1. ERT 316 R EACTION E NGINEERING C HAPTER 5: C OLLECTION AND A NALYSIS OF R ATE D ATA BY ANIS ATIKAH AHMAD

2. O BJECTIVE to obtain the rate law for a specific reaction from data collected in experiment (eg: concentration- time for batch) To find specific rxn rate constant, k To find reaction order

3. B ASIC S TEPS IN ANALYSIS OF RATE DATA

4. A LGORITHM FOR DATA ANALYSIS If 1 of the reactant is in excess, assume its concentration is constant.

5. B ATCH R EACTOR D ATA 1. Differential method

6. B ATCH R EACTOR D ATA 1. Determine α 2. Determine β 3. Determine k A :

7. B ATCH R EACTOR D ATA How to find since we only have data of concentration and time? 3 Methods: Time (min) 050100150 C A (mol/dm 3 ) 0.050.0380.03060.0256 Graphical differentiationNumerical differentiation formulasPolynomial fit

8. G RAPHICAL D IFFERENTIATION Plot a histogram

9. Draw a smooth curve in such a way that: A = B A + C = B + D

10. N UMERICAL DIFFERENTIATION FORMULAS

11. P OLYNOMIAL FIT Fit the concentration-time data to an n th-order polynomial: Find best value of a i Differentiate Eq 1 wrt time: Eq 1

12. B ATCH R EACTOR D ATA 2. Integral method (linear plot) Trial & error to find reaction order. If the order is correct, the plot should be linear

13. B ATCH R EACTOR D ATA 2. Integral method (linear plot)

14. B ATCH R EACTOR D ATA 3. Non-linear regression We want to find the parameter values (α, k ) for which the sum of the squares of the differences, the measured rate ( r m ), and the calculated rate ( r c ) is a minimum. For conc-time data, we can integrate the mole balance equation to obtain:

15. METHOD OF INITIAL RATES C A0 (mol/dm 3 ) -r A (mol/dm 3.)s Determine –r A0 first

16. METHOD OF HALF-LIVES

17. E XAMPLE 5-1 The reaction of triphenyl methyl chloride (trityl) (A) and methanol (B) Trityl (A) + Methanol (B)  Products was carried out in a solution of benzene & pyridine at 25°C. Pyridine reacts with HCl that then precipitates as pyridine hydrochloride thereby making the reaction irreversible. The concentration-time data in table below was obtained in a batch reactor: The initial concentration of methanol was 0.5 mol/dm 3 i. Determine the reaction order with respect to triphenyl methyl chloride. Time (min)050100150200250300 C A (mol/dm 3 ) 0.050.0380.03060.02560.02220.01950.0174 (At t = 0, C A = 0.05 M

18. E XAMPLE 5-1- SOLUTION STEP 1 Postulate a rate law. STEP 2 Select reactor type & corresponding mole balance. Batch reactor Since it is a liquid phase reaction, V = V 0 STEP 3 Process your data in terms of measured variable (in this case: C A ).

19. E XAMPLE 5-1- SOLUTION STEP 4 Look for simplication. Because the concentration of methanol is 10 times the initial concentration of trityl (excess), its concentration is essentially constant. STEP 5 Determine the reaction order. Taking the natural log; The slope

20. F IND t (min)C A (mol/dm 3 )(mol/dm 3.min) 00.05 2.4 3.0 500.038 1.48 1.86 1000.0306 1.00 1.2 1500.0256 0.68 0.8 2000.0222 0.54 0.5 2500.0195 0.42 0.47 3000.0174 GIVEN! (1) (2) From histogram/finite difference method/polynomial

21. G RAPHICAL D IFFERENTIATION 0.5 1 1.5 2 2.5 3

22. P LOT Slope= order of reaction ( α )

23. F IND K ’ Substitute the value of into eg,; C A = 22.2 x 10 -3 mol/dm 3, k’ = 0.125 dm 3 /mol.min