If a polythene sample contains two monodisperse fractions in the ratio 2: 3 with degree of polymerization 100 and 200, respectively, then its weight average molecular weight will be :

Question

If a polythene sample contains two monodisperse fractions in the ratio 2: 3 with degree of polymerization 100 and 200, respectively, then its weight average molecular weight will be : (A) 4900 (B) 4600 (C) 4300 (D) 5200

Tardigrade Admin · Accepted Answer

Given,
Degree of polymerization of first polymer

= 100

Degree of polymerization of second polymer

= 200

n_{1} = 2

n_{2} = 3

Here the polymer is polythene which has a monomer ethylene with molecular mass

28

,
Now,
Degree of polymerization is given as:

D P = \frac{Molar mass of polymer}{molar mass of monomer}

Thus,
Molar mass of first polymer

M_{1} = 100 \times 28 = 2800 g / m o l

Molar mass of second polymer

M_{2} = 200 \times 28 = 5600 g / m o l

Now, The weight average molecular weight is given as:

\overset{ˉ}{M}_{w} = \frac{\sum n _{i} M _{i}^{2}}{\sum n _{i} M _{i}}

Thus, putting all the values we get,

\overline{M}_{w} = \frac{n _{1} M _{1}^{2} + n _{2} M _{2}^{2}}{n _{1} M _{1} + n _{2} M _{2}}

= \frac{2 ( 2800 ) ^{2} + 3 ( 5600 ) ^{2}}{2 \times 2800 + 3 \times 5600} = 4900 g / m o l

Q. If a polythene sample contains two monodisperse fractions in the ratio 2:3 with degree of polymerization 100 and 200, respectively, then its weight average molecular weight will be :

4900

4600

4300

5200

Q. If a polythene sample contains two monodisperse fractions in the ratio $2 : 3$ with degree of polymerization $100$ and $200$ , respectively, then its weight average molecular weight will be :