Free energy exchange

Experimental gas-phase acidities of pyrrole and imidazole reveal that there is a free-energy exchange of Arxnf 298 = 9.3 0.6 kcal mol for deprotonation of imidazole by anionic pyrrole (Equation 1) <2005JPCA11504>. 

Many of these reactions are thermodynamically controlled and proceed under mild conditions. For heterocumulene insertion, the product has additional conjugative stabilization compared with the reagents, and this provides for a favorable free energy exchange for the reaction [e.g., reaction (c)]. A further driving force often derives from the greater polarity of the insertion adduct over its precursors, and the adduct thus frequently precipitates from solution in a nonpolar solvent (cf. 3). 

Thennal equilibrium means free transfer (exchange) of energy in the fonn of heat, mechanical (liydrostatic) equilibrium means free transfer of energy in the fonn of pressure-volume work, and material equilibrium means free transfer... 

Sekiguchi S, Kobori Y, Akiyama K and Tero-Kubota S 1998 Marcus free energy dependence of the sign of exchange interactions in radical ion pairs generated by photoinduced electron transfer reactions J. Am. Chem. Soc. 120 1325-6... 

Finally, exchange is a kinetic process and governed by absolute rate theory. Therefore, study of the rate as a fiinction of temperature can provide thennodynamic data on the transition state, according to equation (B2.4.1)). This equation, in which Ids Boltzmaim s constant and h is Planck s constant, relates tlie observed rate to the Gibbs free energy of activation, AG. ... 

The canonical ensemble corresponds to a system of fixed and V, able to exchange energy with a thennal bath at temperature T, which represents the effects of the surroundings. The thennodynamic potential is the Helmholtz free energy, and it is related to the partition fiinction follows ... 

This section contains a brief review of the molecular version of Marcus theory, as developed by Warshel [81]. The free energy surface for an electron transfer reaction is shown schematically in Eigure 1, where R represents the reactants and A, P represents the products D and A , and the reaction coordinate X is the degree of polarization of the solvent. The subscript o for R and P denotes the equilibrium values of R and P, while P is the Eranck-Condon state on the P-surface. The activation free energy, AG, can be calculated from Marcus theory by Eq. (4). This relation is based on the assumption that the free energy is a parabolic function of the polarization coordinate. Eor self-exchange transfer reactions, we need only X to calculate AG, because AG° = 0. Moreover, we can write... 

The distribution coefficient is an equilibrium constant and, therefore, is subject to the usual thermodynamic treatment of equilibrium systems. By expressing the distribution coefficient in terms of the standard free energy of solute exchange between the phases, the nature of the distribution can be understood and the influence of temperature on the coefficient revealed. However, the distribution of a solute between two phases can also be considered at the molecular level. It is clear that if a solute is distributed more extensively in one phase than the other, then the interactive forces that occur between the solute molecules and the molecules of that phase will be greater than the complementary forces between the solute molecules and those of the other phase. Thus, distribution can be considered to be as a result of differential molecular forces and the magnitude and nature of those intermolecular forces will determine the magnitude of the respective distribution coefficients. Both these explanations of solute distribution will be considered in this chapter, but the classical thermodynamic explanation of distribution will be treated first. 

Rapid exchange of positions was observed for acyl and amidoyl groups in the NMR spectra of compounds 36 in 1-chloronaphthalene solution at high temperatures (170-215°C) (Scheme 18). [72JCS(CC)709]. Crossover experiments clearly indicated the intermolecular exchange. The value of the free-energy barrier was determined as AG = 100 kJ mol at the coales-... 

Using the reaction free energy AG, the cell voltage Aelectrons exchanged during an electrode reaction must be determined from the cell reaction. For the Daniell element (see example), two moles of electrons are released or received, respectively ... 

The fact that in this work a satisfactory linear free energy correlation was obtained for reaction at an ortho position again shows that hydrogen exchange is a reaction of very small steric requirement, as noted elsewhere504. 

A schematic diagram of the free energy changes in an electron exchange reaction, showing the intersection of two parabolas. The lighter curve represents n,c the darker one, eng, ncg. 

In this chapter it is clearly impossible to do more than sample the extensive literature on the carbon acidity of sulfinyl and sulfonyl compounds, as it illuminates the electronic effects of these groups, particularly in connection with linear free-energy relationships. There are three main areas to cover first, as already indicated, equilibrium acidities (pKa values) second, the kinetics of ionization, usually studied through hydrogen isotopic exchange and finally, the kinetics of other reactions proceeding via carbanionic intermediates. 

FIGURE 3.5. The actual free-energy profile for the ground-state surface as a function of the energy gap As. The calculations are done for the CF + CH3C1- C1CH3 + CP exchange reaction (Ref. 11). 

Exchange integrals, 16,27 Exchange reactions, free energy diagram for, 89... 

There is a very special case for self-exchange reactions in which the left side of the equation is identical to the right side. Accordingly, there is no free energy change in the reaction, and the equilibrium constant ( fn) must be unity (Eq. 9.29). 

Monomeric actin binds ATP very tightly with an association constant Ka of 1 O M in low ionic strength buffers in the presence of Ca ions. A polymerization cycle involves addition of the ATP-monomer to the polymer end, hydrolysis of ATP on the incorporated subunit, liberation of Pi in solution, and dissociation of the ADP-monomer. Exchange of ATP for bound ADP occurs on the monomer only, and precedes its involvement in another polymerization cycle. Therefore, monomer-polymer exchange reactions are linked to the expenditure of energy exactly one mol of ATP per mol of actin is incorporated into actin filaments. As a result, up to 40% of the ATP consumed in motile cells is used to maintain the dynamic state of actin. Thus, it is important to understand how the free energy of nucleotide hydrolysis is utilized in cytoskeleton assembly. 

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