Weight fractions

XM(I,2) cols 21-30 measured liquid-phase composition of component one (mole or weight fraction)... 

H = liquid specific enthalpy of the component i X = weight fraction of the component i... 

Xj = mole fraction of component i Xw, = weight fraction of component i M- = molecular weight of the component i = molecular weight of the mixture = absolute viscosity of the mixture... 

C of the mixture in the ideal gas state Cpgp = Cp of the component i in the ideal gas state = weight fraction of component /... 

Compositional data is expressed in two main ways components are shown as a volume fraction or as weight fraction of the total. 

Experiments on sufficiently dilute solutions of non-electrolytes yield Henry s laM>, that the vapour pressure of a volatile solute, i.e. its partial pressure in a gas mixture in equilibrium with the solution, is directly proportional to its concentration, expressed in any units (molar concentrations, molality, mole fraction, weight fraction, etc.) because in sufficiently dilute solution these are all proportional to each other. 

Figure C2.3.8. Self-diffusion coefficients at 45°C for AOT ( ), water ( ) and decane ( ) in ternary AOT, brine (0.6% aqueous NaCl) and decane microemulsion system as a function of composition, a. This compositional parameter, a, is tire weight fraction of decane relative to decane and brine. Reproduced by pennission from figure 3 of [46].

The first and second columns of Table 1.4 give the number of moles of polymer in six different molecular weight fractions. Calculate and for this polymer and evaluate a using both Eqs. (1.7) and (1.18). 

We begin by recognizing that the weight fraction w of n-mers in the polymer mixture at any value of p equals the ratio of the mass of n-mer in the mixture divided by the mass of the total mixture. The former is given by the product uN Mq, where Mq is the molecular weight of the repeat unit the latter is given by NqMq. Therefore we write... 

The weight fraction of n-mers is plotted as a function of n in Fig. 5.6 for several large value of p. Inspection of Fig. 5.6 and comparison with Fig. 5.5 reveals the following ... 

At any p, very small and very large values of n contribute a lower weight fraction to the mixture than do intermediate values of n. This arises because of the product nN in Eq. (5.29) is large for monomers, in which case n... 

Figure 5.6 Weight fraction of n-mers as a function of n for several values of p.

Taylorf carefully fractionated a sample of nylon-6,6 and determined the weight fraction of different n-mers in the resulting mixture. The following results were obtained ... 

Figure 8.5 illustrates the sort of separation this approach predicts. Curve A in Fig. 8.5 shows the weight fraction of various n-mers plotted as a function of n. Comparison with Fig. 6.7 shows that the distribution is typical of those obtained in random polymerization. Curve B shows the distribution of molecular weights in the more dilute phase-the coacervate extract-calculated for the volumes of the two phases in the proportion 100 1. The distribution in the concentrated phase is shown as curve C it is given by the difference between curves A and B. 

Figure 8.5 Theoretical plots of weight fraction n-mers versus n for unfractionated polymer (A), the dilute phase (B), and the concentrated phase (C) (drawn with R = 10 ). (Adapted from Ref. 1.)...

Figure 8.6 Effect of successive fractionations weight fraction n-mer versus n for seven successive precipitates and final residue (calculated for R = 10 ). [Adapted from G. V. Schulz, Z. Phys. Chem. B46 137 (1940) B47.155 (1940).]...

Column 9. Aj/Aj j gives that fraction of the area under the entire curve which has accumulated up to the Nth class. Since the curve is a weight distribution, this is equal to the weight fraction of material in the sample having M < Mj. 

A plot of the last entry versus M gives the integrated form of the distribution function. The more familiar distribution function in terms of weight fraction versus M is given by the derivative of this cumulative curve. It can be obtained from the digitized data by some additional manipulations, as discussed in Ref. 6. 

Progressively smaller molecules have access to successively larger fractions of the internal volume. Therefore, as Vj emerges, consecutive fractions of the polymer come with it. Thus we can write the retention volume for a particular molecule weight fraction as... 

Since K represents the fraction of Vj at which a particular molecular weight fraction emerges from the column, and since In M cc in r we see that this... 

Benoit et al.f prepared a mixture of two different fractions of cellulose nitrate and determined the molecular weight of the mixture by light scattering. The mixture was 25.8% by weight fraction A and 74.2% fraction B, where the individual fractions have the following properties ... 

The T of a polymer can be altered by the copolymerization of two or more monomers. The approximate T value for copolymers can be calculated from a knowledge of the weight fraction W of each monomer type and the T (in degees kelvin) of each homopolymer (12). 

An example of a commercial semibatch polymerization process is the early Union Carbide process for Dynel, one of the first flame-retardant modacryhc fibers (23,24). Dynel, a staple fiber that was wet spun from acetone, was introduced in 1951. The polymer is made up of 40% acrylonitrile and 60% vinyl chloride. The reactivity ratios for this monomer pair are 3.7 and 0.074 for acrylonitrile and vinyl chloride in solution at 60°C. Thus acrylonitrile is much more reactive than vinyl chloride in this copolymerization. In addition, vinyl chloride is a strong chain-transfer agent. To make the Dynel composition of 60% vinyl chloride, the monomer composition must be maintained at 82% vinyl chloride. Since acrylonitrile is consumed much more rapidly than vinyl chloride, if no control is exercised over the monomer composition, the acrylonitrile content of the monomer decreases to approximately 1% after only 25% conversion. The low acrylonitrile content of the monomer required for this process introduces yet another problem. That is, with an acrylonitrile weight fraction of only 0.18 in the unreacted monomer mixture, the low concentration of acrylonitrile becomes a rate-limiting reaction step. Therefore, the overall rate of chain growth is low and under normal conditions, with chain transfer and radical recombination, the molecular weight of the polymer is very low. 

Figure 18 is an entrainment or gas-carryiag capacity chart (25). The operating conditions and particle properties determine the vertical axis the entrainment is read off the dimensionless horizontal axis. For entrainment purposes, the particle density effect is considered through the ratio of the particle density to the density of water. When the entrainable particle-size distribution is smaller than the particle-size distribution of the bed, the entrainment is reduced by the fraction entrainable, ie, the calculated entrainment rate from Figure 18 is multipfled by the weight fraction entrainable. 

The lower molecular weight fractions from this process have been marketed by Montefluos under their trade name Galden. 

By far, the largest commercial use is jewelry. In jewelry, the weight fraction of gold is either expressed as the carat where 24 carat represents 100% or in fineness where 1000 fine represents 100%. Typical carat ranges are from 22-8, the most popular grades in the United States, Europe, and Japan being 18 and 14 carat. 

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