Concentration triangle

Figure 13.5 Adsorption-desorption of ammonia at 280 " C on a model V2O5—WO3/TiO2 catalyst Dashed lines, inlet NH3 concentration triangles, outlet NH3 concentration solid lines, model fit with Temkin-type coverage dependence. Adapted from ref. [3].

In the concentration triangle, points lying on a straight line originating from a vertex correspond to mixtures with a constant ratio of components represented by the other two vertices. The property (y) is normally thought of as projections of lines of constant value on the plane of the concentration triangle. 

Vertices of a triangle similar to a given concentration triangle and centered on the origin, with side of length p ... 

The arrangement of the points in the concentration triangle is shown in Fig. 3.26. Draper and Lawrence suggested for second-order polynomials of Eq. (3.125) as applied to ternary systems, the designs containing from 8 to 15 design points. Parameters for the Draper-Lawrence designs (in fractions of m) at q=3, ni=2 and n2=3, are summarized in Table 3.46. 

The dependence of viscosity at 30 °C on composition is studied for the liquid complex fertilizer consisting of diammonium phosphate, potash and water (NH4)2HP04, K2C03, H20. For the investigation, the region of unsaturated solutions for both salts at 30 °C is selected (Fig. 3.28), the side of the concentration triangle being m=0.5. 

A Draper-Lawrence design containing 13 points is performed (Table 3.51). It is convenient to treat the subregion studied as a concentration triangle in the new coordinate system (X], X2, X3 ) ... 

Lack of fit of the obtained regression model has been checked in control trials 4, 5, 6 and 14, 15, 16, 17 and 18. Three trials 16, 17 and 18 lie inside concentration triangle. The obtained third-order regression model has been adequate in all control trials. For a three-component mixture it is easiest to determine the optimum from geometric interpretation of the regression model. The contour lines of regression model (3.162) are shown in Fig. 3.41. 

Consider first the Al-Fe-Ni system. Generally, the equilibrium phase diagram is known to be helpful in analysing the process of intermetallic layer formation. Projection of the liquidus surface on the concentration triangle and distribution of the phase fields in the solid state for Al-rich Al-Fe-Ni alloys are shown in Fig. 5.15. 

Fig. 51 I(q) versus q for sample F3-PS-PS41-S68 in pure water for different polyion concentration triangles, 1.0 g L-1 diamonds, 2.0 g L squares, 5.0 g L inverted triangles, 10.0 g L-1 circles, 20.0 g L 1...

Figure 3.108. Transmissivity of a solution of 94a in tetrahydrofurane (5.1 x 10 2 M/L, L— 1 cm, d = 0.051 M/L, b — 0.8 cm/GW) as a function of the solute concentration triangle, experimental data solid line is calculated using Eq. (87), an input intensity /(I — 2.21 GW/cm2, and a fitting parameter of (7i = 2.6 x 10 2

Below the temperature of the ternary eutectic point the system formed is a mechanical mixture of the solid phases A, A4B, and C if the composition of the system lies in the triangle A-A4B-C, or A4B, B, and C if the composition of the system lies in the other part of the concentration triangle. 

The phase diagram has four planes pc(A), pc(B), pc(C), and pc(ABC), representing the vertical projections of the planes of the primary crystallization of the individual compounds. The figurative point of the ternary compound ABC lies inside the ternary system A-B-C. There are three boundary lines etj -et2, et2 and etj -etj representing the common crystallization of compounds B, C, and A with AB, respectively. The joints of the figurative point ABC with the apexes of the concentration triangle divide the phase diagram into three simple eutectic ternary systems A-ABC-B, B-ABC-C, and A-ABC-C. The points, where the individual joins of ABC with the apexes cross the boundary lines, form the summits of the boundary lines. 

Example 1. The first example presents analysis of the volume properties of the ternary system, which is experimentally accessible through the whole concentration triangle. 

Example 2. The second example presents the analysis of the volume properties of a ternary system, which is experimentally accessible only in part of the concentration triangle. In order to perform the analysis, the density of one component must be approximated. In addition, the ternary eutectic mixture was chosen for a following component. 

As an example of calculation of the surface tension in the ternary system, KF-KCI-KBF4 is presented. The surface tension of this system was measured by Lubyova et al. (1997) using the maximum bubble pressure method. The system is a simple eutectic system experimentally attainable in the whole concentration triangle. 

The composite isotherms of hexane, benzene and dioxane adsorption from their mixture on silica are presented on Fig. 1. The isotherms of adsorption are expressed by projections of the same adsorption lines on concentration triangle. 

Figure 1. The isotherms of adsorption (projection of lines with equal adsorption on concentration triangle) of dioxane (a), n-hexane (b) and benzene (c) on silica gel from their mixtures. The numbers near the dots and lines are the values of excess adsorption /rmol/m. ...

Inhibition Periods of Polypropylene Oxidations. Although the kinetics of BHT-inhibited polypropylene oxidations may be complex, the consumption of the inhibitor seems to follow simple stoichiometry, at least up to 3 X 10 3M BHT. In Figure 5, the tinh values for polypropylene oxidations [PP]0 = 2.5M, [tert-Bu202]0= 1-2 X 10 2M are plotted against the initial BHT concentrations (triangles). The heavy line close to these... 

Besides the terms of the additive model, the quadratic model of Eq. (7.12) contains cross terms that describe interactions between two components, and for this reason it is usually able to reproduce the response values at the vertices and on the sides of the concentration triangle, since they represent pure and binary mixtures, respectively. It should not surprise us, however, that non-additive effects involving the simultaneous presence of three components will be important to describe... 

Because aU the intervals are different, these inequalities define an irregular hexagon inside the concentration triangle, shown in Fig. 7.8a. The points belonging to this hexagon represent the mixtures that in principle can be studied. With these specifications, the pseudocomponents are defined by the expressions ... 

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