ERT 316 REACTION ENGINEERING

CHAPTER 5: COLLECTION AND ANALYSIS OF RATE DATA

BY

ANIS ATIKAH AHMAD

OBJECTIVE

to obtain the rate law for a specific reaction from data collected in experiment (eg: concentration-time for batch)

BAA CCr 224.0

To find specific rxn rate constant,

k

To find reaction order

BASIC STEPS IN ANALYSIS OF RATE DATA

ALGORITHM FOR DATA ANALYSISIf 1 of the reactant is in excess, assume its

concentration is constant.

BATCH REACTOR DATA

1. Differential method

BATCH REACTOR DATA

1. Determine α

2. Determine β

AA

AA CC

rk

3. Determine

kA :

BATCH REACTOR DATA

How to find since we only have data of

concentration and time?

3 Methods:

dt

dCA

Time (min)

0 50 100 150

CA

(mol/dm3)0.05 0.038 0.0306 0.0256

Graphical differentiation

Numerical differentiation formulas

Polynomial fit

GRAPHICAL DIFFERENTIATION

Plot a histogram

Draw a smooth curve in such a way that:

A = BA + C = B + D

dt

dCA

NUMERICAL DIFFERENTIATION FORMULAS

POLYNOMIAL FIT

Fit the concentration-time data to an nth-order polynomial:

Find best value of ai

Differentiate Eq 1 wrt time:

nnA tatataaC ...2

210 Eq 1

12321 ...32 n

nA tnatataa

dt

dC

BATCH REACTOR DATA

2. Integral method (linear plot)

Trial & error to find reaction order. If the order is correct, the plot should be linear

BATCH REACTOR DATA

2. Integral method (linear plot)

BATCH REACTOR DATA

3. Non-linear regressionWe want to find the parameter values (α,k) for which the sum of the squares of the differences, the measured rate (rm), and the calculated rate (rc) is a minimum.For conc-time data, we can integrate the mole balance equation to obtain:

2

1

1/110

2

1

2 1

N

iiAAmi

N

iAciAmi ktCCCCs

METHOD OF INITIAL RATES

CA0 (mol/dm3)

-rA (mol/dm3.)s

Determine –rA0

first

METHOD OF HALF-LIVES