Essentials Of Materials Science And Engineering, Si Edition
Essentials Of Materials Science And Engineering, Si Edition
4th Edition
ISBN: 9781337629157
Author: Donald R. Askeland, Wendelin J. Wright
Publisher: Cengage Learning
Question
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Chapter 16, Problem 16.15P
Interpretation Introduction

(a)

Interpretation:

The weight average molecular weight and degree of polymerization for the given polymer are 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)

Weight average molecular weight (M¯w) of a polymer is calculated by the formula:

  M¯w=fiMi   ....... (2)

Here, fi is the weight fraction polymer chains in the size range i and Mi is the mean molecular weight of that size range.

Expert Solution
Check Mark

Answer to Problem 16.15P

The weight average molecular weight for the given polymer is 11203.5 g/mol.

The degree of polymerization for the given polymer is 211.

Explanation of Solution

Given information:

A sample of polyacrylonitrile was analyzed and the results are:

  Essentials Of Materials Science And Engineering, Si Edition, Chapter 16, Problem 16.15P , additional homework tip  1

First calculate the total number of chains as:

  Total Chains=iNi=10000+18000+17000+15000+9000+4000=73000

Now, calculate the weight for each of the chain category as:

  Wi=Ni×MiW1=N1×M1=10000×3000=30000000W2=N2×M2=18000×6000=108000000W3=N3×M3=17000×9000=153000000W4=N4×M4=15000×12000=180000000W5=N5×M5=9000×15000=135000000W6=N6×M6=4000×18000=72000000

Calculate the total weight of all the chains as:

  W=iWi=30000000+108000000+153000000+180000000+135000000+72000000=678000000

Calculate the mass fraction for each of the size range as:

  fi=Wi/Wf1=W1/W=30000000/678000000=0.04425f2=W2/W=108000000/678000000=0.15929f3=W3/W=153000000/678000000=0.22566f4=W4/W=180000000/678000000=0.26549f5=W5/W=135000000/678000000=0.19912f6=W6/W=72000000/678000000=0.10619

Now, use formula (2) to calculate the weight average molecular weight of the polymer sample as:

  M¯w=fiMi=f1M1+f2M2+f3M3+f4M4+f5M5+f6M6=( ( 0.04425×3000 )+( 0.15929×6000 )+( 0.22566×9000 ) +( 0.26549×12000 )+( 0.19912×15000 )+( 0.10619×18000 ))=11203.5 g/mol

The repeating unit of the polymer polyacrylonitrile is [C3H3N]. Its molecular weight is:

  (MW)[ C 3 H 3N]=(3×12)+(3×1)+(1×14)=53 g/mol

Now, use equation (1) and calculate the degree of polymerization as:

  nw= M ¯w ( MW ) [ C 3 H 3 N]=11203.5 g/mol53 g/mol211

Interpretation Introduction

(b)

Interpretation:

The number average molecular weight and degree of polymerization for the given polymer are 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)

Number average molecular weight (M¯n) of a polymer is calculated by the formula:

  M¯n=xiMi   ....... (3)

Here, xi is the fraction of total polymer chains in the size range i and Mi is the mean molecular weight of that size range.

Expert Solution
Check Mark

Answer to Problem 16.15P

The number average molecular weight for the given polymer is 9287.67 g/mol.

The degree of polymerization for the given polymer is 175.

Explanation of Solution

Given information:

A sample of polyacrylonitrile was analyzed and the results are:

  Essentials Of Materials Science And Engineering, Si Edition, Chapter 16, Problem 16.15P , additional homework tip  2

First calculate the total number of chains as:

  Total Chains(N)=iNi=10000+18000+17000+15000+9000+4000=73000

Calculate the fraction of chain in each of the size range as:

  xi=Ni/Nx1=N1/N=10000/73000=0.13699x2=N2/N=18000/73000=0.24658x3=N3/N=17000/73000=0.23288x4=N4/N=15000/73000=0.20548x5=N5/N=9000/73000=0.12329x6=N6/N=4000/73000=0.05479

Now, use formula (3) to calculate the number average molecular weight of the polymer sample as:

  M¯n=xiMi=x1M1+x2M2+x3M3+x4M4+x5M5+x6M6=( ( 0.13699×3000 )+( 0.24658×6000 )+( 0.23288×9000 ) +( 0.20548×12000 )+( 0.12329×15000 )+( 0.05479×18000 ))=9287.67 g/mol

The repeating unit of the polymer polyacrylonitrile is [C3H3N]. Its molecular weight is:

  (MW)[ C 3 H 3N]=(3×12)+(3×1)+(1×14)=53 g/mol

Now, use equation (1) and calculate the degree of polymerization as:

  nn= M ¯n ( MW ) [ C 3 H 3 N]=9287.67 g/mol53 g/mol175

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