Eutectic point calculation

E8.12 The melting point of 1,4-dichlorobenzene is 326.4 K and that of naphthalene is 353.4 K. The eutectic point occurs at a temperature of 303.4 K and a mole fraction of naphthalene in the liquid phase of 0.394. Assume ideal liquid solutions, no solid solubility, and ArusCp.m = 0 and calculate AfusHm for 1,4-dichlorobenzene. 

The melting points of pure naphthalene and pure benzene are 80.2°C and 5.4°C, respectively. The average enthalpies of fusion of naphthalene and benzene in the temperature range are 10,040 and 19,200 J mol, respectively. Calculate the temperature and composition for the maphthalene-benzene system that correspond to point B, the eutectic point, in Figure 14.3. 

For the liquidus of InSb(s) there are 13 points from thermal analysis, which include a eutectic point at 494 + 0.5°C and xSb = 0.69 (Liu and Peretti, 1952), as well as three points from dissolution experiments by Hall (cited in Shunk, 1969). The best-fit interaction coefficients, the fit to the liquidus line of InSb(s), liquidus points (Liu and Peretti, 1952), av, and the calculated eutectic temperature and composition are given in Table II. It is emphasized that the values of the interaction coefficients are such that Eqs. 

The attainment of high levels of enantiopurity is not always possible by enzymatic or diaste-reomeric resolutions or by asymmetric syntheses alone. It is however frequently possible to prepare a pure enantiomer from a partially resolved sample by simple recrystallization. For this process to proceed successfully it is necessary that the initial enantiopurity of the mixture is greater than that of the eutectic point in the phase diagram. By utilization of the phase diagram, the optimal quantity of solvent required can be calculated. It is also possible to calculate the maximum expected yield. 

The DSC procedure does not directly measure AT, but can be used to calculate it from the melting curve. At the eutectic point, all of B is in the liquid phase. During the melting of A after the eutectic point the concentration of B varies in the liquid phase. This causes the broadening of the DSC curve. With no solid... 

Equation (7) is obtained from Equation (2) by noting that the solid phase is pure, and therefore the mole fraction and activity coefficient in the solid phase are both unity. The ratio of pure-component fugacities can be obtained from any one of Equations ((3) to (6)), and the activity coefficient in the liquid, Ji, must be estimated. The composition-temperature behavior along the liquidus curves may then be calculated. The eutectic point is found from the intersection of the two liquidus curves. 

Fig. 22.3. Calculation of eutectic point from crystallization or freezing point curves at constant pressure.

In the ternary system KF-K2T1F6-KBF4, the intermediate compound KsTiFy divides the system into two simple eutectic systems. The calculated coordinates of the two ternary eutectic points are ... 

A major point was made after a critical review of numerous reports on reaction rates in frozen systems (50). Kinetic-mechanistic surprises in frozen systems may not require exceptional hypotheses. Concentration effects may account for them. Even if a system appears to be completely solidified and, therefore, not amenable to analysis in terms of unfrozen liquid puddles (51), a liquid phase should still be considered a possibility. A case in point is provided by the efficient electron transfer observed between ferrous and ferric ions in an aqueous system frozen below its putative eutectic point (52). This seemed to require an ice structure in order to bridge the distance between reactants that were calculated to be too far apart for significant reactivity. However, it was pointed out that the assumed eutectic point was based only on the major... 

Calculation of Freezing-Point Depression and the Eutectic Point... 

The phase diagram of a racemic compound (Fig. 2b) is that of a molecular complex, but it is symmetrical about the central vertical line. The racemic compound is a new crystalline species that usually forms eutectic mixtures with the individual enantiomers. The liquidus line between the pure enantiomer and the eutectic point can be calculated by the Schroder-Van... 

In the same way, the solubilities for other temperatures and the other xylene isomers can be calculated. The results for all three systems are shown in Figure 8.4 together with the experimental results. It can be seen that not only the solubilities but also the eutectic points are in good agreement with the experimental findings. This means that the assumption of ideal behavior is reasonable for the systems considered. 

The phase diagram of the ternary system KF-KCI--KBF4 was measured in [3]. It was found that all three binaiy systems and the ternary system are simple eutectic ones. The calculated co-ordinates of the eutectic point in the ternary system is 19.2 mole % KF, 18.4 mole % KCl, 61.4 mole % KBF4 and the temperature of the eutectic crystallization 422 C. The probable inaccuracy in the calculated ternary phase diagram is 6.9 X,... 

In the simplest case of the ideal solution the position of the eutectic point can be calculated not only for binary mixtures but for multicomponent ones... 

Figure 56.1 shows an isothermal ternary phase diagram among two diastereomeric salts, B HA and BxjHA, and an achiral solvent L where the crystalline salts are anhydrous and not miscible. Points A and B represent the solubility of undesired and desired salts, BuHA and Bj HA, respectively. E is the eutectic point where a saturated solution is in equilibrium with both salts in solid phases. The maximum separation efficiency is achieved when the system is at point P. At this point, the separation efficiency e, defined here as the ratio of desired salt in the solid phase to the total desired salt in the system, can be calculated directly from the phase... 

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