (98). A kind of isokinetic relationship was claimed even for enthalpy and entropy of pure substances when relative values referred to those at 298° K are used (99). Enthalpies and entropies of intermolecular interaction were correlated for solutions, pure liquids, and crystals (6). Quite generally, for any temperature-dependent physical quantity, the activation parameters can be computed in a formal way, and correlations between them have been observed for dielectric absorption (100) and resistance of semiconductors (101-105) or fluidity (40, 106). On the other hand, the isokinetic relationship seems to hold in reactions of widely different kinds, starting from elementary processes in the gas phase (107) and including recombination reactions in the solid phase (108), polymerization reactions (109), and inorganic complex formation (110-112), up to such biochemical reactions as denaturation of proteins (113) and even such biological processes as hemolysis of erythrocytes (114). 

The experimental observations on the actinide oxidation-reduction reactions are described, and the empirical results are tabulated. The rate laws have been interpreted in terms of net activation processes, and these have been tabulated togther with the associated activation parameters— aF, AH, and AS. An electrical analog is described which has been useful in interpreting complicated rate laws. Empirical correlations have been found between the formal entropies of the activated complexes and their charges, and for sets of similar reactions, between the hydrogen ion dependence and AF°, between AF and aF°, and between AH and AH°. The kinetic and physical evidence for binuclear species is discussed. 

LINEAR ENTHALPY-ENTROPY OF ACTIVATION PARAMETERS CORRELATION ACCORDING TO EQUATION (5)... 

Some attention has been given to the effect of substituents upon the kinetics of dialkyl peroxide decomposition. The data are presented in Table 67. A linear enthalpy-entropy of activation correlation was made for the decomposition of alkyl peroxides (exclusive of the hydroxyalkyl peroxides) using data in solution and in the gas phase. The isokinetic temperature was found to be 483 °K (210 °C) . No rational explanation was advanced for the substituent effects in solution or the gas phase . However, the discussion of the effect of a chain reaction upon the activation parameters, given in the section on gas phase reactions, should be consulted. The large differences in and log A between the alkyl and the hydroxyalkyl peroxides suggests a change in mechanism. This is supported by the products from the hydroxyalkyl peroxides. A cyclic activated complex was suggested , viz. 

R" = COOMe to 22 dm mol s" for R = H and R" = Ph. The rate constants for addition of PhCF were slightly lower. The rate constants decreased with increasing Ti-ionization potential of the alkyne, except for very electron-deficient alkynes such as dimethyl acetylenedicarboxylate. The correlation indicated that in these additions the carbenes generally behave as electrophiles, whereas with the acetylenedicarboxylate carbenic nu-cleophilicity comes into play. The rate constant of addition of phenylchlorocarbene to 3-hexyne was determined as a function of temperature. The reaction appeared to be entropy controlled Ea = 8.8 + 0.4 kJ mol and AS = -82 J mol" K The corresponding alkenes have rate constants and activation parameters in the same order of magnitude. 

An overview of some basic mathematical techniques for data correlation is to be found herein together with background on several types of physical property correlating techniques and a road map for the use of selected methods. Methods are presented for the correlation of observed experimental data to physical properties such as critical properties, normal boiling point, molar volume, vapor pressure, heats of vaporization and fusion, heat capacity, surface tension, viscosity, thermal conductivity, acentric factor, flammability limits, enthalpy of formation, Gibbs energy, entropy, activity coefficients, Henry s constant, octanol—water partition coefficients, diffusion coefficients, virial coefficients, chemical reactivity, and toxicological parameters. 

Rate coefficients and kinetic parameters for iododeboronation were determined for the benzene- and thiophene-boronic acids, and the results are given in Table 256. The relative reactivities derived from this work correlated well with those obtained in a number of other electrophilic substitutions572, which is perhaps surprising in view of the large variation in the entropies of activation. These differences were explained by Brown et al.132 in terms of the transition state for the phenyl compound occurring earlier along the reaction coordinate than for the... 

