Phases invariant points

As shown in Fig. 18-57, the mutual solubility of two salts can be plotted on the X and Y axes with temperatures as isotherm hues. In the example shown, all the solution compositions corresponding to 100°C with solid-phase sodium chloride present are shown on the Tine DE, All the solution compositions at equihbrium with solid-phase KCl at 100°C are shown by the line EE If both sohd-phase KCl and NaCl are present, the solution composition at equilibrium can only be represented by point E, which is the invariant point (at constant pressure). Connecting all the invariant points results in the mixed-salt hne. The locus of this line is an important consideration in making phase separations. 

When C = 1 and P = 3,/= 0. Thus, if three phases are in equilibrium, there are no degrees of freedom. The T and p conditions at which three phases will be in equilibrium are determined by the system. The equilibrium occurs at a single (T, p) point, commonly referred to as a triple point. Such a point is also referred to as an invariant point because all properties are fixed for the system. For C02 in Figure 8.1, point b is a triple point, with solid, liquid, and gas in equilibrium. 

Below the equilibrium lines, but above the eutectic temperature, a liquid and solid are in equilibrium. Under line ac, solid benzene, and liquid Li, whose composition is given by line ac, are present. Under line be, the phases present are solid 1,4-dimethylbenzene and liquid Li, whose composition is given by line be. Below point c, solid benzene and solid 1,4-dimethylbenzene are present. In the two phase regions, one degree of freedom is present. Thus, specifying T fixes the composition of the liquid, or specifying X2 fixes the temperature.cc Finally, at point c (the eutectic) three phases (solid benzene, solid 1,4-dimethylbenzene, and liquid with x2 = vi.e) are present. This is an invariant point, since no degrees of freedom are present. 

P8.4 The (solid + liquid) phase diagram for (.Yin-C6Hi4 + y2c-C6Hi2) has a eutectic at T = 170.59 K and y2 = 0.3317. A solid phase transition occurs in c-CftH at T— 186.12 K, resulting in a second invariant point in the phase diagram at this temperature and. y2 — 0.6115, where liquid and the two solid forms of c-C6H12 are in equilibrium. A fit of the experimental... 

With the precipitation of bischofite, the system reaches an invariant point at which the mineral assemblage (magnesite, anhydrite, kieserite, carnallite, bischofite, and halite) fully constrains the fluid composition. Further evaporation causes more of these phases (principally bischofite) to form, but the fluid chemistry no longer changes, as can be seen in Figure 24.8. 

At 0 three phases exist in equilibrium, hence F = 0 or 0 is an invariant point. On elevation of the temperature the water phase disappears and the system becomes divariant. Along the line OA the surface film at first solid is observed to melt. No abrupt melting point can however be noted and no break is observed in the line OA. 

From the slopes of the various segments of the curves together with a knowledge of the areas of the molecules at the invariant points it is possible to calculate the latent heat of change from the bulk phase to the surface. 

Invariant behavior occurs at the intersection of three univariant curves. This intersection defines a point at which three phases are in equilibrium. At these so called triple or invariant points, there are no degrees of freedom and both temperature and pressure assume fixed values. 

In equation (11.31), AHm and A Vm are the molar enthalpy and molar volume changes associated with the change in phase, and dp/dT gives the slope of the equilibrium lines. Point b is the triple point for CO2. It is an invariant point, since, according to the Gibbs phase rule... 

Thus, in the melting process, the solid hydrate melts by decomposing to solid H2O and a liquid solution. This liquid has the composition given by point p, known as the peritectic point. It is an invariant point, since three phases... 

Fig. 2.7 The pseudosysiem CaO-CjS-C,A7-C4AF, showing the primary phase volume of C3S. For details of invariant points P1-P8, see Table 2.1. After Lea and Parker (L4). with later modifications.

The possible types of invariant reactions were illustrated in Table 11.2. These reactions, or their absence, determine the positions and shapes of the areas, known as phase fields, in a phase diagram. Three-phase equilibrium is only allowed at a single point (an invariant point) in a binary system that is, three-phase fields are not allowed. Binary systems however, may contain both single-phase and two-phase fields, and when a two-phase field does exist, it must be located between two single-phase fields. 

There are some important geometrical constraints for the phase equilibria topology in isobarothermal sections of ternary systems. For example, the Dutch physical chemist Franciscus Antonius Hubertus Schreinemakers (1864-1945) developed rules that determine the arrangement of stable and metastable univariant equilibria where they intersect at an invariant point (Schreinemakers, 1912, 1915). (Incidentally, Schreinemakers also authored the third volume of Die Heterogenen Gleichgewichte von Standpunkte des Phosenlehre.) Schreinemakers found that the extrapolations of one-phase field boundaries must either both fall inside a three-phase field or one inside each of the two two-phase fields. There are actually a number of Schreinemakers mles that are helpful for... 

Invariant Point Confirmation. The weight percentages of the prepared complexes, arbitrarily chosen within the three-phase, solid-liquid-liquid region, are tabulated in Table III. Tabulated in the same table are the weight percentages of the denser liquid layers and those of the less dense layers. 

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