Q12.126CP - Chemistry: Molecular Nature Of Matter And Change

Question

Polytetrafluoroethylene (Teflon) has a repeat unit with the formula ${\mathbf{F}}_2\mathbf{C}\mathbf{—}{\mathbf{CF}}_2$ . A sample of the polymer consists of fractions with the following distribution of chains:

(a) Determine the molar mass of each fraction. 

(b) Determine the number-average molar mass of the sample. 

(c) Another type of average molar mass of a polymer sample is called the weight-average molar mass: 

 ${\mathbf{\chi }}_w\mathbf{=}\frac{\mathbf{\pi }\mathbf{ }\mathbf{(}\mathbf{\chi }\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{fraction}\mathbf{ }\mathbf{\times }\mathbf{ }\mathbf{mass}\mathbf{ }\mathbf{of}\mathbf{ }\mathbf{fraction}\mathbf{)}}{\mathrm{total} \mathrm{mass} \mathrm{of} \mathrm{all} \mathrm{fractions}}$

Calculate the weight-average molar mass of the above sample.

Step-by-Step Solution

Answer

a. The molar mass of each fraction:

Fraction 1: 27.3mole

Fraction 2: 132mole

Fraction 3: 368mole

Fraction 4: 338.1mole

Fraction 5: 157.5mole

Fraction 6: 57.5mole

 

b. The number-average molar mass of the sample is 189.65.

 

c. The weight-average molar mass of the sample is 0.66.

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:

${\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}$

Here,

${\mathbf{{\rm M}}}_{\mathrm{polymer}}$  is the polymer mass.

${\mathbf{M}}_{\mathrm{repeat}}$   is the repeating unit’s mass.

 n is the degree of polymerization.

 

Step 2: Subpart (a) The molar mass of each fraction.

Molar Mass of the molecule  ${\text{F}}_{\text{2}}{\text{C—CF}}_{\text{2}}$,

 

 $\begin{array}{c}\mathrm{Molar} \mathrm{Mass} \mathrm{of} \mathrm{molecule}=2\times \mathrm{C}+4\times \mathrm{F}\\ \mathrm{Molar} \mathrm{Mass} \mathrm{of} \mathrm{molecule}=2\times 12+4\times 19\\ \mathrm{Molar} \mathrm{Mass} \mathrm{of} \mathrm{molecule}=100\mathrm{g}/\mathrm{mole}\end{array}$

 

The repeating units of the molecule ${\text{F}}_{\text{2}}{\text{C—CF}}_{\text{2}}$  :

Fraction 1:

 $\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{\times }\mathbf{273}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{27}\mathbf{.}\mathbf{3}\mathbf{mole}\end{array}$

 

 

Fraction 2:

 $\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{40}\mathbf{\times }\mathbf{330}\\ \mathrm{Mpolymer}=132\mathrm{mole}\end{array}$

 

 

Fraction 3:

$\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{00}\mathbf{\times }\mathbf{368}\\ \mathrm{Mpolymer}=368\mathrm{mole}\end{array}$

Fraction 4:

  $\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{70}\mathbf{\times }\mathbf{483}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{338}\mathbf{.}\mathbf{1}\mathbf{mole}\end{array}$

 

 

Fraction 5:

 $\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{30}\mathbf{\times }\mathbf{525}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{157}\mathbf{.}\mathbf{5}\mathbf{mole}\end{array}$

Fraction 6:

$\begin{array}{c}{\mathbf{{\rm M}}}_{\mathrm{polymer}}\mathbf{=}{\mathbf{M}}_{\mathrm{repeat}}\mathbf{\times }\mathbf{n}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{10}\mathbf{\times }\mathbf{575}\\ \mathbf{Mpolymer}\mathbf{=}\mathbf{57}\mathbf{.}\mathbf{5}\mathbf{mole}\end{array}$

 

Step 3: Subpart (b) The number-average molar mass of the sample.

$\begin{array}{c}\mathbf{Average}\mathbf{ }\mathbf{Moalr}\mathbf{ }\mathbf{Mass}\mathbf{=}\frac{\sum \mathbf{Molar}\mathbf{ }\mathbf{Mass}}{N}\\ \mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\frac{\mathbf{27}\mathbf{.}\mathbf{3}\mathbf{+}\mathbf{132}\mathbf{+}\mathbf{368}\mathbf{+}\mathbf{338}\mathbf{.}\mathbf{1}\mathbf{+}\mathbf{157}\mathbf{.}\mathbf{5}\mathbf{+}\mathbf{57}\mathbf{.}\mathbf{5}\mathbf{+}\mathbf{57}\mathbf{.}\mathbf{5}}{6}\\ \mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\frac{\mathbf{1137}\mathbf{.}\mathbf{9}\mathbf{mole}}{6}\\ \mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\mathbf{189}\mathbf{.}\mathbf{65}\end{array}$

Step 4: Subpart (c) The weight-average molar mass of the given sample.

$\begin{array}{c}\mathbf{Weight}\mathbf{ }\mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\frac{\sum \mathbf{Molar}\mathbf{ }\mathbf{Mass}}{N}\\ \mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\left(\frac{\begin{array}{l}27.3\times 0.10+132\times 0.40\\ +368\times 1.00+338.1\times 0.70\\ +157.5\times 0.30+57.5\times 0.10\end{array}}{1080.4}\right)\end{array}$

$\begin{array}{c}\mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\frac{\mathbf{2}\mathbf{.}\mathbf{73}\mathbf{+}\mathbf{52}\mathbf{.}\mathbf{8}\mathbf{+}\mathbf{368}\mathbf{+}\mathbf{236}\mathbf{.}\mathbf{67}\mathbf{+}\mathbf{47}\mathbf{.}\mathbf{25}\mathbf{+}\mathbf{5}\mathbf{.}\mathbf{75}}{\mathbf{1080}\mathbf{.}\mathbf{4}}\\ \mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\frac{\mathbf{713}\mathbf{.}\mathbf{2}}{\mathbf{1080}\mathbf{.}\mathbf{4}}\\ \mathbf{Average}\mathbf{ }\mathbf{Molar}\mathbf{ }\mathbf{Mass}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{66}\end{array}$