The number-average molecular weight of polystyrene is 500,000 g/mol. Compute the number-degree of polymerization (molecular structure of polystyrene is C8 H8).
The Correct Answer and Explanation is:
To calculate the number-degree of polymerization (DPn) for polystyrene, we can use the following relationship:DPn=MnM0\text{DPn} = \frac{M_n}{M_0}DPn=M0Mn
Where:
- MnM_nMn is the number-average molecular weight of the polymer.
- M0M_0M0 is the molecular weight of a single monomer unit.
Step 1: Find the molecular weight of the monomer (C₈H₈)
The molecular weight of the monomer is calculated by adding up the atomic weights of carbon (C) and hydrogen (H) atoms in the monomer structure (C₈H₈).
- Carbon (C) has an atomic weight of approximately 12 g/mol.
- Hydrogen (H) has an atomic weight of approximately 1 g/mol.
The molecular weight of the monomer (C₈H₈) is:M0=(8×12)+(8×1)=96+8=104 g/molM_0 = (8 \times 12) + (8 \times 1) = 96 + 8 = 104 \, \text{g/mol}M0=(8×12)+(8×1)=96+8=104g/mol
Step 2: Use the number-average molecular weight (Mₙ) of polystyrene
The number-average molecular weight (MnM_nMn) of the polystyrene is given as 500,000 g/mol.
Step 3: Calculate the number-degree of polymerization (DPn)
Now that we have both values, we can substitute them into the formula:DPn=MnM0=500,000 g/mol104 g/mol=4807.69\text{DPn} = \frac{M_n}{M_0} = \frac{500,000 \, \text{g/mol}}{104 \, \text{g/mol}} = 4807.69DPn=M0Mn=104g/mol500,000g/mol=4807.69
Thus, the number-degree of polymerization (DPn) of polystyrene is approximately 4808.
Explanation:
The number-degree of polymerization represents the average number of monomer units in a polymer chain. In this case, for polystyrene with a molecular weight of 500,000 g/mol and a monomer molecular weight of 104 g/mol, the average polymer chain contains about 4808 monomer units. This gives us an understanding of the polymer’s size and how many repeating units are in the structure.
