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    Lucas Hernández Karla Berenice
    The document calculates the activation energy of a second-order chemical reaction using nonlinear regression analysis of experimental rate constant (kexp) data collected at different temperatures. It finds the pre-exponential factor (A), activation energy (E), and frequency factor (ko) that provide the best fit between the calculated rate constants (kcalc) and kexp. The best-fit values are A = 3.54×1012 L/(mol∙s), E = 196,367 J/mol (196.4 kJ/mol), and ko = 0.169 L/(mol∙s) with a high coefficient of determination (R2 = 0.9996744).

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    © All Rights Reserved
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    Untitled

    Uploaded by

    Lucas Hernández Karla Berenice
    20 views8 pages
    The document calculates the activation energy of a second-order chemical reaction using nonlinear regression analysis of experimental rate constant (kexp) data collected at different temperatures. It finds the pre-exponential factor (A), activation energy (E), and frequency factor (ko) that provide the best fit between the calculated rate constants (kcalc) and kexp. The best-fit values are A = 3.54×1012 L/(mol∙s), E = 196,367 J/mol (196.4 kJ/mol), and ko = 0.169 L/(mol∙s) with a high coefficient of determination (R2 = 0.9996744).

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    © © All Rights Reserved

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    The document calculates the activation energy of a second-order chemical reaction using nonlinear regression analysis of experimental rate constant (kexp) data collected at different temperatures. It finds the pre-exponential factor (A), activation energy (E), and frequency factor (ko) that provide the best fit between the calculated rate constants (kcalc) and kexp. The best-fit values are A = 3.54×1012 L/(mol∙s), E = 196,367 J/mol (196.4 kJ/mol), and ko = 0.169 L/(mol∙s) with a high coefficient of determination (R2 = 0.9996744).

    Copyright:

    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd
    Download as xlsx, pdf, or txt
    20 views8 pages

    Untitled

    Uploaded by

    Lucas Hernández Karla Berenice
    The document calculates the activation energy of a second-order chemical reaction using nonlinear regression analysis of experimental rate constant (kexp) data collected at different temperatures. It finds the pre-exponential factor (A), activation energy (E), and frequency factor (ko) that provide the best fit between the calculated rate constants (kcalc) and kexp. The best-fit values are A = 3.54×1012 L/(mol∙s), E = 196,367 J/mol (196.4 kJ/mol), and ko = 0.169 L/(mol∙s) with a high coefficient of determination (R2 = 0.9996744).

    Copyright:

    © All Rights Reserved
    Download as XLSX, PDF, TXT or read online from Scribd
    Download as xlsx, pdf, or txt
    of 8

    Calculate activation energy by nonlinear regression

    k=koexp(-E(1/T-1/To)/R) To = 770 K R= 8.314 J/(mol K)


    k=Aexp(-E/(RT)) A=koexp(E/(RTo)
    ko = 0.169 L/(mol s) A= 3.54E+12 L/(mol s)
    E= 196,367 J/mol E= 196.4 kJ/mol
    T(K) kexp kcalc (kexp-kcalc)2 (kexp-kmean)2 1000/T ln(kexp) ln(kcalc)
    700 0.011 0.008 9.93E-06 0.3187 1.43 -4.51 -4.85
    730 0.035 0.031 1.29E-05 0.2921 1.37 -3.35 -3.46
    760 0.105 0.113 5.84E-05 0.2214 1.32 -2.25 -2.18
    790 0.343 0.367 5.59E-04 0.0541 1.27 -1.07 -1.00
    810 0.789 0.767 4.80E-04 0.0456 1.23 -0.24 -0.27
    840 2.17 2.173 1.08E-05 2.5424 1.19 0.77 0.78
    kmean= 0.5755
    SS= 0.00113 3.4742 =SSmean

