Q12.113P - Chemistry: Molecular Nature Of Matter And Change

Question

The repeat unit in a polystyrene coffee cup has the formula ${\mathbf{C}}_6{\mathbf{H}}_5{\mathbf{CHCH}}_2$. If the molar mass of the polymer is $\mathbf{3}\mathbf{.}\mathbf{5}\mathbf{\times }{\mathbf{10}}^5\mathbf{g}\mathbf{/}\mathbf{mole}$  g/mole, what is the degree of polymerization?

Step-by-Step Solution

Answer

The molar mass of the molecule is 104 g/mole and the number of the repeat units is $\mathbf{3}\mathbf{.}\mathbf{37}\mathbf{\times }{\mathbf{10}}^3\mathbf{g}\mathbf{/}\mathbf{mole}$ .

Step 1: Definition

A polymer may be defined as a complex molecule that is formed by the addition or condensation of the small units called monomers. Polymer mass is the mass of the complex molecule which contained many types of similar or different monomers. The mass of the polymer is very high.

Polymer mass can be calculated by the formula:

$\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ {\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}\mathrm{Polymer}\mathrm{mass}, \\ {\mathbf{M}}_{\mathrm{repeat}} =\mathrm{Repeating}\mathrm{the}\mathrm{unit}’\mathrm{s}\mathrm{massn} \\ \mathrm{n}=\mathrm{degree}\mathrm{of}\mathrm{polymerization}.\end{array}$

Step 2: Explanation

Molar Mass of the molecule : ${\mathbf{C}}_6{\mathbf{H}}_5{\mathbf{CHCH}}_2$

 $\begin{array}{l}\mathrm{Molar} \mathrm{Mass} \mathrm{of} \mathrm{molecule}=8\times \mathrm{C}+8\times \mathrm{H}\\ \mathrm{Molar} \mathrm{Mass} \mathrm{of} \mathrm{molecule}=8\times 12+8\times 1\\ \mathrm{Molar} \mathrm{Mass} \mathrm{of} \mathrm{molecule}=104\mathrm{g}/\mathrm{mole}\end{array}$

 

 

The repeating units of the molecule  : ${\text{C}}_{\text{6}}{\text{H}}_{\text{5}}{\text{CHCH}}_{\text{2}}$

 $\begin{array}{l}{\mathrm{{\rm M}}}_{\mathrm{polymer}}={\mathrm{M}}_{\mathrm{repeat}}\times \mathrm{n}\\ 3.5\times {10}^5\mathrm{g}/\mathrm{mole}=104\mathrm{g}/\mathrm{mole}\times \mathrm{n}\\ \mathrm{n}=\frac{3.5\times {10}^5\mathrm{g}/\mathrm{mole}}{104\mathrm{g}/\mathrm{mole}}\\ \mathrm{n}=3.37\times {10}^3\mathrm{repeatunits}\end{array}$