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