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  • 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 : <div

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 : 

Option: 1

4900


Option: 2

4600


Option: 3

4300


Option: 4

5200


Answers (1)

best_answer

Given,
Degree of polymerization of first polymer =100
Degree of polymerization of second polymer =200
\begin{aligned} & n_1=2 \\ & n_2=3 \end{aligned}
Here the polymer is polythene which has monomer ethylene with molecular mass 28,
Now,
The degree of polymerization is given as:

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

Thus,
Molar mass of first polymer

M_{1}=100 \times 28=2800 \mathrm{~g} / \mathrm{mol}

Molar mass of second polymer

M_{1}=200 \times 28=5600 \mathrm{~g} / \mathrm{mol}

Now, The weight average molecular weight is given as:

\overline{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}}

\overline{M}_{w}=\frac{2(2800)^{2}+3(5600)^{2}}{2 \times 2800+3 \times 5600}=4900 \mathrm{~g} / \mathrm{mol}

Option 1 is correct.

Posted by

shivangi.shekhar

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