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Use the data provided for tert-Butyl hydroperoxide, AIBN, and Potassium persulfate. a) Plot the relationships between kd (s-1) and T (Kelvin) for each compound.  b) Using an Arrhenius fit, what is the activation energy of decomposition for these initiators c) What is the half-life (in hours) of each compound at the highest temperature data point given Need part C please, but if all can be done it would be appreciated

Use the data provided for tert-Butyl hydroperoxide, AIBN, and Potassium persulfate. a) Plot the relationships between kd (s-1) and T (Kelvin) for each compound.  b) Using an Arrhenius fit, what is the activation energy of decomposition for these initiators c) What is the half-life (in hours) of each compound at the highest temperature data point given Need part C please, but if all can be done it would be appreciated

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Use the data provided for tert-Butyl hydroperoxide, AIBN, and Potassium persulfate.

a) Plot the relationships between kd (s-1) and T (Kelvin) for each compound. 

b) Using an Arrhenius fit, what is the activation energy of decomposition for these initiators

c) What is the half-life (in hours) of each compound at the highest temperature data point given

Need part C please, but if all can be done it would be appreciated

4 Applications: Free Radical Initiators Thermal Initiators: Decomposition Rate and Half-Life (continued) Table 1: Decompositon Rates and 10-Hour Half-life Temperatures of Common Thermal Initiators (arranged alphabetically by initiator) Aldrich Cat. No. Initiator 44,146-5 tert-Amyl peroxybenzoate 11,816-8 4,4-Azobis(4-cyanovaleric acid) 38,021-0 1,1'-Azobis(cyclohexanecarbonitrile) 44,109-0 2,2¹-Azobisisobutyronitrile (AIBN) 17,998-1 Benzoyl peroxide² 44,169-4 2,2-Bis(tert-butylperoxy)butane 38,814-9 1,1-Bis( tert-butylperoxy)cyclohexane 38,809-2 2,5-Bis(tert-butylperoxy)-2,5- 32,953-3 44,171-6 38,808-4 41,666-5 tert-Butyl hydroperoxide dimethylhexane 2,5-Bis(tert-Butylperoxy)- 2,5-dimethyl-3-hexyne Bis(1-(tert-butylperoxy)-1- methylethyl)benzene 1,1-Bis (tert-butylperoxy)-3,3,5- trimethylcyclohexane 38,807-6 tert-Butyl peracetate 16,852-1 tert-Butyl peroxide 15,904-2 tert-Butyl peroxybenzoate 44,147-3 tert-Butylperoxy isopropyl carbonate 24,750-2 Cumene hydroperoxide 28,908-6 Cyclohexanone peroxide 32,954-1 Dicumyl peroxide 29,078-5 Lauroyl peroxide 44,182-1 2,4- Pentanedione peroxide 26,933-6 Peracetic acid 21,622-4 Potassium persulfate³ Solvent Acetone Water Water Toluene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Water 0.1M NaOH T(°C) 70 69 80 80 95 102 50 70 100 60 78 100 93 115 145 130 160 170 183 85 100 130 80 100 130 100 130 115 145 40 60 85 80 50 60 80 90 k (s.¹) 4.6 x 10-5 1.9 x 10-5 9.0 x 10-5 6.5 x 10-5 5.4 x 10-5 1.3 x 10+ 2.2 x 10⁰ 3.2 x 10-5 1.5 X 10-³ 2.0 x 10-6 2.3 x 10-5 5.0 x 10* 1.9 x 10-5 1.1 x 10-5 4.7 x 10+ 3 x 10-7 6.6 x 10-6 2.0 x 10-5 3.1 x 10-5 1.2 x 10⁰ 1.5 x 10-5 5.7 x 10+ 7.8 x 10-⁹ 8.8 x 10-7 3.0 x 10-5 1.1 x 10-5 3.5 x 10- 4.0 x 10 6.6 x 10€ 4.9 x 10 9.2 x 10€ 3.8 x 10+ 6.9 x 10 9.5 x 10-7 3.2 x 10-6 9.2 x 10-5 3.5 x 104 10h Half-life °C (Solvent) 99 (benzene) 69 (water) 88 (toluene) 65 (toluene) 70 (benzene) 100 (benzene) 120 (benzene) 125 (benzene) 115 (benzene) 85 (dibutyl phthalate) 170 (benzene) 100 (benzene) 125 (benzene) 103 (benzene) 98 (aliphatic hydrocarbons) 135 (toluene) 90 (benzene) 115 (benzene) 65 (benzene) 125 (triethyl phosphate) 135 (toluene) 60 (H₂O) 70 (0.1M NaOH) ¹"Polymer Handbook", Eds. Brandrup, J; Immergut, E.H.; Grulke, E.A., 4th Edition, John Wiley, New York, 1999, II/2-69; Aldrich Catalog No. 241,247-3. ²Amines can significantly increase the decomposition rates of peroxides, e.g., addition of N,N-dimethyl aniline to benzoyl peroxide causes the latter to decompose rapidly at room temperature. *Persulfate decomposition is pH dependent. • Polymer Products from Aldrich
