Mass number average

The mean values of molar masses, number average,, and mass average,, can be calculated by means of equations... 

An average molecular mass (viscosity average) An average molecular mass (number average) Molecular dimensions and an average molecular mass (weight average) Molecular mass distribution... 

The chromatogram was calibrated using the result of the analysis of MALDI-ToF spectra of selected fractions (see Table 5.1). The average molar masses (number average molecular weight (M ) and MJ of the copolymer were measured using the Caliber software distributed by Polymer Lab. The type of calibration selected by Montaudo and co-workers [10] was a narrow standards the calibration function was polynomial of order 1 and the calculation method was area based . 

M average molar mass number-average molar mass (Mn) weight-average... 

The solute molecular weight enters the van t Hoff equation as the factor of proportionality between the number of solute particles that the osmotic pressure counts and the mass of solute which is known from the preparation of the solution. The molecular weight that is obtained from measurements on poly disperse systems is a number average quantity. 

Lead, atomic number 82, is a member of Group 14 (IVA) of the Periodic Table. Ordinary lead is bluish grey and is a mixture of isotopes of mass number 204 (15%), 206 (23.6%), 207 (22.6%), and 208 (52.3%). The average atomic weight of lead from different origins may vary as much as 0.04 units. The stable isotopes are products of decay of three naturally radioactive elements (see Radioactivity, natural) comes from the uranium series (see Uraniumand... 

However, a moments consideration makes clear that over half the mass of the polymer consists of the molecule with the molecular weight of 100000 and that this would have an important influence on the properties of the polymer mass not reflected in the number average figure which is in any case totally unrepresentative of any of the molecules. In this case the weight average molecular weight will be... 

Figure I 6.34 Degree of polymerization distribution molar distribution ( ) with number average degree of polymerization (dp = 140 glucose unimers) mass distribution ( ) with weight average degree of polymerization dp = 1242 glucose unimers.

The average atomic mass shown in the periodic table is not equal to the mass number. 

The number-average molar mass of thermoplastic polyesters varies from about 20,000 for film and fiber applications to 40,000 for injection-molding or blowmolding resins. Relationships between intrinsic or molten viscosity and molar mass have been published for PET,131-136 PBT,135,137 and PEN.138... 

The rigid and soft blocks used in polyesteredier diermoplastic elastomers (polyesteretlier TPEs) are typically PBT and poly(oxyteti amethylene) (PTMO), respectively, witii block number-average molar mass varying between 1000 and 3000. They are obtained by the melt reaction between dimethyl terephthalate, butanediol, and dihydroxy-terminated PTMO in the conditions typical of a PBT syndiesis. 

Thermoplastic linear polyesters, 18 Thermoplastic polyesters, 20-29, 31 commercial (table), 21-22 number-average molar mass of, 45... 

Fig. 13. Yields of nuclei in the fission of U230, as a function of mass number. The points are averages of reported experimental values, and the curve is the result of a simple theoretical calculation described in the text.

Figure 5. Number average degree of polymerization vs, conversion for hatch-mass styrene polymerization (4j...

Gelation occurs at relatively low conversions of monomer to polymer hence the number-average molar mass at the gel point is low. By contrast, however, the weight-average molar mass becomes infinite at the gel point. 

The methods by which polymers are prepared result in a mixture of molecular sizes whose properties depend on the average size of the molecules present. In principle there are a number of ways in which such an average can be calculated. The most straightforward is the simple arithmetic mean, usually called the number average molar mass, M. This is defined by the expression... 

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