Eyring plots

Estimate the activation energy of the relaxation process responsible for the deformation of polycarbonate from figure 8.9  

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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)...

In these calculations T is taken in the middle of the experimental range k is the Boltzmann constant and h is Planck s constant. From Eq. (5-48) it can be seen that a plot of ln(A /7 ) against 1/7" has a slope of — A7/ /7 such a graph is called an Eyring plot. 

Figure 8.27 An Eyring plot of In(k/T) (as y ) against 1 IT (as V). The data relate to the rate of hydrolysing a biological molecule in the temperature range 300-500 K...

Kinetic data on the influence of the reaction temperature on the enantioselectivity using chiral bases and prochiral alkenes revealed a nonlinearity of the modified Eyring plot [16]. The observed change in the linearity and the existence of an inversion point indicated that two different transition states are involved, inconsistent with a concerted [3+2] mechanism. Sharpless therefore renewed the postulate of a reversibly formed oxetane intermediate followed by irreversible rearrangement to the product. 

Figure 15.4 Eyring plots for reaction 1 2 (see figure 15.3) in the forward (squares) and reverse (circles) directions.

The strong curvature of the Eyring plots at temperatures below 35°C (see ref. 19a, Table V and Figure 6) points to hydrogen-bonded interactions between catalyst molecules, as already observed in 1969 by Uskokovic (52) in the H nuclear magnetic resonance (NMR) spectrum of dihydroquinine. 

Fig. 6. Curved Eyring plot of second-order rate constants k for the [Fe(CN)g] oxidation of spinach PCu(I) in 50 50 (v/v) Me0H-H20 solvent at temperatures 25 to — 35°C (reproduced with permission from Ref. [105])...

Fig. 2.3 Arrhenius ( ) and Eyring ( ) plots of data for the exchange of a single dmso molecule with Ga(dmso) + in CD3NO2. Nmr line-broadening was used for the higher temperatures and stopped-flow nmr experiments for the lower temperatures. For the Arrhenius plot, the slope and intercept (at T = 0) are -9.2 x 10 and +31,4 respectively, leading to = 76 kJ mol" and logA = 13.6. For the Eyring plot, the slope and intercept are —8.77 x 10 and +24.4 respeetively, leading to A// = 73 kJ mol" and AS = 5 J K" mol" .

Fig. 2.12 Examples of non-linear Arrhenius (or Eyring) plots (a) 1u(A oh)7 " ) vs T for the base hydrolysis of trans-Co(en)2ClJ. Curvature may result when k, k2 and A// , not equalling A// in the conjugate-base mechanism (Sec. 4.3.4). Reprinted with permission from C. Blakeley and M. L. Tobe, J. Chem. Soc. Dalton Trans. 1775 (1987). (b) nk vs T for iron removal from C- and N-terminal monoferric transferrin (lower and upper scales respectively). Transferrin contains two iron binding sites = 35 A apart. Either of the two sites, designated C- and N-terminal, can be exclusively labelled by Fe(lll) ions and these may be removed by a strong ligand such as a catechol (see Sec. 4.11). Reprinted with permission from S. A. Kretschmar and K. N. Raymond, J. Amer. Chem. Soc. 108, 6212 (1986). (1986) American Chemical Society.

Cryokinetic studies of the plastocyanin-ferricyanide redox reactions in 50 50 v/v MeOH + H2O, pH = 7.0, p = 0.1 M reveal an Eyring plot shown for the second-order rate constant k from 25 °C to -35°C. The reaction is irreversible over the whole temperature range and there is no evidence for a change in the Cu(I) active site. Recalling that these reactions may involve consecutive steps, explain the deviation from a linear Eyring plot. F. A. Armstrong, P. C. Driscoll, H. G. Ellul, S. E. Jackson and A. M. Lannon, J. Chem. Soc. Chem. Communs. 234 (1988). 

In Eqn. (4.48), when Ar i > k, proton transfer is a pre-equilibrium and when A j < k, the act of deprotonation becomes rate-limiting. Since these processes are likely to have different heats of activation, in the intermediate region, A , = Atj, the heat of activation is changing and the Eyring plot will be curved. See Sec. 2.6. 

Similarly, vesicular reactivity is dependent on bilayer fluidity and Arrhenius (or Eyring) plots for the decarboxylation of 6-NBIC show a break around Tm. " For the Kemp elimination in different bilayers, it was found that the bilayer for which kinetic data had been gathered below its was least effective as a catalyst. Ester hydrolysis has also been found to be faster above r. For the decarboxylation of 6-NBIC, the increase in catalytic efficiency was attributed to different aggregate surface dynamics based on the observation that vesicles above showed intermediate activation parameters between vesicles below and micelles. One could, of course, discuss causality here considering the fact that many of the bilayer... 

Fig. 1, Eyring plot of log(rate/temperature) vs (1/temperature) for the chemical exchange of the aldehyde proton in furfural. Crosses represent measured rates and the straight line is the...

In fast exchange, we must measure Tz for the coalesced line, and then calculate the exchange rates from that. Standard CPMG and Tip methods may be difficult to implement, but the offset-saturation experiment can be done on essentially any spectrometer. These Tz measurements can often extend the high-temperature side of the Eyring plot by substantial amounts, particularly in the case of unequally populated systems. Taken together with the other methods, they provide excellent data. 

The absolute and relative rates of decomposition of tcrt-butyl phenylperacetates were measured in CDCI3 at 60, 70, 80, 90, 100 and 110°C and Hammett correlations were obtained (Table 3). An Eyring plot gave the activation parameters (Table 4). 

Figure 5.70 Eyring plot for polycarbonate. Reprinted, by permission, from N. G. McCmm, C. P. Buckley, and C. B. BucknaU, Principles of Polymer Engineering, 2nd ed., p. 191. Copyright 1997 by Oxford University Press.

FIGURE 1 Eyring plots (solid lines) for reactions of homologous series of five molecules obtained with kinetic experiments carried out at constant temperature (plain markers) (simulated data from ref. 14). 

One analysis of experimental data involves carrying out rate constant measurements at a series of temperatures, and then plotting iQ(k/T) against l/T (a so-called Eyring plot). We may rearrange Eq. (15.28) to... 

Another important point that must be borne in mind is that failure to account for tunneling, or to recognize its contribution in die first place, can lead to significant errors in the interpretation of experimental data. For example, Watson (1990) analyzed an Eyring plot of apparent rate constants for methane metathesis by methyllutetiocene (Figure 15.5) to infer... 

Additional data on density and diameter effects is provided by Kegler (Ref 4) for RDX/TNT and HMX/TNT mixts. Fig 5 shows the variation of D (VQ in Kegler s notation) with initial density p with charge diameter 0 as a parameter. Fig 6 shows the variation of D with 1/0 (Eyring plot) with initial density as a parameter. Also shown are reaction zone widths as computed by the Eyring method... 

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... 

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