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
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
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
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