Polystyrene Molecular Weight Calculation

The number average molecular weight (Mn) relates to the number average degree of polymerization (DPn) and the molecular weight of the repeating unit (M0).

Formula

The calculation uses the formula:

$ M_n = DP_n \times M_0 $

Given Values

• Number Average Degree of Polymerization, DPn = 1000
• Repeating Unit: Styrene ($C_8H_8$)

Repeating Unit Molecular Weight (M0)

The molecular weight of the styrene unit ($M_0$) is calculated using standard atomic weights (C $\approx 12.011$ g/mol, H $\approx 1.008$ g/mol):

$ M_0 = (8 \times 12.011) + (8 \times 1.008) \approx 104.15 \text{ g/mol} $

Number Average Molecular Weight (Mn)

Substituting the values:

$ M_n = 1000 \times 104.15 \text{ g/mol} \approx 104150 \text{ g/mol} $

This calculated value is approximately $1.04 \times 10^5$ g/mol.

Conclusion

The correct answer is Option B ($9.01 \times 10^4$ g/mol).