Question

In a recent year, 2.84 billion kilograms of polystyrene were produced in the United States. Polystyrene is the addition polymer formed from the styrene monomer, ${\mathbf{C}}_{\mathbf{6}}{\mathbf{H}}_{\mathbf{5}}\mathbf{CH}\mathbf{=}{\mathbf{CH}}_{\mathbf{2}}$. How many styrene monomer units were incorporated in that 2.84 billion kilograms of polymer?

Short answer

Thus, the number of styrene monomers units incorporated in 2.84 billion kilograms of polymer are $2.73\times {10}^{10}$.

Step-by-step solution

Polystyrene

Polystyrene is a synthetic polymer that can be synthesized by the addition polymerization of styrene monomer. It is a liquid hydrocarbon and is generally manufactured from petroleum.

Explanation

The chemical equation for the formation of polystyrene from styrene is as shown:

Formation of polystyrene

Since nothing is lost in addition to polymerization, the weight of one unit of polystyrene is the same as that of styrene.

The weight of the polystyrene is given as 2.84 billion kilograms, i.e.,.

The mass of one styrene unit is 104.15 g.

The number of styrene monomer units is calculated by taking the ratio of the weight of polystyrene by the mass of one styrene unit as follows:

$$\begin{gathered} Numberofstyrenemonomer=\frac{Massofpolystyrene}{Massof onestyrene} \\ =\frac{2.84\times {10}^{9}kg}{104.15g}\times \frac{1000g}{1kg} \\ =2.73\times {10}^{10}monomer \end{gathered}$$

Therefore, the number of styrene monomers units incorporated in 2.84 billion kilograms of polymer are $2.73\times {10}^{10}$.