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ERT 316 R EACTION E NGINEERING C HAPTER 5: C OLLECTION AND A NALYSIS OF R ATE D ATA BY ANIS ATIKAH AHMAD
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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
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B ASIC S TEPS IN ANALYSIS OF RATE DATA
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A LGORITHM FOR DATA ANALYSIS If 1 of the reactant is in excess, assume its concentration is constant.
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B ATCH R EACTOR D ATA 1. Differential method
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B ATCH R EACTOR D ATA 1. Determine α 2. Determine β 3. Determine k A :
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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
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G RAPHICAL D IFFERENTIATION Plot a histogram
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Draw a smooth curve in such a way that: A = B A + C = B + D
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N UMERICAL DIFFERENTIATION FORMULAS
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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
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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
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B ATCH R EACTOR D ATA 2. Integral method (linear plot)
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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:
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METHOD OF INITIAL RATES C A0 (mol/dm 3 ) -r A (mol/dm 3.)s Determine –r A0 first
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METHOD OF HALF-LIVES
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