4.6 A polymer P having number-average and weight-average molecular weights of 120,000 and 300,000, respectively, was cut into fractions A and B by fractional precipitation. If A and B have number-average molecular weights of 90,000 and 130,000, respectively, what are the weight fractions of A and B obtained from the initial polymer P? If A and B have the same polydispersity, what is the polydisper- sity index ?
4.6 A polymer P having number-average and weight-average molecular weights of 120,000 and 300,000, respectively, was cut into fractions A and B by fractional precipitation. If A and B have number-average molecular weights of 90,000 and 130,000, respectively, what are the weight fractions of A and B obtained from the initial polymer P? If A and B have the same polydispersity, what is the polydisper- sity index ?
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
Related questions
Question
![231
Polymer Molecular Weights
polydispersity index ?
[Ans. WB = 60 g; I = 1.92]
4.6 A polymer P having number-average and weight-average molecular weights of
120,000 and 300,000, respectively, was cut into fractions A and B by fractional
precipitation. If A and B have number-average molecular weights of 90,000 and
130,000, respectively, what are the weight fractions of A and B obtained from the
initial polymer P ? If A and B have the same polydispersity, what is the polydisper-
sity index ?
[Ans. WA = 0.19; wg = 0,81; I = 2.45]
4.7 By fractional precipitation, 200 g of polymer P with the most probable distribution
and a number-average molecular weight M = 150,000 is separated into two frac-
tions, A and B, the former weighing 68.0 g. Light scattering of A gives a molecular
weight of 250,000. If the polydispersity index of A is the same as that of B, what is
the number-average molecular weight of B ?
[Ans. (M„)B = 143,300]
4.8 For end-group analysis, 0.8632 g of a carboxy) terminated polybutadiene (CTPB)
sample dissolved in 1:3 mixture of ethanol and toluene consumed 5.2 ml of 0.1240
N alcoholic potassium hydroxide solution in titration using phenolphthalein as the
indicator. Calculate the molar mass of the polymer.
[Ans. 2672 g mol-!)
A linear polyester was synthesized from a mixture of diacid and glycol with car-
boxyl to hydroxyl ratio greater than unity. A sample of the polyester (3.5 g) re-
quires titration with 23 mL of N/50 KOH to reach a phenolphthalein end point. By
vapor-pressure osmometry the molecular weight of the polymer was determined to be
12,000. Calculate the average carboxyl functionality of the polymer (that is, average
number of carboxyl groups per polymer molecule).
[Ans. 1.6]
4.9
4.10 About 1 g (dry) of a sample of polyester polyol of M, = 3,000 was treated with bro-
moacetyl bromide (BrCH2COBr) to convert the hydroxyl end groups to bromoacetyl
end groups. The treated polymer was found to contain 4.88% Br by elemental analy-
sis. Estimate the average number of hydroxyl groups on each molecule of the polyol.
[Ans. 2.0]
4.11 A polyol for polyurethane foam was synthesized by polymerizing propylene oxide
by using glycerol as the initiator (see Chapter on "Ring-Opening Polymerization").
For analysis, a sample of this polyol was reacted with phenyl isocyanate to convert
the hydroxyl groups to urethanes which were then analyzed for nitrogen. The nitro-
gen content of the treated polymer was found to be 1.523%. Estimate the hydroxyl
equivalent weight and molecular weight of the polyol.
[Ans. OH equiv. = 800 g (mol OH)-'; M, = 2,400]
4.12 The molecular weight of a polymer determined by an osmotic pressure measurement
in a theta solvent is 20,000. What osmotic pressure (atm) would be expected at a
concentration of 1.20 g/dL and 30°C? Would there be a difference in molecular](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F270f44e4-e962-45cd-8799-3cb18f49e5d1%2Fc1bf520a-b7bb-469c-b3e7-bd57a95175e9%2F8q3lve_processed.jpeg&w=3840&q=75)
Transcribed Image Text:231
Polymer Molecular Weights
polydispersity index ?
[Ans. WB = 60 g; I = 1.92]
4.6 A polymer P having number-average and weight-average molecular weights of
120,000 and 300,000, respectively, was cut into fractions A and B by fractional
precipitation. If A and B have number-average molecular weights of 90,000 and
130,000, respectively, what are the weight fractions of A and B obtained from the
initial polymer P ? If A and B have the same polydispersity, what is the polydisper-
sity index ?
[Ans. WA = 0.19; wg = 0,81; I = 2.45]
4.7 By fractional precipitation, 200 g of polymer P with the most probable distribution
and a number-average molecular weight M = 150,000 is separated into two frac-
tions, A and B, the former weighing 68.0 g. Light scattering of A gives a molecular
weight of 250,000. If the polydispersity index of A is the same as that of B, what is
the number-average molecular weight of B ?
[Ans. (M„)B = 143,300]
4.8 For end-group analysis, 0.8632 g of a carboxy) terminated polybutadiene (CTPB)
sample dissolved in 1:3 mixture of ethanol and toluene consumed 5.2 ml of 0.1240
N alcoholic potassium hydroxide solution in titration using phenolphthalein as the
indicator. Calculate the molar mass of the polymer.
[Ans. 2672 g mol-!)
A linear polyester was synthesized from a mixture of diacid and glycol with car-
boxyl to hydroxyl ratio greater than unity. A sample of the polyester (3.5 g) re-
quires titration with 23 mL of N/50 KOH to reach a phenolphthalein end point. By
vapor-pressure osmometry the molecular weight of the polymer was determined to be
12,000. Calculate the average carboxyl functionality of the polymer (that is, average
number of carboxyl groups per polymer molecule).
