1. Lecture 11 Thursday 2/7/08 Determining the Rate Law from Experimental Data Integral Method Graphical Method Nonlinear Least Regression Multiple Reactions The Four Types What’s New to Our Algorithm Reactions in Series

20. Levenspiel Plot

21. Two steps to get Step 1: Rate Law Step 2: Stoichiometry Step 3: Combine to get

26. Finding Rate Laws, Multiple Reactions Slope = α CACA dC A /dt ln t(min)0123 C A (mol/L)10.70.50.35 0.30.20.15 Find the f(t) of using equal area differentiation.1.2.3 t 123 Areas equal for both sides of the histogram CACA 10.70.50.35 -dC A /dt0.350.250.1750.12 Plot –dC A /dt as a function of C A α = slope ln CACA Slope = α dC A /dt

27. Regression Method C meas 10.70.50.35 C Calc 10.50.330.25 (C c -C m )0-0.2-0.17-0.10 (C c -C m ) 2 00.040.0290.01 Guess values for α and k and solve for measured data points then sum squared differences for α = 2, k = 1 → S 2 = 0.079 for α = 2, k = 2 → S 2 = 0.27 etc. until S 2 is a minimum

28. 4 Types of Multiple Reactions Series: A → B → C Parallel: A → D, A → U Independent: A → B, C → D Complex: A + B →C + D, A + C → E With multiple reactors, either molar flow or number of moles must be used (no conversion!) FlowBatch Rates: rate law for each reaction net rates: the sum of rates for each reaction given

29. example: 1) A + B → C + D-r 1A = k 1A C A C B -r 2A = k 1A C A C C 2) A + B → Eetc…. relative rates: only applied to a given reaction Stoich: example: A → B → C (1) A → B k 1 (2) B → C k 2 1) mole balance:2) rates: V=V 0 (constant batch) laws net rates