Molar mass weight average, defined

This is the simplest average it is the mass of the specimen divided by the total number of moles present. Properties that depend on the total number of molecules in the specimen, independent of their size, correlate with The weight average molar mass M is defined as... 

The weight-average molar mass (M ) is defined as the sum of the products of the molar mass of each fraction multiplied by its weight fraction ... 

Alternatively we can define the weight-average molar mass where we take terms inM , i.e. 

The leading parameter that characterizes the distributions of randomly branched samples is an exponent Tthat is defined in the next section. The average procedures for the z-average of the mean square radius of gyration and the weight average molar mass results in the relationship [7]... 

Figure 6.10 Effect of CITREM on the molecular and thermodynamic parameters of maltodextrin SA-2 (DE = 2) in aqueous medium (phosphate buffer, pH = 7.2, ionic strength = 0.05 M 20 °C) (a) weight average molar mass, Mw (b) radius of gyration, Ra (c) structure sensitive parameter, p, characterizing die architecture of maltodextrin associates (d) second virial coefficient, A2 or A2, on the basis of the weight ( ) and molal (A) scales, respectively. The parameter R is defined as the molar ratio of surfactant to glucose monomer units in the polysaccharide. The indicated cmc value refers to the cmc of the pure CITREM solution. Reproduced from Anokhina et al. (2007) with permission.

For conversions lower than xgei the average molar mass of the polymer exhibits a continuous increase. The first two moments of the molar mass distribution are the number-average molar mass, Mn, and the mass-average molar mass, Mw, respectively. Mn is defined in terms of the number contribution of every species to the whole population. The weight factor used to define this average is the molar fraction. Mw is defined in terms of the mass contribution of every species to the whole mass, so that the mass fraction is the weight factor used in its definition. 

As agreed by the IUPAC Commission on Atomic Weights and Isotopic Abundances in 1979 [42] the relative atomic mass (atomic weight) of an element, E, can be defined for any specified sample. It is the average mass of its atoms in the sample divided by the unified atomic mass unit1 or alternatively the molar mass of its atoms divided by the standard molar mass M = Lmu = 1 gmol-1 ... 

In addition to the molar mass, this analysis also provides information about the radius of gyration of larger partides, which is a measure of the shape and size of the molecule. This quantity is defined as the weight-average distance of the individual elements of die molecule from the centre of mass ... 

Because of the results to be presented to illustrate composition drift, we prefer to define the average weight fraction of styrene Ws(V) in equation 5. Determinations of Ks, Ka, and Kb were reported previously (J7). It was demonstrated that for the range of molar masses studied there was no dependence of refractometer proportionality constants on chain length or end group structure. 

The polydispersity index is defined as the ratio of the weight-average and number-average molar masses Monodisperse samples with... 

In order to quantify the chain length, the molar mass (or molecular weight) must be defined statistically. The number average molar mass, M, is given by ... 

The dimensionless quantity relative molecular mass (molecular weight), defined as the average mass of the molecule divided by one twelfth the mass of an atom of the nuclide c, is often used in polymer chemistry and called the molecular weight. In this book, the quantity molar mass is also used and the appropriate SI units are given. 

From light-scattering measurements, a method depending on the size rather than the number of molecules, a weight-average molar mass M is obtained. This is defined as... 

Assuming that a polymer has a molar-mass distribution defined by (m) = ae ", where n m)Am represents the fraction of molecules with molar masses between m and m + Am, show that a = b and calculate (i) the number- and weight-average molar masses, and hence the polydispersity index and (ii) the molar mass at the mode (maximum) of the distribution function. 

Weight-average molecular weight A polymer molar mass average which is the mean value of the weight distribution of molecular sizes, defined as M = LNiMf l = "LwiMirLwi, where Nj, Mi and Wi are the number of molecules, the molar mass, and the total with of the molecular species. 

The most important averages of molar masses are defined by simple moments of the distribution fimctions of the molar masses w M)- H M) or n(M) h(M). Hydrodynamic methods, as a rule, yield more complex molar-mass averages. According to the statistical weighting factor, mean values of molar masses listed in Table 4.1.1 can be determined as shown in Table 4.2.1. 

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