Final answer:
The fraction of the possible crosslink sites bonded to sulfur crosslinks is 0.29%.
Step-by-step explanation:
To find the fraction of the possible crosslink sites that are bonded to sulfur crosslinks, we need to calculate the number of crosslinks formed using the given information.
20 kg of polybutadiene is vulcanized with 4.8 kg of sulfur. Assuming that, on average, 4.5 sulfur atoms participate in each crosslink, we can calculate the number of crosslinks formed by dividing the total mass of sulfur by the average number of sulfur atoms per crosslink.
Number of crosslinks = 4.8 kg sulfur / (4.5 sulfur atoms/crosslink) = 1.0667 crosslinks
Next, we calculate the total number of possible crosslink sites by dividing the mass of polybutadiene by the molecular weight of polybutadiene.
Molecular weight of polybutadiene: 4 carbon atoms * 12.01 g/mol + 6 hydrogen atoms * 1.01 g/mol = 54.06 g/mol
Number of possible crosslink sites = 20 kg polybutadiene / (54.06 g/mol) = 369.85 crosslink sites
Finally, we calculate the fraction of crosslink sites bonded to sulfur by dividing the number of crosslinks by the number of possible crosslink sites.
Fraction of crosslink sites bonded to sulfur = 1.0667 crosslinks / 369.85 crosslink sites = 0.0029 or 0.29%