Chapter 16, Problem 16.6P

Interpretation Introduction

(a)

Interpretation:

The type of polymerization in the given reaction is to be identified.

Concept Introduction:

Polymers are the large molecules which are made up of many small repeating units bonded together in linear, branched or cross-linked manner.

They are of two types: natural and synthetic. Natural polymers are those which occur naturally, and synthetic polymers are those which are synthesized or man-made.

A process by which the monomer units chemically react together to form chains or three-dimensional structures is known as polymerization.

In condensation polymerization, when monomers react to produce the polymer a by-product is formed which is a small molecule like ${\text{H}}_2\text{O or HCl}$.

In addition-polymerization no by-product is formed during the chain formation and the reaction propagates due to the presence of the catalyst.

Answer to Problem 16.6P

The given reaction is a type of condensation polymerization.

Explanation of Solution

Given information:

The reaction to produce Kevlar $\left({\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2\right)$ from paraphenylene diamine and terephthaloyl chloride is:

  

The reaction for the formation of Kevlar is:

  

In this reaction, $2$ molecules of $\text{HCl}$ is formed for every molecule of Kevlar. Therefore, the given reaction is a type of condensation polymerization.

Interpretation Introduction

(b)

Interpretation:

The required weight of terephthaloyl chloride is to be calculated which is completely combined with $1\text{ kg}$ of paraphenylene diamine.

Concept Introduction:

Stoichiometry is the calculation of the reactants and the products involved in aa chemical reaction. It is based on the law of mass conservation. According to the stoichiometry, total mass of the reactants equals the total mass of the products.

Number of moles $\left(n\right)$ of a substance is calculates as:

  $n=\frac{m}{\text{MW}}$  ...... (1)

Here, $m$ is the mass of the substance in ' $\text{g}$ ' and $\text{MW}$ is the molar mass of the substance in $\text{g/mol}$.

Answer to Problem 16.6P

The amount of terephthaloyl chloride required to completely react with $1\text{ kg}$ of paraphenylene diamine is $1.88\text{ kg}$.

Explanation of Solution

Given information:

The reaction for the production of Kevlar $\left({\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2\right)$ from paraphenylene diamine and terephthaloyl chloride is:

  

The reaction is $100\%$ efficient and $1\text{ kg}$ of paraphenylene diamine is reacted.

The basis of the calculations is taken as $1\text{ kg}$ of paraphenylene diamine.

Molecular formula of paraphenylene diamine is ${\text{C}}_6{\text{H}}_8{\text{N}}_2$. Its molecular weight will be

  $\begin{array}{c}{\left(\text{MW}\right)}_{{\text{C}}_6{\text{H}}_8{\text{N}}_2}=\left(6\times 12\right)+\left(8\times 1\right)+\left(2\times 14\right)\\ =108\text{ g/mol}\end{array}$

Now, using equation (1), calculate the moles present in $\text{1 kg}$ paraphenylene diamine as:

  $\begin{array}{c}{n}_{{\text{C}}_6{\text{H}}_8{\text{N}}_2}=\frac{m_{{\text{C}}_6{\text{H}}_8{\text{N}}_2}}{{\left(\text{MW}\right)}_{{\text{C}}_6{\text{H}}_8{\text{N}}_2}}\\ =\frac{1\text{ kg}\times \frac{{10}^3\text{ g}}{\text{kg}}}{108\text{ g/mol}}\\ =9.26\text{ mol}\end{array}$

Molecular formula of terephthaloyl chloride is ${\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2$. Its molecular weight will be

  $\begin{array}{c}{\left(\text{MW}\right)}_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}=\left(8\times 12\right)+\left(4\times 1\right)+\left(2\times 35.5\right)+\left(2\times 16\right)\\ =203\text{ g/mol}\end{array}$

As it is given that the reaction has $100\%$ efficiency, this means that all the paraphenylene diamine reacts with terephthaloyl chloride to produce Kevlar.

According to the stoichiometry of the given reaction, $9.26\text{ mol}$ of paraphenylene diamine will completely react with $9.26\text{ mol}$ of terephthaloyl chloride.

Use equation (1) to calculate the mass of terephthaloyl chloride as:

  $\begin{array}{c}{n}_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}=\frac{m_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}}{{\left(\text{MW}\right)}_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}}\\ m_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}=n_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}\times {\left(\text{MW}\right)}_{{\text{C}}_8{\text{H}}_4{\text{Cl}}_2{\text{O}}_2}\\ =\left(9.26\text{ mol}\right)\times \left(203\text{ g/mol}\right)\\ =1879.78\text{ g}\\ =1.88\text{ kg}\end{array}$

Therefore, $1.88\text{ kg}$ of terephthaloyl chloride is required to completely react with $1\text{ kg}$ of paraphenylene diamine.

Interpretation Introduction

(c)

Interpretation:

The amount of Kevlar produced is to be calculated.

Concept Introduction:

The reaction for the production of Kevlar $\left({\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2\right)$ from paraphenylene diamine and terephthaloyl chloride is:

  

The reaction is $100\%$ efficient and $1\text{ kg}$ of paraphenylene diamine is reacted.

Answer to Problem 16.6P

The amount of Kevlar produced is $2.20\text{ kg}$.

Explanation of Solution

Given information:

The reaction for the production of Kevlar $\left({\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2\right)$ from paraphenylene diamine and terephthaloyl chloride is:

  

The reaction is $100\%$ efficient and $1\text{ kg}$ of paraphenylene diamine is reacted.

Molecular formula of Kevlar is ${\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2$. Its molecular weight will be

  $\begin{array}{c}{\left(\text{MW}\right)}_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}=\left(14\times 12\right)+\left(10\times 1\right)+\left(2\times 14\right)+\left(2\times 16\right)\\ =238\text{ g/mol}\end{array}$

As it is given that the reaction has $100\%$ efficiency, this means that all the paraphenylene diamine reacts with terephthaloyl chloride to produce Kevlar.

According to the stoichiometry of the given reaction, $9.26\text{ mol}$ of paraphenylene diamine will completely react with $9.26\text{ mol}$ of terephthaloyl chloride to produce $9.26\text{ mol}$ of Kevlar.

Use equation (1) to calculate the mass of Kevlar as:

  $\begin{array}{c}{n}_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}=\frac{m_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}}{{\left(\text{MW}\right)}_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}}\\ m_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}=n_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}\times {\left(\text{MW}\right)}_{{\text{C}}_{14}{\text{H}}_{10}{\text{N}}_2{\text{O}}_2}\\ =\left(9.26\text{ mol}\right)\times \left(238\text{ g/mol}\right)\\ =2203.88\text{ g}\\ =2.20\text{ kg}\end{array}$

Therefore, $2.20\text{ kg}$ of Kevlar is produced when $1\text{ kg}$ of paraphenylene diamine reacts.