Answer:
a)Number average molecular weight is 50, 500 g/mol
b) Weight average molecular weight is 99, 019.8 g/mol
Step-by-step explanation:
We have a polymer P made up of two monodisperse fractions.
A with molecular weight of MA = 1000 g/mol and B with MB =100000 g/mol.
The batch contains an equal mole fraction of each component A and B.
Let's suppose a total number (Nt) of mols 2 moles. Equal fraction means XA = 0.5 and XB =0.5
Nt = 2 mol
Na = 2*0.5 = 1 mol
Nb = 2*0.5 = 1 mol.
So, we have 1 mol of A, 1 mol of B and 2 moles in total.
a) The number average molecular weight (NAM) is calculate using the mole numbers of each component. In this case, we will multiple each component molecular weight by the number of moles of each one. After that we will sum them and finally to divide by the total number of moles.
NAM = (Na*MA + Nb*MB)/(Nt)
NAM = (1 mol *1000 g/mol + 1*100000 g/mol ) /(2 mol)
NAM = 50500 g/mol
The number average molecular weight for the polymer P is 50,500 g/mol
b) Weight average molecular weight (WAM) is calculated using the mass quantities of each component. Weight mass of A (WA), weight mass of B (WB) are calculate using the moles of A, B and their molecular weights respectively. Total Weight (WT)
WA = Na*MA = 1 mol *1000 g/mol = 1000 g A
WB = Nb*MB = 1mol * 100000 g/mol = 100 000 gB
WT = WA + WB = 101 000 g
Now we will calculate average molecular using weights, we will multiple each component molecular weight by the mass of each one. After that we will sum them and finally to divide by the total mass.
WAM = (WA*MA + WB*MB)/(WT)
WAM = (1000 g *1000 g/mol + 100000 g*100000 g/mol )/(101 000 g)
WAM = 99 019.8 g/mol
The weight average molecular weight for polymer P is 99, 019.8 g/mol