ChE 452 Lecture 04
Measuring Rate Data
1
Objective

General concepts in measurement of rate
data



Compendium of methods (language)
Direct vs indirect
Design of experiments
2
General Approach
Initiate reaction
measure concentration vs time
fit data to calculate rates
1
C o n c e n tra tio n
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
1
2
3
4
5
6
Time, Hours
3
Rate Measurements: An
Old Topic
1.1
C o n c e n tra tio n
1
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
2
4
6
8
10
12
Time, Hours
Figure 3.1 Wilhelmy’s [1850] measurements of
the changes in sucrose concentration in grape
juice after acid is added.
4
Many Methods To Do
Measurements


Techniques include: conventional,
stopped flow, temperature jump…
Differ via time scale of reaction


Need to mix reactants and initiate reaction
before reaction is done
Different techniques used for fast reactions
than slow ones
5
Batch Methods To Measure
Reaction Rates
Conventional
1)
2)
Stopped flow
1)
2)
3)
Temperature jump
1)
2)
3)
Mix reactants together in a batch reactor
Measure concentration versus time
Set of continuous-flow systems where
reactants are fed into the reactor, and
flow out again so quickly that there is
negligible reaction
Stop the flow so that the reactants can
react
Measure conversion versus time
Mix reactants at such a low temperature
that the reaction rate is negligible
Use CO2 laser to suddenly heat reactants
Measure concentration vs time
10 sec or more
10-1 sec or more
10-6 sec or more
Table 3.1
6
Batch Methods
Continued
Shock tube
1)
2)
3)
4)
Flash photolysis
1)
2)
3)
NMR
1)
2)
Put 10-1 atm of one reactant and 10 atm of 10-3 to 10-5 sec
helium on one side of a diaphragm
Put 10-3 atm of the other reactant on the
other side of the diaphragm
Suddenly break the diaphragm so that the
gas flows from the high-pressure side to
the low-pressure side
Measure the reactant concentration vs
time
Put the reactants into a vessel under
10-9 to 10-1 sec
conditions where reaction is negligible
Pulse a laser or flash lamp to start reaction
Measure the reactant concentration vs
time
Initiate a change with a magnetic pulse
Measure the decay of spins with the NMR
10-2 to 10-9 sec
7
Flow Methods To Measure
Reaction Rates
Conventional flow
system
1)
2)
Molecular beam
1)
2)
Continuously feed reactants into a
10-3 sec or more
reactor – CSTR or plug flow
Measure the steady state reaction rate
Direct beams of reactants toward each 10-13 to 10-9 sec
other in a vacuum system
Measure the steady state reaction
rate
8
How Do You Decide What
Experimental Method To Use?
Key Issues:
• Direct method or indirect method
• Can measurement be done on an
appropriate time scale?
9
Direct vs Indirect Methods
Recall – rate equation is the rate as a function of
the concentrations
•
•
Direct method - any method where you actually
measure the rate as a function of concentration
Indirect method - a method where you measure
some other property (i.e. concentration vs time)
and infer a rate equation.
10
Example: Consider Arsine
Doping Of Silicon
2A sH 3  2A s  3H 2
Silicon
Pressure Gauge
3-zone oven
W afers
Door
To Pump
(Loadlock)
Feed
H older
(boat)
Figure 3.6 A typical arsine
decomposition reactor.
11
Direct Measurement
PA sH
3
= P
k t
0
 e 1
A sH 3
M icrobalance
W afer
H eat
Lam p
F eed
E xhaust
Figure 3.7 A possible apparatus
to examine the decomposition of
arsine (AsH3) on silicon.
12
Indirect Measurement
P ressure, x2, torr
100
10
0
5
10
15
20
25
30
35
T im e, H ours
Figure 3.8 Typical batch data
for reaction(3.7). Data of
Tamaru[1955].
13
A Comparison Of The Advantages And
Disadvantages Of Direct And Indirect Methods
Direct Method
Indirect Method
Advantages
•
Get rate equation directly
•
Easy to fit data to a rate law
•
High confidence on final rate
equation
Disadvantages
•
Must infer rate equation
•
Hard to analyze rate data
•
Low confidence on final rate
equation
Disadvantages
•
Difficult experiment
•
Need many runs
•
Not suitable for very fast or
very slow reactions
Advantages
•
Easier experiment
•
Can do a few runs and get
important information
•
Suitable for all reactions
including very fast or very
slow ones
14
Other Notation
Direct method
• differential method
• differential reactor
Indirect method
• integral method
15
Initial Rate Method




