Equilibria graphical presentation

It is obvious from the graphical presentation in Fig. 7 that the cation [2S ] and the anion [2 ] exist in equilibrium with the covalent hydrocarbon [28-2] as well as the radical [28-] and [2-] as formulated in (35). In other words, the THF solution is a unique system in which one can observe four elemental species of organic compounds, i.e. covalent molecule, cation, anion and radical, at the same time. 

Next we shall consider the graphical presentation of solubility equilibria. From recent work on the system Cu2+-H20-C02 (see appendix), we know the equilibrium constants which relate the solids CuO (tenorite), CuC03 Cu(OH)2 (malachite), and (Cu(C03))2 Cu(OH)2 (azurite) with the dissolved species H+(OH ), C02, HCO3", C032", Cu2+, CuOH Cu2(OH)22+, Cu(OH)3", Cu(OH)42", CuC03, and Cu(C03)22 . The data refer to pure water and hold for 25 °C. Choosing H+ and co2... 

This suggests a useful graphical presentation of the design of an adiabatic tubular reactor. In Fig. 8.8 the equilibrium line Fe and the curve of maximum reaction rate in an adiabatic bed, are shown. The broken lines are adiabatic paths. Let and be the extent and temperature at a point on Then the adiabatic path through such a point is... 

Sillen, L. G., "Graphic Presentation of Equilibrium Data," Chapter 8 in Treatise on Analytical Chemistry, Part I, Vol. 2, L M. Kolthoff and P. J. Elving, eds., Wiley-Interscience, New York, 1959. 

Graphical presentation of redox equilibria, like the graphical treatment of acid-base, complexation, and precipitation equilibria is helpful in understanding complicated problems and in obtaining approximate solutions to equilibrium questions. For redox systems in natural waters the equilibrium condition is truly a boundary condition. In many cases, natural systems are not at equilibrium from a redox standpoint. The diagrams usually present an idea of what is possible, not necessarily of the existing or imminent situation. The graphical presentations of redox equilibria are seldom simple because redox reactions usually involve... 

Sillen LG (1959) Graphical presentation of equilibrium data. Kapitel 8. hr Kolthoff IM, Elving PJ, Sandell EB (eds) Treatise on analytical chemistry. The hiterscience Encyclopedia, New York... 

The relationship between boiling lens and h/x diagram are graphically presented in Fig. 5.2-12. In principle, the intensive quantity temperature is replaced by the extensive quantity enthalpy. The isotherms drawn between dew point and boiling point lines represent the phase equilibrium. 

Gas-liquid equilibrium of ternary mixtures is graphically presented by distillation lines. Distillation lines constimte a sequence of equilibrium stages. Beginning with... 

Figure 2. Noncompetitive inhibition. Rapid Equilibrium Random bisubstrate system with an inhibitor noncompetitive with B. Graphical presentation of Eq. (S-io), with A as a constant and B as a variable substrate.

Piguire 4. Product inhibition by Q in the Rapid Equilibrium Ordered Bi Bi system. Graphical presentation of Eq. (8.14), with B as a constant and A as a variable substrate. 

The chapter by Gruber deals with thermodynamic equilibrium considerations. It develops a graphical method for presenting these results, and touches on the potentially important problem of carbon-laydown on the catalyst. 

For three-component (C = 3) or ternary systems the Gibbs phase rule reads Ph + F = C + 2 = 5. In the simplest case the components of the system are three elements, but a ternary system may for example also have three oxides or fluorides as components. As a rule of thumb the number of independent components in a system can be determined by the number of elements in the system. If the oxidation state of all elements are equal in all phases, the number of components is reduced by 1. The Gibbs phase rule implies that five phases will coexist in invariant phase equilibria, four in univariant and three in divariant phase equilibria. With only a single phase present F = 4, and the equilibrium state of a ternary system can only be represented graphically by reducing the number of intensive variables. 

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