Question

A sample of natural rubber (cis-1,4-polyisoprene) is vulcanized such that one of every 240 chain carbon atoms is cross-linked. The formula unit of the isoprene monomer is \( C_5H_8 \) (molecular weight = 68 g/mol). The average molecular weight (rounded off to nearest integer) between cross-links is \(\underline{\hspace{2cm}}\) g/mol.

Hint:

To calculate the average molecular weight between cross-links in polymers, multiply the molecular weight of the repeat unit by the number of repeat units per cross-link.

Answer 1

Correct Answer: 4000

The average molecular weight between cross-links is given by:
\[ M_{\text{cross-link}} = \frac{M_{\text{molecule}} \times 240}{1} \] where:
- \( M_{\text{molecule}} = 68 \, \text{g/mol} \).
Substituting the value:
\[ M_{\text{cross-link}} = \frac{68 \times 240}{1} = 16320 \, \text{g/mol}. \] Thus, the average molecular weight between cross-links is approximately \( 16320 \, \text{g/mol} \).