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

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

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Answer: aExplanation: 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.

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

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Answer: b

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.

What does the ratio of number to weight average degree of polymerization for a bifunctional system represent?

a) degree of polymerization

b) breadth of molecular size

c) extent of reaction

d) none of the mentioned

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Answer: bExplanation: The ratio, commonly, is used to represent the molecular size distribution, which is given by (1+p).

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

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Answer: a

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.

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

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Answer: d

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.

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

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Answer: a

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).

What is the maximum attainable degree of polymerization for 5% stoichiometric imbalance?

a) 52

b) 41

c) 63

d) 56

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Answer: bExplanation: 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.

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

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Answer: c

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.

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

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Answer: a

Explanation: The probability is given by,

Pn= pn-1(1-p)

= (0.98)3(0.02)

= 0.0189.

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

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Answer: cExplanation: 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.

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

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Answer: cExplanation: 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.

What is the ratio of number to weight distribution function for a bifunctional system?

a) N0/n

b) N0

c) N

d) n/ N0

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Answer: a

Explanation: For a bifunctional system,

Nn= N0(1-p)2pn-1

Wn= n(1-p)2pn-1

So, the ratio comes out to be N0/n.