ChE 452 Lecture 04Measuring Rate Data

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Objective

General concepts in measurement of rate data Compendium of methods (language) Direct vs indirect Design of experiments

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General Approach

Initiate reactionmeasure concentration vs timefit data to calculate rates

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Time, Hours

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Rate Measurements: An Old Topic

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Time, Hours

00.10.20.30.40.50.60.70.80.91

1.1

Co

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ntr

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Figure 3.1 Wilhelmy’s [1850] measurements of the changes in sucrose concentration in grape juice after acid is added.

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

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Batch Methods To Measure Reaction Rates

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Conventional 1) Mix reactants together in a batch reactor

2) Measure concentration versus time

10 sec or more

Stopped flow 1) Set of continuous-flow systems where reactants are fed into the reactor, and flow out again so quickly that there is negligible reaction

2) Stop the flow so that the reactants can react

3) Measure conversion versus time

10-1 sec or more

Temperature jump

1) Mix reactants at such a low temperature that the reaction rate is negligible

2) Use CO2 laser to suddenly heat reactants

3) Measure concentration vs time

10-6 sec or more

Table 3.1

Batch Methods Continued

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Shock tube 1) Put 10-1 atm of one reactant and 10 atm of helium on one side of a diaphragm

2) Put 10-3 atm of the other reactant on the other side of the diaphragm

3) Suddenly break the diaphragm so that the gas flows from the high-pressure side to the low-pressure side

4) Measure the reactant concentration vs time

10-3 to 10-5 sec

Flash photolysis

1) Put the reactants into a vessel under conditions where reaction is negligible

2) Pulse a laser or flash lamp to start reaction

3) Measure the reactant concentration vs time

10-9 to 10-1 sec

NMR 1) Initiate a change with a magnetic pulse

2) Measure the decay of spins with the NMR

10-2 to 10-9 sec

Flow Methods To Measure Reaction Rates

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Conventional flow system

1) Continuously feed reactants into a reactor – CSTR or plug flow

2) Measure the steady state reaction rate

10-3 sec or more

Molecular beam 1) Direct beams of reactants toward each other in a vacuum system

2) Measure the steady state reaction rate

10-13 to 10-9 sec

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?

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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.

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Example: Consider Arsine Doping Of Silicon

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To Pump

Feed

SiliconWafers

Holder(boat)

3-zone ovenPressure Gauge

Door(Loadlock)

Figure 3.6 A typical arsine decomposition reactor.

2AsH 2As 3H3 2

Direct Measurement

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P = P eAsH AsH0 k t

3 31

ExhaustFeed

Wafer

Microbalance

HeatLamp

Figure 3.7 A possible apparatus to examine the decomposition of arsine (AsH3) on silicon.

Indirect Measurement

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0 5 10 15 20 25 30 3510

100

Time, Hours

Pre

ssur

e, x

2, to

rr

Figure 3.8 Typical batch data for reaction(3.7). Data of Tamaru[1955].

A Comparison Of The Advantages And Disadvantages Of Direct And Indirect

Methods

Direct Method Advantages

• Get rate equation directly• Easy to fit data to a rate law• High confidence on final rate

equation

Disadvantages• Difficult experiment• Need many runs• Not suitable for very fast or

very slow reactions

Indirect MethodDisadvantages

• Must infer rate equation• Hard to analyze rate data• Low confidence on final

rate equation

Advantages• Easier experiment• Can do a few runs and

get important information• Suitable for all reactions

including very fast or very slow ones

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Other Notation

Direct method• differential method• differential reactor

Indirect method• integral method

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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

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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.

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Analysis Of Data From A Differential Reactor

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0.020

0.100

10 100

Oxygen Pressure (Torr)

Etc

h R

ate

(mic

rons

/min

)

Metallic Color

Oxide Color

Slope = 0.5

0.030

0.040

0.050

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0.080

0.010

General method – least squares with rate vs time data

Figure 3.10 The rate of copper etching as a function of the oxygen concentration. Data of Steger and Masel [1998].

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

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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?

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Usual Technique: Initial Rate Method

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•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

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

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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

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Example: How Does Temperature And Concentration Affect Selectivity Of A

Reaction Pick two values of each variable

Temperature + = higher temperatureTemperature - = lower temperatureConcentration + = higher concentrationConcentration - = lower concentration

Look at all possibilities

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Table of All Possibilities

Run # T C Result

1 + + 30%

2 + - 40%

3 - + 60%

4 - - 50%

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How Do We Analyze The Data?

Look at the deviation from the mean Calculate row averages

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For Our Example, Mean=45%

Run # T C Deviation

1 + + -15%

2 + - -5%

3 - + +15%

4 - - +5%

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Calculate Row Averages

Run # T C Deviation

1 + + -15%

2 + - -5%

3 - + +15%

4 - - +5%

=+(-15%) +(-

5%) -(+15%)-(+5%)=-40%

=+(-15%) -(-5%)

+(+15%)-(+5%)=0%

+5%

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First Conclusion

Want temperature to be low Cannot tell about concentration

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Calculate Row Averages

Run # T C Deviation

1 + + -15%

2 + - -5%

3 - + +15%

4 - - +5%

=+(-15%) +(-

5%) -(+15%)-(+5%)=-40%

=+(-15%) -(-5%)

+(+15%)-(+5%)=0%

+5%

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Is It True That We Do Not Care About Concentration?

Run # T C Deviation

1 + + -15%

2 + - -5%

3 - + +15%

4 - - +5%

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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

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%

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Want T – and TC -

Can Extend Process To Several Variables

Run A B C D1 + + + +2 + + + -3 + + - +4 + + - -5 + - + +6 + - + -7 + - - +8 + - - -9 - + + +

10 - + + -11 - + - +12 - + - -13 - - + +14 - - + -15 - - - +16 - - - -

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Gives too many runs

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

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Echip Software Example

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Software Setup

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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!

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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)

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Class Question

What did you learn new today?

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