Gibbs energy profile

I.2. Energetics of the Benzylation by o-QM in the Gas Phase and in Aqueous Solution The Gibbs energy profiles for the NH3, H20, and H2S addition reactions to o-QM, in the gas phase and in aqueous solutions, both in the presence (water-catalyzed mechanism) and in the absence of an ancillary water molecule (uncatalyzed mechanism) have been explored, and are displayed in Scheme 2.3.13... 

SCHEME 2.3 Gibbs energy profiles for the benzylation of NH3 (a), H20 (b), and H2S (c) by o-QM in the gas phase (continuous line), water-catalyzed (S4-S6) and uncatalyzed (S1-S3), and in aqueous solution (dotted line, Slaq-S6aq) optimizing both reagents and TSs in aqueous solution [B3LYP-C-PCM/6-311 +G(d,p)]. Data are taken from Ref. [13]. 

Figure 6.6. Gibbs energy profiles of the outer-sphere one-electron transfer process (4) in the Butler -Volmer formalism at electrode potential Ej (a) and electrode potential E2 (b).

Figure 6.8. Gibbs energy profiles of a proton discharge process resulting in a metal-hydrogen bond formation. The difference in the Gibbs energy of adsorption of hydrogen between metal 1 to metal 2 lowers the activation barrier for the discharge and makes metal 2 the electrocatalytically more favorable (active) electrode material.

Fig. 10. Standard Gibbs energy profile along the axis of an ion transfer across the liquid-liquid interface in the absence (1) and presence (2) of an additional potential barrier at the interface. The broken line represents the contribution of the long-range electrostatic forces the solid line corresponds to the sum of the long- and short-range contributions X2 Helmholtz planes in the aqueous and the organic solvent phases.

Fig. 11. Standard Gibbs energy profile (solid line) for an ion transfer across the sharp interface calculated through a non-Boltzmann sampling using a total of 1.6 ns molecular dynamics trajectories. The crosses denote half of the average ion-solvent electrostatic energy. (After [128]).

Fig. 7.3 Gibbs energy profile for the formation of an activated complex 7 in a bimolecular heteronuclear reaction (A) and a bimolecular homonuclear reaction (B).

The Gibbs energy profile involved in formation of the transition state for atom transfer is that shown in fig. 7.3. When the attacking nucleophile is the same as the leaving group, then the profile is that for a homonuclear bimolecular reaction. This type of system can be studied using radioactive isotopes. 

Macroscopic thermodynamic models have been presented to give the Gibbs energy profile of the particle, as a function of its position along the interfacial normal [198, 199]. If the aqueous phase (z < 0) is treated as the reference state and line tension at the three-phase boundary is neglected, then... 

Figure 1 Gibbs energy profile illustrating the relationship between the decrease in energy of activation and the exergonicity of a reaction. Reaction II has a larger Gibbs energy of activation and is less exergonic than reaction I.

Fig. 13 Electrostatic Gibbs energy profiles for ion transfer across the ITIES boundary. Solid lines finite-size ion profiles in units of (ze) /eio, ei = 78 and different values of si. Dashed lines profile for the point change model in the same units, ei = 78, ez = 10 [25]. (Reproduced by permission of Elsevier Sequoia S. A.)...

Fig. 8 Standard Gibbs energy profile for global ion-transfer reactions.

Fig. 10 Standard Gibbs energy profile for an elementary ion-transfer reaction.

We can show the energy changes that occur during a reaction by a Gibbs energy profile. 

FIGURE 3.21 A calculated Gibbs energy profile for the ORR shown at different values of the electrode potential relative to the SHE. Close to equilibrium (dashes), the profile contains two uphill sequences, corresponding to step 1 and steps 3 and 4. Below an electrode potential of 0.78 V all steps in the sequence are downhill, as shown by the profile in the middle (short dashes). (Adapted from Chem. Phys., 319(1), Rossmeisl, J., Logadottir, A., and Nprskov, J. K. Electrolysis of water on (oxidized) metal surfaces, 178-184, Figure 2, Copyright (2005) Elsevier. With permission.)... 

There are two challenges associated with the Gibbs energy profile shown in Figure 3.21 and the correlation between and AG (Oad) shown in Figure 3.20. 

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