Eyring plot equation

Figure B2.4.2. Eyring plot of log(rate/7) versus (1/7), where Jis absolute temperature, for the cis-trans isomerism of the aldehyde group in fiirfiiral. Rates were obtained from tln-ee different experiments measurements (squares), bandshapes (triangles) and selective inversions (circles). The line is a linear regression to the data. The slope of the line is A H IR, and the intercept at 1/J = 0 is A S IR, where R is the gas constant. A and A are the enthalpy and entropy of activation, according to equation (B2.4.1)...

The value for P3 was obtained from AH (from Eyring plots) because E = AH + RT. AG° was taken as equal to AH°, and from literature values of AH° estimates of PA were obtained. The constants Pj-P4 were then derived from the experimental data and the foregoing equation. 

For the 1,2,4,6-tetramethylpiperidine equilibrium 123 124, AH° = 1.0 kcal mol-1, and for the N-methylpiperidine equilibrium, AH° = 0.88 kcal mol 1 and refer to measurements made on pure liquids. These values are much lower than those obtained by most other techniques (Table XI) and it is agreed2 that values of AH0 obtained by spectroscopic methods are more reliable than those from ultrasonic techniques. AH (axial -> transition state) values, however, are in agreement with those from other methods, and for Af-methylpiperidine a value of 5.02 kcal mol-1 has been obtained from Eyring plots and a value of 5.76kcal mol l, using the foregoing equation.171... 

Recently, kinetic studies have shown that the catalytic osmylation of alkenes in the presence of cinchona derivatives as chiral amine catalysts (vide infra) is first order with respect to 0s04 and alkene, but shows saturation behavior with respect to the amine ligand42. The influence of the reaction temperature on the enantioselectivity of these reactions has also been studied. Eyring plots according to the equation ... 

Fig. 8 Comparison of Eyring plots of kopt (circles) calculated using Equation (14) with CESR (squares) for Hyl4NA + (24+, open symbols), Hy2DU+ (20+, filled symbols), and Hy2BI+ (21+, symbols with a cross).

From equation 25.6, a plot of ln(k/r) against /T (an Eyring plot) is linear the activation parameters AH and AG can be determined as shown in Figure 25.1. 

Fig. 25.1 An Eyring plot allows the activation parameters AH and A5 to be determined from the temperature dependence of the rate constant the dotted part of the line represents an extrapolation. See equation 25.6 for definitions of quantities.

In Section 25.2 we discussed activation parameters, including A// and A5, and showed how these can be determined from an Eyring plot Figure 25.1) which derives from the equation above relating k to AG. ... 

As for the derivation of Eqs. 122,123 and 124 only the transitions 1—>2 have been counted, these equations do not describe recovery processes, where the transitions 2 —>1 are important as well. These approximations have been made for convenience s sake, but neither imply a limitation for the model, nor are they essential to the results of the calculations. Equation 124 is the well-known formula for the relaxation time of an Eyring process. In Fig. 65 the relaxation time for this plastic shear transition has been plotted versus the stress for two temperature values. It can be observed from this figure that in the limit of low temperatures, the relaxation time changes very abruptly at the shear yield stress Ty = U0/Q.. Below this stress the relaxation time is very long, which corresponds with an approximation of elastic behaviour. 

From the derivative of these plots, the potential dependence of a was obtained and the for each disulfide was estimated, using the approach described in Section 2. The double-layer uncorrected E° values and corresponding standard rate constants were optimized by reproducing the experimental curves by digital simulation. The data are reported in Table 11. By using the Eyring equation (4) with the pertinent pre-exponential... 

The quantities AH and AS are obtained by plotting In A/T against /T (equation 37, right), obtained by combining equation 36 and the Eyring equation (equation 37, left). 

The Eyring equation is usually used in the logarithmic form (6) to have a linear plot of kinetic data. The intercept gives the AS value and the slope gives the APP value ... 

The complete Eyring equation (good for all values of r ) is plotted in Figure 2.18, illustrating that the net current is the sum of two opposing exponen-... 

Under the assumption that AH and A are independent of T, their values can be obtained from the slope and intercept, respectively, of a semi-log plot by the use of equation (4) (Eyring equation). 

Kinetic traces acquired under pseudo-first-order conditions can be fitted to exponential functions, and the observed rate constants, kobs, can be calculated. The second-order rate constants can be obtained from the slopes of the linear plots of kobs versus [hgand] (e.g. the ligand-binding reactions). The activation parameters can be determined through a systematic variation of temperature and pressure. The activation enthalpies and entropies, AH and A5, are calculated using the Eyring equation (1), and the volumes of activation, AV, calculated from the slope of In kobs versus pressure (under certain conditions). 

In this form, the Eyring equation shows that the activation volume for a given single flow process can be obtained direetly by plotting the flow stress against the logarithm of strain rate at constant temperature, provided that the observed strain rate is due entirely to that flow process. This version of the Eyring equation is implied in the expression of... 

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