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Collection & Analysis of Rate Data

Dicky Dermawanwww.dickydermawan.net78.net

dickydermawan@gmail.com

ITK-329 Kinetika & Katalisis

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Types of Reactors for obtaining Rate Data

Batch, primarily for homogeneous reactions:Measured: C(t), P((t) and/or V(t)

Unsteady-state operation

Differential reactor, for heterogeneous reactionsMeasured: Product concentration @ different

feed condition Steady-state operation

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Methods for Analyzing Rate Data

Differential Method Integral Method Half-lives Method Method of Initial Rates Linear and Nonlinear Regression (Least-

Square Analysis

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Differential Method

Applicable when reaction condition are such that the rate is essentially a function of the concentration of only one reactant

Can be used coupled with method of excess

Outline of the procedure: combining the definition of rate reaction with the assumed

AA Ckr- productA

BAA CCkr- productBA

dt

)V/N(d

dt

dN

V

1r AAA

dt

dCr AA

AA Ckr- AA

AA

Cln)kln(dt

dCln

Ckdt

dC

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Determining The Derivative

Graphical Differentiation

Differentiation of a polynomial fit to the data

Numerical differentiation

y = 0.4781x - 1.5944R2 = 0.9974

-3

-3

-2

-2

-1

-1

0

-3 -2 -1 0 1 2

ln CA

ln (

-DC

A/D

t)

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Graphical Differential

-

0.05

0.10

0.15

0.20

0.25

0.30

0.35

0.40

0.45

0.50

0 5 10 15 20

t, menit

- d

C A/d

t

1nn

1n,An,An

1n

A

tt

CC

dt

dC

t, min CA, mol/L

0 4.00 3 2.89 5 2.25 8 1.45 10 1.00 12 0.65 15 0.25

17.5 0.07

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Differentiation of a Polynomial Fit to The Data

y = 0.01x2 - 0.3992x + 3.999R2 = 1

-

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

4.50

0 5 10 15 20

t, min

CA

, m

ol/L

399,0t02,0dt

dC

999,3t399,0t01,0C

A

2A

Thus….

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Numerical Method

t, min CA, mol/L

0 4.00 3 2.89 5 2.25 8 1.45 10 1.00 12 0.65 15 0.25

17.5 0.07

t2

C3C4C

dt

dC point Last

t2

CC

dt

dCpoint t Intermedia

t2

CC4C3-

dt

dC point Initial

5A4AA3

t

A

)1i(A1)A(i

t

A

2A1AA0

t

A

5

i

0

D

D

D

Only applicable for uniform sampling interval

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Example: P5-3A1

The irreversible isomerizationA B

was carried out in a batch reactor and the following concentration – time data were obtained.

Determine the reaction order and the specific reaction rate k using differential method

Check the goodness of the fit.

t, min CA, mol/L

0 4.00 3 2.89 5 2.25 8 1.45 10 1.00 12 0.65 15 0.25

17.5 0.07

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Example: P5-51

The reaction

A B + C

was carried out in a constant-volume batch reactor where the following concentration – time measurements were recorded as a function of time.

Determine the reaction order and the specific reaction rate k using differential method

Check the goodness of the fit.

t, min CA, mol/L

0 2.00 5 1.60 9 1.35 15 1.10 22 0.87 30 0.70 40 0.53 60 0.35

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Integral Method

Most often used when the reaction order is known

Outline of the procedure:– Guess the reaction order, then integral data

the combining differential concentration-time equation; find the appropriate linear plot

– (Essen’s Method) If the assumed rate law is correct, the plot should be linear; otherwise assume other rate equation and repeat the procedure

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Intagral Metode of van’t Hoff

Pada aplikasi metode integral oleh Essen, tidak dibuat kurva dari hasil integrasi, melainkan………

Dihitung harga k dari setiap data point; bila hasilnya kira-kira konstan, maka dapat disimpulkan bahwa orde reaksi yang dipostulasikan sudah tepat.

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Example: P5-3A2

The irreversible isomerizationA B

was carried out in a batch reactor and the following concentration – time data were obtained.

Determine the reaction order and the specific reaction rate k using integral method

Check the goodness of the fit.

t, min CA, mol/L

0 4.00 3 2.89 5 2.25 8 1.45 10 1.00 12 0.65 15 0.25

17.5 0.07

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Example: P5-52

The reaction

A B + C

was carried out in a constant-volume batch reactor where the following concentration – time measurements were recorded as a function of time.

