1. Collection and Analysis of Rate Data

2. Determining the Rate Law
Example: Reaction of triphenyl methyl chloride (trityl) (A) and methanol (B)
A B  C D
was carried out in a solution of bezene and pyridine at 25OC. Pyridine reacts with HCl that then precipitates as pyridine hydrochloride thereby making the reaction irreversible.
The concentration-time data in Table was obtained as in a batch reactor
At t=0, CA = 0.05M)
Time (min 50
100
150
200
250
300
Concentration of A (mole/dm3) X 38
30.6
25.6
22.2
19.5
17.4

3. The initial concentration of methanol was 0.5 mole/dm3
Part (1): Determine the reaction with respect to triphenyll methyl chloride.
Part (2): In a separate set of reaction the reaction order wrt methanol was found to be first order. Determine the specific reaction constant

4. Solution
Part (1) Find the reaction order wrt trityl.
Step 1 Postulate rate law
Step 2 Process your data in terms of the measured variables, which in this case is CA
Step 3 Look for simplification. Concentration of methanol is 10 times the initial concentration of triphenyl methyl chloride, its concentration is essentially constant.
CB = CB0

5. Substituting CB in equation
Where
Step 4 Apply the CRE algorithm
Mole balance
Rate Law

6. V = V0 Stoichiometry: Liquid
Combine: mole balance, rate law and stoichiometry
Taking the natural log on both sides of equation

7. Slope of vs will yield reaction order a
Slope of vs will yield reaction order a with respect to triphenyl methyl chloride (A).
Step 5 Find as a function of CA from the concentration-time data.

8. could be find in three ways
Graphical Method
Finite Differential Method
Polynomial Method

9. Graphical Method t (min) CAx103 (mol/dm3) (mol/dm3 - min) 50 3.0 2.4050
3.0
2.40 38
1.86
1.48
100
30.6
1.20
1.00
150
25.6
0.80
0.68
200
22.2
0.50
0.54
250
19.5
0.47
0.42
300
17.4

10. Graphical Method
The derivative –dCA/dt is determined by calculating and plotting (-DCA/Dt) as a function of time, t, and using differential technique (Appendix A.2) to determine (-dCA/dt) as a function of CA.

11. Graphical Method
First calculate the ratio (-DCA/Dt) from the first two columns of the Table.
The result is written the third column
Next plot the third column as a function of first column. i.e., (-DCA/Dt) versus t.
Using the equal-area differentiation, the value of (-dCA/dt) is read off the figure. The value is put in the fourth column of the Table.

12. Graphical Method

13. Graphical Method

14. Finite Difference Method

15. Summary Table
Graphical
Finite Difference
t (min)
(mol/dm3-min)
(mol/dm3)
3.0
2.86 50
1.86
1.94 38
100
1.20
1.24
30.6
150
0.80
0.84
25.6
200
0.68
0.61
22.2
250
0.54
0.48
19.5
300
0.42
0.36
17.4

16. Plot column 2 and 3 ( ) as a function of column 4
(CA X 1,000) on log scale.
We could substitute parameter values into Excel to find  and k’.

17. To evaluate k’ we can derivative and CAP=0.5X10-3 mol/dm3, which is
Then

18. Excel Plot

19. Excel Plot Graphical method Slope = 2.05 Finite Difference Method
The reaction is consider as Second order