Intrinsic free

An intrinsic free energy of activation, which would exist if the reactants and products had the same AG° This is a kinetic part, called the intrinsic barrier AG ,... 

For the most part, equations don t tell most people much. But this one is different. It tells everybody exactly how to decide what s going to happen. There are just two things (and only two things) that go into this decision. First, there s how much AG is built into the system—certain chemical reactions are just intrinsically more favorable. This factor shows up in AG°. Second, there s the size of the actual products/reac-tants ratio. If it s large enough, it can overcome even a large intrinsic free-energy difference. 

Overall, steric and electronic factors, which are seen to be small, are found to work in opposite directions and, to some degree, cancel each other out. Consequently, the intrinsic free activation barriers and reaction free energies (AG nt, AG nt), respectively, span a small range for catalysts I-IV and differ by less than l.Okcalmol-1. Thus, oxidative coupling represents the one process (beside allylic isomerization, cf. Section 5.3) among all the critical elementary steps of the C8-cyclodimer channel, that is least influenced by electronic and steric factors. 

Among catalysts I-IV, which predominantly catalyze the generation of cyclodimer products, the overall lowest intrinsic free-energy barrier of 20.5 kcal mol-1 (AG nt) for 2a -> 8a appears for catalyst IV with L = P(OPh)3, where both electronic and steric factors are seen to assist the formation of VCH to a similar amount. Reductive elimination involves a higher intrinsic barrier (AG nt) for catalysts bearing moderately bulky, donor phosphines,... 

The chemical or intrinsic free energy term is reflected in the pHp2C this pHpzc varies for every oxide depending on each oxide s proton affinity. The Coulombic term, however, is approximately the same for different oxides (AG°ou) = ZF /) at a given ApH and at a given ionic strength. This will be discussed further in Chapter 3.8. 

Relationships having the same form as eq 14 can also be written for the enthalpic and entropic contributions to the intrinsic free energy barriers (10). Provided that the reactions are adiabatic and the conventional collision model applies, eq 14 can be written in the familiar form relating the rate constants of electrochemical exchange and homogeneous self-exchange reactions (13) ... 

Intrinsic free energy of activation for homogeneous self-exchange, obtained from values of corr giVen in Table 1 using AGih = "RT ln(kcorr/Zh) where 2 x 1()11, -1 ... 

Individual operator sites are denoted O if vacant, or R2 if occupied by a repressor dimer. Pairwise interactions between adjacent occupied sites are denoted ( ) AG 2 and AG23 the free energies of cooperative interaction between adjacent occupied sites, defined as the difference between AG, for any species and the sum of the intrinsic free enei es of binding to occupied sites. 

In this paper we will not pursue such formal developments any further, and instead use mean field ideas and heuristic arguments to motivate the choice of the appropriate free energy functional. We represent the intrinsic free energy functional in the form of an effective 2D step Hamiltonian H and imagine on physical grounds that it has the... 

Technically this means rather more than bad conductor . Metals conduct electricity because some of their electrons come free of their parent atoms and are at liberty to roam through the material. Their motion corresponds to an electrical current. A semiconductor also has wandering electrons, but only a few. They are not intrinsically free, but can be shaken loose from their atoms by mild heat some are liberated at room temperature. So a semiconductor becomes a better conductor the hotter it is. Metals, in contrast, become poorer conductors when hot, because they gain no more mobile electrons from a rise in temperature and the dominant effect is simply that hot, vibrating atoms obstruct the movement of the free electrons. 

Early research with irradiated paprika (Beczner et al, 1973), white pepper, nutmeg and ginger (Tjaberg etal., 1972) concluded that the technique was not suitable for the detection of these spices since the free radicals formed were short lived and could not be distinguished from intrinsic free radicals already present in the non-irradiated samples. More recently, a radiation-induced stable EPR signal has been observed for up to three months in paprika, white mustard and chilli (Stachowicz et al1992). 

F[n] is the intrinsic free energy (here simply the intrinsic energy because the entropic contribution TS vanishes at T = 0) that we have met before, and carries with it all of the standard consequences. 

The 7r-bonding hypothesis is further supported by calculations of the differences in intrinsic free energy of adsorption, i.e., AGacjs, with the effect of displaced water molecules subtracted. For a series of butyl, phenyl and naphthyl derivatives these were found to be —6-4, —8-9, and —12 4 kcal mole-1, respectively. 

An intrinsic free energy of activation, which would exist if the reactants... 

T calls the intrinsic free energy, N symbolizes the particle number. In the case of the inhomogeneous fluid the grand potential becomes to a function of the density function, to the functional n[p]. It can be formulated for the adsorbed molecular fluid which is influenced by the external potential. 

Despite these problems of saturation of vibrational bands IR spectroscopy, described in the next subsection, has been recently shown to nevertheless remain an especially powerful method to observe H2O molecules. Special recently proposed set-ups can avoid saturation in the whole conventional IR region, thus taking full advantage of the power of IR to study H-bond networks. They are first described, before the contribution of recent time-resolved nonlinear IR spectroscopy is examined. Other methods such as NIR or Raman spectroscopy, which are intrinsically free of this saturation effects can also be used to study the HjO molecule. They are often limited to some specific problems, as they do not display the power of ordinary IR spectroscopy for the study of H-bonds or of H2O molecules and cannot consequently be considered as general methods. They are described in the last subsection of this section on vibrational spectroscopy. 

The elementary kinetic constant k is therefore the product of a term calculated from a difference of intrinsic free enthalpies 12 and a ratio of symmetry numbers, which we will call single-events number ne — 0 ob/[Pg.276]

Or as an energy model14 for the reactants and activated complexes composed of intrinsic free enthalpy components and symmetry number (see below). 

The intrinsic free enthalpy is the free enthalpy minus the symmetry entropic contributions. 

To calculate the free enthalpy of an ion, we need to know its symmetry number and its intrinsic free enthalpy. The symmetry number can be calculated methodically and algorithmically. The intrinsic free enthalpy is obtained from the assumptions of the single-events theory. For an ion, the intrinsic free enthalpy calculations involve two parameters ... 

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