Combined weight-fraction

Bromine (128 g., 0.80 mole) is added dropwise to the well-stirred mixture over a period of 40 minutes (Note 4). After all the bromine has been added, the molten mixture is stirred at 80-85° on a steam bath for 1 hour, or until it solidifies if that happens first (Note 5). The complex is added in portions to a well-stirred mixture of 1.3 1. of cracked ice and 100 ml. of concentrated hydrochloric acid in a 2-1. beaker (Note 6). Part of the cold aqueous layer is added to the reaction flask to decompose whatever part of the reaction mixture remains there, and the resulting mixture is added to the beaker. The dark oil that settles out is extracted from the mixture with four 150-ml. portions of ether. The extracts are combined, washed consecutively with 100 ml. of water and 100 ml. of 5% aqueous sodium bicarbonate solution, dried with anhydrous sodium sulfate, and transferred to a short-necked distillation flask. The ether is removed by distillation at atmospheric pressure, and crude 3-bromo-acetophenone is stripped from a few grams of heavy dark residue by distillation at reduced pressure. The colorless distillate is carefully fractionated in a column 20 cm. long and 1.5 cm. in diameter that is filled with Carborundum or Heli-Pak filling. 4 hc combined middle fractions of constant refractive index are taken as 3-l)romoaccto])lu iu)nc weight, 94 -100 g. (70-75%) l).p. 75 76°/0.5 mm. tif 1.57,38 1.5742 m.]). 7 8° (Notes 7 and 8). 

Equation 1-5 was written for a sample containing a single element upon which monochromatic x-rays are incident. In so far as x-ray absorption is an atomic property, the mass absorption coefficients for other samples are additive functions of the weight-fractions of the elements, free or combined, that are present that is,... 

For large values of z a fully developed case is reached in which the velocities are only functions of r and 0. In the fully developed case the weight fraction polymer increases linearly in z with the same slope for all r and 0. An implicit finite difference scheme was used to solve the model equations, and for the fully developed case the finite difference method was combined with a continuation method in order to efficiently obtain solutions as a function of the parameters (see Reference 14). It was determined that except for very large Grashof... 

For detector 2 ( X = 235 nm) the response is assumed to be a linear combination of the weight fraction of each component in the copolymer. That is ... 

By using two or more polymerization catalysts simultaneously, polymer chemists can produce copolymers tvith a bimodal composition distribution. This is made possible by the fact that no two catalysts incorporate monomers at exactly the same rate. The net result is that short chain branches may be preferentially incorporated into either the higher or lower molecular weight fractions. Polymer manufacturers can obtain a similar result by operating two polymerization reactors in series. Each reactor produces a resin with a different copolymer distribution, which are combined to form a bimodal product. Copolymers with a bimodal composition distribution provide enhanced toughness when extruded into films. 

The kidneys receive a disproportionate fraction of cardiac output. Although the combined weight of the kidneys accounts for less than 1% of total body weight, these organs receive 20 to 25% of the cardiac output. This magnitude of blood flow, which is in profound excess to their metabolic needs, enables them to carry out their multiple homeostatic functions more efficiently. Assuming a resting cardiac output of 5 1/min, the renal blood flow (RBF) is approximately 1.1 1/min. 

The carboxylic acids were combined with hexylamlne and water in order to study the association structures formed. The hexyl-amine was chosen because it did not by Itself form a liquid crystalline phase with water. Fig. 3A. Water dissolves in the amine to a maximum of 60% to form an isotropic solution. The liquid crystal is formed first at a certain octanoic acid amine ratio, approximately 0.1. The liquid crystalline phase forms a large region reaching to a weight fraction of 0.61 of the acid, corresponding to a 1 1 molar ratio of the two species. 

Typically, the liquidus lines of a binary system curve down and intersect with the solidus line at the eutectic point, where a liquid coexists with the solid phases of both components. In this sense, the mixture of two solvents should have an expanded liquid range with a lower melting temperature than that of either solvent individually. As Figure 4 shows, the most popular solvent combination used for lithium ion technology, LiPFe/EC/DMC, has liquidus lines below the mp of either EC or DMC, and the eutectic point lies at —7.6 °C with molar fractions of - 0.30 EC and "-"0.70 DMC. This composition corresponds to volume fractions of 0.24 EC and 0.76 DMC or weight fractions of 0.28 EC and 0.71 DMC. Due to the high mp of both EC (36 X) and DMC (4.6 X), this low-temperature limit is rather high and needs improvement if applications in cold environments are to be considered. 

These equations are general and apply equally for multifunctional reactions such as that of Af with B, or that of Ay with A—A and B B. Depending on which of these reactant combinations is involved, the value of a will be appropriately determined by the parameters r,f, p, and p. For convenience the size distributions in the reaction of equivalent amounts of trifunctional reactants alone, that is, where a p, will be considered. A comparison of Eqs. 2-89 and 2-166 shows that the weight distribution of branched polymers is broader than that of linear polymers at equivalent extents of reaction. Furthermore, the distribution for the branched polymers becomes increasingly broader as the functionality of the multifunctional reactant increases. The distributions also broaden with increasing values of a. This is seen in Fig. 2-17, which shows the weight fraction of x-mers as a function of a for the polymerization involving only trifunctional reactants. 

Consider the situation where one polymer molecule is produced from each kinetic chain. This is the case for termination by disproportionation or chain transfer or a combination of the two, but without combination. The molecular weight distributions are derived in this case in exactly the same manner as for linear step polymerization (Sec. 2-7). Equations 2-86, 2-88, 2-89, 2-27, 2-96, and 2-97 describe the number-fraction, number, and weight-fraction... 

The combined characterization results for all of the SAN samples (including the one polystyrene sample), i.e., weight fraction of AN mer units and [p] in... 

Combine your information to make a single, rough plot of AS i /R versus At what weight fraction is the difference in the entropy of mixing between an ideal and athermal polymer solution the greatest for this system ... 

We now introduce two terms which will become very important in subsequent discussions N, the number of moles of gaseous detonation products per gram of explosive, and G, the weight fraction of explosive going over to gaseous products. From the definitions, NM=G, so that after combining constants, kH—A and ( kH=B, the equation may now take the general form... 

We can now compare these calculated values with test results. Technical brochures issued by raw material manufacturers supply an abundance of data on their products, also on the tensile moduli of the virgin polymers and on those containing a certain weight fraction of glass fibres. Combination of these data for a number of polymers (POM, PPE/PS, PC, PBTP, PET, PA-6) results in Figure 9.16. We can read from this... 

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