Engineering Questions with Answers - Multiple Choice Questions

# Polymer Engineering MCQ’s – Distribution of Molecular Weight in Linear Polycondensation

1 - Question

Which of the following expressions correctly represents the number distribution function for a linear polycondensation reaction?(Here N0 and p are total number of initial monomer molecules and extent of reaction initially)
a) Nn=N0(1-p)2pn-1
b) Nn=N0(1-p)pn-1
c) Nn= N0pn-1
d) Nn0n(1-p)2pn
Explanation: The probability Pn of formation of polymer molecule with n degree of polymerization is given by, Pn=pn-1(1-p) Where, Pn= Nn/N, and also N= N0(1-p), so the value on Nn comes out to be, Nn= N0(1-p)2pn-1.

2 - Question

Find the value of number average degree of polymerization for a mixture of polymers at 90% completion of reaction?
a) 0.1
b) 10
c) 100
d) 1.1

Explanation: The expression for Xn is given by,
Xn= 1/(1-p)
= 1/0.1
= 10
Thus, the value of number average degree of polymerization is 10.

3 - Question

What does the ratio of number to weight average degree of polymerization for a bifunctional system represent?
a) degree of polymerization
c) extent of reaction
d) none of the mentioned
Explanation: The ratio, commonly, is used to represent the molecular size distribution, which is given by (1+p).

4 - Question

What are the values of number and weight average degree of polymerization for a bifunctional system at 95% completion of reaction?
a) 20, 39
b) 10,39
c) 2,3.9
d) 25,35

Explanation: The expressions for number and weight average degree of polymerization are given by,
Xn= 1/(1-p)
Xw= (1+p)/(1-p)
By putting the value of p, value of Xn and Xw can be calculated.

5 - Question

80 moles of monomers react to prepare Nylon 12. After completion of 8 hrs, 4 moles of monomers are still left. What is the weight average molecular weight of polymer system?
a) 1263
b) 197
c) 3940
d) 7683

Explanation: The extent of reaction is-
p= 80-4/80 = 0.95
Thus, Xw= (1+p)/(1-p) = 39
Mw= Xw Mo= 197*39= 7683.

6 - Question

What are the number average molecular weights of Nylon 66 and Nylon 11, when the conversion is 90%?
a) 2260, 1830
b) 4294, 3477
c) 2586, 1830
d) 3477, 4200

Explanation: The value of Xn is given by,
Xn= 1/(1-p) = 1/(1-0.9)
= 10
Thus, for Nylon 66, Mn= 226*10=2260
For Nylon 11, Mn= 183*10= 1830
(226 and 183 are the molecular weights of the repeating units of polymer Nylon 66 and Nylon 11, respectively).

7 - Question

What is the maximum attainable degree of polymerization for 5% stoichiometric imbalance?
a) 52
b) 41
c) 63
d) 56
Explanation: For 5% impurity, the maximum attainable degree of polymerization will be, Xn= [1+(100/105)]/[1-(100/105)] Thus, Xn will be equal to 41.

8 - Question

Hydroxy caproic acids are used to polyester molecules. Due to improper purification of reactants, 2% of acid impurity was found. What is the number average degree of polymerization for 95% completion of reaction?
a) 2526
b) 2280
c) 1912
d) 1270

Explanation:For 2% acid impurity, r= 100/102= 0.98
Then, Xn is given by,
Xn= (1+r)/(1+r-2rp)
= 16.78
Thus, Mn= 114*16.78= 1912.

9 - Question

What is the probability of having tetramers in the preparation of Nylon 12, when 98% of functional groups have reacted?
a) 0.0189
b) 0.05
c) 0.256
d) 1

Explanation: The probability is given by,
Pn= pn-1(1-p)
= (0.98)3(0.02)
= 0.0189.

10 - Question

Which curve in the given figure possibly represents the highest value of conversion for bifunctional polycondensation? a) 1
b) 2
c) 3
d) Cannot be determined

Explanation: Curve 3 possibly represents the highest conversion because the steepness of number fraction distribution curve falls with increasing value of p and the 3rd curve here is the most flattened one.

11 - Question

Consider the following graph plotted between weight fraction of molecules and degree of polymerization. What may be the possible value of p for the curve with highest peak? a) 0.95
b) 0.99
c) 0.89
d) 0.92

Explanation: For a given value of p, Wn passes through a maximum and the maximum shifts to a higher value of n as the value of p increases. Therefore, the broadest curve represents highest p and the curve with highest peak represents the curve with lowest value of p.

12 - Question

What is the ratio of number to weight distribution function for a bifunctional system?
a) N0/n
b) N0
c) N
d) n/ N0