Equilibrium-distribution diagram

Isopolytungstate anions isolated from solution in the form of crystalline salts are listed in Table 4. Several other species undoubtedly remain to be characterized, but analysis of aqueous polytungstate equilibria is complicated by the extreme range of rates involved. Many apparently stable isopolytungstates may be kinetic intermediates. For this reason, no equilibrium distribution diagrams, will be given, nor would such diagrams provide a useful... 

Equation (3-31) relates the interfacial concentrations to each other. So, it is valid only at that point on the equilibrium-distribution curve which represents the local interfacial compositions. For the purpose of locating that point, rewrite equation (3-31) as a continuous relation between the variables in the equilibrium-distribution diagram, namely xA and yA ... 

These values are plotted on the equilibrium-distribution diagram, as shown in Figure 3.7. The resulting curve intersects the equilibrium curve to give the interface compositions xA. - 0.231 and yA = 0.494. This solution agrees with the solution obtained previously by the algebraic method. 

Figure 3.9 is the equilibrium-distribution diagram for this system at a pressure of 1 atm. Point P (yA G, xAL) represents the bulk concentration of both phases, and... 

Equilibrium data (Boobar, et al. 1951) have been converted to a solvent-free basis and are given in Table 7.4 (Treybal, 1980). These are plotted in the form of a Janecke diagram in Figure 7.19. The corresponding equilibrium distribution diagram is Figure 7.20. From the problem statement, F =F= 1000 kg/h, XF - 0.6 wt fraction of styrene,... 

Figure 7.20 Equilibrium-distribution diagram and minimum number of stages for Example 7.6.

The equilibrium constants given above for the hydrolysis and protolysis reactions of cis- and trans-DDP can be employed to construct distribution diagrams of various species as a function of the pH. In human blood plasma ([Cl-] = 0.1 M) the dichloro species predominates at about pH 7.4 for both cis- and frans-DDP (Figure 4). By contrast, in intracellular conditions ([Cl ]ambient = 0.004 M) the hydrolysis products dominate, but the distribution behavior of the two isomers is quite... 

Figure 9.2. Schematic diagram of equilibrium distribution of iodine between water and carbon tetrachloride at fixed temperature and pressure.

Consideration of the energy level diagram of Fig. 1 leads to the conclusion that there must be a mechanism by which the Boltzmann thermal equilibrium distribution can be maintained during resonance absorption. For, if there were no such mechanism, upon application of a field Hi at the resonance frequency initial absorption of energy would occur, but would... 

Rudd, R. E Briggs, G. A. D Sutton, A. R, Medeiros-Ribeiro, G., and Williams, R. S. (2007). Equilibrium distributions and the nanostructure diagram for epitaxial quantum dots. /. Comput. Theor. Nanosci. 4, 335-47. [300]... 

Equilibria. The equilibrium distributions of butane, pentane, and hexane isomers have been experimentally determined (5, 16) and are diagrammed in Figure 2. In each case, lower temperatures favor the more highly branched structures. At the approximately 200° F. temperature usually employed for isomerization, the butane equilibrium mixture contains about 75% isobutane. That for pentane contains about 85% isopentane.. In the case of hexane, the equilibrium product contains about 50% neohexane and has a Motor octane rating of about 82. In all cases, of course, the yield of the desired isomers can be increased by fractionation and recycle. 

Further clarification is obtained from Figure 2 where the relations are depicted by a composition diagram where the vapor phase composition is the ordinate and the condensed phase composition is the abscissa. A straight line with a slope equal to the equilibrium distribution constant KiD is the locus of all equilibrium compositions. The curved line represents a set of nonequilibrium conditions for condensation out of the vapor phase. The departure from equilibrium can be projected on either axis, and the lengths of the projections correspond to the two expressions for potential difference shown above. Refs. 2 and 10 treat the boundary layer in detail. 

Firsly, the concentration dependence of the diffusion coefficient can be neglected. Secondly, the concentration of components at the interfaces of any growing layer can be assumed to be equal to the limits of the homogeneity range of a compound according to the equilibrium phase diagram of the A-B binary system. Thirdly, the concentration distribution of the components across a compound layer at any moment of time can reasonably be assumed to be close to linear (Fig. 1.22a), so that... 

