Stoichiometric line

The carbon monoxide concentration contours for 50 atm and 700 °K (Figure 9) indicate that the equilibrium CO leakage will not be high if equilibrium is reached when the initial composition is near the stoichiometric line. 

Dislocations Dislocations are stoichiometric line defects. A dislocation marks the boundary between the slipped and unslipped parts of crystal. The simplest type of dislocation is an edge dislocation, involving an extra layer of atoms in a crystal (Fig. 25.2). The atoms in the layers above and below the half-plane distort beyond its edge and are no longer planar. The direction of the edge of the half-plane into the crystal is know as the line of dislocation. Another form of dislocation, known as a screw dislocation, occurs when an extra step is formed at the surface of a crystal, causing a mismatch that extends spirally through the crystal. 

The stoichiometric line represents all stoichiometric combinations of fuel plus oxygen. The combustion reaction can be written in the form... 

The stoichiometric line is drawn from this point to the pure nitrogen apex. 

The LOC can be estimated by reading the oxygen concentration at the intersection of the stoichiometric line and a horizontal line drawn through the LFL (see appendix C). This is equivalent to the equation... 

Use expression 6-15 to locate the stoichiometric point on the oxygen axis, and draw the stoichiometric line from this point to the 100% nitrogen apex. 

Locate the LOC on the oxygen axis, and draw a line parallel to the fuel axis until it intersects with the stoichiometric line. Draw a point at this intersection. 

One might suggest an even more optimized procedure. This involves first pumping air into the vessel until a point is reached on the air stoichiometric line above the UFL. This is followed... 

Figure 7-6 Estimating a target fuel concentration at point S for taking a vessel out of service. Point M is the intersection of the LFL line with the stoichiometric line.

An expression to estimate ISOC using the intersection of the minimum oxygen concentration and the stoichiometric line is also found using a similar procedure. The analytical result is... 

A useful application of this result is shown in Figure AC-5. Suppose that we wish to find the oxygen concentration at the point where the LFL intersects the stoichiometric line shown. The oxygen concentration in question is shown as point X in Figure AC-5. The stoichiometric combustion equation is represented by... 

Figure AC-5 Determining the oxygen concentration X at the intersection of the LFL and the stoichiometric line.

For most compounds detailed flammability zone data are not available. In this case an estimate can be made of the location of point S, as shown in Figure AC-6. Point S can be approximated by a line starting at the pure air point and connecting through a point at the intersection of the LFL with the stoichiometric line. Equation AC-7 can be used to determine the gas composition at point S. Referring to Figure AC-2, we know the gas composition at points R and M and wish to calculate the gas composition at point S. Let A represent the fuel and C the oxy-... 

Another approach is to estimate the fuel concentration at point S by extending the line from point R through the intersection of the LOC and the stoichiometric line. The result is... 

This initial condition is rather idealized. In reality, one would expect to see partially premixed zones with f = fst and 7 = 0 which will move towards 7 = 1 along the stoichiometric line. The movement along lines of constant f corresponds to premixed combustion, and occurs at a rate that is controlled by the interaction between molecular diffusion and chemical reactions (i.e., the laminar flame speed). 

Equation (81) can also be used to predict the existence of reactive arheotropes provided that the mixture is in permanent chemical equilibrium - that is, the Damkohler number is sufficiently large. The condition which must be fulfilled has been given by Frey and Stichlmair [30], who concluded that the slope of the nonreacting residue curve must coincide with the slope of the stoichiometric lines of the chemical reaction, given by the stoichiometric coefficients vu... 

The relation (A.3) describes the so-called stoichiometric lines converging into a pole 71, whose location can be determined by the following relation ... 

The mass-balance problem can be solved graphically. The median connecting the vertex C with the AB edge corresponds to the transformation of an equimolar AB mixture into C. Extending this line with an equal segment gives the position of the pole n of coordinates (0,1) and (1,0). From this point, stoichiometric lines can be drawn for any initial composition of the reaction mixtures. When the reaction preserves the number of moles (v, = 0) the stoichiometric lines are parallel. 

For example, the AB mixture expressed in Figure A.1 by XA and XB mole fractions on the AB edge leads at equilibrium to a mixture (xA, xB, xc) obtained by intersecting the equilibrium curve with the stoichiometric line passing through the initial mixture. Conversely, a ternary mixture where a chemical reaction at equilibrium takes place may be described only by two transformed composition variables. 

Figure A.2 (right) emphasizes a particular position where phase equilibrium and stoichiometric lines are collinear. In other words the liquid composition remains unchanged because the resulting vapor, after condensation, is converted into the original composition. This point is a potential reactive azeotrope, but when the composition satisfies chemical equilibrium too it becomes a true reactive azeotrope. Some examples of residue curve maps are presented below. Ideal mixtures are used to illustrate the basic features, which may be applied to some important industrial applications.

Figure A.3 also illustrates graphically the formation of a reactive azeotrope as the point where a particular stoichiometric line becomes tangential to the nonreac-tive residue curve and intersects simultaneously the chemical equilibrium curve.

The mathematical solution of Eq. (A.15) is tedious. An elegant graphical solution has been proposed by Stichlmair and Fair [1]. The occurrence of a reactive azeotrope is expressed geometrically by the necessary condition that the tangent to the residue (distillation) curve be collinear with the stoichiometric line. Such points form the locus of potential reactive azeotropes. In order to become a true reactive azeotrope the intersection point must also belong to the chemical equilibrium... 

Consider the Al-S system shown in Figure 11.8. This phase diagram displays several features that are typical of many binary metal chalcogenides. There is only one stoichiometric line compound (bipartite phase) at room temperature, AI2S3. However, at one atm. 

It Is Instructive to compare these behaviors In a phase diagram (Figure 7). For all systems of polymers and particles, there Is a line of compositions where the polymers exactly saturate the surfaces of all particles. If the spheres are large. It will take many macromolecules to saturate the surface of each one If they are small, one macromolecule will saturate many spheres and hold them In a necklace. On either side of the stoichiometric line, the behaviors of oxide particles and surfactant micelles diverge ... 

Oxide particles Above the stoichiometric line, excess polymer coexists with fully covered spheres. Below the stoichiometric line, excess spheres cause unlimited bridging and the separation of a concentrated gel from the pure solvent. Then at even lower polymer concentrations, below the optimum flocculation concentration (o.f.c.), the gel can no longer accommodate all the spheres, and some are rejected. 

Surfactant micelles Above the stoichiometric line, loose necklaces are formed where all the excess length of polymer Is In the bridges (19-21). Below the stoichiometric line, the necklaces are overloaded with bound spheres, and excess spheres are rejected they coexist In the solution with the tight necklaces. No phase separation Is observed. 

TiSi2 is a stoichiometric line compound of ordered orthorhombic C 54 type of structure, space group F ddd (Pearson symbol oF24). The unit cell of... 

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