Isothermal solubility curves

The isothermal solubility curve of mixtures of potassium sulphate and sulphuric acid expresses the composition of the soln. at 25° in equilibrium with the solid phase or phases, when the mol. ratio of K2SO4 and SO3 per 1000 grms. of soln. are plotted as co-ordinates. The ranges of stability in the ternary system K20—S03—H20, are diagrammed in Fig. 51, where the conditions have been studied in the vicinity of the SOs-apex, as far as the formation of KHS207, hut not as far as the well-known potassium pyrosulphate. The meaning of the diagram... 

FIGURE 6.1 Solubility curves for various types of crystallization systems Curve A, isothermal solubility curve B, positive temperature coefficient of solubility curve C, negative temperature coefficient of solubility. 

SCF and the solubility of the solid in the SCF. Therefore, the isothermal solubility curves deviate from linearity as the SCF approaches a highly compressed constant density, at which point the solid solubility reaches a limiting value. The solubility curves also deviate from linearity as the UCEP for the solid-SCF mixture is approached. This deviation from linearity near the system UCEP is clearly shown in the work of Schmitt and Reid (1984) for the naphthalene-ethylene system. Finally, the solubility curves will deviate from linearity if there are specific solute-solvent interactions, such as acid-base interactions or hydrogen bonding (Schmitt, 1984). 

In the preceding chapter we considered the changes in the solubility of double salts and of mixtures of their constituent salts with the temperature noting, more especially, the relationships between the two systems at the transition point. It is now proposed to conclude the study of the three-component systems by discussing very briefly the solubility relations at constant temperature, or the isothermal solubility curves. In this way fresh light will be thrown on the change in the solubility of one component by the addition of another component, and also on the conditions of formation and stable existence of double salts in solution. With the help of these isothermal curves, also, the phenomena of crystallisation at constant temperature—phenomena which have not only a scientific interest but also an important bearing on the industrial pieparation of double salts— will be more clearly understood. ... 

Isothermal Evaporation.— The isothermal solubility curves are of great importance for obtaining an insight into the behaviour of a solu-... 

Application to the Characterisation of Racemates.— The form of the isothermal solubility curves is also of great value for determining whether an inactive substance is a racemic compound or a conglomerate of equal proportions of the optical antipodes. ... 

As has already been pointed out, the formation of racemic compounds from the two enantiomorphous isomerides, is analogous to the formation of double salts. The isothermal solubility curves also have a similar form. In the case of the latter, indeed, the relationships are simplified by the fact that the two enantiomorphous forms have identical solubility, and the solubility cur 7-es are therefore symmetrical to the line bisecting the angle of the co-ordinates. Further, with the exception of the partially racemic compounds to be mentioned later, there is no transition interval. 

In Fig. 128 are given diagrammatically two isothermal solubility curves for optically active substances. From what has been said in the immediately preceding pages, the figure ought really to explain itself. The upper isothermal acb represents the solubility relations... 

Space Model for Camallite.—Interesting and important as the isothermal solubility curves are, they are insufficient for the purpose of obtaining a clear insight into the complete behaviour of the systems of two salts and water. A short description will, therefore, be given here of the representation in space of the solubility relations of potassium and magnesium chlorides, and of the double salt which they form, carnallite, ... 

If the evaporation is carried out at some other temperature, say 100 , the corresponding isothermal solubility curve must be constructed. 

Systems which have a ternary C.S.T. Refer to Fig. 2.9. In this case, the curve through the plait points Pi, P2, P3, P4, and Pb reaches a ternary maximum at Pe, which then becomes a true ternary C.S.T. The curve continues through P5 to P7, the binary C.S.T. Projections of the isotherms onto the base of the figure are indicated in Fig. 2.10. It is clear that for temperatures between that at P7 and Pe, such as that at plait points, Pb and P5, while the binary pairs show individually complete miscibility. An example of this type of system is that of water-phenol-acetone with a ternary C.S.T. at 92 C., and a binary C.S.T. (water-phenol) at 66 C. (42). 

Figure 26 shows the ternary phase diagrams (solubility isotherms) for three types of solid solution. The solubilities of the pure enantiomers are equal to SA, and the solid-liquid equilibria are represented by the curves ArA. The point r represents the equilibrium for the pseudoracemate, R, whose solubility is equal to 2Sd. In Fig. 26a the pseudoracemate has the same solubility as the enantiomers, that is, 2Sd = SA, and the solubility curve AA is a straight line parallel to the base of the triangle. In Figs. 26b and c, the solid solutions including the pseudoracemate are, respectively, more and less soluble than the enantiomers. 