Start with multiple parallel reactors
Fill each with a different
concentration
Let reaction go & measure conversion
vs time
Get rate from slope extrapolated to
zero
16
Next: Start Analysis Of Data
From Indirect Reactors:
Which is easier to analyze?
• Direct method (rate vs concentration
• Indirect method (concentration vs time)
Direct is easier to analyze.
17
E tch R ate (m icrons/m in)
Analysis Of Data From A
Differential Reactor
0 .1 0 0
0 .0 8 0
0 .0 6 0
0 .0 5 0
General method –
least squares with
rate vs time data
Slo pe = 0 .5
0 .0 4 0
0 .0 3 0
0 .0 2 0
M eta llic C o lo r
O x id e C o lo r
0 .0 1 0
10
100
O x y g en Pressu re (T o rr)
Figure 3.10 The rate of copper
etching as a function of the
oxygen concentration. Data of
Steger and Masel [1998].
18
Next: Multiple Variable Analysis

Rates of reaction usually strongly
effected by many variables


Temperature: concentration, solvents,
inpurities, catalysts, ……
So far only consider one variable:
Concentration
19
Example: Develop A Rate Equation
For The Growth Of Grass
Variables
• Sunlight
• Rain
• Amount of grass seed
• Number of birds and insects
• Fertilizer
• Soil type
• Soil bacteria
How do we proceed to measure a rate?
20
Usual Technique: Initial Rate
Method
Start with multiple parallel reactors
•Fill each with a different concentration
•Let reaction go & measure conversion
vs time
•Get rate from slope extrapolated to
zero
•
21
If We Have Several Variables,
What Do We Measure?
General approach
 Take some preliminary data to determine
what variables are important


Usually requires multiple iterations
Take more detailed measurements on the
variables that are most important
22
Design Of Experiments To Determine
Which Variables Are Important





2n designs
Pick two values of each of the variables
Look at two possibilities for each variable
Do experiments for all combinations
Do analysis to decide which variables are
important
23

Example: How Does Temperature And
Concentration Affect Selectivity Of A
Reaction
Pick two values of each variable
Temperature + = higher temperature
Temperature - = lower temperature
Concentration + = higher concentration
Concentration - = lower concentration

Look at all possibilities
24
Table of All Possibilities
Run #
T
C
Result
1
+
+
30%
2
+
-
40%
3
-
+
60%
4
-
-
50%
25
How Do We Analyze The Data?


Look at the deviation from the mean
Calculate row averages
26
For Our Example, Mean=45%
Run #
T
C
Deviation
1
+
+
-15%
2
+
-
-5%
3
-
+
+15%
4
-
-
+5%
27
Calculate Row Averages
Run #
T
C
Deviation
1
+
+
-15%
2
3
+
-
+
-5%
+15%
4
=+(-15%) =+(-15%)
+(-5%)
-(-5%)
-(+15%)
+(+15%)
-(+5%)
-(+5%)
=-40%
=0%
+5%
+5%
28
First Conclusion


Want temperature to be low
Cannot tell about concentration
29
Calculate Row Averages
Run #
T
C
Deviation
1
+
+
-15%
2
3
+
-
+
-5%
+15%
4
=+(-15%) =+(-15%)
+(-5%)
-(-5%)
-(+15%)
+(+15%)
-(+5%)
-(+5%)
=-40%
=0%
+5%
+5%
30
Is It True That We Do Not Care
About Concentration?
Run #
T
C
Deviation
1
+
+
-15%
2
+
-
-5%
3
-
+
+15%
4
-
-
+5%
Answer no: If the temperature is low, can improve
conversion by keeping the concentration high – it is
just that the opposite effect occurs when the
temperature is high
31
Lets Examine The Effect Of TC
(Simultaneous Variation of T+C)
Run #
T
C
TC
Deviation
1
+
+
+
-15%
2
+
-
-
-5%
3
-
+
-
+15%
4
-
-
+
+5%
-40%
0
-20
+5%
Want T – and TC 32
Can Extend Process To Several
Variables
Run
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
A
+
+
+
+
+
+
+
+
-
B
+
+
+
+
+
+
+
+
-
C
+
+
+
+
+
+
+
+
-
D
+
+
+
+
+
+
+
+
-
Gives too many runs
33
Software To Help

Concept: we usually want to fit the data
to a simple function:
Response=C1+C2A+C3B+…
Only need enough runs to fit constants
accurately
34
Echip Software Example
35
Software Setup
36
Number of Runs
Substantially Reduced


4 variables, 4 values with 3 replicates
gives (4)4 + 3*4 = 268 runs
Echip achieves almost the same accuracy
with 23 runs!
37
Summary


Single variables use ANOVA to check
models
Multivariable problems



Use design of experiments to see which
variables are important (2n) designs
Software can simplify runs
Use variances to fit models (automatic in
software)
38
Class Question

What did you learn new today?
39