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

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 reactions Measured: Product different feed condition Steady-state operation

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

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

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

Graphical Differential

Differentiation of a Polynomial Fit to The Data
Thus….

Numerical Method Only applicable for uniform sampling interval

Example: P5-3A1 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.

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.

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

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.

Example: P5-3A2 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.

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.

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

L3-14 Constant 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 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.

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 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 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.

L5-18 Constant Pressure Batch Reactor
The homogeneous gas reaction: A  2 B is 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.

Quiz 1 Basic Concept Selasa, 10 Oktober 2006

Half-lives Method @ t = t1/2  NA = ½ NA0 @ V = V0  CA = ½ CA0

L3-8 Half-lives Method Find the overall order of the reaction:
2 H2 + 2 NO  N2 + 2 H2O From the following constant-volume data using equimolar amounts of hydrogen and nitric oxide:

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: Determine a rate equation that fits these data

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

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

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.

Fitting Data from Differential Reactors
Using very small catalyst weight W & large volumetric flow rates 0 Low conversion X CA ~ CA0

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 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

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: b. Which rate law best describe the data?

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

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

Nonlinear Regression for Example P5-3A1

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

Paramaecium Growth

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