The Thermodynamic Situation

The exchange of energy connected with a chemical or electrochemical reaction is described by thermodynamic laws and data, as shown in Chapter 1 of this book. Since these laws apply only to the state of 

Monobasic sulfate Dibasic sulfate PbOPbSO 2PbOPbS04 6.28-7.31  

Substance Molecular weight Specific weight Electrical resistance 

The specific resistance of the oxides depends on pressure (cf. Ref. [5], Table 2.3). 

Equation 6.8 represents by definition the zero point of the electrochemical potential scale (standard hydrogen electrode, often denoted SHE). 

Eq is the decomposition voltage of water. Above this value, water is not stable but decomposes with formation of oxygen (O2). 

At small pH values, the curve A is below the H2/H curve, which means that lead is not stable in an aqueous solution under these conditions, but is converted into Pb ions, and simultaneously water is decomposed with formation of hydrogen H2. 

---

A survey of the thermodynamic situation is provided by so-called Pourbaix diagrams [10], which show equilibrium potentials versus the pH value. Figure 1 shows such a diagram for lead and its oxides in a very simplified form that considers only the standard concentrations of the dissolved components. The complete diagram contains a great number of parallel lines that express the various concentrations. 

Hydrogen oxidation according to Eq. (5) is possible above 0 V. If hydrogen evolution occurs at the negative electrode and the H2 evolved reaches the positive electrode, from the thermodynamic situation the reaction that is to be expected is ... 

Direct metalation of 2,6-disubstituted pyridines has also been reported to occur at the 4-position under certain conditions. Thus the 2,6-bistrimeth-ylsilyl chromium tricarbonyl compound 96 gave the 4-lithio derivative 102 [91JCS(P1)501], and 2,6-dichloropyridine gave mainly the 4-lithio derivative 103 under kinetic deprotonation conditions, in contrast to the thermodynamic situation where 3-lithiation was preferred (91JOC4793). 

At a rough surface of a solid without electron defects, the molecules of oxygen do not dissociate faster into their atoms than in air because no electron interchanges take place. In contrast to the homogeneous gas phase, the thermodynamic situation at the surface of a suitable catalyst is quite different. Due to the electron affinity of oxygen, the electron can be transferred to the chemisorbing oxygen... 

Figure 2. The thermodynamic situation upon solidification of a multemary system. The vertical lines designate principal reaction pathways, the dashed tangent lines illustrate the compositional changes arising from an equilibrium solidification at the respective pathways (interrupt lines on the vertical arrows). The narrow areas of existence designate stable phases with a finite phase width, the area designated metastable indicates the existence of a single phase solid which is unstable at ambient conditions.

At the macroscopic level, information is quantified via multivariable functions, line integrals, and probability distributions—the tools central to Chapters 3 through 5. The thermodynamic situations that admit analytical solutions are rare. Approximations are necessary with the assistance of computer programming and spreadsheets. 

The conversion is limited by the chemical equilibrium. The thermodynamic situation for the simultaneous reaction and distillation is qualitatively given in figure 1 showing a mole fraction tetrahedron for this system. 

Thus, it turns out that the curvature parameter required for the numerical calculation to obtain critical gradients in the order of the experiment is quite reasonable and corresponds to the thermodynamic situation of the Al-Co system. Especially, for the polymorphic nucleation mode without shape optimization, we find almost exact agreement. The value of a = 8 x 10 J/atom for the polymorphic mode without... 

---