Linear free energy plots

An even better correlation can be obtained by combining the steric radical diameter term with the Taft cr, constant. The use of linear free energy plots of the Hammett type to correlate orientation is discussed in detail in Section 8. 

There was a slight rate acceleration with an inductive removal of electrons from the a-carbon. A correlation of the chemical shift of the a-proton in CCI4 with Taft (7 constants was made, and a fairly good linear free energy plot of the relative rate coefficients was obtained with a. This indicates a modest increase in rate by electron withdrawing substituents. 

Fig. 6. Linear free energy plot of the rates of ionization of alkyl chlorides (shaded points are corrected to achieve limiting values) versus the calorimetric heats of ionization in SO2CIF...

FIGURE 4. Linear free-energy plot of log /Ch vs protonation of 1-substituted... 

I thank Werner Stumm, Walter Schneider, and James J. Morgan. Their advice, support, and encouragement in front of different activation barriers made this journey into the world of rust and heterogeneity possible. A nice linear free-energy plot by Rene Schwarzenbach convinced me to calculate Figure 8. 

Fig. 13. (A) Linear free energy plot relating the log of the rate of formation of Tyr-AMP (kj) to (he log of the equilibrium constant (Kj) at the active site of tyrosyl-tRNA synthetase for several mutants. The slope is 0.83 with a correlation coefficient of 0.99. (B) The same data as shown in (A) is plotted to illustrate the correlation between log and log k-i. The slope provides a fi value of 0.8 with a correlation coefficient of 0.69. [Reprinted with permission from Refs. (69) and (71).]...

Hammett a constants also have been successfully correlated with reduction rate constants. For example, the reduction rate constants of a series of 4-substituted nitrobenzenes in anaerobic sediment-water systems and the Hammett a constants exhibited a positive correlation (Delgado and Wolfe, 1992). The slopes of the linear-free energy plots for a river sediment, pond sediment, and aquifer material were similar, suggesting that reduction was occurring through the same mechanism in each of these systems. 

The four general approaches to mechanism determination to be mentioned here are the use of linear free energy plots and plots of activation enthalpies against activation entropies, the determination of volumes of activation, the search for transient intermediates, and the study of solvent variation on rates. The last topic is covered in Part II Chapter 6, the other three here. 

The use of linear free energy plots to estimate the position of the transition state along the reaction co-ordinate has been discussed in theoretical and organic terms. ... 

Comparison of base hydrolysis, racemisation, and proton exchange rates for [CoX(trenen)] +, where X = Cl , N3-, or OHg, and trenen is the quinquedentate ligand (19) indicates an nlcb mechanism for base hydrolysis. The demonstration of linear free energy plots (AG vs. AC ) of... 

The difference in mechanism, D for ligand replacement except when the leaving group is water (/ mechanism), adumbrated above, is also indicated by the different isokinetic plots obtained for the two types of reaction and illustrated in connection with the investigation of the kinetics of dissociation and of formation of thiourea complexes.The slope of the linear free energy plot connecting rates and equilibrium constants for reaction of pentacyanoaquoferrate(II) with a series of cobalt(III) complexes also indicates a dissociative mechanism for these reactions. 

Selectivity has a strong bearing on linear free energy plots commonly used to determine outer-sphere behavior. A dependence of the slope of these plots on the difference between Er values for reductants considered has been noted but does not appear to have general application. 

The scope of this mechanism for the reaction of a series of nucleophiles with hydroperoxides has been reviewed and a linear free-energy plot of ogkz against logArj derived for acid-catalysed oxidations. The reaction of l-aIkyl-3-aryl-thioureas with HgOa yields 1,2,4-thiadiazoles which rearrange in acidic solutions to thiazolyl-guanidines. The formation of amidinothioureas as precursors of the thiadiazoles has, however, been established. 

The ki term is very small, though it is significant for the cw-complex it corresponds to the rate constant for aquation in acidic solution. Rates of hydroxide ion attack here are much less than for analogous cobalt(m) complexes. An mechanism is thought to operate for base hydrolysis of [Cr(NH3)5X] +, with X = Cl, Br, or I. Kinetic results for the complex [Cr(NH3)6F] + now show that the point for this complex lies on the same linear free energy plot of logarithms of second-order rate constants against pK values of the acids HX as the points for [Cr(NH3)sX] with X = Cl, Br, or I. Thus base hydrolysis of all four halide complexes would seem to have a common mechanism. ... 

Catalysis.— In 1965 Langford reported that a linear free-energy plot of logarithms of aquation rate constants against logarithms of stability constants for a series of [Co(NH3)gX]2+ complexes had a slope of 1.0. This suggested that... 

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