Molar mass definition

The above two examples of the polymerization of styrene contrast the prototypical controlled and uncontrolled polymerizations. Controlled polymerizations offer simple molar mass control, the ability to define the polymer end groups, and give polymer samples with narrow molar mass distributions. Molar mass definition in uncontrolled polymerizations is more difficult, polymer end groups are determined by inherent termination (and transfer) reactions, and the molar mass distributions are typically broader. There is much contemporary interest in developing polymerization reactions that are controlled because of the precision with which macromolecules can be designed. Many chapters are dedicated to these endeavors with controlled radical polymerization receiving the most attention recently. 

FIGURE 9.9 Definition of column test parameters using a SEC chromatogram of a polymer standard mixture (PSS Polystyrene ReadyCal) and a low molar mass compound (BHT). 

A mole represents not only a specific number of particles but also a definite mass of a substance as represented by its formula (0,02, H20, NaCl,. . . ). The molar mass, MM, in grams per mole, is numerically equal to the sum of the masses (in amu) of the atoms in the formula. 

Finally, the definition of molar mass (MM = mitt) gives... 

By definition, the molar mass of the end groups should be included in the molecular weight of a polymer but the corresponding quantity is not included in the degree of polymerization. 

E.29 The king of Zirconia is naturally fond of the element zirconium and has established an independent definition of the mole based on zirconium. The mass of one zirconium-90 atom is 1.4929 X 10 22 g. If zirconium were the standard used for molar mass (instead of carbon-12), 1 mol would be defined as the amount of substance that contains the same number of entities as there are atoms in exactly 90 g of zirconium-90. In that case, what would be (a) the molar mass of carbon-12 (b) the (average) molar mass of gold ... 

Why do polymers not have definite molar masses How does the fact that polymers have average molar masses affect their melting points ... 

Polymers generally do not have definite molecular masses because there is no fixed point at which the chainlengthening process will cease. There is no fixed molar mass, only an average molar mass. Because there is no one unique compound, there is no one unique melting point, rather a range of melting points. 

At pH 3.0, all enzymatic activities are lower than the ones at pH 6.0. This effect is especially marked for the PL because its optimum pH value is definitely higher than those of PG and PE (Table 1). PG is very efficient in depolymerising the polygalacturonic acid. The solution viscosity reaches its minimum value, which corresponds to a rather low molar mass, after 40 min at both pH 4.1 and 6.0. 

Basic definitions Let X be some property of a polymer chain such as the degree of polymerization, molar mass, radius of gyration, or comonomer content of a copolymer, etc. In general, the polymer is heterogeneous with respect to X, which can assume discrete values X,. We now define for molecules with X = X,-. 

Special care has to be taken if the polymer is only soluble in a solvent mixture or if a certain property, e.g., a definite value of the second virial coefficient, needs to be adjusted by adding another solvent. In this case the analysis is complicated due to the different refractive indices of the solvent components [32]. In case of a binary solvent mixture we find, that formally Equation (42) is still valid. The refractive index increment needs to be replaced by an increment accounting for a complex formation of the polymer and the solvent mixture, when one of the solvents adsorbs preferentially on the polymer. Instead of measuring the true molar mass Mw the apparent molar mass Mapp is measured. How large the difference is depends on the difference between the refractive index increments ([dn/dc) — (dn/dc)A>0. (dn/dc)fl is the increment determined in the mixed solvents in osmotic equilibrium, while (dn/dc)A0 is determined for infinite dilution of the polymer in solvent A. For clarity we omitted the fixed parameters such as temperature, T, and pressure, p. 

Since effects of radioactive decay on the molar mass can be neglected, q>bas Sr can be replaced with an excellent precision by expressed through equation (1.3.2) as a function of mass fractions / and concentrations CSr requires... 

It is shown that model, end-linked networks cannot be perfect networks. Simply from the mechanism of formation, post-gel intramolecular reaction must occur and some of this leads to the formation of inelastic loops. Data on the small-strain, shear moduli of trifunctional and tetrafunctional polyurethane networks from polyols of various molar masses, and the extents of reaction at gelation occurring during their formation are considered in more detail than hitherto. The networks, prepared in bulk and at various dilutions in solvent, show extents of reaction at gelation which indicate pre-gel intramolecular reaction and small-strain moduli which are lower than those expected for perfect network structures. From the systematic variations of moduli and gel points with dilution of preparation, it is deduced that the networks follow affine behaviour at small strains and that even in the limit of no pre-gel intramolecular reaction, the occurrence of post-gel intramolecular reaction means that network defects still occur. In addition, from the variation of defects with polyol molar mass it is demonstrated that defects will still persist in the limit of infinite molar mass. In this limit, theoretical arguments are used to define the minimal significant structures which must be considered for the definition of the properties and structures of real networks. 

Note 2 Any molar-mass average can be defined in terms of mass fractions or mole fractions. In this document only a few of the important molar-mass averages are given in terms of the mass fractions, Wi, of the species with molar mass M. These definitions are most closely related to the experimental determination of molar-mass averages. 

Definitions of Basic Terms Relating to Low-Molar-Mass and Polymer Liquid Crystals... 

Definitions of basic terms relating to low-molar-mass and polymer liquid crystals (lUPAC Recommendations 200 ), Pure Appl. Chem. 73, 845-895 (2001). 

Solve these kinds of problems by using the definition of molarity and conversion factors. In parts (b) and (c), you must first convert your mass in grams to moles. To do so, you divide by the molar mass from the periodic table (flip to Chapter 7 for details). In addition, be sure you convert milliliters to liters. 

By definition, molar volume V, liquid density plL, and molar mass Mi are related by... 

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