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15 Collection & Analysis of Rate Data Dicky Dermawan ITK-329 Kinetika & Katalisis

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16 Types of Reactors for obtaining Rate Data Batch, primarily for homogeneous reactions: Batch, primarily for homogeneous reactions: Measured: C(t), P((t) and/or V(t) Unsteady-state operation Differential reactor, for heterogeneous reactions Differential reactor, for heterogeneous reactions Measured: Product different feed condition Steady-state operation Steady-state operation

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17 Methods for Analyzing Rate Data Differential Method Differential Method Differential Method Differential Method Integral Method Integral Method Integral Method Integral Method Half-lives Method Half-lives Method Half-lives Method Half-lives Method Method of Initial Rates Method of Initial Rates Method of Initial Rates Method of Initial Rates Linear and Nonlinear Regression (Least- Square Analysis Linear and Nonlinear Regression (Least- Square AnalysisRegression

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18 Differential Method Applicable when reaction condition are such that the rate is essentially a function of the concentration of only one reactant 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 Can be used coupled with method of excess Outline of the procedure: combining the definition of rate reaction with the assumed Outline of the procedure: combining the definition of rate reaction with the assumed

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19 Determining The Derivative Graphical Differentiation Graphical Differentiation Differentiation of a polynomial fit to the data Differentiation of a polynomial fit to the data Numerical differentiation Numerical differentiation

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20 Graphical Differential

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21 Differentiation of a Polynomial Fit to The Data Thus….

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22 Numerical Method Only applicable for uniform sampling interval

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23 Example: P5-3A 1 The irreversible isomerization A 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.

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24 Example: P5-5 1 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.

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25 Integral Method Most often used when the reaction order is known Most often used when the reaction order is known Outline of the procedure: 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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26 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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27 Example: P5-3A 2 The irreversible isomerization A 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.

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28 Example: P5-5 2 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.

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29 Process your data in terms of measured variable Look for simplifications! Unfortunately, The problem is not that easy….

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30 L3-14 Constant Volume Batch Reactor A small reaction bomb fitted with a sensitive pressure-measuring device is flushed out at 25 o C, a temperature low enough that the reaction does not proceed to any appreciable extent. The temperature is then raised as rapidly as possible to 100 o C by plunging the bomb into boiling water, and the readings in Table P14 are obtained. The stoichiometry of the reaction is 2 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.

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31 L3-19 Constant 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 14 o C, a temperature low enough that the reaction does not proceed to any appreciable extent. The temperature is then raised as rapidly as possible to 100 o C, and the readings in Table P19 are obtained. The stoichiometry of the reaction is A 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.

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32 L5-18 Constant Pressure Batch Reactor The homogeneous gas reaction: A 2 B A 2 B is run at 100 o C 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.

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33 Quiz 1 Basic Concept Selasa, 10 Oktober 2006

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34 Half-lives t = t 1/2 N A = ½ N V = V 0 C A = ½ C A0

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35 L3-8 Half-lives Method Find the overall order of the reaction: 2 H NO N H 2 O From the following constant-volume data using equimolar amounts of hydrogen and nitric oxide:

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36 U2-Half-lives Method The thermal decomposition of nitrous oxide (N 2 O) in the gas phase at 1030 K is studied in a constant-volume vessel at various initial pressures of N 2 O. The half-life data so obtained are as follows: Determine a rate equation that fits these data

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37 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

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38 Method of Initial Rates Reversible reaction, viz. A B If 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

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39 H3-7. Metode laju awal Data laju awal,, berikut ini dilaporkan untuk reaksi fasa gas antara diborana dengan aseton pada suhu 114 o C: B 2 H Me 2 CO 2(Me 2 CHO) 2 BH Bila dipostulasikan persamaan laju reaksi berbentuk tentukan n, m, dan k. tentukan n, m, dan k.

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40 Fitting Data from Differential Reactors Using very small catalyst weight W & large volumetric flow rates 0 Low conversion X C A ~ C A0

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41 Fitting Data from Differential Reactors: Example 5-4 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 H 2 + CO CH H 2 O was carried out at 500 o F 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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42 Fitting Data from Differential Reactors: P5-19C The dehydrogenation of methylcyclohexane (M) to produce toluene (T) was carried out over a 0.3% Pt/Al 2 O 3 catalyst in a differential catalytic reactor. The reaction is carried out in the presence of hydrogen (H 2 ) to avoid coking [J. Phys. Chem., 64, 1559 (1960)] a. Determine the model parameters for each of the following rate laws: b. Which rate law best describe the data?

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

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44 Linear & Nonlinear Regression: Goodness of Fit R square R square Variance Variance F test F test

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45 Nonlinear Regression for Example P5-3A1

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46 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 concentration Eadie – Hofstee Plot(rearragement) Nonlinear least square

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47 Paramaecium Growth

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48 Assignment Analyze the previous data to fit kinetic model: Using linear & nonlinear least square Compare the variance of your results

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