Determine the reaction order and the specific reaction rate k using integral method

Check the goodness of the fit.

t, min CA, mol/L

0 2.00 5 1.60 9 1.35 15 1.10 22 0.87 30 0.70 40 0.53 60 0.35

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Process your data in terms of measured variable

Look for simplifications!

Unfortunately,The problem is not that easy….

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L3-14Constant Volume Batch Reactor

A small reaction bomb fitted with a sensitive pressure-measuring device is flushed out at 25oC, a temperature low enough that the reaction does not proceed to any appreciable extent. The temperature is then raised as rapidly as possible to 100oC by plunging the bomb into boiling water, and the readings in Table P14 are obtained.

The stoichiometry of the reaction is2 A B

After leaving the bomb in the bath over the weekend the contents are analyzed for A; none can be found.

Find a rate equation in units of moles, liters, and minutes which will satisfactorily fit the data.

t, min P, atm1 1.1402 1.0403 0.9824 0.9405 0.9056 0.8707 0.8508 0.8329 0.815

10 0.80015 0.75420 0.728

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L3-19Constant Volume Batch Reactor with Inert in the Reactant

A small reaction bomb fitted with a sensitive pressure-measuring device is flushed out & filled with a mixture of 76.94% reactant A and 23.06% inert at 1-atm pressure at 14oC, a temperature low enough that the reaction does not proceed to any appreciable extent. The temperature is then raised as rapidly as possible to 100oC, and the readings in Table P19 are obtained.

The stoichiometry of the reaction isA 2 R

After sufficient time the reaction proceeds to completion.

Find a rate equation in units of moles, liters, and minutes which will satisfactorily fit the data.

t, min P, atm0.5 1.5001.0 1.6501.5 1.7602.0 1.8402.5 1.9003.0 1.9503.5 1.9904.0 2.0255.0 2.0806.0 2.1207.0 2.1508.0 2.175

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L5-18Constant Pressure Batch Reactor

The homogeneous gas reaction:

A 2 Bis run at 100oC at a

constant pressure of 1 atm in an experimental batch reactor.

The data in Table P18 were obtained starting with pure A.

Find the rate equation.

t, min V/V0, atm

0 1.0001 1.2002 1.3503 1.4804 1.5805 1.6606 1.7207 7.7808 1.8209 1.86010 1.88011 1.91012 1.92013 1.94014 1.950

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Quiz 1Basic Concept

Selasa, 10 Oktober 2006

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Half-lives Method@ t = t1/2 NA = ½ NA0

@ V = V0 CA = ½ CA0

2/10A

0A

t

0

C2/1

CAAAAA

A dtkdCCdtkdCCCkdt

dC

2/1

10A

10A

2/1

C2/1

C

1A tk

1

CC2/1)0t(k

1

C0A

0A

2/1

10A

1

2/1

10A

10A

1

tk1

C12tk

1

CC2

2/11

0A

1

tC1k

12

0A

1

2/1 Cln)1(1k

12lntln

5

7

9

11

13

15

17

200 250 300 350

ln CA0

ln t

1/2

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L3-8 Half-lives Method

Find the overall order of the reaction:

2 H2 + 2 NO N2 + 2 H2OFrom the following constant-volume data using

equimolar amounts of hydrogen and nitric oxide:

Initial Total Pressure, mmHg 200 240 280 320 360Half-life, sec 265 186 115 104 67

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U2-Half-lives Method

The thermal decomposition of nitrous oxide (N2O) in the gas phase at 1030 K is studied in a constant-volume vessel at various initial pressures of N2O. The half-life data so obtained are as follows:

p0, mmHg 52,5 139 290 360 t½ , s 860 470 255 212

Determine a rate equation that fits these data

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L3-29 Half-lives Method

Determine the complete rate equation in units of moles, liters, and seconds for the thermal decomposition of tetrahydrofuran from the half-life data in Table P29

Initial Total Pressure, mmHg Half-life, sec Temp. oC214 14.5 569204 67 530280 17.3 560130 39 550206 47 539

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Method of Initial Rates

Reversible reaction, viz. A BIf follows simple order rate law:

Data analysis should take into account the influence of the reverse reaction.

However……This is not the case at the initial moment when

we start the experiment with only A or B

BBAAA CkCkr

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H3-7. Metode laju awal

Data laju awal, , berikut ini dilaporkan untuk reaksi fasa gas antara diborana dengan aseton pada suhu 114oC:

B2H6 + 4 Me2CO 2(Me2CHO)2BH

Bila dipostulasikan persamaan laju reaksi berbentuk

tentukan n, m, dan k.

