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 3

Rate Measurements: An Old Topic 4 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 5

Batch Methods To Measure Reaction Rates 6 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 sec or more Temperature jump 1) Mix reactants at such a low temperature that the reaction rate is negligible 2) Use CO 2 laser to suddenly heat reactants 3) Measure concentration vs time sec or more Table 3.1

Batch Methods Continued 7 Shock tube 1) Put atm of one reactant and 10 atm of helium on one side of a diaphragm 2) Put 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 to 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 to sec NMR 1) Initiate a change with a magnetic pulse 2) Measure the decay of spins with the NMR to sec

Flow Methods To Measure Reaction Rates 8 Conventional flow system 1) Continuously feed reactants into a reactor – CSTR or plug flow 2) Measure the steady state reaction rate sec or more Molecular beam 1) Direct beams of reactants toward each other in a vacuum system 2) Measure the steady state reaction rate to 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? 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 11 Figure 3.6 A typical arsine decomposition reactor.

Direct Measurement 12 Figure 3.7 A possible apparatus to examine the decomposition of arsine (AsH 3 ) on silicon.

Indirect Measurement 13 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 Method Disadvantages 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 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

Analysis Of Data From A Differential Reactor 18 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 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 21 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 22

Design Of Experiments To Determine Which Variables Are Important 2 n 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 #TCResult 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 #TCDeviation % 2+--5% % 4--+5% 27

Calculate Row Averages Run #TCDeviation % 2+--5% % 4--+5% =+(-15%) +(-5%) -(+15%) -(+5%) =-40% =+(-15%) -(-5%) +(+15%) -(+5%) =0% +5% 28

First Conclusion Want temperature to be low Cannot tell about concentration 29

Calculate Row Averages Run #TCDeviation % 2+--5% % 4--+5% =+(-15%) +(-5%) -(+15%) -(+5%) =-40% =+(-15%) -(-5%) +(+15%) -(+5%) =0% +5% 30

Is It True That We Do Not Care About Concentration? Run #TCDeviation % 2+--5% % 4--+5% 31 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 #TCTCDeviation % % % % -40%0-20+5% 32 Want T – and TC -

Can Extend Process To Several Variables RunABCD Gives too many runs

Software To Help Concept: we usually want to fit the data to a simple function: Response=C 1 +C 2 A+C 3 B+… 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 (2 n ) designs Software can simplify runs Use variances to fit models (automatic in software) 38

Class Question What did you learn new today? 39