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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.
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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)
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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)
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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.
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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)
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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