[Ans. 1.6]
4.9
4.10 About 1 g (dry) of a sample of polyester polyol of M, = 3,000 was treated with bro-
moacetyl bromide (BrCH2COBr) to convert the hydroxyl end groups to bromoacetyl
end groups. The treated polymer was found to contain 4.88% Br by elemental analy-
sis. Estimate the average number of hydroxyl groups on each molecule of the polyol.
[Ans. 2.0]
4.11 A polyol for polyurethane foam was synthesized by polymerizing propylene oxide
by using glycerol as the initiator (see Chapter on "Ring-Opening Polymerization").
For analysis, a sample of this polyol was reacted with phenyl isocyanate to convert
the hydroxyl groups to urethanes which were then analyzed for nitrogen. The nitro-
gen content of the treated polymer was found to be 1.523%. Estimate the hydroxyl
equivalent weight and molecular weight of the polyol.
[Ans. OH equiv. = 800 g (mol OH)-'; M, = 2,400]
4.12 The molecular weight of a polymer determined by an osmotic pressure measurement
in a theta solvent is 20,000. What osmotic pressure (atm) would be expected at a
concentration of 1.20 g/dL and 30°C? Would there be a difference in molecular
![If a polymer sample contains an equal number of moles of species with degrees of
polymerization x = 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, what are the number-average and
weight-average degrees of polymerization ?
[Ans. DP = 5.5; DP, = 7]
EXERCISES
4.1
4.2 One gram of polymer A (DPn = 1000, DP = 2000) is mixed with 2 g of polymer B
(DP
= 2000, DP,= 5000). Calculate the degree of polymerization of the mixture
that would be derived from osmotic pressure measurements at several concentrations.
[Ans. DPn = 1500; DPw = 4000]
%3D
4.3 Polyethylenes A, B, and C from three sources are to be blended to achieve a weight-
average molecular weight of 210,000 and polydispersity index (PDI) of 3.0. How
much of each polymer should be used to obtain 10,000 kg blend ?
Weight-average mol. wt.
130,000
Polyethylene
PDI
A
2.50
2.00
220,000
400,000
[Hint: Mw = Ewi(Mw)i; 1/Mn = Ewi/(Mn)i; PDI = Mw[Mn.]
[Ans. A = 1892 kg, B = 5776 kg, C = 2332 kg; (Total 10,000 kg)]
2.50
%3D
4.4 Polymer samples A and B are monodisperse polyisobutylenes, while sample C is a
polydisperse polyisobutylene. Sample A is known to have a molecular weight twice
that of B and M,, for sample C is given as 1.8×10³. Deduce the M for sample C
from the following two measurements on a mixture of all three samples. The mixture
contains 30 g of A, 40 g of B, and 30 g of C. Light scattering measurements give
a molecular weight of 94,000, while the measurement of osmotic pressure gives a
molecular weight of 50,000.
[Ans. 48,000 g mol-]
4.5 By a fractional precipitation a polymer A with most probable distribution (I =2.0)
and an osmotic molecular weight of 120,000 is separated into two fractions B and
C with molecular weights, 200,000 and 300,000, respectively, determined by light
scattering. Calculate the weight of B that would be obtained from 100 g of initial
polymer A. If both B and C have the same polydispersity, what is the value of the
%3D](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F270f44e4-e962-45cd-8799-3cb18f49e5d1%2Fc1bf520a-b7bb-469c-b3e7-bd57a95175e9%2F04rhrw7_processed.jpeg&w=3840&q=75)
Transcribed Image Text:If a polymer sample contains an equal number of moles of species with degrees of
polymerization x = 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10, what are the number-average and
weight-average degrees of polymerization ?
[Ans. DP = 5.5; DP, = 7]
EXERCISES
4.1
4.2 One gram of polymer A (DPn = 1000, DP = 2000) is mixed with 2 g of polymer B
(DP
= 2000, DP,= 5000). Calculate the degree of polymerization of the mixture
that would be derived from osmotic pressure measurements at several concentrations.
[Ans. DPn = 1500; DPw = 4000]
%3D
4.3 Polyethylenes A, B, and C from three sources are to be blended to achieve a weight-
average molecular weight of 210,000 and polydispersity index (PDI) of 3.0. How
much of each polymer should be used to obtain 10,000 kg blend ?
Weight-average mol. wt.
130,000
Polyethylene
PDI
A
2.50
2.00
220,000
400,000
[Hint: Mw = Ewi(Mw)i; 1/Mn = Ewi/(Mn)i; PDI = Mw[Mn.]
[Ans. A = 1892 kg, B = 5776 kg, C = 2332 kg; (Total 10,000 kg)]
2.50
%3D
4.4 Polymer samples A and B are monodisperse polyisobutylenes, while sample C is a
polydisperse polyisobutylene. Sample A is known to have a molecular weight twice
that of B and M,, for sample C is given as 1.8×10³. Deduce the M for sample C
from the following two measurements on a mixture of all three samples. The mixture
contains 30 g of A, 40 g of B, and 30 g of C. Light scattering measurements give
a molecular weight of 94,000, while the measurement of osmotic pressure gives a
molecular weight of 50,000.
[Ans. 48,000 g mol-]
4.5 By a fractional precipitation a polymer A with most probable distribution (I =2.0)
and an osmotic molecular weight of 120,000 is separated into two fractions B and
C with molecular weights, 200,000 and 300,000, respectively, determined by light
scattering. Calculate the weight of B that would be obtained from 100 g of initial
polymer A. If both B and C have the same polydispersity, what is the value of the
%3D
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