Activity diagrams construction

Figure 1.96. Log /oj-pH diagram constructed for temperature = 200°C, ionic strength = 1, ES = 10 m, and EC = 10 m. Solid line represents aqueous sulfur and carbon species boundaries which are loci of equal molalities. Dashed lines represent the stability boundaries for some minerals. Ad adularia. Bn bomite, Cp chalcopyrite, Ht hematite, Ka kaolinite, Mt magnetite, Po pyrrhotite, Py pyrite, Se sericite. Heavy dashed lines (1), (2), and (3) are iso-activity lines for ZnCOs component in carbonate in equilibrium with sphalerite (1) 4 co3=0-1- (2) 4 ,co3=0-01- (3) 4 co3 =0-001 (Shikazono, 1977b).

Helgeson (1967) constructed an activity diagram depicting chemical equilibrium points (albite-sericite-K-feldspar and albite-sericite-Na-montmorillonite) of NazO-K20-Si02-Al203-H20 system at elevated temperatures. At these points,... 

Table 8.25 Equilibrium constants used for construction of figure 8.31 (activity diagram). ...

In order to construct the activity diagrams in a rigorous fashion, a certain amount of information must be available. Some experimental data for the mica-feldspar-kaolinite-gibbsite-montmorillonite relations are available. Data for the other minerals are often inferred from measurements of natural chemical parameters (K+, SiC, H+ concentrations in solutions) in situations where the different minerals are assumed to be stable. The relations between minerals can also be calculated as a function of K+, SiO and pH using thermochemical data for the participating phase (Hess, 1966) when they are known with precision. Frequently it is... 

Thus, the foregoing shows how the real activation energies must be calculated—they can be derived from potential energy diagrams constructed on the assumption that the latent equilibrium heat of the electrode process is zero. 

Using these equations, the stability fields of the minerals in this system can be shown on activity diagram and chemical potential diagram (Figs. 1.3,1.4, and 1.5). Thermochemical data that can be used for constructing stabihty diagrams are presented in Table 1.1. 

Figure 17.10 Construction of a two helix truncated Z domain, (a) Diagram of the three-helix bundle Z domain of protein A (blue) bound to the Fc fragment of IgG (green). The third helix stabilizes the two Fc-binding helices, (b) Three phage-display libraries of the truncated Z-domaln peptide were selected for binding to the Fc. First, four residues at the former helix 3 interface ("exoface") were sorted the consensus sequence from this library was used as the template for an "intrafece" library, in which residues between helices 1 and 2 were randomized. The most active sequence from this library was used as a template for five libraries in which residues on the Fc-binding face ("interface") were randomized. Colored residues were randomized blue residues were conserved as the wild-type amino acid while yellow residues reached a nonwild-type consensus, [(b) Adapted from A.C. Braisted and J.A. Wells,...

A more complete analysis of interacting molecules would examine all of the involved MOs in a similar wty. A correlation diagram would be constructed to determine which reactant orbital is transformed into wfiich product orbital. Reactions which permit smooth transformation of the reactant orbitals to product orbitals without intervention of high-energy transition states or intermediates can be identified in this way. If no such transformation is possible, a much higher activation energy is likely since the absence of a smooth transformation implies that bonds must be broken before they can be reformed. This treatment is more complete than the frontier orbital treatment because it focuses attention not only on the reactants but also on the products. We will describe this method of analysis in more detail in Chapter 11. The qualitative approach that has been described here is a useful and simple wty to apply MO theory to reactivity problems, and we will employ it in subsequent chapters to problems in reactivity that are best described in MO terms. I... 

It should be noted that Fig. 1.15 (top) is based entirely on thermodynamic data and is therefore correctly described as an equilibrium diagram, since it shows the phases (nature and activity) that exist at equilibrium. However, the concepts implicit in the terms corrosion, immunity and passivity lie outside the realm of thermodynamics, and, for example, passivity involves both thermodynamic and kinetic concepts it follows that Fig. 1.15 (bottom) cannot be regarded as a true equilibrium diagram, although it is based on one that has been constructed entirely from thermodynamic data. 

The equilibrium potentials and E, can be calculated from the standard electrode potentials of the H /Hj and M/M " " equilibria taking into account the pH and although the pH may be determined an arbitrary value must be used for the activity of metal ions, and 0 1 = 1 is not unreasonable when the metal is corroding actively, since it is the activity in the diffusion layer rather than that in the bulk solution that is significant. From these data it is possible to construct an Evans diagram for the corrosion of a single metal in an acid solution, and a similar approach may be adopted when dissolved O2 or another oxidant is the cathode reactant. 

Figure 1.120. Probable ranges of sulfur and oxygen activities for the Te-type and Se-type deposits. The diagram was constructed mainly based on Heald et al. (1987). Temperature = 250°C (Shikazono et al., 1990).

CPM is an important scheduling aid, but from it alone a schedule cannot be devised. To schedule a project, after a CPM or PERT diagram has been constructed the planner must evaluate the work force and special equipment needed for each activity. Then he must devise a scheduling plan that will maintain a fairly even level of labor and assure the most efficient use of specialty items. 

To construct such a diagram, a set of defect reaction equations is formulated and expressions for the equilibrium constants of each are obtained. The assumption that the defects are noninteracting allows the law of mass action in its simplest form, with concentrations instead of activities, to be used for this purpose. To simplify matters, only one defect reaction is considered to be dominant in any particular composition region, this being chosen from knowledge of the chemical attributes of the system under consideration. The simplified equilibrium expressions are then used to construct plots of the logarithm of defect concentration against an experimental variable such as the log (partial pressure) of the components. The procedure is best illustrated by an example. 

Figure A.15 Energy diagram for the adsorption of a simple diatomic molecule on a d-metal. Chemisorption orbitals are constructed from both the bonding and the antibonding levels of the molecule. As the latter becomes partially occupied, the intramolecular bond of the adsorbate has been activated.

A large number of publications deal with the construction and interpretation of potential -pH (Pourbaix) diagrams, and some of these have been included in Table HJ. Most of these studies avoid the question of activity coefficients because the stability fields are calculated for arbitrarily specified activities of the species in solution. 

Phase diagrams are often constructed to provide a visual picture of the existence and extent of the presence of solid and liquid phases in binary, ternary and other mixtures of substances. Phase diagrams are normally two-component (binary) representations but multicomponent phase diagrams can also be constructed. Interactions between active substances and excipients can often be evaluated using phase diagrams. 

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