Free energy plots

Some representative plots of entropies of adsorption are shown in Fig. XVII-23, in general, T AS2 is comparable to Ah2, so that the entropy contribution to the free energy of adsorption is important. Notice in Figs. XVII-23 i and b how nearly the entropy plot is a mirror image of the enthalpy plot. As a consequence, the maxima and minima in the separate plots tend to cancel to give a smoothly varying free energy plot, that is, adsorption isotherm. 

Fig. 10 Free energy plot for an electron-transfer reaction.

Fig. 11 Free energy plot for an atom-transfer reaction in solution. Diffusive motion along the solvent coordinate opens the opportunity for a favourable atom transfer.

Now, it is the forward rate constant that is almost invariant (because there is a common nucleophile H2O), whereas k is very sensitive to the nucleophilic character of X, i.e. it is an associative type reaction. Selectivity would be expected to lead to curved free energy plots but these have not yet been observed. 

Figure 2.1 Unary phase diagram (top) and Gibbs free energy plot (bottom) for elemental sulfur. Reprinted, by permission, from D. R. Gaskell, Introduction to Metallurgical Thermodynamics, 2nd ed., p. 178, Copyright 1981 by Hemisphere Publishing Corporation.

For the excited singlet state of rhodamine as product state the free energy plot of the reverse electron transfer from the reduced dye to the hole (dashed curve in Fig. 31) is a mirror image to the free energy plot of the forward reaction relative to AG° =0. We immediately see from Figs. 31 and 32 that this reverse reaction is very fast at phenanthrene and slower at chrysene. It is still slower at anthracene and extremely slow at perylene. At phenanthrene this reverse reaction can compete with the dissociation of the hole from the reduced dye as is borne out by the recombination controlled current in this system (Fig. 27). 

When in addition the singlet spin state is not preserved even though the reduced dye-hole pair is formed from the two singlet states XD and xCo we have to consider similar free energy plots for the reverse electron transfer reactions lead-... 

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. 

In general, if A 7 is small, as is likely to be the case for homogeneous solutions, the free energy, plotted as a function of composition, forms a broad, shallow U-shaped curve, and the ranges of composition over which the single phases are... 

As per the glycolysis pathway, the energy drops in the free energy plot were as shown below (Fig. 9.3)... 

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...

Fig. 11 represents the two-dimensional section of the energy landscape with the free energy plotted against the conformational coordinate. The CGU can... 

The manifest linearity of the majority of free energy plots is paradoxical because the constant slope would indicate that the transition structure is substituent independent. Variation in structure might be expected to occur due to the change in substituent and thus yield curved relationships as indicated in Section 6.1. The relationship between reactivity and selectivity is based on a very simple model, to which most reactions do not conform because they involve not only at least two major bonding changes but solvation changes as well. 

Alternative definitions parallel mechanisms can be diagnosed when the observed rate on one side of the break-point in a free energy plot is greater than that calculated from the correlation on the other side. Parallel mechanisms are diagnosed if the non-linear free energy correlation exhibits a concave upwards curvature. 

A stepwise mechanism where an addition intermediate is formed (Scheme 34) can be excluded because it would also predict a break in the free energy plot (Figure 28). 

Where is the local slope of the free-energy plot. From the above equation AGjj does not depend linearly on AG°gi instead, three free-energy regions can be distinguished, depending on the magnitude of AG%/4(AG j)q (Fig. 1). 

These adiabaticity factors are reasonable considering the poor overlap expected for the Eu 4f-orbitals and illustrate the utility of Eq. (g) in rationalizing rate patterns observed for very exothermic reactions. More generally, because the fi2 correction depends on not on the slope of the free-energy plot can be... 

Figure 12.06 Free energy plot indicating the behaviour of AG for various fluctuations AC (After Shewman, 1969).

Figure 6-2. Left Correlations between photo-induced hole transport rate constants and structural distances in synthetic capped hair-pin double-strand oligonucleotides for charge separation (open symbols) and charge recombination (filled symbols). Right Free energy plots for charge separation (filled symbols) and recombination (open symbols) Circles and triangles represent different sensitizer molecular units. Reprinted from ref. 52 with permission.

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