Answer:
Mn = 43,783
Mw = 60,000
Mz = 73,333
narrow distribution = 1.37
Explanation:
The molecular weights of these fractions increase from 20,000 to 100,000 in increments of 20,000. This means their Mi is respectively: (The molar weight (Mi) of the fractions)
Fraction 1 : Mi = 20 *10^3
Fraction 2: Mi = 40 *10^3
Fraction 3 : Mi = 60 *10^3
Fraction 4: Mi = 80 *10^3
Fraction 5 : Mi = 100 *10^3
The ΣMi = 300*10^-3
The Wi (mass of the fractions is for all the fractions the same, let's say 1)
So Wi = 1+1+1+1+1 = 5
Since number of moles = mass / Molar mass
The number of moles is respectively: ni = Wi/Mi (x10^5)
Fraction 1 : ni = Wi/Mi = 1/20000 = 5
Fraction 2: ni = 1/40000 = 2.5
Fraction 3 : ni =1/60000 = 1.67
Fraction 4: ni = 1/80000 = 1.25
Fraction 5 : ni= 1/100000 = 1
The Σni = 11.42
Mn = ΣWi/ni = 5/11.42*10^-5 = 43,783
Mw = (ΣWi * Mi)/ΣWi = 300,000 /5 = 60,000
Mz = (ΣWi * Mi²)/ΣWi *Mi = (4*10^8 +16*10^8 +36*10^8 +64*10^8 +100*10^8) /300,000 =73,333
Mz/Mn = narrow distribution =60,000/43,783 = 1.37