From this analysis it is clear that the trade-off between kinetics and thermodynamics is not at all obvious. Consider a monotropic, dimorphic system (for simplicity) whose solubility diagram is shown schematically in Fig. 2.10. It is quite clear that for the occurrence domain given by solution compositions and temperatures that lie between the form II and I solubility curves only polymorph I can crystallize. However, the outcome of an isothermal crystallization that follows the crystallization pathway indicated by the vector in Fig. 2.10 is not so obvious since the initial solution is now supersaturated with respect to both polymorphic structures, with thermodynamics favouring form I and kinetics (i.e. supersaturation) form II. 

Figure 6 displays a first P-x Naci diagram depicting binodal and spinodal isotherms at 623 K, 350°C. The equation of state reproduces well the tabulated data by Bischoff for the solubility curves L(G) and G(L). The pressures of the diffusion spinodal curves Sp(L) and Sp(G) decrease with increasing XNaci mole fractions (note also that the spinodal curves run through the stability field of... 

On continuing to alter the temperature in the same direction as before, the relative shifting of the solubility curves becomes more marked, as shown in Fig. 124. At the temperature of this isothermal, the solution saturated for the double salt now lies in a region of distinct unsaturation with respect to the single salts and the double salt can now exist as solid phase in contact with solu- tions containing both relatively more of A (curve ED), and relatively more of B (curve DF), than is contained in the double salt itself. 

Water vapour has anomalous solubility characteristic, because of the strong hydrogen bonding between the molecules. Figure 11.2 shows that the sorption isotherms can curve steeply upwards as the relative pressure approaches 1. However, hydrophobic polymers such as polyolefins still obey Henry s law. 

Until for example, the substance S is added isothermally to the binary mixture, according to point M, the ratio AM/MB will change if the liquid phase with the highest concentration of S disappears. Now the ternary system is homogeneous. This is true at point M, the saturation point. Similarly, this is valid for points P, P and Q, Q. Curve A, M, P, Q, B is the line connecting the saturation points or the solubility curve, solubility isotherm or binodal curve (Fig. 1-11). 

Figure 12.5 Effect of temperature on the solubility curves and the co-crystal domain in the ternary phase diagram of (a) a congruently melting cocrystal (c/.. Figure 12.1(a)) and (b) an incongruently melting co-crystal cf, Figure 12.1(b)). Ideal miscibility of all components in the liquid phase is assumed. The eutectic grooves are indicated by continuous lines, the peritectic groove by a dashed line. The two-phase regions in the 75 °C isothermal cross section are shaded.

Fig. 6.6 shows two isothermal p — Xi) sections of the phase diagram. The two-phase region is located above the helium solubility curves of phases ( ) and ("), on the left- and right-hand sides of the critical line. 

Fig. 6.6. Isotherms in the (p—X2) plane of the mercury-helium phases diagram at 1490 C and 1518 C. Dot-dash curve is the critical line connecting critical points open circles), heavy solid lines represent solubility curves and are extrapolated (dashed curves) to p = 11 g cm". Coordinates of selected tie lines light solid lines) are given in Table 6.1.

This type is exemplified by the system chlorobenzene (A)-water (B)-methyl ethyl ketone (C), where A and C arc completely soluble, while the pairs A-B and B-C show only limited solubility. Refer to Fig. 10.5a, a typical isotherm. At the prevailing temperature, points K and J represent the mutual solubilities of A and B and points H and L those of B and C. Curves KRH (A-rich) and JEL (B-rich) are the ternary solubility curves, and mixtures outside the band between these curves form homogeneous single-phase liquid solutions. Mixtures such as Af, inside the heterogeneous area, form two liquid phases at equilibrium at E and R, joined on the diagram by a tie line. The corresponding distribution curve is shown in Fig. 10.5i>. 

The peculiar features shown by the sorption isotherms of ethanol in PTMSP are followed also by the solubility curves for methanol in PTMSP, which are presented in Figure 5. As in the case of ethanol, the methanol solubility coefBcient in the low pressure limit. So, is orders of magnitude lower than for alkanes, and the sorption isotherms are characterised by the previously mentioned S shape. 

Tjf = (T/Tc). The 12 "C (T = 1.01) isotherm of p vs. shows a rapid rise in p by more than an order of magnitude around Pr = 1.0. The shape of this curve is quite similar to that of the naphthalene solubility curve, suggesting that the solvent power of ethylene for naphthalene is directly related to the SCF solvent density near T Pc. 

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