Respuesta :
Explanation:
Formula to calculate degree of polymerization is as follows.
Degree of polymerization (DP) = [tex]\frac{\text{Number average molecular weight}}{\text{Average unit molecular weight}}[/tex]
DP = [tex]\frac{\bar{M_{n}}}{m}[/tex]
1000 = [tex]\frac{\bar{M_{n}}}{104.12}[/tex]
[tex]\bar{M_{n}}[/tex] = 104150
Formula to calculate average repeat molecular weight of co-polymer is as follows.
[tex]\bar{m} = \sum{f_{j}m_{j}}[/tex]
where, [tex]f_{j}[/tex] = mole fraction of each component
Moles of styrene = [tex]\frac{mass}{\text{molar mass}}[/tex]
= [tex]\frac{100 g}{104.12 g/mol}[/tex]
= 0.96 mol
Moles of toulene = [tex]\frac{900 g}{92.15 g/mol}[/tex]
= 9.77 mol
Therefore, mole fraction will be calculated as follows.
[tex]f_{1} = \frac{0.96}{0.96 + 9.77}[/tex]
= 0.0895
[tex]f_{2} = \frac{9.77}{0.96 + 9.77}[/tex]
= 0.910
[tex]\bar{m} = 0.0895 \times 104.12 g/mol + 0.910 \times 92.15 g/mol[/tex]
= 93.22 g/mol
Hence, DP = [tex]\frac{\bar{M_{n}}}{\bar{m}}[/tex]
= [tex]\frac{104150}{93.22 g/mol}[/tex]
= 1117
Thus, we can conclude that the number-average degree of polymerization is 1117.
