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5 - In-Situ Methods for Kinetic Analysis Experimental Kinetic

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5 - In-Situ Methods for Kinetic Analysis Experimental Kinetic Powered By Docstoc
					                                                                                                                          Autumn 2004


In-Situ Methods for Kinetic Analysis

    •     Ideally, we would like to have a probe that can “ride along” with the
          molecules as the reaction proceeds, so that we have a virtually
          continuous account of the changing concentrations of species.

    •     What sort of probe can we use?

          Any method that gives an accurate measurement of some property of the
          system that is proportional to concentration or proportional to rate.

           – Differential (or derivative) methods measure a property that is
             proportional to the instantaneous reaction rate.

           – Integral methods measure a property that is proportional to
             concentration.




                                                                                                                                                            1




                                                                                                                          Autumn 2004
Experimental Kinetic Measurements

•       Any method which measures differences in a property as a function of time
        will provide a more dramatic picture to the eye than one which measures
        accumulation (e.g. integral techniques).
•       Features of the reaction profile are are more difficult to pick out by eye from a
        measure of % conversion vs. time compared to rate vs. time.
         – The induction period of rising rate lasts until ca. 10% conversion, but this appears
           only as a slight bend in the conversion plot.
         – The shoulder in rate at high conversion is also hard to spot in the conversion curve.

                                                                                    14                                    100

                                                                                    12
                                                                                                                                % Conversion of Substrate




                                                 dCi                                                                      80
                 rate of change of species i =                                      10
                                                  dt
                                                                    Reaction Rate




                                                                                                                          60
                                                                                     8

                                                   C
                                               1 i ,t " dCi %                        6
                                                                                                                          40

                                              Ci ,0 C(0 # dt &
          % conversion of species i = 100 !             $    ' dt
                                                                                     4
                                                     i,
                                                                                                                          20
                                                                                     2

                                                                                     0                                    0
                                                                                         0   10   20       30   40   50
                                                                                                   Time (min)

                                                                                                                                                            2
                                                                                                   Autumn 2004


Integral Methods for Collecting Rate Data

•       Sample collection and analysis:
         – sampling is conventionally used        to obtain                          !Ci Ci " Ci "1
                                                                            rate =       =
           initial rate data                                                          !t   t i " t i "1

         – one rate datum point for every two samples taken!
•       In-situ methods: spectroscopic
         – (FTIR, UV,Raman, etc)
         – usually measure concentrations by relying on                              Ai = ! bCi
           Beer’s Law.
         – to obtain reaction rate, we must take the derivative
           of concentration, dc/dt
•       In-situ methods: Gas uptake measurements: P = f(t)
         – ideal gas law gives relationship between pressure                            ni   P
            and concentration                                                   Ci =       =
                                                                                        V RT
         – applicable to reactions where one of the reactants
           (or products) is gaseous (hydrogenations,
           oxidations, some polymerizations)
                                                                                                            3




                                                                                                   Autumn 2004


Differential Methods

    •    In-situ methods: reaction calorimetry                                                t

          – measures reaction enthalpy, q, as a                       dCi
                                                                                              " q(t )dt
                                                         q = !HrxnV         % conversion =    0
             function of time                                          dt                     tf


          – The heat consumed or evolved in a                                                 " q(t )dt
                                                                                              0

             reaction is directly propotional to the
             reaction rate
          – Each datum point is a (rate, time) pair
          – Each datum point can be thought of as
             an “initial rate” measurement at a
             different substrate concentration.
          – Conversion may be obtained by
             integrating the heat flow curve.




                                                                                                            4
                                                                                                                                                                                                                                                         Autumn 2004


Example : In-situ FTIR Spectroscopy

                                                                                   H                             H                                                       H
                                  N                               H2               N                        H2   N                        H2                             N
                                                  H                                                     H                H                                                              H
                                                  N                                                     N                N                                                              N
                                  N           C                                    N         C                   N   C                                                   N         C
                                                                                                                 H                                                       H
                                              O                                              O                       O                                                             O

                                                                                  Possible intermediate species
                            monitor !C=O
                                                                                                                                                                                          pyrazine
                                                                                                                                                                         0.5            carboxamide
                                                                                                                                                                                        1677 cm--1
                                                      1661 cm-1




                                                                                                                                                                                                                                              piperazine


                                                                                            1602 cm-1
                                                                                                                                                                         0.4                                                                 carboxamide




