Number average molar mass definition

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. 

In dilute solutions the osmotic pressure is given by tt = (LNJN )(RT/V) in which is the total number of molecules. Show that in view of Eq. (35.31), the definition of v, that we can write n = (wRT/V)/(M where w is the total mass and jy is the number-average molar mass. 

The sum 2, (c,/ in Equation (9-8) is also contained in the definition of the number-average molar mass = 2,c,7S,[c,7(Af,) ] given in equation (8-44). If this expression is inserted into Equation (9-8), it is seen that osmotic pressure measurements give the number-average molar mass ... 

Let s denote with D(x) the ratio between the weight-average and the number-average molar mass in fraction x. Using the definitions, D(x) becomes ... 

A normal polymer sample contains molecules with a variety of lengths and it is only possible to quote an average value of the molar mass. A typical distribution of molar mass is shown in Fig. 1.3. Often the exact form of the distribution is not known and it is conventional to describe it in terms of either a number average molar mass, M or a weight average molar mass, My. Both of these parameters can be measured experimentally. In the definition of M and M , it is envisaged that the distribution of molar mass... 

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 ... 

---