Essentials Of Materials Science And Engineering
Essentials Of Materials Science And Engineering
4th Edition
ISBN: 9781337670845
Author: ASKELAND
Publisher: Cengage
Question
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Chapter 16, Problem 16.14P
Interpretation Introduction

(a)

Interpretation:

The number of polyethylene chains in the given rope is to be calculated.

Concept Introduction:

The molecular weight of a polymer is not fixed. It has a certain range under which its molecular weight falls. For a linear polymer, degree of polymerization represents the average length of the polymer. Degree of polymerization is defined as:

  Degree of polymerization=average molecular weight of polymermolecular weight of repeating unitn= ( MW ) av. ( MW ) repeating unit   ....... (1)

The formula to calculate number of chains in the given mass of polymer is:

  Number of chains=m×NA( MW)av.   ....... (2)

Here, m is the mass of the polymer, NA is the Avogadro's number, and (MW)av. is the average molecular mass of the polymer.

Expert Solution
Check Mark

Answer to Problem 16.14P

The number of polyethylene chains in the given rope is 3.487×1021 chains.

Explanation of Solution

Given information:

A rope made up of polyethylene weighs 0.25 lb per foot. One chain of this polymer contains 7000 repeat units.

The length of the rope is 10 ft.

The repeating unit of polyethylene is [C2H4]. Its molecular weight is:

  (MW)[ C 2 H 4]=(2×12)+(4×1)=28 g/mol

Now, use equation (1) and calculate the average molecular weight of polytetrafluoroethylene as:

  n= ( MW ) av. ( MW ) [ C 2 H 4 ]7000= ( MW ) av.28 g/mol(MW)av.=196000 g/mol

Calculate the mass of 10 ft polyethylene rope as:

  m=(0.25 lb ft× 454 g lb)×(10 ft)=1135 g

Calculate the number of chains in the given rope of polyethylene using equation (2) as:

  Number of chains=m×NA ( MW ) av.=( 1135 g)( 6.023× 10 23  chains/mol)196000 g/mol=3.487×1021 chains

Interpretation Introduction

(b)

Interpretation:

The total length of chains in the given rope is to be calculated.

Concept Introduction:

The formula to calculate the length (L) of 1 chain of a polymer is:

  L=n×Lrepeat unit+(n1)×LC-C   ....... (3)

Here, n is the number of repeating units in the polymer chain, Lrepeat unit is the length of one repeating unit, and LC-C is the length between two carbon atoms in the chain.

Expert Solution
Check Mark

Answer to Problem 16.14P

The total length of chains in the given rope is 9.637×1012 km.

Explanation of Solution

Given information:

A rope made up of polyethylene weighs 0.25 lb per foot. One chain of this polymer contains 7000 repeat units.

The length of the rope is 10 ft .The length between each carbon atom is approximately 0.15 nm and length of each repeat unit is 0.24495 nm.

From the given data:

  n=7000Lrepeat unit=0.24495 nmLC-C=0.15 nm

Use equation (3) to calculate the length of 1 polymer chain as:

  L=n×Lrepeat unit+(n1)×LC-C

Substituting the values:

  =7000×(0.24495 nm)+(70001)×(0.15 nm)=2764.5 nm

Now, calculate the total length of the chains in the given polymer rope as:

  LTotal=(3.487× 10 21 chains)×(2764.5 nm)=9.637×1024 nm=9.637×1012 km

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