Mole fraction ratio

The integration is performed graphically as shown in Figure 3.9 by plotting In gB against the mole fraction ratio XB/XA. 

Since dosage forms contain more than just active drug, it is of practical interest to understand how the various components from a multicomponent solid influence their own dissolution and release. Nelson [18] was one of the first pharma-ceuticists to ponder this question and perform the initial dissolution studies. Unfortunately, Nelson initially considered the dissolution of interacting solids (benzoic acid + trisodium phosphate), which is a more complicated and more complex situation than simple multicomponent dissolution of noninteracting solids. Nelson did show that for his benzoic acid and trisodium phosphate pellets, there was a maximum increase in benzoic acid dissolution in water at a mole fraction ratio of 2 1 (benzoic acid trisodium phosphate) and that the benzoic acid dissolution rate associated with the maximum rate was some 40 times greater than that of benzoic acid alone. 

For convenience in representing other local mole fraction ratios, we introduce additional notation as follows ... 

In addition, Hemy s law constants may be expressed as a mole fraction ratio between the air and aqueous phases (Leighton and Calo, 1981) ... 

Within the frame of the present first series of experiments it was almost always oxygen which was injected into supercritical water-methane mixtures. There were several reasons for this first choice. One of these was the desire, to study rich flames and their possible products first. Often the water to methane mole fraction ratio was 0.7 to 0.3. But mixtures down to a methane mole fraction of 0.1 were also used. It was possible, however, to inject oxygen and methane simultaneously into the supercritical water and produce a flame. Not possible was the production of true premixed flames. After a retraction of the thin inner nozzle capillary of the burner (see Fig. 1 b) the two gases could be mixed just below the reaction cell, but the flame reaction proceeded from the nozzle tip in the cell back towards this mixing point immediately. 

There are two rather striking features—the large magnitudes of the maxima in the case of the fully N-substituted acetamides or pyrrolidones which extend from about 1 to 2 cp. for the pure amides to between 4 and 5 cp. at the maxima, and the three families of curves, according to which specific mole fraction ratios the respective maxima occur. The fully N-substituted acetamides, N,N-dimethylacetamide (DMA), N,N-diethylacetamide (DEA), N,N-di-n-propylacetamide (Dn-PA), and N,N-diisopropylacetamide (Di-PA), together with N,N-diethylformamide with... 

Henry s law constant Hx = Hypc where pc = gas-phase pressure Henry s law constant Hy = Xnn T/Xnn water (mole fraction ratio for compound i) ionic strength... 

The initial predictive method by Wilcox et al. (1941) was based on distribution coefficients (sometimes called Kvsi values) for hydrates on a water-free basis. With a substantial degree of intuition, Katz determined that hydrates were solid solutions that might be treated similar to an ideal liquid solution. Establishment of the Kvsj value (defined as the component mole fraction ratio in the gas to the hydrate phase) for each of a number of components enabled the user to determine the pressure and temperature of hydrate formation from mixtures. These Kysi value charts were generated in advance of the determination of hydrate crystal structure. The method is discussed in detail in Section 4.2.2. 

The subscript r refers to a reference phase, which is present at thermodynamic equilibrium. Implementation of conditions (1) to (3) results in the following expression for the mole fraction ratio ... 

Gupta (1990) showed that, by defining the mole fraction ratio in terms of the distribution coefficient as... 

Replacing the mole fraction ratio in Equation 5.40 with Equation 5.42, we... 

Key ratio is the mole fraction ratio of the light key to the heavy key,... 

Fig. 31. Burning velocities of hydrogen + nitrogen + oxygen flames having. 02.u 0.0460 and T = 336 K, showing dependence on the initial mole fraction ratio Xhj,u/Xn2,u (after Dixon-Lewis et al. [158]). Line represents values calculated by Dixon-Lewisetal. and x, additional calculations using sets 1 and 3 of rate coefficients in Table 30 and +, additional calculations using set 2 of Table 30 (+ at each end). (By courtesy of The Royal Society.)...

Xi/X2)a is the mole fraction ratio of species 1 and 2 for the entire monolayer and f(Di) a continuous distribution such that /(Di)dDj gives the number of surface regions having a potential minimum for the surface-molecule interaction in the range Dj Di -f dD. In the limit when... 

Furthermore, when VjF =, no finite separation whatsoever occurs, albeit a dew-point type calculation will give a value for the degree or sharpness of separation in terms of mole fraction ratios or A-values. When F/F — 0, again no finite separation occurs, albeit... 

The samples used in the present study are (1) a copolymer consisting of p-hydroxybenzoic acid (HBA) and 6-hydroxy-2-naphthoic acid (HNA) in the mole fraction ratios 73 27 and (2) a polymer which contains HBA, HNA, terephthalic acid (TA) and hydroquinone (HQ) in the ratios 57 41 1 1. It will be shown later that the incorporation of the small amount of TA and HQ into the latter structure makes the material less shear—thinning than the copolymer containing only HBA and HNA, when examined theologically. It is generally believed that a random sequence distribution of monomers occurs in both... 

Exercise 2.6,2. Show that the mole fraction ratio of Nj to Hj remains constant only if 7 = 1. 

At a particular temperature and pressure the exponential term is a constant, and the mole fraction ratio in the two coexisting phases will equal a constant, or... 

In other words, the mole fraction ratio of / in the coexisting phases at equilibrium for a given T and P should be constant. This is Nernst s law (cf. Lewis and Randall 1961). K is also called the distribution coefficient, often symbolized by >, and is used in the study of trace element partitioning between coexisting mineral solid solutions. 

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