Transcribed Image Text:4 Applications: Free Radical Initiators Thermal Initiators: Decomposition Rate and Half-Life (continued) Table 1: Decompositon Rates and 10-Hour Half-life Temperatures of Common Thermal Initiators (arranged alphabetically by initiator) Aldrich Cat. No. Initiator 44,146-5 tert-Amyl peroxybenzoate 11,816-8 4,4-Azobis(4-cyanovaleric acid) 38,021-0 1,1'-Azobis(cyclohexanecarbonitrile) 44,109-0 2,2¹-Azobisisobutyronitrile (AIBN) 17,998-1 Benzoyl peroxide² 44,169-4 2,2-Bis(tert-butylperoxy)butane 38,814-9 1,1-Bis( tert-butylperoxy)cyclohexane 38,809-2 2,5-Bis(tert-butylperoxy)-2,5- 32,953-3 44,171-6 38,808-4 41,666-5 tert-Butyl hydroperoxide dimethylhexane 2,5-Bis(tert-Butylperoxy)- 2,5-dimethyl-3-hexyne Bis(1-(tert-butylperoxy)-1- methylethyl)benzene 1,1-Bis (tert-butylperoxy)-3,3,5- trimethylcyclohexane 38,807-6 tert-Butyl peracetate 16,852-1 tert-Butyl peroxide 15,904-2 tert-Butyl peroxybenzoate 44,147-3 tert-Butylperoxy isopropyl carbonate 24,750-2 Cumene hydroperoxide 28,908-6 Cyclohexanone peroxide 32,954-1 Dicumyl peroxide 29,078-5 Lauroyl peroxide 44,182-1 2,4- Pentanedione peroxide 26,933-6 Peracetic acid 21,622-4 Potassium persulfate³ Solvent Acetone Water Water Toluene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Benzene Water 0.1M NaOH T(°C) 70 69 80 80 95 102 50 70 100 60 78 100 93 115 145 130 160 170 183 85 100 130 80 100 130 100 130 115 145 40 60 85 80 50 60 80 90 k (s.¹) 4.6 x 10-5 1.9 x 10-5 9.0 x 10-5 6.5 x 10-5 5.4 x 10-5 1.3 x 10+ 2.2 x 10⁰ 3.2 x 10-5 1.5 X 10-³ 2.0 x 10-6 2.3 x 10-5 5.0 x 10* 1.9 x 10-5 1.1 x 10-5 4.7 x 10+ 3 x 10-7 6.6 x 10-6 2.0 x 10-5 3.1 x 10-5 1.2 x 10⁰ 1.5 x 10-5 5.7 x 10+ 7.8 x 10-⁹ 8.8 x 10-7 3.0 x 10-5 1.1 x 10-5 3.5 x 10- 4.0 x 10 6.6 x 10€ 4.9 x 10 9.2 x 10€ 3.8 x 10+ 6.9 x 10 9.5 x 10-7 3.2 x 10-6 9.2 x 10-5 3.5 x 104 10h Half-life °C (Solvent) 99 (benzene) 69 (water) 88 (toluene) 65 (toluene) 70 (benzene) 100 (benzene) 120 (benzene) 125 (benzene) 115 (benzene) 85 (dibutyl phthalate) 170 (benzene) 100 (benzene) 125 (benzene) 103 (benzene) 98 (aliphatic hydrocarbons) 135 (toluene) 90 (benzene) 115 (benzene) 65 (benzene) 125 (triethyl phosphate) 135 (toluene) 60 (H₂O) 70 (0.1M NaOH) ¹"Polymer Handbook", Eds. Brandrup, J; Immergut, E.H.; Grulke, E.A., 4th Edition, John Wiley, New York, 1999, II/2-69; Aldrich Catalog No. 241,247-3. ²Amines can significantly increase the decomposition rates of peroxides, e.g., addition of N,N-dimethyl aniline to benzoyl peroxide causes the latter to decompose rapidly at room temperature. *Persulfate decomposition is pH dependent. • Polymer Products from Aldrich
A ALDRICH Applications: Free Radical Initiators. Thermal Initiators: Decomposition Rate and Half-Life ww Ideally, a thermal free radical initiator should be relatively stable at room temperature but should decompose rapidly enough at the polymer-processing temperature to ensure a practical reaction rate. In addition to temperature, the decomposition rate (k) of the initiator will depend on the solvent/monomer system used. The confining effect of solvent molecules (the cage effect) causes secondary "wastage" reactions including recombination of radicals to regenerate the initiator. The cage effect becomes more significant as viscosity increases. The most