Mixture point

If two gas mixtures R and S are combined, the resulting mixture composition lies on a line connecting the points R and S on the flammability diagram. The location of the final mixture on the straight line depends on the relative moles in the mixtures combined If mixture S has more moles, the final mixture point will lie closer to point S. This is identical to the lever rule used for phase diagrams. 

Figure AC-3 The location of the mixture point M depends on the relative masses of mixtures R and S.

Point T, however, will separate into two liquid phases. If the extractor consists of one true equilibrium stage, this mixture (point T) separates into two phases represented by points R and E. 

Effects of the Four Taste Substances. The concentration of MSG equivalent in the umami intensity to an MSG-IMP mixture (point of subjective equality) was determined both in pure water and in the four taste solutions. The results are shown in Table V. The equi-umami concentration of MSG obtained in the presence of each of the four taste substances was almost the same as that in pure water. Thus the synergistic effects of umami substances were seen to be unaffected by the four taste substances. 

Figure 8.6 illustrates the relationship between Euclidean and mixture-factor space for three variables. Here, we see that the set of the mixture points lying on... 

The absence of HFS in the EPR spectrum of 10 min activated mixture points to the appearance of weak exchange interaction between V ions (localized centres), probably, through electron gas (delocalized electrons) - C-S-C relaxation [80,81]. 

The studies described above illustrate the difficulties in predicting the effects of mixtures, even when all components are chemically similar. In these studies, exposures to lipophilic mixtures of very similar compounds produced expected effects in one study and unanticipated effects in different body organs in the other studies. These studies, as well as others describing the effects of lipophile/hydrophile mixtures, point out the need to limit exposures to aromatic hydrocarbons. 

Figure 5.10. Equilibration paths during mass transfer in the system glycerol (1), water (2), and acetone (3) in a batch extraction cell. The point M is the mixture point and P represents the plait point. Experimental data correspond to Run C of Krishna et al. (1985).

The given feed and solvent compositions are used to locate points Qq and Lg on the phase diagram. The mixture point M is then located based on the ratio of flow rates (the graphical solution is shown only schematically in Figure 11.2) ... 

Thus, if the feed and solvent compositions and flow rates are known, the mixture point M can be determined (Figure 11.4). The solvent and feed points Lq and 2jv+i are first plotted at their known compositions, and a straight line is drawn through them. The mixture point, M, is located on the basis of the lever arm rule ... 

L Liquid phase solvent and extract M Mixture point N Number of stages Q Liquid phase feed and raffinate R Raffinate 5 Solvent X Mole fraction A Difference point... 

If an experiment is performed at an overall composition equal to x in figure 3.2d, the vapor-liquid envelope is first intersected along the dew point curve at low pressures. The vapor-liquid envelope is again intersected at its highest pressure, which corresponds to the mixture critical point at T2 and x. This mixture critical point is identified with the intersection of the dashed curve in figure 3.2b and the vertical isotherm at T2. At the critical mixture point, the dew point and bubble point curves coincide and all the properties of each of the phases become identical. Rowlinson and Swinton (1982) show that P-x loops must have rounded tops at the mixture critical point, i.e., (dPldx)T = 0. This means that if the dew point curve is being experimentally determined, a rapid increase in the solubility of the heavy component will be observed at pressures close to the mixture critical point. The maximum pressure of the P-x loop will depend on the difference in the molecular sizes and interaction energies of the two components. 

The critical mixture curve is measured in the following manner (Occhio-grosso et al., 1986). At a temperature slightly higher than the UCEP temperature, a vapor-liquid mixture at a fixed overall concentration is compressed to a single phase. The pressure is then isothermally decreased very slowly until the system becomes turbid and a second phase just begins to precipitate. A critical mixture point is obtained if critical opalescence is observed during the transition process and if two phases of equal volume are present when the mixture phase-separates. 

Figure 7.8-1 illustrates this process. For example, if one begins with pure B and titrates into it pure species C, then the resulting mixture composition moves from the B apex in Fig, 7,8-1 toward the C apex. This titration is carried out until turbidity results in the mixture (point 1). Subsequently, species A is added until clarity in the mixture is achieved aud the composition is ai point 2 in Fig. 7.8-1. Coniinuerion of this process lends to points 3, 4, and 5 as indicated. Subsequently, the other side of the solubility curve may be generated by starting with an aliquot of pure C and then titrating into it successive amonnis of B and A until tuibidity is achieved and removed, respectively.

Any point on a side of the triangle represents a binary mixture. Point D, for example, is a binary mixture containing 80% A and 20% B. All points on the line DC represent mixtures containing the same ratio of A to B and can be considered as mixtures originally at D to which C has been added. 

Equation 9.8 suggests the use of a 2 factorial design to study the effect of the temperature. Equation 9.9 would require a first-order Scheffe design at each temperature (simplex vertices). In fact two independent measurements of solubility were carried out at each point. Also unreplicated test points were set up at the midpoints of the binary mixtures (points 7-12) that would allow use of a more complex model, if necessary. The resulting design is given in table 9.14. 

Fig. 4. Analysis of the experimental data for a CO NO =1 1 mixture. Points are experimental data, curves are calculated by equations (13)-(15) at y = 1.

Figure 7.4. Phase diagrams for type I (top) and type II (bottom) binary mixtures with carbon dioxide as one component (L = liquid and v = vapor). The UCST line indicates the temperature at which the two immiscible liquids merge to form a single liquid phase. The critical mixture curve is the locus of critical mixture points spanning the entire composition range. (From ref. [44] American Chemical Society).

The temperature-concentration diagram in Figure 9.27 illustrates the mixing of a saturated solution A and unsaturated solution B to give a mixture with a composition and temperature represented by a point somewhere along line AB, determined by the mixture rule (section 4.4). A supersaturated mixture will be produced if the relative flowrates result in the mixture point lying in the sector below the solubility curve. For example, if A and B are mixed at equal mass flowrates, a supersaturated mixture Mi would be produced (distance AMi = BMi). For the mixture to enter the unsaturated zone, the B A ratio would have to exceed about 7 2 in the case illustrated. The unsaturated mixture M2, for example, is the result of an 8 1 B A ratio (AM2 = 8BM2). 

If an additional 80 g is added to the 15 g of water present, then it is easy to compute the mass fractions in the system, giving the point (0.05, 0.95) this mixture is displayed as point 3 in Figure 2.5. Note that by the addition of more water, we have moved from point 2 to 3. It is clear that additional water added to the system reduces the concentration of NaCl in solution, and hence the mixture point will lie closer to the point (1.0, 0.0), which is the coordinate representing pure water. 

Initial Batch Points from region Bj are chosen as starting points for further batches, similar to Section 3.2.3. The specific mixture point used is not important, and so a point located near the center of region Bj shall be utilized. This is given by point Xj in Figure 3.3(a). 

Finally, a mixture point residing in the concave region is chosen wherefrom further batch experiments may be run. 

Entrants were provided with the experimental bubble points for 15 mixture compositions of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea) and ethanol at 283.17 K, and properties of the pure materials at 343.13 K. The challenge was to compute bubble points for seven mixture compositions at 343.13 K, using any experimental data for the pure components but the only mixture points at 283.17 K. Entries using any theory/modeling/simulation method were accepted. Entries were judged based on the criterion. 

---