Calculate the number-average molecular weight of a random nitrile rubber [poly (acrylonitrile-butadiene) copolymer] in which the fraction of butadiene repeat units is 0.27; assume that this concentration corresponds to a degree of polymerization of 2000.

106,504 g/mol

Explanation:

The two repeat units at the polymer are the acrylonitrile and the butadiene. If the fraction of repeat of butadiene is 0.27, the fraction of repeat of units of acrylonitrile must be 0.73.

The acrylonitrile repeat unit has 3 carbons atoms, 1 nitrogen atom, and 3 hydrogen atoms. So, the molecular weigth for it is:

mac = 3*mC + 1*mN + 3*mH

mC = 12 g/mol; mN = 14 g/mol; mH = 1g/mol

mac = 3*12 + 14 + 3*1 = 53 g/mol

The butadiene repeat unit has 4 carbons atoms and 6 hydrogen atoms. Thus, the molecular weight is:

mbu = 4*12 + 6*1 = 54 g/mol

The average repeat unit molecular weight is the fractions multiplied by the molecular weight of the repeat unities:

m = 0.73*53 + 0.27*54 = 53.27 g/mol

The number-average molecular weight is the average repeat unit molecular weight multiplied by the degree of polymerization:

M = 53.27*2000

M = 106,504 g/mol