Composition fractional

F, V, and L moles/unit time and their mole-fraction compositions are, respectively, w, y, and x. ... 

Simultaneous solution by the Newton-Raphson method yields x = 0.9121, y = 0.6328. Accordingly, the fractional compositions are ... 

Filter aids should have a narrow fractional composition. Fine particles increase the hydraulic resistance of the filter aid, whereas coarse particles exhibit poor separation. Desired particle-size distributions are normally prepared by air classification, in which the finer size fractions are removed. 

LiNbOj appeared in the treated mixtures that contained more than a 0.33 mol fraction of Nb02F. This indicates that the system is not pseudo-binary in mixtures with higher Nb02F mol fraction compositions. 

FIGURE 10 JO The fractional composition of the species in carbonic acid as a function of pH. Note that the more fully protonated species are dominant at lower pH. 

FIGURE 19.5 The fractional composition of a solution of alanine, a typical amino acid, as a function of pH. Notice that the concentration of the molecular form is extremely low at all pH values its concentration had to be multiplied by a factor of 10 l for it to be visible on the graph. Amino acids are present almost entirely in ionic form in aqueous solution. 

Consider the binary batch distillation column, represented in Fig. 3.58, and based on that of Luyben (1973, 1990). The still contains Mb moles with liquid mole fraction composition xg. The liquid holdup on each plate n of the column is M with liquid composition x and a corresponding vapour phase composition y,. The liquid flow from plate to plate varies along the column with consequent variations in M . Overhead vapours are condensed in a total condenser and the condensate collected in a reflux drum with a liquid holdup volume Mg and liquid composition xq. From here part of the condensate is returned to the top plate of the column as reflux at the rate Lq and composition xq. Product is removed from the reflux drum at a composition xd and rate D which is controlled by a simple proportional controller acting on the reflux drum level and is proportional to Md-... 

The system is ideal, with equilibrium described by a constant relative volatility, the liquid components have equal molar latent heats of evaporation and there are no heat losses or heat of mixing effects on the plates. Hence the concept of constant molar overflow (excluding dynamic effects) and the use of mole fraction compositions are allowable. 

Assuming the equilibrium to be expressed in terms of relative volatilities a, and theoretical plate behaviour, the relation between the vapour and liquid mole fraction compositions leaving the plate is given by... 

The results of the calculation are thus the mole fraction compositions, yA and yB, together with the total volumetric flow rate G, as steady-state functions of reactor length. 

When considering the composition inhomogeneity of Markovian copolymers, the finiteness of the chemical size of macromolecules cannot be ignored, because fractional composition distribution W(/ f) in the limit / -> oo turns out to be equal to the Dirac delta function 5(f - X). For macromolecules of finite size f2> 1 the function W(/ f) is the Gaussian distribution whose center and dispersion (Eq. 2) are described by relationships (Eq. 8) and the following one... 

The majority of work done on VGCF reinforced composites has been carbon/carbon (CC) composites [20-26], These composites were made by densifying VGCF preforms using chemical vapor infiltration techniques and/or pitch infiltration techniques. Preforms were typically prepared using furfuryl alcohol as the binder. Composites thus made have either uni-directional (ID) fiber reinforcement or two-directional, orthogonal (0/90) fiber reinforcement (2D). Composite specimens were heated at a temperature near 3000 °C before characterization. Effects of fiber volume fraction, composite density, and densification method on composite thermal conductivity were addressed. The results of these investigations are summarized below. 

A The mole fraction composition of each component is that component s partial pressure divided by the total pressure. Again, we note that the vapor is richer in the more volatile component. 

Organic Fraction Composition Conversion Factor (mgCOD mgDM-1)... 

Considering the multistage industrial unit, in any equilibrium stage, the quantity of solution in the underflow may be a function of the concentration of the solution in the thickener, and the concentration of the overflow solution will be the same as that in the underflow. If the curved line EF (Figure 10.18) represents the experimentally determined composition of the underflow for various concentrations, any point f on this line represents the composition of a mixture of pure B with a solution of composition g, and Of/fg is the ratio of solution to solids in the underflow. If the amount of solution removed in the underflow is not affected by its concentration, the fractional composition of the underflow with respect to the insoluble material B (xB) is a constant, and is represented by a straight line, through E, parallel to the hypotenuse, such as EF. Point E represents the composition of the underflow when the solution is infinitely weak, that is when it contains pure solvent. If K is the mass of solution removed in the underflow per unit mass of solids, the ordinate of E is given by ... 

The point representing the stream F will be a difference point, since it will represent the composition of the stream which must be added to w h to give W h r In general, in a countercurrent flow system of this sort, the net flow of all the constituents will not be in the same direction. Thus one or more of the fractional compositions in this difference stream will be negative, and the difference point will lie outside the triangle. A balance on the whole system, as shown in Figure 10.19, gives ... 

The fractional composition of the stream flowing to the right with respect to one of the components is given by ... 

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