02 determination of rate law part 1

8/12/2019 02 Determination of Rate Law Part 1

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Constant-volume of batch reactor

Integral method of analysis of data

Differential method of analysis of data

TOPIC 2

Determination of Rate Law


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Constant volume of batch reactor refer to volume of

reaction mixture, not the volume of the reactor.

It also known as constant-densityreaction system.

The measure of reaction rate of component ibecomes

For ideal gas

therefore,

*This means the rate of

reaction of a

component can be

given by the rate of

change of concentration

or partial pressure

[1]

[2]


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SayA, converted to something else, or the fraction ofAreacted away. We call this, simply, the conversion ofA,with symbolXA.

Suppose that NA0is the initial amount ofAin the reactorat time t = 0, and that NAis the amount present at timet. Then the conversion of A in the constant volumesystem is given by

The Conversion


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and

We will develop the equations in this chapter in terms of

concentration of reaction components and also in terms

of conversions. Later we will relateXAand CAfor the more general case

where the volume of the system does not stay constant.

[7]

[8]


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The integral method of analysis always puts a particularrate equation to the test bythe with the

.

If the fit is unsatisfactory, another rate equation is. This procedure is shown and used

in the cases next treated.

It should be noted that the integral method is especially

useful for fitting simple reaction types corresponding to.


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Consider the reaction

Irreversible Unimolecular-Type

First-Order Reactions

[9]

For this reaction. Separating and integrating we obtain

[11]


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In terms of conversion (see Eqs. 7 and 8), the rate

equation, Eq. 10, becomes

which on rearranging and integrating gives

[12]

Or


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A plot of, as shown in Fig.

below.

If the experimental data seems to be better fitted by a

curve than by a straight line,

because the first-order reaction

.


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Integral Method Rate Analysis

We could integrate the combined mole balanceand rate law to plot reaction rate data in terms of

concentration vs. time for 0, 1st, and 2nd order

reactions.


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Zero order

First order


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For irreversible reaction, the reaction order andspecific rate constant can be determined by

.

It is applicable when the rate is essentially a functionof the concentration of only .

Consider a reaction carried out isothermally in a

constant volume batch reactor and the concentration

is as a function of time.

AA kCr

PA


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Combine mole balance and rate law:

The reaction order can be found by taking the natural

logarithm of both side

AA

ACk

dt

dC

AA

ACk

dt

dClnlnln


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: Graphical differentiation

Numerical differentiation

Differentiation of a polynomial fit to the data

FAKULTI OF CHEMICALENGINEERING, UiTM CHE584/594

16


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Graphical Method

This method accentuates measurement error!

time (s) 0 t1 t2 t3

concentration(mol/dm3)

CAo CA1 CA2 CA3


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Numerical Method Can be used when the data points in the independent

variable are equally spaced.

dCA/dt can be calculated by

Initial point

Interior points

Last point

time (s) 0 t1 t2 t3 t4 t5

concentration

(mol/dm3)CAo CA1 CA2 CA3 CA4 CA5

ttttt 1201

t

CCC

dt

dCAAA

t

A

2

43210

0

112

1

iAiA

t

ACC

tdt

dC

i

543

5

34

2

1

AAA

ACCC

tdt

dC


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02 determination of rate law part 1

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