Question

The average degree of polymerization of polystyrene is 1000. The number average molecular weight of polystyrene is:

• A. \(1.03 \times 10^{5}\)
• B. \(9.01 \times 10^{4}\)
• C. \(1.03 \times 10^{4}\)
• D. \(9.8 \times 10^{5}\)

Hint:

Always double-check the monomer structure. For styrene, it's a benzene ring attached to an ethylene group (\(C_8H_8\)). Memorizing common monomer molecular weights (Ethylene: 28, Styrene: 104, Vinyl Chloride: 62.5) saves time!

Answer 1

The Correct Option is A

Concept: The Degree of Polymerization (\(DP\) or \(X_n\)) represents the number of repeating monomer units in a polymer chain. The number average molecular weight (\(\bar{M}_n\)) is calculated by multiplying the degree of polymerization by the molecular weight of the single repeating unit (\(M_0\)). \[ \bar{M}_n = DP \times M_0 \]

Step 1: Determine the molecular weight of the monomer unit.
Polystyrene is made from the monomer Styrene (\(C_8H_8\)). The repeating unit is \(-[CH_2-CH(C_6H_5)]-\). Calculation of \(M_0\):
• Carbon (C): \(8 \times 12 = 96~g/mol\)
• Hydrogen (H): \(8 \times 1 = 8~g/mol\)
• \(M_0 = 96 + 8 = 104~g/mol\)

Step 2: Calculate the number average molecular weight.
Given \(DP = 1000\): \[ \bar{M}_n = 1000 \times 104 = 104,000~g/mol \] \[ \bar{M}_n = 1.04 \times 10^{5}~g/mol \] The closest value among the provided options is \(1.03 \times 10^{5}\).