# Polymer Engineering Questions and Answers – Kinetics of Chain Polymerization Initiated by a Free Radical Initiator

This set of Polymer Engineering Multiple Choice Questions & Answers focuses on “Kinetics of Chain Polymerization Initiated by a Free Radical Initiator “.

1. How many initiator fragments are present in the dead polymer formed by combination mode of chain termination?
a) 2
b) 1
c) 3
d) 0

Explanation: The combination reaction is given by-
R~~~ CH2CHY + YHC−CH2 ~~~~~R → R ~~~CH2−CHY─CHY─CH2 ~~~ R.

2. What is the initiator efficiency in chain initiation step of free radical polymerization?
a) fraction of unreacted monomers
b) extent of reaction
c) fraction of radicals actually contributing
d) number of initiator molecules

Explanation: the initiator efficiency is the fraction of free radicals actually contributing in chain initiation and is less than unity.

3. What is the expression for the rate of chain initiation of free radical chain growth polymerization?
a) fkd[I]
b) 2fkd[I]
c) kd[I]/2
d) kd[I]

Explanation: The expression is given by-
Ri= 2fkd[I] where f is the initiator efficiency, and the factor 2 is introduced because for decomposition of one initiator molecule, two initiator radicals are formed.

4. The data for bulk chain polymerization having potassium persulfate as initiator is given-
[I] = 5 mol/m3
[M] = 5.3*103 mol/m3
kp2/kt = 0.85*10-6 m3/ mol-s
What is the initial rate of polymerization, if potassium persulfate decomposes at a rate of 2.2*10-6 m3 s/ mol?
a) 0.012
b) 0.0162
c) 0.05
d) 0.1

Explanation: The initial rate of polymerization is here, expressed as, Rp=[(kp2/kt)fkd]0.5[I]0.5[M].
Assuming f=1, and substituting all the values, we get Rp as 0.0162 m3/ mol-s.

5. What is the rate chain initiation reaction for initiator efficiency of 0.8, when concentration and decomposition rate of benzoyl peroxide are 4 mol/m3 and 3.24*10-6 m3/ mol-s-1, respectively?
a) 2.07*10-5
b) 1.57*10-5
c) 3.27*10-5
d) 1.03*10-5

Explanation: The rate expression for chain initiation is given by-
Ri= 2fkd[I] By substituting the values, rate can be calculated.

6. What is the expression for rate of termination reaction of free radical polymerization?
a) kt[M]2
b) 2kt[M]2
c) 2fkt[M
d) fkt[M

Explanation: The rate expression for termination reaction is given by- Rt = 2kt[M]2
The factor 2 is used for the disappearance of chain radicals at each incidence of termination reaction.

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7. Consider following data for bulk polymerization, with benzoyl peroxide as initiator.
[I] = 6 mol/m3
[M] = 6.56*103 mol/m3
kp2/kt = 1.5*10-6 m3/ mol-s
What is the initiator efficiency if initial rate of polymerization is 0.0256 m3/ mol-s benzoyl peroxide decomposes at a rate of 3.2* 10-6 m3/ mol-s-1?
a) 0.7
b) 0.53
c) 0.26
d) 0.82

Explanation: The initial rate of polymerization is given by-
Rp =[( kp2/kt)fkd]0.5[I]0.5[M] Squaring both the sides and then substituting the values given, f is obtained as 0.53.

8. How does polymerization rate at a given monomer concentration vary, if rate of chain initiation is tripled?
a) doubled
b) tripled
c) increment by factor of 30.5
d) remains constant

Explanation: The rate equation of overall polymerization clears that the polymerization rate at a given monomer concentration is dependent on the square root of rate of chain initiation.

9. Which order kinetics does the rate of polymer formation, in free radical polymerization, follow corresponding to monomer concentration?
a) 1
b) 0
c) 2
d) 3

Explanation: The rate of polymer formation is given by-
Rp =[( kp2/kt)fkd]0.5[I]0.5[M] This proves that rate of polymer formation is first order in monomer concentration.

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