Answer to Question #227852 in General Chemistry for Paul

Question

A 50-g polymer sample was fractionated into six samples of different weights given in the table below. The viscosity-average molecular weight, Mv, of each was determined and is included in the table. Estimate the number-average and weight-average molecular weights of the original sample. For these calculations, assume that the molecular-weight distribution of each fraction is extremely narrow and can be considered to be monodisperse. Would you classify the molecular-weight distribution of the original sample as narrow or broad? Fraction Weight (g)Mv 1,500 35,000 75,000 150,000 400,000 850,000 1.0 5.0 21.0 15.0 6.5 1.5 2 4

Answer 1

By definition, the differential numerical function MMR-rn (M) is equal to the ratio of the numerical fraction of macromolecules (dn) having a molecular weight in the range from M to M dM to the value of this interval (dM), i.e. rn(M) = dn/dM; similarly, the differential mass function MMR - rw(M) is determined by the ratio rw(M) = dw/dM, where dw is the mass fraction of macromolecules of molecular weight lying in the range from M up to M dM.