Consider first the Al-Fe-Ni system. Generally, the equilibrium phase diagram is known to be helpful in analysing the process of intermetallic layer formation. Projection of the liquidus surface on the concentration triangle and distribution of the phase fields in the solid state for Al-rich Al-Fe-Ni alloys are shown in Fig. 5.15. 

Your task in this problem will be to use a spreadsheet to generate a Txy diagram for a two-component system, using Raoult s law to express the vapor-liquid equilibrium distribution of each species. The spreadsheet will be constructed for the chloroform-benzene system at 1 atm (for which Raouit s law is not a very good approximation), but it can then be used for any other system by substituting different Antoine equation constants. 

The equilibrium distributions of butane, pentane, and hexane isomers have been experimentally determined (6,21) and are diagrammed in... 

Figure 4.1 illustrates the equilibrium distribution of the carbonate solutes as a function of pH (cf. Sections 3.6-3.9). The constmction of the double logarithmic diagram has been explained in connection with Figure 3.4. The equations 5, 6, 7, and 8 of Table 4.2 can be drawn graphically as linear asymptotes in different pH ranges. For example, for the equations (see 5 and 6 of Table 4.2) ...

Figure 5.8a gives the proportions of SO2 in the gas and aqueous phase as a function of pH. For pH < 5, sulfur dioxide occurs mainly in the gas phase for pH > 7, it occurs mainly in the solution phase. The fraction of SO2 in the aqueous phase is given in Figure 5.8b as a function of q (water content) for a few pH values. The double logarithmic graphic representation is particulariy convenient to plot the equilibrium distribution of the aqueous sf>ecies (Figure 5.8c). For a sketch of this diagram it is convenient to recall the following ...

The assessed Si-Sb system is primarily based on the experimental work of Rohan et al. [84], Thurmond and Kowalchik [85], Song et al. [86], Nobili et al. [87] and Sato et al. [88]. The equilibrium distribution coefficients as a function of Sb content were also given by Trumbore et al. [89]. The assessed phase diagram was thermodynamically modeled, primarily based on the work mentioned above, see Fig. 13.10. 

A simplified representation of the phase equilibrium is the distribution diagram (Fig. 2.7). As demonstrated, the distribution equilibrium curve can be developed out of the triangular diagram. The slope of the equilibrium curve represents the distribution coefficient K. The position of the binodal curve and its tie lines in the liquid-liquid equilibrium is only determined by the activity coefficient. 

The formation of a stable dizinc(II) complex of 20 in aqueous solution is demonstrated by potentiometric titration experiments. Figure 26 shows the distribution diagram of the species present at the equilibrium in solution containing 20 and 2 equiv. of Zn , over the 2-12 pH range. The dimetallic species [Zn 2(20)] begins to form at pH = 5.5 and reaches its maximum concentration (85%) at pH = 7.5. This species should be more correctly written [Zn"2(20)(H2O)2]", as the remaining axial... 

The formation of 1 1 complexes between Ni(II) and ligand 6 (indicated in the following as LH2) in an MeCN/H20 mixture (4 1, v/v), at varying pH, is illustrated by the distribution diagram shown in Fig. 10. The concentration profiles of the species present at the equilibrium over the 2-12 pH interval were calculated from the pertinent complexation constants, which had been... 

Fig. 10. The distribution diagram of the species present at the equilibrium in a solution containing equimolar amounts of Ni(II) and of the heteroditopic ligand 6 (% concentration in the left vertical axis). Relevant species to the translocation process are [Ni(II)(LH2)]2+, 90% at pH = 7.5, in which the Ni(II) center occupies compartment B, and [Ni(II)(L)], 100% at pH > 9.5, in which Ni(II) has moved to the doubly deprotonated A2- compartment. When in the A2- compartment, the Ni(II) center shows a square-planar stereochemistry (low-spin, yellow, d-d absorption band at 450 nm, s = 103 M-1 cm-1) full triangles indicate the variation with pH of the intensity of such an absorption band (molar absorbance on the right vertical axis)...

---