                                                                                                                                                   IR Intensity (a.u.)
                                  1677 cm-1




                                                                                                                                                                                                                                                1661 cm--1
                                                                                                                                                                         0.3
                                                                                                                                                                                                            1602 cm--1
                                                                                                                                                                         0.2                        Intermediate


                                                                                                                                                                         0.1


                                                                                                                                                                         0.0
                                                                                                                                                                               0                   100                       200                 300               400
                                                                                                                                                                                                                          Time (min)



                    FTIR can give a concentration profile of reactants, intermediates, and products
                    over the course of the reaction
                                                                                                                                                                                    Sun, et al., Thermochim. Acta, 1996, 289, 189.                                                      5




                                                                                                                                                                                                                                                         Autumn 2004


Example : Hydrogen Uptake Measurements

                    hydrogen reservoir P = f(t)

                                                                                                                                                                               N                                                    N
                    constant pressure reactor                                                                                                                                                      H2

                                                                                                                                                                                              Ir catalyst
                                                                                          P
                                                                                                                                                                                                            O

                                                                                                                                                                                                                            PF6
                                                                                                                                                                                                        N

                                                                          metering                                                                                                          Ph2P
                                                                                                                                                                                                    Ir
                                                                                                                                                                                                    (COD)2      C(CH3)2

                                                                           valve
                                                                                                                                          25                                                                                                             0,1




calibration curve between reservoir                                                                                                                                                                                                                      0,08
                                                                                                                                          20
pressure and moles substrate consumed
                                                                                                                                                                                                                                                                Reaction Rate (dP/dt)
                                                                                                                         Pressure (bar)




                                                                                                                                                                                                                                  reservoir pressure
                    5                                                                                                                                                                                                                                    0,06
                             y = -0,0092018 + 203,59x R= 0,99864

                                                                                                                                          15
                    4
                                                                                                                                                                                                                                                         0,04
                                                                                                                                                                                                                          reaction rate
  uptake (bar H2)




                    3                                                                                                                                                                                                     (derivative of pressure)
                                                                                                                                          10
                                                                                                                                                                                                                                                         0,02
                    2                                                                                                                                                               reactor pressure



                    1                                                                                                                     5                                                                                                              0
                                                                       Reaction conditions:
                                                                                                                                               0                                   50                       100                     150                200
                                                                       10-20 °C
                                                                       2-7 bar reactor pressure
                                                                                                                                                                                               Time (min)
                    0
                        0         0,005               0,01                0,015                 0,02
                                                                                                                                      Rosner, Pfaltz, Blackmond
                              substrate consumed (moles substrate by GC)
                                                                                                                                                                                                                                                                                        6
                                                                                                                                                                                                                                                                 Autumn 2004


 Example : Reaction Calorimetry

    •             Differential methods of measurement highlight rapid
                  changes

                                                            O                                                OH
                                                                                           H2
                                                                         O                                             O
                                                                                                                                                                                                                                                 dCi
                                                                                       Pt catalyst
                                                                                     chiral modifier
                                                                                                              *
                                                                                                                                                                                                                          q = !Hrxn "V "
                                                                     O                                            O                                                                                                                               dt
                                                                                                                                                                                                                                                          t

                                                                                                                                                                                                                                                          # q(t )dt
             100
                                                                                                                                        2.0
                                                                                                                                                                                                                   % conversion = 100 "                   0
                                                                                                                                                                                                                                                          tf
              80                                                                            rising reaction rate observed in
                                                                                            the heat flow curve is not as
                                                                                            noticeable from partial heat flow           1.5
                                                                                                                                                                                                                                                          # q(t )dt




                                                                                                                                              Reaction Rate
Conversion




                                                                                            curve or from analytical                                                                                                                                      0
              60                                                                            samples


                                                                                                  This line is NOT a fit to the         1.0
              40                                                                                  analytical data points! It comes
                                                                                                  from the integral of the heat flow
                                                                                                  curve.
              20                                                                                                                        0.5
                                                                                                                                                                                                                   heat flow calorimetry gives kinetic
                                                                                                                                                                                                                   AND thermodynamic information
               0                                                                                                                        0                                                                          about the reaction
                    0                                                             100         200                                 300
                                                                                     Time (min)
                                                                                                                                                                                                                                                                          7




                                                                                                                                                                                                                                                                 Autumn 2004


   Developing a “Graphical Rate Equation”

              •     We can turn our integral measurement into a differential curve (and vice
                    versa) by differentiating it (or integrating it).

