Three Types of Diagrams

Plot and use y-x, temperature-composition, enthalpy-composition diagrams explain the relationship between these three types of diagrams... 

Three types of diagrams have been shown for describing mono-protic acid-base systems. These methods reinforce the conclusions of Chapter 3 about the importance of various terms in the complete equation (3-2). It is unlikely that one would plot these graphs from scratch to solve a problem. But, once available, they do help choose among approximate and more complete methods of solution. 

Figure 1.4 presents the phase equilibria in a hypothetical unary system represented on each of the three types of diagrams. The plot of P versus... 

Figure 1.8 presents the phase equilibria in a hypothetical binary eutectic system similar to that in Figure 1.7, represented on each of the three types of diagrams. This diagram is similar to those for the Ag-Cu and Ni-Cr systems. The plot of T versus ub is a Type 1 diagram and the three-phase equilibrium a-L-(3 is represented by a point. The plot of T versus Ab is a Type 2 diagram and the a-L-(3 equilibrium is represented by three points on a line, the eutectic isotherm. The plot of S versus Xb is a Type 3 diagram and the a-L-(3 equilibrium is represented by an area. Note that the forms of these diagrams correspond to those for the unary system in Figure 1.4. (Numerous examples of the three types of phase diagrams are given for unary, binary and ternary systems in Chapter 13 of Reference [2], Reference [5] and Chapter 2 of Reference [8].

Figure Al.7.9. Schematic diagram illustrating three types of adsorption sites.

Three types of binary equilibrium cui ves are shown in Fig. 13-27. The y-x diagram is almost always plotted for the component that is the more volatile (denoted by the subscript 1) in the region where distillation is to take place. Cui ve A shows the most usual case, in which component 1 remains more volatile over the entire composition range. Cui ve B is typical of many systems (ethanol-water, for example) in which the component that is more volatile at lowvalues of X becomes less volatile than the other component at high values of X. The vapor and liquid compositions are identical for the homogeneous azeotrope where cui ve B crosses the 45° diagonal. A heterogeneous azeotrope is formed with two liquid phases by cui ve C,... 

The method of construction of this type of diagram will be illustrated using the general case of the three component system metal-sulphur-oxygen (M-S-O) whose values of AG for the reactions between the various condensed phases are given in Talile 7.37 on page 7 191. 

In addition to forming different ways in which t/-orbitals can combine to form bonds, (b) Place the three types of d-d bonds—[Pg.256]

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. 

Fig. 26 Isothermal solubility diagrams of the three types of pseudoracemates (see text). The appearance of the tie lines is shown in the right half of the triangles. (Reproduced with permission of the copyright owner, John Wiley and Sons, Inc., New York, from Ref. 141, p. 197.)...

Figure 1. Melting point diagrams for the three types of enantiomer systems (only the liquidus curves are shown).

Comparison of phase diagrams (see Section A.2.1.1.1. for the three types of crystalline racemic forms) of different but structurally very similar compounds can be used to establish absolute configurations in two instances196 ... 

Three types of isochron diagrams are used in discussions of short-lived radionuclides. An internal isochron is one based entirely on measurements from the object being dated. By measuring several minerals with different parent/daughter elemental ratios, one can obtain an array of data that gives both the initial ratio (NR/Ns)a and the initial isotopic ratio of the daughter element Figure 8.25 shows an example of an internal isochron for an... 

Ribbon diagrams of the three types of HIV-1 RT crystal structures, (a) Structure of the HIV-1 RT/DNA/Fab ternary complex... 

The small difference between the energies of S0 and T may easily be overturned by the effects of substituents on the carbene center. Figure 7.6 shows the interaction diagrams which are relevant to the interaction of the carbene center with each of the three types of substituent. Because of more favorable overlap, the interaction of the carbon 2p orbital with substituent p or n orbitals is expected to dominate. The spn orbital which lies in the nodal plane of the substituent p or n orbital will not interact except more weakly with substituent a orbitals. Its energy is shown in Figure 7.6 as unperturbed by the substituent. 

Figure 7.10 shows the interaction diagrams which are relevant to the interaction of the nitrenium ion with each of the three types of substituent. The 2p and spn orbitals of the nitrenium ion are lower in energy than the analogous orbitals of a carbene. Several differences in the effects of substituents ensue ...

Often the essentials of phase diagrams in P,7,x-space are represented in a P,7-projection. In this type of diagrams only non-variant (F=0) and monovariant (F=l) equilibria can be represented. Since pressure and temperature of phases in equilibrium are equal, a four-phase equilibrium is now represented by one point and a three-phase equilibrium with one curve. Also the critical curve and the azeotropic curve are projected as a curve on the P, 7-plane. A four-phase point is the point of intersection of four three-phase curves. The point of intersection of a three-phase curve and a critical curve is a so-called critical endpoint. In this intersection point both the three-phase curve and the critical curve terminate. 

Saio, Kato, and Nomoto (1988) recently examined under what conditions a massive star undergoes a blue-red-blue evolution. The evolution of a star of initial mass 20 M0 star in the HR diagram is shown in Figure 1 from the zero-age main-sequence through carbon ignition at the center. The metallicity in the envelope was assumed to be Z = 0.005 and the Schwarzschild criterion was adopted. The star shows the three types of evolutionary path (A, B, C) depending on the mass loss, metallicity, and the change in the helium abundance Y in the envelope. 

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