important indicator of activity of an initiator is its half-life (t2). It is the time required to reduce the original initator content of a solution by 50%, at a given temperature. Fig 1: Relationship of Half Life (t) to Decomposition Rate (k.). L=85d 20d 200d 1y- 2y- k x 10⁰ 8.5d- 10d- 20d 40d 60d- x 10 20h 24h 40h 60h 120h- x 10° 120m- 200m - 5h- 10h x 10 12m 20m- 30m- 40m 80m Assuming first order decomposition kinetics, which is tru for most free radical organic initiators, the half-life (₁/2) related to the initiator decomposition rate (k) as follows t₁/2 = In2/k Table I lists the decomposition rate (k) data¹ for sever commonly used free radical initiators, at specific temper tures and solvents. To further assist you in your selection a thermal initiator, the temperature corresponding to a hour half-life in a specific solvent is also shown. Fig. relates the initiator decomposition rate (k.) in s¹ to th half-life for a broad range of k, values, including those four in Table I. x 10 How to read the chart: See circled example: Half lives are to the left of each vertical line. A half life of 200s has a rate constant of 3.4 x 10-³ 70s 80s 120s 200s 10m - x 10¹ 7s 10s 20s 30s- 40s- Key: y = years d = days h = hours x 10° 0.75s- m minutes s seconds 1s 3s 5s x 10' 0.07s 0.12s 0.25s- 0.35s 0.5s x 10° 10 = 9 8 7 6 5 4 3 2 This chart is reprinted with permission from Wiley Interscience 1 The Link to All Your Polymer Needs
Transcribed Image Text:A ALDRICH Applications: Free Radical Initiators. Thermal Initiators: Decomposition Rate and Half-Life ww Ideally, a thermal free radical initiator should be relatively stable at room temperature but should decompose rapidly enough at the polymer-processing temperature to ensure a practical reaction rate. In addition to temperature, the decomposition rate (k) of the initiator will depend on the solvent/monomer system used. The confining effect of solvent molecules (the cage effect) causes secondary "wastage" reactions including recombination of radicals to regenerate the initiator. The cage effect becomes more significant as viscosity increases. The most important indicator of activity of an initiator is its half-life (t2). It is the time required to reduce the original initator content of a solution by 50%, at a given temperature. Fig 1: Relationship of Half Life (t) to Decomposition Rate (k.). L=85d 20d 200d 1y- 2y- k x 10⁰ 8.5d- 10d- 20d 40d 60d- x 10 20h 24h 40h 60h 120h- x 10° 120m- 200m - 5h- 10h x 10 12m 20m- 30m- 40m 80m Assuming first order decomposition kinetics, which is tru for most free radical organic initiators, the half-life (₁/2) related to the initiator decomposition rate (k) as follows t₁/2 = In2/k Table I lists the decomposition rate (k) data¹ for sever commonly used free radical initiators, at specific temper tures and solvents. To further assist you in your selection a thermal initiator, the temperature corresponding to a hour half-life in a specific solvent is also shown. Fig. relates the initiator decomposition rate (k.) in s¹ to th half-life for a broad range of k, values, including those four in Table I. x 10 How to read the chart: See circled example: Half lives are to the left of each vertical line. A half life of 200s has a rate constant of 3.4 x 10-³ 70s 80s 120s 200s 10m - x 10¹ 7s 10s 20s 30s- 40s- Key: y = years d = days h = hours x 10° 0.75s- m minutes s seconds 1s 3s 5s x 10' 0.07s 0.12s 0.25s- 0.35s 0.5s x 10° 10 = 9 8 7 6 5 4 3 2 This chart is reprinted with permission from Wiley Interscience 1 The Link to All Your Polymer Needs
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