Fraction and weighting

Weight (or Mass) Basis. The terms weight fraction and weight percent" are often used as synonymous for mass fraction and mass percent, respectively. If the total... 

In the sections that follow the techniques used for reducing experimental quantities to weight fractions and weight fraction activity coefficients are described. For the solvents, pure component liquid densities and second virial coefficients were often required and were obtained from Daubert and Danner (1990). 

Therefore, table 4B.1 gives the raw data from Selleck et al. (1952) only for the water content of the H2S-rich phase. The data presented are exactly those from the original document. Thus the pressure is in psia, and both weight fraction and mole fraction of H2S are given. To obtain the mole fraction and weight fraction of water in the sample, merely subtract the value in the table from one. 

An interesting property relating to mole fractions and weight fractions appears if we apply (20.43) and (20.44) to a two-phase system. It follows that if the mole fractions of i are the same in the two phases, then the weight fractions are also equal. In other words, for each of the components... 

The number-average is the common average used, for example, to determine the average denomination of the coins in your pocket. The number traction of each type of coin (n ) is multiplied by its denomination Mm)-Substituting Eq. (1.27) into Eq. (1.23) shows that the ratio of the molar mass of a polymer with AT monomers and the number-average molar mass Mn relates the number fraction and weight fraction of molecules ... 

A discussion of the thermodynamics and kinetics of solubility hrst requires a discussion of the method hy which solubility is reported. The solubility of a substance may be dehned in many different types of units, each of which represents an expression of the quantity of solute dissolved in a solution at a given temperature. Solutions are said to be saturated if the solvent has dissolved the maximal amount of solute permissible at a particular temperature, and clearly an unsaturated solution is one for which the concentration is less than the saturated concentration. Under certain conditions, metastable solutions that are supersaturated can be prepared, where the concentration exceeds that of a saturated solution. The most commonly encountered units in pharmaceutical applications are molarity, normality, molality, mole fraction, and weight or volume percentages. 

Problem 5.16 In a synthesis of polyester from 2 moles of terephthalic acid, 1 mol of ethylene glycol and 1 mol of butylene glycol, the reaction was stopped at 99.5% conversion of the acid. Determine (a) M and M , of the polyester and (b) mole fraction and weight fraction of species containing 20 monomer units. 

The number fraction and weight fraction distributions [63] are readily shown to be... 

Problem 8.8 1-VinyInaphthalene is polymerized anionically at 25°C in a tetrahy-drofuran solution containing initially 4 x 10 M C4HgLi and 0.20 M 1-vinyInaphthal-ene. Show graphically the number fraction and weight fraction distributions of... 

Figure 8.2 Number fraction and weight fraction distribution of the degree of polymerization with i/ = 50 for anionic "living" polymers and for free-radical polymerization (with termination by disproportionation). (Problem 8.8)...

While we could do UNIFAC calculations at all compositions for each of the candidate compounds, we will adopt a further simplification here. We will use the simpler van Laar equations with the parameters obtained to match the infinite-dilution activity coefficients from the UNIFAC model. From such a calculation, we find that the mole fractions and weight fractions of the additives needed to attain a freezing point of —25X are as follows ... 

Figures 3.10c and 3.10d are representations of the same ternary system in terms of weight fraction and weight ratios of the solute. In Fig. 3.10d the ratio of coordinates for each point on the curve is a distribution coefficient K p.= YfiXf. If K p were a constant, independent of concentration, the curve would be a straight line. In addition to their other uses, x-y or X-Y curves can be used to obtain interpolate tie lines, since only a limited number of tie lines can be shown on triangular graphs. Because of this, x-y ot X-Y diagrams are often referred to as distribution diagrams. Numerous other methods for correlating tie-line data for interpolation and extrapolation purposes exist.

Samples. Hytrel types 7246, 6346, SS26 and 4056 were obtained in both powder and pellet form from the du Pont Company. The mole fraction and weight per cent of hard segments in these sampies has been determined by solution state NMR (13). The... 

Mole Fraction and Weight Per Cent Hard Segments in Hytrel Samples... 

The solute, A, is initially dissolved in diluent, D, in the feed. Solute is extracted with solvent, S. The entering solvent stream is often presaturated with diluent. Streams with high concentrations of diluent are called raffinate, while streams with high concentrations of solvent are the extract. The nomenclature in both wei t fraction and weight ratio units is given in Table 13-2. 

In order that the deviation from ideality expressed as the activity coefficient may be significant, the selection of a reference for systems should be consistent. The activity coefficient depends, besides the variables of state associated with it, on the concentration units employed (mole fraction, molality etc.). In the case of polymer solutions volume fractions segment fractions and weight fractions Wt are the most convenient [15]. 

Fig. 22. Rigid amorphous, mobile amorphous, and crystallinity changes in PPS with crystallization temperatures (166). Mobile amorphous fraction rigid amorphous fraction and weight fraction crystallinity A.

The simplest possible type of three-dimensional polymer is that formed by stepwise homopolymerization of a multifunctional monomer, snch as etheri cation of pentaerythritol, or by stepwise copolymerization of equimolar amounts of two monomers having the same fnnctionality /, snch as the condensation of a trihydric alcohol with an equimolar proportion of a tribasic acid, all three functional groups on each monomer being equally reactive. For such polymerizations, the number Nx, the number or mole fraction %, and weight fraction Wx of x-mer molecules in the reaction system are given (Ghosh, 1990 Odian, 1991), respectively, by... 

Figure 1.56. Number fraction and weight fraction of the Poisson distribution. Af and M are also indicated.

Under the condition of known physical and mechanical properties of components, the effect of the component considers only the volume fraction and weight fractions of the fillers as variables regardless of the influence of shape, orientation, size, and other variables of the components. 

A basic parameter in all gas-solid systems is the size of the particles present in the system. At first glance, determination of particle size may seem like an easy task. On taking up a handful of sand, inspection by eye tells one that an average particle size could probably be determined with ease. A simple technique would be to sieve the sand into different fractions and weight average the results according to the sieve openings. This technique is probably sufficient for a number of situations, but there are many more where this procedure is not applicable. 

Figure 4.4 Changes of the complex viscosity, volume fraction and weight percent of PES in the DCEBA/DDM/PES mixture with 10wt% PES at different isothermal curing...

The mole fraction and weight fraction distributions for step polymerizations in which there is a stoichiometric imbalance are similar to those just derived for the case of exactly equivalent stoichiometry. Thus all linear step polymerizations lead to essentially the same form of molar mass distribution. 

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