Gibbs free energy of activation, and

The standard entropy difference between the reactant(s) of a reaction and the activated complex of the transition state, at the same temperature and pressure. Entropy of activation is symbolized by either A5 or and is equal to (A// - AG )IT where A// is the enthalpy of activation, AG is the Gibbs free energy of activation, and T is the absolute temperature (provided that all rate constants other than first-order are expressed in temperature-independent concentration units such as molarity). Technically, this quantity is the entropy of activation at constant pressure, and from this value, the entropy of activation at constant volume can be deduced. See Transition-State Theory (Thermodynamics) Gibbs Free Energy of Activation Enthalpy of Activation Volume of Activation Entropy and Enthalpy of Activation (Enzymatic)... 

The Gibbs free energy of activation and Gibbs free energy of reaction are determined as with the enthalpy and internal energy discussed previously. 

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. ... 

Fig. 16. A. Plot of log iNa as a function of T 1 (°K) using the experimental values of the rate constants and the location of the binding sites in Eq. 4. The Gibbs free energy of activation is calculated from Eq. 3 the AS are taken to be zero, and the current is calculated by means of Eq. 4. The purpose is to demonstrate that multibarrier channel transport can be seen as single rate process with average values for the enthalpies of activation. Non-linearity of such a plot is then taken to arise form the dynamic nature of the channel.

We shall reformulate Eq. (7-54) on thermodynamic grounds, introducing A//, AS, and AG, the standard Gibbs free energy of activation. These expressions also follow from Eq. (7-37). 

The Gibbs free energy of activation, AG, may be separated into enthalpic and entropic terms, if required, by using another relationship from equilibrium thermodynamics,... 

Schematic representation of the Gibbs free energies for activation and reaction of reactants A + B+. . . to form products M + N+. . . via the transition state [A, B,.. . ]. ...

Modern theoretical developments in the theory of proton-transfer reactions suggest that such linear Bronsted plots are only a first approximation when the range of the P-KHA-values is narrow. When a wider range of bases is used, the curve obtained should be such that the Gibbs free energy of activation AG fits the Marcus eqn (6). This equation was derived (Cohen and Marcus, 1968 ... 

In this context, the solvent influence on the C—N rotational barrier in N,N-dimethylformamide, Mc2N—CH=0 <-> Me2N+=CH—0 , is noteworthy [280]. For this rotation, the Gibbs free energy of activation in the gas phase AG =81 kJ/mol) is much smaller than in polar HBD solvents such as water AG = 92 kJ/mol). Thus, the rate of amide bond rotation decreases as the polarity and the HBD ability of the solvent increases. This can be attributed to the change in dipole moment on rotation, whereby a polar solvent stabilizes the ground state with the higher dipole moment fi = 3.8 D) in preference to the less dipolar activated complex [280]. 

Fig. 9.1 Reaction profile for peptide bond cis-trans isomerization. The kinetic constants for the trans to cis (k, J and cis to trans (kM>) isomerization are dependent on the Gibbs free energy of activation (AG ). The ground state energy difference AG° (G°as - C°mm) determines the population of the cis and trans isomers in the equilibrium state.

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