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

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

B ASIC S TEPS IN ANALYSIS OF RATE DATA

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

B ATCH R EACTOR D ATA 1. Differential method

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

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

G RAPHICAL D IFFERENTIATION Plot a histogram

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

N UMERICAL DIFFERENTIATION FORMULAS

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

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

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

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:

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

METHOD OF HALF-LIVES

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) C A (mol/dm 3 ) (At t = 0, C A = 0.05 M

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 ).

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

F IND t (min)C A (mol/dm 3 )(mol/dm 3.min) GIVEN! (1) (2) From histogram/finite difference method/polynomial

G RAPHICAL D IFFERENTIATION

P LOT Slope= order of reaction ( α )

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