Fifteen kilogram of polychloroprene is vulcanized with \(5.2 \mathrm{kg}\) sulfur. What fraction of the possible crosslink sites is bonded to sulfur crosslinks, assuming that, on the average, 5.5 sulfur atoms participate in each crosslink?

Understanding the molar mass of chemical substances is crucial when analysing chemical reactions and it is the first step of our vulcanization problem. The molar mass is the mass of one mole of a substance, measured in grams per mole (g/mol). It is calculated by summing the atomic masses of all the atoms in a molecule. In the case of polychloroprene which is composed of carbon (C), hydrogen (H), and chlorine (Cl) atoms, we calculate its molar mass by adding together the atomic masses of these elements, multiplied by the number of times each element appears in one molecule.

For sulfur (S8), the process is similar - since it exists naturally as an octatomic molecule, its molar mass is eight times the atomic mass of a single sulfur atom. To convert the mass given in kilograms to moles, we divide by the molar mass. This fundamental conversion is key to all further stoichiometric calculations in chemistry, since it allows chemists to count molecules by weighing them, providing a link between the macroscopic quantities that we can measure and the microscopic quantities that dictate chemical behavior.

Chemical crosslinking is a process where polymer chains are linked together to form a three-dimensional network, enhancing the material's properties, such as elasticity, thermal stability, and mechanical strength. Vulcanization, the process being explored in our problem, is a type of chemical crosslinking where sulfurs forms bonds with the polymer chains of polychloroprene.

During vulcanization, the sulfur atoms act as bridges between the long-chain molecules. The ratio of sulfur atoms to possible crosslink sites determines the degree of crosslinking—with more crosslinking usually resulting in a tougher material. Analyzing the number of sulfur atoms participating in each crosslink and the total number of moles of sulfur provides insight into the extent of crosslinking within the polymer. The effectiveness of vulcanization is a significant topic in materials science, particularly in the manufacturing of products like tires and industrial belts where such properties are critical.

Stoichiometry is the calculation of reactants and products in chemical reactions. It is based on the conservation of mass where the amount of each element must be the same in both the starting materials and the final products. In our scenario, stoichiometry applies in determining the fraction of polychloroprene's crosslink sites that react with sulfur.

Using stoichiometry, we deduced that not all crosslink sites on the polymer were occupied by sulfur—signifying a partial vulcanization. This information is pertinent when evaluating the mechanical properties of the vulcanized material; a lower degree of crosslinking might result in a less durable material. Understanding stoichiometry not only helps us grasp theoretical concepts but also has practical implications in producing materials with desired characteristics by controlling reaction conditions and ratios of reactants.