The number-average molecular weight of a polystyrene is 500,000 g/mol. Compute the degree of polymerization.
The correct answer and explanation is :
To compute the degree of polymerization (DP) of polystyrene, we use the formula:
[
DP = \frac{M_n}{M_0}
]
where:
- ( M_n ) = number-average molecular weight of the polymer (500,000 g/mol)
- ( M_0 ) = molecular weight of the repeating unit (for polystyrene, the repeating unit is styrene, which has a molecular weight of 104.15 g/mol)
Calculation:
[
DP = \frac{500,000}{104.15} \approx 4,800
]
Explanation:
The degree of polymerization refers to the number of monomeric units in a polymer chain. It helps determine the physical properties of the polymer, such as strength, toughness, and viscosity.
For polystyrene, each repeating unit (monomer) is styrene (C₈H₈), which has a molecular weight of 104.15 g/mol. Since the given polymer has a number-average molecular weight ((M_n)) of 500,000 g/mol, we divide this by the molecular weight of the monomer to find how many monomers are linked together in an average polymer chain.
A higher DP means longer polymer chains, leading to improved mechanical properties such as higher tensile strength, increased viscosity, and better impact resistance. However, beyond a certain limit, excessive polymer chain length may hinder processability due to high viscosity.
In practical applications, polystyrene is widely used in packaging, insulation, and disposable containers due to its lightweight and moldability. The molecular weight and degree of polymerization significantly influence its end-use properties.