Standard free-energy of reaction

Table 16-5 The standard free energy of reaction, AG , for the main environmental redox reactions...

If two reactions differ in maximum work by a certain amount 8wm (= -SAG ), it follows from the Brpnsted relation [when taking into account the Arrhenius equation and the known relation between the equilibrium constant and the Gibbs standard free energy of reaction, A m = exp(-AGm/J r)] that their activation energies will differ by a fraction of this work, with the opposite sign ... 

Similarly, the change of standard free energy of reaction (4-12b) is For ethyl xanthate... 

Standard free energy of reaction and the equilibrium constant 1187... 

The algebraic sum of the standard chemical potentials is called the standard free energy of reaction and is denoted as ArG°. In our case ... 

In the literature (e.g., Thauer et al. 1977 Hanselmann, 1991) you find the AfG°(aq) values at 25°C for all the species involved in reaction Eq. 1. Note that by convention, the free energies of formation of the elements in their naturally occurring most stable form, as well as of the proton in aqueous solution, are set to zero. From these values, calculate the standard free energy of reaction Eq. 1 ... 

Does a positive standard free energy of reaction, ArG°, mean that a given reaction does not occur spontaneously under any condition ... 

In the literature you find all the necessary AfC°(aq) values for the species involved in the two reactions. See Illustrative Example 12.1 for a detailed description of how to make the necessary calculations.The resulting standard free energies of reaction are ... 

Table 14.2 Standard Reduction Potentials and Average Standard Free Energies of Reaction (per Electron Transferred) at 25 °C of Some Redox Couples that Are Important in Natural Redox Processes (The reactions are ordered in decreasing 1 h(W) values.)a...

Hence, the standard free energy of reaction Eq. 6 can now be calculated (note that we omit AfG (aq) which is zero) ... 

Finally, we should note that the E value of a multielectron transfer half reaction is given by the average of the respective standard one-electron reduction potentials. This is easy to rationalize when recalling that the overall standard free energy of reaction of a sequence of reaction steps is given by the sum of the ArG° values of each step. Hence, we may write ... 

Figure 14.9 Energetic considerations for the reduction of nitrobenzene to nitrosobenzene (Ar = C6H5) with HS as electron donor at environmental ( W ) standard conditions. Note that ArG°(W)= -nF A (W). ArG,°(W) is the standard free energy of reaction for the transfer of the first electron ArG° is the overall standard free energy of reaction for the transfer of both electrons.

A more exact analysis of the effect of solvent variation and hence of solvent—solute interactions could be obtained through the thermodynamic transfer functions.21 The application of these to the equilibrium situation can be seen by referring to Figure 6. SAG, is defined as the difference in standard free energy of reaction between the two solvents A and B (equation 32), which by reference to Figure 6 leads to equation (33) ... 

The standard free energy of formation of a substance is the standard free energy of reaction per mole of compound when it is formed from its elements in their most stable forms. The sign of AG f tells us whether a compound is stable or unstable with respect to its elements. Standard free energies of formation are used to calculate standard reaction free energies by using Eq. 21. 

The assumptions, equations and several applications of a recently formulated theory of electron transfer reactions of solvated electrons are outlined. The relationship of the reorganization terms to those of ordinary electron exchange and electrochemical reactions is described, together with the role played by an effective standard free energy of reaction. Applications include prediction of conditions under which chemiluminescence might be found and description of conditions under which reactions might not be diffusion-controlled. 

In this last equation AF0,lntisthe standard free energy of reaction AF°f in the prevailing medium, corrected for the translational free energy loss when the oriented center, in which the electron formerly resided, disappears during the formation of product from the centered distribution on the hypersurface. This corrected AF° constitutes the driving force for reaction at the mean separation distance R ... 

Quantitative structure/activity relationships (QSARs) for hydrolysis are based on the application of linear free energy relationships (LFERs) (Well, 1968). An LFER is an empirical correlation between the standard free energy of reaction (AG0), or activation energy (Ea) for a series of compounds undergoing the same type of reaction by the same mechanism, and the reaction rate constant. The rate constants vary in a way that molecular descriptors can correlate. 

Linear free energy relationship (LFER) — For various series of similar chemical reactions it has been empirically found that linear relationships hold between the series of free energies (-> Gibbs energy) of activation AG and the series of the standard free energies of reactions AGf, i.e., between the series of log fc (k -rate constants) and log K (Kt - equilibrium constants) (z labels the compounds of a series). Such relations correlate the - kinetics and -> thermodynamics of these reactions, and thus they are of fundamental importance. The LFER s can be formulated with the so-called Leffler-Grunwald operator dR ... 

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