Ten kilograms of polybutadiene is vulcanized with \(4.8 \mathrm{~kg}\) sulfur. What fraction of the possible crosslink sites is bonded to sulfur crosslinks, assuming that, on the average, \(4.5\) sulfur atoms participate in each crosslink?

Understanding the calculation of crosslink sites is critical for assessing the strength and flexibility of vulcanized polymers such as polybutadiene. In the vulcanization process, crosslinks are formed between polymer chains through the addition of sulfur, which provides the necessary rigidity and strength to the material.

Let's break down the concept of 'crosslink sites'. A crosslink site is a point on a polymer chain where bonding with another chain or sulfur atom can occur. For polybutadiene, every molecule has two sites where these bonds can be made because each molecule contains two double bonds capable of reaction.

In a given sample, the number of available crosslink sites is directly proportional to the number of moles of the polymer; specifically, it's double the number of moles because of the two reactive sites per molecule. The step-by-step solution presents a clear approach to calculate how many such sites are actually used in forming crosslinks with sulfur atoms for a set mass of polybutadiene.

Example Calculation:

• Determine the number of moles of polybutadiene.
• Identify the number of possible crosslink sites per molecule (which is two for polybutadiene).
• Multiply the number of moles by the number of sites to get the total possible crosslinks.

Determining what fraction of these sites are involved in sulfur crosslinking gives insights into the extent of vulcanization, which in turn affects the material properties of the final product.

Molar mass is a fundamental concept in chemistry, including polymer chemistry. It represents the mass of one mole of a substance - be it a single molecule like water or a complex polymer chain like polybutadiene. The molar mass is critical for comparing different substances and for converting between mass and moles, which is often necessary for stoichiometric calculations.

To determine the molar mass of polybutadiene, one would sum the molar masses of all the atoms in its repeating unit, which includes carbon and hydrogen in this case. Since a polybutadiene molecule has four carbon atoms and six hydrogen atoms, the calculation involves multiplying the number of each type of atom by its atomic mass and then summing the results.

Steps for Calculating Molar Mass of Polybutadiene:

• Identify the chemical formula for one repeat unit (C4H6 for polybutadiene).
• Look up the atomic masses of carbon (12.01 g/mol) and hydrogen (1.01 g/mol).
• Multiply the atomic mass of each atom by the number of times it appears in the formula and add these values together.

Knowing the molar mass allows for the conversion of masses to moles, which is essential for understanding the amounts of reactants and products in chemical reactions, such as those involved in the vulcanization of polybutadiene.

Stoichiometry in polymer chemistry deals with the quantitative relationships between reactants and products in polymerization reactions, including vulcanization. It involves calculations based on balanced equations to predict the amounts of substances consumed and produced. For vulcanized polybutadiene, understanding stoichiometry is necessary to determine how much sulfur is needed to achieve a certain degree of crosslinking.

The stoichiometric principles allow for the precise calculation of the number of sulfur atoms that participate in forming crosslinks with the available sites on the polybutadiene chains. This is vital for predicting the resulting material's properties and for ensuring that there isn't an excessive or insufficient amount of sulfur, both of which can lead to suboptimal product qualities.

In the exercise provided, stoichiometry is used to:

• Calculate the number of moles of polybutadiene and sulfur required.
• Assess the average number of sulfur atoms involved in each crosslink.
• Find out the total number of crosslinks formed.
• Determine the fraction of crosslink sites actually used in the vulcanization process.

By mastering stoichiometry, one can optimize the vulcanization process for producing polybutadiene with the desired strength and elasticity, which is crucial in various industrial applications such as tire manufacturing.