              •     The raw data are called the “primary data” and the derivative (or integral)
                    curve is called the “processed” data.
                                                                                                                                                              fraction conversion or relative rate
                    fraction conversion or relative rate




                                                                     a                                                                                                                                         b
                                                            1                                                                                                                                         1

                                                                                                                                                                                                                                      processed data:
                                                           0.8                                                                                                                                       0,8                            fraction conversion
                                                                                                          primary data:
                                                                                                       fraction conversion
                                                           0.6                                                                                                                                       0,6


                                                           0.4                                                                                                                                       0,4

                                                                                                          processed data:                                                                                                               primary data:
                                                           0.2                                              reaction rate                                                                            0,2                                reaction rate

                                                            0                                                                                                                                         0
                                                                 0           10     20       30         40        50         60                                                                            0         40      80         120         160
                                                                                                                                                                                                                           time (min)
                                                                                         time (min)




                                                                                                                                                                                                                                                                          8
                                                                                                                                                                                                                                                                                             Autumn 2004


Developing a “Graphical Rate Equation”

            •             We make kinetic measurements as a function of time, but a reaction rate
                          law gives rate as a function of concentration (or fraction conversion).

            •             If we combine our primary and processed data, we can develop a plot of
                          rate vs. conversion (or concentration) -- a “graphical rate equation”.
                              fraction conversion or relative rate




                                                                               a




                                                                                                                                                                       fraction conversion or relative rate
                                                                      1                                                                                                                                                   b
                                                                                                                                                                                                                  1

                                                                     0.8                                                                                                                                                                             processed data:
                                                                                                               primary data:                                                                                  0,8                                  fraction conversion
                                                                                                            fraction conversion
                                                                     0.6
                                                                                                                                                                                                              0,6

                                                                     0.4
                                                                                                                                                                                                              0,4
                                                                                                               processed data:
                                                                     0.2                                         reaction rate                                                                                0,2
                                                                                                                                                                                                                                                      primary data:
                                                                                                                                                                                                                                                      reaction rate

                                                                      0                                                                                                                                           0
                                                                           0       10     20      30         40        50         60                                                                                  0          40     80            120         160
                                                                                                                                                                                                                                      time (min)
                                                                                               time (min)




                     1
                                a                                                                                                                                 1                                           b
                    0.8
                                                                                                                                                                 0.8




                                                                                                                                                 relative rate
    relative rate




                    0.6
                                                                                                                                                                 0.6


                    0.4                                                                                                                                          0.4


                    0.2                                                                                                                                          0.2
                                                                                                              first order kinetics                                                                                                                                    first order kinetics

                     0                                                                                                                                            0
                          0                                                0.02         0.04        0.06            0.08               0.1                             0                                                      0.05           0.1                0.15                0.2
                                                                                                                                                                                                                                      [substrate] (M)
                                                                                         [substrate] (M)                                                                                                                                                                                              9




                                                                                                                                                                                                                                                                                             Autumn 2004


Reaction Progress Kinetic Analysis

•                   Reaction progress kinetic analysis compared to classical kinetic methods:
                          – we construct the entire rate vs. concentration curve from a single
                            experiment rather than a series of initial rate experiments.
                          – We make use of a visual approach (compare to integrating rate equations!)
                            to assess the reaction’s “driving forces”.


•                   In this example, the plot of rate vs.                                                                                    •       In this example, the plot of rate vs.
                    concentration is linear, showing that                                                                                            concentration shows curvature,
                    the reaction obeys first order kinetics.                                                                                         suggesting that the rate law is more
                                                                                                                                                     complex than a simple integer order.


                     1
                                a                                                                                                                                 1                                           b
                    0.8
                                                                                                                                                                 0.8
                                                                                                                                                 relative rate
    relative rate




                    0.6
                                                                                                                                                                 0.6


                    0.4                                                                                                                                          0.4


                    0.2                                                                                                                                          0.2
                                                                                                              first order kinetics                                                                                                                                    first order kinetics

                     0                                                                                                                                            0
                          0                                                0.02         0.04        0.06            0.08               0.1                             0                                                      0.05           0.1                0.15                0.2
                                                                                                                                                                                                                                      [substrate] (M)
                                                                                         [substrate] (M)                                                                                                                                                                                             10

				
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