Collection and Analysis Collection and Analysis of Rate Dataof Rate Data

Determining the Rate LawDetermining the Rate Law Example: Reaction of triphenyl methyl chloride (trityl) (A) and Example: Reaction of triphenyl methyl chloride (trityl) (A) and

methanol (B)methanol (B)

A + B A + B C + D C + D

was carried out in a solution of bezene and pyridine at 25was carried out in a solution of bezene and pyridine at 25OOC. Pyridine C. Pyridine reacts with HCl that then precipitates as pyridine hydrochloride reacts with HCl that then precipitates as pyridine hydrochloride thereby making the reaction irreversible.thereby making the reaction irreversible.

The concentration-time data in Table was obtained as in a batch The concentration-time data in Table was obtained as in a batch reactorreactor

At t=0, CAt t=0, CAA = 0.05M) = 0.05M)

(C6H5)3CCl + CH3OH (C6H5)CCH3 + HCl

O

Time (minTime (min 00 5050 100100 150150 200200 250250 300300

Concentration of A Concentration of A (mole/dm3) X (mole/dm3) X

5050 3838 30.630.6 25.625.6 22.222.2 19.519.5 17.417.4

The initial concentration of methanol was 0.5 mole/dmThe initial concentration of methanol was 0.5 mole/dm33

Part (1):Part (1): Determine the reaction with respect to triphenyll Determine the reaction with respect to triphenyll methyl chloride. methyl chloride.

Part (2):Part (2): In a separate set of reaction the reaction order In a separate set of reaction the reaction order wrt wrt methanol was found to be first order. Determine methanol was found to be first order. Determine

the specific reaction constantthe specific reaction constant

SolutionSolutionPart (1)Part (1) Find the reaction order wrt trityl.Find the reaction order wrt trityl.

Step 1Step 1 Postulate rate law Postulate rate law

Step 2Step 2 Process your data in terms of the measured Process your data in terms of the measured variables, which in this case is variables, which in this case is CA

Step 3Step 3 Look for simplification. Concentration of Look for simplification. Concentration of methanol is methanol is 10 times the initial concentration of triphenyl 10 times the initial concentration of triphenyl

methyl chloride, its concentration is essentially methyl chloride, its concentration is essentially constant.constant.

CB = CB0

BAA CkCr

Substituting CSubstituting CBB in equation in equation

Where Where

Step 4Step 4 Apply the CRE algorithmApply the CRE algorithm

Mole balanceMole balance

Rate LawRate Law

AA Ckr

0BkCk

Vrdt

dNA

A

AA Ckr

Stoichiometry: LiquidStoichiometry: Liquid

V = V0

Combine: mole balance, rate law and stoichiometry

Taking the natural log on both sides of equation

0V

NC AA

A

A Ckdt

dC

AA Ck

dt

dClnlnln

Slope of Slope of vsvs will yield reaction order will yield reaction order with respect to triphenyl methyl chloride (A).with respect to triphenyl methyl chloride (A).

Step 5Step 5 Find as a function of Find as a function of CA from the from the concentration-time data.concentration-time data.

dt

dCAln ACln

dt

dCA

could be find in three wayscould be find in three ways

a)a) Graphical MethodGraphical Method

b)b) Finite Differential MethodFinite Differential Method

c)c) Polynomial MethodPolynomial Method

dt

dCA

Graphical MethodGraphical Method

t (min)t (min) CCAAx10x1033 (mol/dm (mol/dm33)) (mol/dm3 - min)(mol/dm3 - min) (mol/dm3 - min)(mol/dm3 - min)

00 5050 3.03.0

2.402.40

5050 3838 1.861.86

1.481.48

100100 30.630.6 1.201.20

1.001.00

150150 25.625.6 0.800.80

0.680.68

200200 22.222.2 0.500.50

0.540.54

250250 19.519.5 0.470.47

0.420.42

300300 17.417.4

410

t

CA 410dt

dCA

Graphical MethodGraphical Method

The derivative The derivative –dCA/dt is determined by calculating is determined by calculating and plotting (and plotting (-CA/t) as a function of time, ) as a function of time, t, and , and

using differential technique (Appendix A.2) to using differential technique (Appendix A.2) to determine (determine (-dCA/dt) as a function of ) as a function of CA..

.minmol/dm104.21024.0

10050

5038

343

3

12

12

tt

CC

t

C AAA

Graphical MethodGraphical Method

First calculate the ratio (First calculate the ratio (-CA/t) from the first two columns ) from the first two columns of the Table. of the Table.

The result is written the third columnThe result is written the third column

Next plot the third column as a function of first column. i.e., Next plot the third column as a function of first column. i.e., ((-CA/t) versus ) versus t..

Using the equal-area differentiation, the value of (Using the equal-area differentiation, the value of (-dCA/dt) is ) is read off the figure. The value is put in the fourth column of read off the figure. The value is put in the fourth column of the Table.the Table.

Graphical MethodGraphical Method

Graphical MethodGraphical Method

0

0.5

1

1.5

2

2.5

3

3.5

4

0 50 100 150 200 250 300 350

dt

dCA410

t

CA

410

mindm

mol3

mint

Finite Difference MethodFinite Difference Method

t=0

t=50

t

CCC

dt

dC AAA

t

A

2

43 210

0

.minmol/dm1086.2

100

106.30384503

34

3

/minmol/dm1086.2 34dt

dCA

100

10506.30

2

302

1

t

CC

dt

dC AA

t

A

/minmol/dm1094.1 34

Summary TableSummary TableGraphicalGraphical Finite DifferenceFinite Difference

t (min)t (min) (mol/dm(mol/dm33-min)-min) (mol/dm(mol/dm33-min)-min) (mol/dm(mol/dm33))

00 3.03.0 2.862.86 5050

5050 1.861.86 1.941.94 3838

100100 1.201.20 1.241.24 30.630.6

150150 0.800.80 0.840.84 25.625.6

200200 0.680.68 0.610.61 22.222.2

250250 0.540.54 0.480.48 19.519.5

300300 0.420.42 0.360.36 17.417.4

410dt

dCA 410dt

dCA 000,1AC

Plot column 2 and 3 ( ) as a function of column 4 Plot column 2 and 3 ( ) as a function of column 4

((CA X 1,000) on log scale.) on log scale.

We could substitute parameter values into Excel to find We could substitute parameter values into Excel to find and and ’.

410dt

dCA

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

Then

min.mol/dm105.0 34

P

A

dt

dC

2AP

P

A

C

dtdC

k

min/mol.dm125.0mol/dm1020

min.mol/dm105.0 333

34

Excel PlotExcel Plot

0.1

1

10

10 100

99.10013.0 AA C

dt

dC

410

dt

dCA

.mindm

mol3

34 mol/dm10C A

Excel PlotExcel Plot

Graphical methodGraphical method

Slope = 2.05Slope = 2.05 Finite Difference MethodFinite Difference Method

Slope = 1.996Slope = 1.996

The reaction is consider as The reaction is consider as Second order