Tekanan awal (torr) Tempuhan

B2H6 Me2CO Laju awal x1000,

torr/sec 1 6,0 20,0 0,5 2 8,0 20,0 0,63 3 10,0 20,0 0,83 4 12,0 20,0 1,00 5 16,0 20,0 1,28 6 10,0 10,0 0,33 7 10,0 20,0 0,80 8 10,0 40,0 1,50 9 10,0 60,0 2,21

10 10,0 100,0 3,33

nmCO2Me6H2B

PPkLaju

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Fitting Data from Differential Reactors

Using very small catalyst weight W & large volumetric flow rates 0

Low conversion X CA ~ CA0

W'rFF AA0A W

FF'r A0A

A

W

XF'r 0A

A

W

F'r

P

AP

A

W

C'r P0

AP

A

)C(f'r 0AA

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Fitting Data from Differential Reactors: Example 5-4

Run PCO, atm PH2, atm CCH4, mol/L

1 1.00 1.0 2.44 x 10-4

2 1.80 1.0 4.40 x 10-4

3 4.08 1.0 10.0 x 10-4

4 1.00 0.1 1.65 x 10-4

5 1.00 0.5 2.47 x 10-4

6 1.00 4.0 1.75 x 10-4

The formation of methane from carbon monoxide and hydrogen using a nickel catalyst was studied by Pursley. (J.A.Pursley, Ph.D thesis, University of Michigan).

The reaction: 3 H2 + CO CH4 + 2 H2O

was carried out at 500oF using 10 g catalyst at volumetric flow rate 300 L/min in a differential reactor where the effluent concentration of methane was measured.

Relate the rate of reaction to the exit methane concentration

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Fitting Data from Differential Reactors: P5-19C

The dehydrogenation of methylcyclohexane (M) to produce toluene (T) was carried out over a 0.3% Pt/Al2O3 catalyst in a differential catalytic reactor. The reaction is carried out in the presence of hydrogen (H2) to avoid coking [J. Phys. Chem., 64, 1559 (1960)]

a. Determine the model parameters for each of the following rate laws:

2HMM PPk'r- )1(

MM

MM PK1

Pk'r- )2(

2MM

HMM

PK1

PPk'r- )3( 2

22

2

HHMM

HMM PKPK1

PPk'r- )4(

b. Which rate law best describe the data?

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Fitting Data from Differential Reactors: P5-19C (cont’)

PH2 [atm] PM [atm] rT' [mol toluene.(s-1).(kg cat)-1

1 1 1.21.5 1 1.250.5 1 1.30.5 0.5 1.11 0.25 0.92

0.5 0.1 0.643 3 1.271 4 1.283 2 1.254 1 1.3

0.5 0.25 0.942 0.05 0.41

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Linear & Nonlinear Regression:Goodness of Fit

R square

data

2data

2

2

YY

)X(fY

1R

Variance

dof

SSEV

F test

model the in parameters of no. - point data of no.dof

model better in iancevar

model weakerin iancevarFinvers

model) worsefor dof model, better for dof,F(FDIST1confidence% inverse

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Nonlinear Regression for Example P5-3A1

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Case: Paramaecium Growth

The following table shows some data for the growth rate of paramaecium as a function of the paramaecium concentration.

Fit the data to Monod’s law (Monod, 1942)

Using:Linear least square:

Lineweaver – Burke Plot(reciprocal)difficulty in low

concentrationEadie – Hofstee Plot (rearragement)

Nonlinear least square

]par[K1

]par[Kkr

2

21P

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Paramaecium Growth

Conc.,

N/cm3

Rate,

N/cm3.hour

Conc.,

N/cm3

Rate,

N/cm3.hour

Conc.,

N/cm3

Rate,

N/cm3.hour

2.0 10.4 16.0 36.0 46.0 96.03.6 12.8 16.6 46.4 46.2 124.84.0 23.2 19.0 59.2 47.4 117.65.2 17.6 20.0 62.4 55.0 112.07.8 46.4 23.8 62.4 57.0 127.28.0 23.2 26.0 57.6 61.0 116.08.0 46.4 30.4 108.8 61.6 111.2

11.0 32.0 31.0 80.0 71.0 124.014.4 34.4 31.2 61.6 74.0 116.015.6 44.8 31.6 109.6 76.4 116.015.6 63.2 39.2 103.2

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Assignment

Analyze the previous data to fit kinetic model:

Using linear & nonlinear least square

Compare the variance of your results

5.12

21P

]par[K1

]par[Kkr