Transfer Gibbs free energy

The relevant quantities are the transfer activity coefficients, wfs related t0 the standard molar transfer Gibbs free energies by ... 

Static dielectric constant Force constant Viscosity Electron transfer Gibbs free energy... 

If we were to place a piece of zinc metal into an aqueous copper(II) sulfate solution, we would see a layer of metallic copper begin to deposit on the surface of the zinc (see Fig. K.5). If we could watch the reaction at the atomic level, we would see that, as the reaction takes place, electrons are transferred from the Zn atoms to adjacent Cu2 r ions in the solution. These electrons reduce the Cu2+ ions to Cu atoms, which stick to the surface of the zinc or form a finely divided solid deposit in the beaker. The piece of zinc slowly disappears as its atoms give up electrons and form colorless Zn2+ ions that drift off into the solution. The Gibbs free energy of the system decreases as electrons are transferred and the reaction approaches equilibrium. However, although energy is released as heat, no electrical work is done. 

The units of AG are joules (or kilojoules), with a value that depends not only on E, but also on the amount n (in moles) of electrons transferred in the reaction. Thus, in reaction A, n = 2 mol. As in the discussion of the relation between Gibbs free energy and equilibrium constants (Section 9.3), we shall sometimes need to use this relation in its molar form, with n interpreted as a pure number (its value with the unit mol struck out). Then we write... 

The intrinsic aqueous solubility S of a drug X is related to the Gibbs free energy AGs i of the transfer of the drug X from its lowest free energy crystalline form to a saturated solution of the neutral form of X in water by the simple equation ... 

For two relatively immiscible solvents log P can be considered [1] proportional to the molar Gibbs free energy of transfer between octanol and water ... 

Fig. 12.2. Free energy data for electron transfer between the protein cytochrome c and the small acceptor microperoxidase-8 (MP8), from recent simulations [47]. Top Gibbs free energy derivative versus the coupling parameter A. The data correspond to solvated cytochrome c the MP8 contribution is not shown (adapted from [47]) Bottom the Marcus diabatic free energy curves. The simulation data correspond to cyt c and MP8, infinitely separated in aqueous solution. The curves intersect at 77 = 0, as they should. The reaction free energy is decomposed into a static and relaxation component, using the two steps shown by arrows a static, vertical step, then relaxation into the product state. All free energies in kcalmol-1. Adapted with permission from reference [88]...

The computation of chemical equilibria can be posed as an optimization problem with linear side conditions. For any infinitesimal process in which the amounts of species present may be changed by either the transfer of species to or from a phase or by chemical reaction, the change in the Gibbs free energy is... 

Electrode reactions are inner-sphere reactions because they involve adsorption on electrode surfaces. The electrode can act as an electron source (cathode) or an electron sink (anode). A complete electrochemical cell consists of two electrode reactions. Reactants are oxidized at the anode and reduced at the cathode. Each individual reaction is called a half cell reaction. The driving force for electron transfer across an electrochemical cell is the Gibbs free energy difference between the two half cell reactions. The Gibbs free energy difference is defined below in terms of electrode potential,... 

In principle, Gibbs free energies of transfer for trihalides can be obtained from solubilities in water and in nonaqueous or mixed aqueous solutions. However, there are two major obstacles here. The first is the prevalence of hydrates and solvates. This may complicate the calculation of AGtr(LnX3) values, for application of the standard formula connecting AGt, with solubilities requires that the composition of the solid phase be the same in equilibrium with the two solvent media in question. The other major hurdle is that solubilities of the trichlorides, tribromides, and triiodides in water are so high that knowledge of activity coefficients, which indeed are known to be far from unity 4b), is essential (201). These can, indeed, be measured, but such measurements require much time, care, and patience. 

As indicated in the previous section, the derivation of Gibbs free energies of transfer, and thence of entropies of transfer, from trichloride... 

The Gibbs Free Energy change accompanying the transfer of dnB moles of B from a reservoir in which it is present in its standard state to the equilibrium mixtures is... 

The signal generated by the complex is governed by several physical phenomena associated with the matrix thickness. As soon as the probe is placed in contact with the analyte, external mass transfer controls the movement of the analyte toward the surface of the optical probe.(S4) The osmotic pressure and Gibbs free energy dictate the permeation of the analyte into the matrix. Once the analyte has penetrated the matrix, internal mass transfer resistance controls the movement of the analyte in the matrix. Eventually, the probe reaches a steady state of equilibrium with molecules continuously moving in and out of the matrix. 

It is apparent from early observations [93] that there are at least two different effects exerted by temperature on chromatographic separations. One effect is the influence on the viscosity and on the diffusion coefficient of the solute raising the temperature reduces the viscosity of the mobile phase and also increases the diffusion coefficient of the solute in both the mobile and the stationary phase. This is largely a kinetic effect, which improves the mobile phase mass transfer, and thus the chromatographic efficiency (N). The other completely different temperature effect is the influence on the selectivity factor (a), which usually decreases, as the temperature is increased (thermodynamic effect). This occurs because the partition coefficients and therefore, the Gibbs free energy difference (AG°) of the transfer of the analyte between the stationary and the mobile phase vary with temperature. 

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