# 5 - In-Situ Methods for Kinetic Analysis Experimental Kinetic

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```					                                                                                                                          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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