1. Collection and Analysis of Rate Data
Dr. AKM Shafiqul Islam

2. Types of Chemical Reactions
Two types of reaction for rate data
The Batch reactor, which is used primarily for homogenous reaction
The Differential reactor, which is used for solid-fluid heterogeneous reactions

3. Batch Reaction
In Batch reaction experiments, concentration, pressure, and or volume are usually measured and recorded at the different times during the course of reaction.
Measurements on the differential reactor are made during steady-state operation. The product concentrations are monitored for different sets of feed conditions

4. Rate law A B rA = the rate of formation of species A per unit volume
-rA = the rate of a disappearance of species A per unit volume
rB = the rate of formation of species B per unit volume

5. Example, A  B
If B is being created at a rate of 0.2 moles per decimeter cubed per second, i.e., the rate of formation of B is, rB = 0.2 mole/dm3/s
Then A is disappearing at the same rate: -rA = 0.2 mole/dm3/s the rate of formation of A is rA = -0.2 mole/dm3/s

6. Power Law Model & Elementary Rate Laws
The dependence of reaction rate, -rA on the concentration of the species present fn(Cj)
The order of a reaction refers to the powers to which the concentrations are raised in the kinetic rate law
Here a order with respect to reactant A and b order with respect to reactant B

7. Steps in Analyzing Rate Data
Postulate a rate law
Power law models for homogenous reactions
Langmuir-Hinshelwood models or heterogeneous reactions

8. Select reactor type and corresponding mole balance
If batch reactor use mole balance on Reactant A
TE5-1.1
If different PBR use mole balance on product P (AP)
TE5-1.2

9. Process your data in terms of measured variable (e.g., NA, CA or PA)
If possible write your mole balance in terms of the measured variable
Look for simplifications
For example, if one of the reactant is excess, assume its concentration is constant. If the gas phase mole fraction of reactant is small, set e0

10. For a batch reactor, calculate –rA as function of concentration CA to determine reaction order
Differential analysis
Combine the mole balance and power law model
(TE5-1.3)
(TE5-1.4)

11. taking the natural log (TE5-1.5) Find from CA versus t data by
Graphical method
Finite differential method
Polynominal
Plot vs dt and find reaction order a which
Find k

12. For the combined mole balance and rate law is
Integral method
For the combined mole balance and rate law is
(TE5-1.4)
Guess a and integrate equation
Nonlinear regression (Polymath)
Integrate equation (TES5-1.4) to obtain
(TE5-1.6)

13. For differential PBR calculate as a function of and
Calculate as a function of reactant concentration
Choose model, e.g.,
Use nonlinear regression to find the best model and model parameters
Analyze the rate model for “goodness of fit”.

14. Batch Reactor Data
Batch reactors are used primarily to determine rate law parameters for homogeneous reactions
Determination is achieved by measuring concentration as a function of time
Use differential, integral and nonlinear regression method of data analysis to determine reaction order, a and specific reaction rate constant, k

15. if reaction is irreversible, it is possible to determine reaction order a and the specific rate constant by either nonlinear regression or numerically differentiating concentration vs time data
Example, for the decomposition reaction
A  Products
The differential method may be used

16. It is possible to determine the relationship between and the concentration of other reactants
For irreversible reaction
A + B  Products
with the rate law
Where a and b are both unknown, the reaction could first be run in an excess of B so that CB remains essentially unchanged during the course of the reaction

17. Where
After determining a, the reaction is carried out in excess of A, for which the rate law is approximated as

18. Once a and b are determined, kA can be calculated from the measurement of –rA at known concetration of A and B
Both a and b can be determined by using method of excess, coupled with a differential analysis of data for batch system

19. Differential Method of Analysis
Consider a reaction carried out isothermally in a constant-volume batch reactor and concentration recorded as a function of time. By combining the mole
After taking natural log on both side of the equation

20. The reaction order can be found from a ln-ln plot ofvs

21. Three Ways to Determine (-dCA/dt) from Concentration-Time Data
Graphical differentiation
Numerical differentiation
Differentiation of a Polynomial fit to the data

22. Graphical Method
The graphical method involves plotting –DCA/Dn as a function of t and then using equal-area differentiation to obtain –dCA/dt.

23. concentration (mol/dm3)
Numerical differentiation
Numerical differentiation formulas can be used when the data points in the independent variables are equally spread, such as t1 – t0 = t2 – t1 = Dt
time (s) t1 t2 t3
concentration (mol/dm3)
CAo
CA1
CA2
CA3

24. The three-point differentiation formulas
Initial point:
Interior points:
Last point:

25. Polynomial Fit
Another technique to differentiate the data is to first fit the concentration-time data to the nth-order polynomial:
CA = ao + a1t + a2t2 + a3t3 +a4t4
Many software package program that will calculate best values for the constants ai only by entering concentration-time data

26. After determining the constants, ai, the differentiate equation with respect to time can get
The concentration and the time rate of change of concentration are both known at any time t