Relative activation enthalpies (Aif) in Table 2 were converted to o% kx k ) at 298 K, and were plotted against Hammett a constants. Here, we used enthalpies, because the size of the entropy and hence the free energy depend much on low frequencies, which are less reliable than higher frequencies, especially for compounds with weak interactions such as TS (8). The use of free energy (AG ) gave similar correlations with more scattered points. As for the Hammett o constant, we used dual-parameter o constants in the form of the Yukawa-Tsuno equation (LArSR equation) (9) as defined in eq 3. Here, the apparent a constant (aapp) has a variable resonance contribution parameter (r), which varies depending on the nature of the reaction examined for t-cumyl... 

Pearson et al. (1952) employed this approach to derive a series of substituent parameters for electron-deficient reactions of substituted benzenes. These constants, designated as sigmae, were based on a study of the Beckmann rearrangement of -substituted acetophenone oximes. These authors considered the rates of the rearrangement reaction of the oximes to deviate from the Hammett eq. (1). It is pertinent that, with the sole exception of the yi-OMe group, the deviations were not major. The entropy of activation, AS, for the -anisyl derivative was, however, 20 e.u. different from the essentially constant values for the other substituents. To remedy the deviations, Pearson and his associates suggested the sigmae constants. It was indicated that these constants were more suitable for the correlations of electron-deficient reactions than the conventional cr-values. 

Examinations of possible correlations between the volume of activation and the entropy of activation for series of similar reactions have been reported for reactions of transition metal coordination compounds, such as solvent exchange, ligand substitution, or isomerization.163 167 A limiting factor in a potential correlation may be the lack of precision that often attends experimental determination of the entropy of activation. Attention has been drawn specifically to the qualitative nature of the correlations between the two parameters for solvent exchange at some 3 + cations, and at square planar Pd2+ and Pt2+ ions.168... 

The data for this solvent were not used to calculate the parameters in Table 54. Similarly the data for decarboxylation of oxanilic acid in anisole were not used for the AH -AS correlation. With the reported AH value of 32.6 kcal.mole , the entropy of activation is calculated to be 3.59 0.03 eu compared to the reported value of 11.1 eu. In the decarboxylation of malonic acid, the data obtained with pyridine and ) -mercaptopropionic acid solvents deviated considerably from the plots and were not included in the correlation. The data for malonic acid decarboxylation appeared to be best correlated by two lines. One line was described by the following solvents acids, phenols, nitro-aromatics, benzaldehyde, and the melt the other line involved amines, alcohols, dimethylsulfoxide and triethyl phosphate. The latter line was not as well defined as the former. However, it was our intention to correlate as many solvents as possible with a minimum number of lines. The data for decarboxylation of malonic acid in water and in benzyl alcohol fell between these two lines and were not included in either correlation. The data for decarboxylation of benzylmalonic acid also appeared to be best correlated with two lines. One line was defined by the cresols, acids and the melt, while the other line was defined by the amines. Decarboxylation of cinnamalmalonic acid was correlated by two lines as indicated in Table 54. Similarly j8-resorcylic acid was correlated by two lines. The separation of data into parallel lines is presumably due to multiple solvation mechanisms . In support of this interpretation it is seen that when two lines are observed, acids fall into one line and amines into the other. It is not unexpected that the solvation mechanisms for these two classes of solvents would differ. It is interesting to note that all of the nitrogen containing acids are correlated reasonably well with one line for both basic and acidic solvents. Also the AHq values fall in a rather narrow range for all of the acids. From the values of p in Table 54, there appears to be little correlation between this parameter and the melting point of the acids, contrary to prior reports " ... 

On generating CA, MCOO, and DCOO parameters, it was observed that solvent activity representation was generally improved, but except for nonane, predicted solvent activities were consistently low. This indicated an over influence of the Flory-Huggins term, and effective counts of 100 and 5.6 were used for the resin and nonane components in the final correlation. The reduction of the entropy contribution for the resin can be justified on the basis that orientative effects are operating the behavior of nonane is somewhat anomalous. 

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