Activation Gibbs free energy

The Hammett equation is the best-known example of a linear free-energy relationship (LEER), that is an equation which implies a linear relationship between free energies (Gibbs energies) of reaction or activation for two related processes71. It describes the influence of polar meta- or para-substituents on reactivity for side-chain reactions of benzene derivatives. 

Gibbs free energy change Transition state activation free energy Henry s constant Enthalpy change... 

Fats, rancidity, 328 Favorskii rearrangement, 294 Fenton s reagent, 306 Ferrocene, 275 Field effects, 22, 152, 364 Flash photolysis, 304 Fluorination, 121,140,170, 315, 326 Free energy, Gibbs, 34 change and K, 35, 359 of activation, 38, 359 standard, 35... 

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 ... 

Fugacity, also see below f = Henrian activity coefficient F = Free Energy, Gibbs Free Energy F = Farady Constant g = Gas... 

For chemical rate processes, equation (2) applies, where AG is the standard free energy (Gibbs energy) of activation. 

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. ... 

When the expanded expression for Gibb s free energy is substituted for AG. as shown in Eq. 4, it becomes possible to calculate the enthalpy and entropy of activation when rates are available across a range of temperatures. These parameters are calculated in Table 6 using the data supplied by Zavitsas and Ferrero [80,85,90]. 

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.

The partial molar entropy of a component may be measured from the temperature dependence of the activity at constant composition the partial molar enthalpy is then determined as a difference between the partial molar Gibbs free energy and the product of temperature and partial molar entropy. As a consequence, entropy and enthalpy data derived from equilibrium measurements generally have much larger errors than do the data for the free energy. Calorimetric techniques should be used whenever possible to measure the enthalpy of solution. Such techniques are relatively easy for liquid metallic solutions, but decidedly difficult for solid solutions. The most accurate data on solid metallic solutions have been obtained by the indirect method of measuring the heats of dissolution of both the alloy and the mechanical mixture of the components into a liquid metal solvent.05... 

For a detailed discussion of the calculation of activities (and excess Gibbs free energies) from freezing point measurements, see R. L. Snow. J. B. Ott. J. R. Goates. K. N. Marsh, S. O Shea, and R. N. Stokes. "(Solid + Liquid) and (Vapor + Liquid) Phase Equilibria and Excess Enthalpies for (Benzene + //-Tetradecane), (Benzene + //-Hexadecane). (Cyclohexane + //-Tetradecane), and (Cyclohexane +//-Hexadecane) at 293.15, 298.15, and... 

Since these mixing processes occur at constant pressure, // is the heat evolved or absorbed upon mixing. It is usually measured in a mixing calorimeter. The excess Gibbs free energy, is usually obtained from phase equilibria measurements that yield the activity of each component in the mixtureb and S is then obtained from equation (7.17). The excess volumes are usually obtained... 

Transition state theory gives the Gibbs free energy of activation from either of the forms as... 

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). 

These techniques are known as linear free energy relations, LFER. Imagine that one has determined the rate constants, or the Gibbs free energies of activation, for a series of reactions. The reactions are all the same, save for (for example) a different substituent on each reactant. The substituent is not a direct participant in the reaction. In an LFER, the values of log k or AG are correlated with some characteristic of the substituent as manifested in another reaction series. If the correlation is successful, then the two series of reactions have a common denominator. This technique has proved to be a powerful one for systematizing reactivity. We shall see a number of such correlations. 

Gibbs (free) energy of activation (AG ), 10, 84, 165 heat capacity of activation (ACP ), 160-161... 

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