    R2= 0.9996744 Run# 4


    SE= 0.0168179 Expected Run# 4
    df= 4

    T(K) X matrix Xt*Xinv


    700 0.04654 -1.226E-07 0.1605 -75582.3
    730 0.18623 -2.688E-07 -75582.3 36784345267
    760 0.66791 -2.315E-07
    790 2.17396 1.450E-06 S e2 0.000283
    810 4.54831 5.917E-06 Sko 0.006738
    840 12.88611 2.829E-05 SEact 3225.5
    ¶k/¶ko ¶k/¶E alpha 5%
    tval 2.776

    parameter value +/- 95% confidence intervals


    ko 0.169 +/- 0.019
    E(J/mol) 196,367 +/- 8,956
    E(kJ/mol) 196.4 +/- 9.0
    A 3.54E+12 +/- 0.40E+12
    University of Colorado Boulder
    Data from S.M. Walas, Chemical Reaction Engineering Handbook of Solved Problems, Gordon and Breach Publishe
    Second-order reaction

    1.0

    kexp-kcalc
    0.0032 0.0
    0.0036
    -0.0076
    -0.0236 -1.0
    0.0219
    -0.0033
    -2.0
    ln(k)

    -3.0

    -4.0

    -5.0
    1.15 1.20 1.25 1.30 1.35 1.40 1.45
    1000/T(K)

    kexp-kcalc
    0.0300

    0.0200

    0.0100

    0.0000
    680 700 720 740 760 780 800 820 840 860

    -0.0100

    -0.0200

    -0.0300
    Gordon and Breach Publishers, p188 (1995)

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    Calculate activation energy by nonlinear regression
    k=koexp(-E(1/T-1/To)/R) To = 770 K R= 8.314 J/(mol K)
    k=Aexp(-E/(RT)) A=koexp(E/(RTo)
    ko = 0 L/(mol s) A= 3.54E+12
    E= 196367 J/mol E= 196.4
    T(K) kexp kcalc (kexp-kcalc)2 (kexp-kmean)2 1000/T
    700 0.011 0.008 9.93E-06 0.3187 1.43
    730 0.035 0.031 1.29E-05 0.2921 1.37
    760 0.105 0.113 5.84E-05 0.2214 1.32
    790 0.343 0.367 5.59E-04 0.0541 1.27
    810 0.789 0.767 4.80E-04 0.0456 1.23
    840 2.17 2.173 1.08E-05 2.5424 1.19
    kmean= 0.5755
    SS= 0.00113 3.4742 =SSmean

    R2= 0.9996744 Run#


    SE= 0.0168179 Expected Run#
    df= 4

    T(K) X matrix Xt*Xinv


    700 0.04654 -1.226E-07 0.1605 -75582.3
    730 0.18623 -2.688E-07 -75582.3 36784345266.8064
    760 0.66791 -2.315E-07
    790 2.17396 1.450E-06 S e2 0.000283
    810 4.54831 5.917E-06 Sko 0.006738
    840 12.88611 2.829E-05 SEact 3225.5
    ¶k/¶ko ¶k/¶E alpha 5%
    tval 2.776

    parameter value +/- 95% confidence intervals


    ko 0.169
    E(J/mol) 196,367
    E(kJ/mol) 196.4
    A 3.54E+12
    University of Colorado Boulder
    Data from S.M. Walas, Chemical Reaction Engineering Handbook of Solved Problems, Gordon and Breac
    Second-order reaction
    L/(mol s)
    1.0
    kJ/mol
    ln(kexp) ln(kcalc)kexp-kcalc
    -4.51 -4.85 ### 0.0
    -3.35 -3.46 ###
    -2.25 -2.18 ###
    -1.07 -1.00 ### -1.0
    -0.24 -0.27 ###
    0.77 0.78 ###
    -2.0
    ln(k)

    4 -3.0
    4

    -4.0

    -5.0
    1.15 1.20 1.25 1.30 1.35 1.40 1.45
    1000/T(K)

    kexp-kcalc
    0.0300

    0.0200
    95% confidence intervals
    +/- 0.019 0.0100
    +/- 8,956
    +/- 9.0 0.0000
    680 700 720 740 760 780 800 820 840 860
    +/- 0.40E+12
    -0.0100

    -0.0200

    -0.0300
    Problems, Gordon and Breach Publishers, p188 (1995)

    .40 1.45

    840 860

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