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Lecture 11

Lecture 11. Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place. Today’s lecture. Determining the Rate Law from Experimental Data Integral Method Differential (Graphical) Method

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Lecture 11

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  1. Lecture 11 Chemical Reaction Engineering (CRE) is the field that studies the rates and mechanisms of chemical reactions and the design of the reactors in which they take place.

  2. Today’slecture • Determining the Rate Law from Experimental Data • Integral Method • Differential (Graphical) Method • Nonlinear Least Regression • Multiple Reactions • The Four Types • What’s New to Our Algorithm • Reactions in Series

  3. Integral Method A  Products MoleBalance: Rate Law: Stochiometry: Combine: Consider the followingreaction that occurs in a constantvolumeBatchReactor: (Wewillwithdrawsamples and record the concentration of A as a function of time.)

  4. Finallyweshouldalsouse the formula to plotreaction rate data in terms of conversion vs. time for 0, 1st and 2nd order reactions. Derivation Equationsused to Plot 0, 1st and 2nd order reactions. Thesetypes of plots are usuallyused to determine the values k for runs at varioustemperatures and thenused to determine the activationenergy.

  5. Finding the Rate law (Integral Method) Guess and check for α = 0, 1, 2 and check against experimental plot CA 1/CA ln(CA0/CA) t t t

  6. Differential Method Taking the natural log of The reaction order can be found from a ln-ln plot of: ln Slope = α ln

  7. Methods for finding the slope of log-log and semi-log graph papers may be found at http://www.physics.uoguelph.ca/tutorials/GLP/. However, we are usually given concentration as a function of time from batch reactor experiments:

  8. Three Ways to determine (-dCA/dt) from Concentration-Time Data • Graphical differentiation • Numerical differentiation formulas • Differentiation of a polynomial fit to the data 1. Graphical

  9. The methodaccentuatesmeasurementerror!

  10. Example - Finding Rate Law Areas equal for both sides of the histogram .3 .2 .1 t 1 2 3

  11. Example - Finding Rate Law Find the f(t) of using equal area differentiation Plot –dCA/dt as a function of CA ln dCA/dt ln Slope = α CA

  12. Non-LinearLeast-SquareAnalysis We want to find the parameter values (α, k, E) for which the sum of the squares of the differences, the measured rate (rm), and the calculated rate (rc) is a minimum. That is wewant to be a minimum.

  13. Non-LinearLeast-SquareAnalysis For concentration-time data, we can integrate the mole balance equation for to obtain

  14. Non-LinearLeast-SquareAnalysis Wefind the values of alpha and k whichminimize s2

  15. Regression Method Guess values forα and k and solve for measured data points then sum squared differences: for α= 2, k = 1 → S2 = 0.07 for α = 2, k = 2 → S2 = 0.27 etc. until S2 is a minimum

  16. Residuals

  17. End of Lecture 11

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