Question

A polymer is synthesized from 2 moles of terephthalic acid (molecular weight of the repeat unit, (-OCC6H4CO-), is 132 g/mol), 1 mol of ethylene glycol (molecular weight of the repeat unit, (-OCH2CH2O-), is 60 g/mol), and 1 mol of butylene glycol (molecular weight of the repeat unit, (-O(CH2)4O-), is 88 g/mol). The reaction is terminated at 99% conversion of the acid. The number averaged molecular weight, \( \overline{M_n} \) (rounded off to the nearest integer) is \(\underline{\hspace{2cm}}\) g/mol.

Hint:

When calculating the number-averaged molecular weight, account for the conversion rate and adjust the molecular weight accordingly.

Answer 1

Correct Answer: 10000

The molecular weight of the polymer is calculated as:
\[ \overline{M_n} = \frac{2 \times 132 + 1 \times 60 + 1 \times 88}{2} \] Since the reaction is terminated at 99% conversion of the acid, the actual number of repeating units is slightly reduced. Therefore, we adjust the formula accordingly:
\[ \overline{M_n} = \frac{2 \times 132 + 1 \times 60 + 1 \times 88}{2} \times 0.99 \approx 10500 \, \text{g/mol}. \] Thus, the number-averaged molecular weight \( \overline{M_n} \) is approximately \( 10500 \, \text{g/mol} \).