Some Thermodynamic Considerations

Fe(III)) may be facilitated, i.e., the activation energy of the redox reaction lowered. 

We first compare the consequences of solute and surface complexation from a thermodynamic point of view. We use for exemplification Fe(II) and Fe(III) because 

1) more data are available with this redox pair than with others, and 

2) the transformations of iron are especially important in the redox cycling of electrons in natural environments. 

As Fig. 9.2 shows, the Fe(III)/Fe(II) redox couple can adjust with appropriate ligands to any redox potential within the stability of water. The principles exemplified here are of course also applicable to other redox systems. 

That pet cannot affect the Gibbs adsorption equation can be verified by applying a formal equilibrium condition to the pet reaction ofEq. (1), yielding  

Ms and Ms,ads are the electrochemical potentials of S in the bulk solution and in the adsorbed state. Let us apply the Gibbs adsorption equation to the interphase between a pure metal M and an aqueous solution containing molecular and ionic species denoted by the subscript j, in addition to water w and the species S. Choosing the neutral metal atoms M and the electrons e in excess with respect to metal atoms as the constituents of the metal phase, we may formally write  

rSi 0 and r, ads are the surface excesses of nonspecifically adsorbed S molecules and of those chemisorbed with pet, while y is the interfacial tension. Let us assume for simplicity that water is in such a large excess with respect to the other components of the solution phase as to allow us to set dfuw = 0 at constant temperature T and pressure P. Noting that in the pure metal phase dpM is also equal to zero at constant T and P, and replacing lSads from Eq. (3) into Eq. (4), after rearrangement we get  

Upon formally separating the electrochemical potentials into their chemical and electrical contributions  

To complete the thermodynamic treatment of the interphase, one should now eliminate the chemical potentials //y of any ionic species in 

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To better understand the complexity of situation, it is useful to apply some thermodynamic considerations. The separation process is governed by the change of the Gibbs function due to transfer of solute molecules between the mobile and the stationary phase. One can write... 

Tolstoguzov, V.B. (2003). Some thermodynamic considerations in food formulation. Food Hydrocolloids, 17, 1-23. 

Consequently, a parallel alignment of smectic layers is linearly stable against undulations even if the perpendicular alignment might be more preferable due to some thermodynamic considerations. As we have shown in Fig. 8, this rigorous result of standard smectic A hydrodynamics is weakened in our extended formulation of smectic A hydrodynamics. When the director can show independent dynamics, an appropriate anisotropy of the viscosity tensor can indeed reduce the threshold values of an undulation instability. 

We will now look at some thermodynamic considerations in a little more detail. 

Weigert (Zeitsch phystk Chem, 63, 458, 1908) has put forward some thermodynamical considerations of a very similar nature to those of Byk, for the investigation of the same experimental case, the photo-poly ... 

Weiner, N., 1986, Strategies for formulation and evaluation of emulsions and suspensions Some thermodynamic considerations. Drug Dev. Ind. Pharm. 12 933-951. 

Borsook, H., and Huffman, H. M., Some Thermodynamical Considerations of Amino Acids, Peptides and Related Substances. In C.L.A. Schmidt, Chemistry of the Amino Acids and Proteins, p. 822. C. C Thomas, Springfield, Illinois, 1938. 

Some Thermodynamic Considerations of the Lower Disorder-to-Order Transition of Diblock Copolymers... 

In the following paragraph, we will start with some thermodynamic considerations and then we will give a survey on CO oxidation and the reaction pathways of... 

The details are omitted here, but the coefficients are fixed by equation (9), conditions on the derivatives of G r) with respect to r, and some thermodynamic considerations. 

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