Chap 2 CRE.ppt

8/14/2019 Chap 2 CRE.ppt

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Chapter 2KINETICS OF HOMOGENEOUS REACTIONS

Simple Reactor Types

The Rate Equation

CONCENTRATION-DEPENDENT TERM OF A RATE EQUATION

- Single and Mul tiple Reactions- Elementary and Nonelementary Reactions

- Molecularity and Order of Reaction

- Representation of an Elementary Reaction- Representation of a Nonelementary Reaction

- Testing Kinetic Models


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TEMPERATURE-DEPENDENT TERM OF A RATE EQUATION

- Temperature Dependency from Arrhenius' Law

- Comparison of Theories with Arrhenius' Law- Activation Energy and Temperature Dependency


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Assume we have the following reaction:

aA + bB rR + sS

The most useful measure of reaction rate for reactant A

is then

The Rate Equation

[1]


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The rates of reaction of all materials are related by

Experience shows that the rate of reaction isinfluenced by the composition and the energy ofthe material. By energy we mean the temperature.

By considering the temperature, we can write

[2]


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Concentration-dependent Term of a Rate Equation

Single and Multiple Reactions

When a single stoichiometric equation and single rate

equation are chosen to represent the progress of the reaction,

we have asingle reaction. When more than one

stoichiometric equation is chosen to represent the observedchanges, then more than one kinetic expression is needed to

follow the changing composition of all the reaction

components, and we have multiple reactions.

Single reaction such as: AB


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Multiple reactions may be classified as:

Series reactions,Parallel reactions,

and more complicated schemes, an example of which is


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Elementary and Nonelementary Reactions

Consider a single reaction with stoichiometric equation

The rate of disappearance of A is given by

Such reaction is called elementary reaction

Elementary reactions: the rate equation corresponds to a

stoichiometric equations

H2+I22HI -rH2=k[H2][I2]


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When there is no direct correspondence between

stoichiometry and rate, then we have nonelementary

reactions. The classical example of a nonelementary reaction

is that between hydrogen and bromine,

which has a rate expression

[3]

Nonelementary reactions:no direct correspondencebetween stoichiometry and rate


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Molecularity and Order of Reaction

The molecularity of an elementary reaction is the

number of molecules involved in the reaction, and this

has been found to have the values of one, two, or

occasionally three.

Note that the molecularity refers only to an elementaryreaction.

Let us say, materials A, B, . . . , D, can be approximated

by an expression of the following type:

[4]


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where a, b, . . . , d are not necessarily related to the

stoichiometric coefficients. These powers are the order of

the reaction. Thus, the reaction is

Rate Constant k

When the rate expression for a homogeneous chemical

reaction is written in the form of Eq. 4, the dimensions ofthe rate constant kfor the nth-order reaction are

[5]


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Representation of an Elementary Reaction

In expressing a rate using partial pressure:

Elementary reactions are often represented by an equationshowing both the molecularity and the rate constant. Forexample,

which for a first-order reaction becomes simply

[7]

[6]


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The rate of reaction is:

And the rate of reaction for Eq. 8, if the rate is measured in

terms of B, is:

[8]

If it refers to D, the rate equation is


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Or if it refers to the product T, then

But from the stoichiometry

hence,

[9]


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Representation of a Nonelementary Reaction

A nonelementary reaction is one whose stoichiometry

does not match its kinetics. For example,


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Temperature-dependent Term of a Rate Equation

Temperature Dependency from Arrhenius' Law

For many reactions, and particularly elementary

reactions, the rate expression can be written as a

product of a temperature-dependent term and acomposition dependent term, or

For such reactions the temperature-dependent term, the

reaction rate constant, has been found in practically all

cases to be well represented by Arrhenius' law:

[33]


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At the same concentration, but at two differenttemperatures, Arrhenius' law indicates that

[34]

where

k, is the frequency or pre-exponential factor and

E is the activation energy of the reaction.

[35]


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The below expression summarizes the predictions of thesimpler versions of the collision and transition state theoriesfor the temperature dependency of the rate constant.

For more complicated versions mcan be as great as 3 or 4.Now, because the exponential term is so much moretemperature-sensitive than the pre-exponential term, thevariation of the latter with temperature is effectively

masked, and we have in effect

Comparison of Theories with Arrhenius' Law

[35]

[36]

This shows that Arrhenius' law is a good approximation to the

temperature dependency of both collision and transition-state theories


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The temperature dependency of reactions is determinedby the activation energy and temperature level of the

reaction, as illustrated inFig. 2.2and Table 2.1.

Activation Energy and Temperature Dependency


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1. From Arrhenius' law a plot of lnkvs1/Tgives astraight line, with large slope for largeEand small

slope for smallE (slope =E/R).

2. Reactions with high activation energies are very

temperature-sensitive; reactions with low activation

energies are relatively temperature-insensitive.

3. k0 does not affect the temperature sensitivity.

These findings are summarized as follows:


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Milk is pasteurized if it is heated to 63oC for 30

min, but if it is heated to 74C it only needs 15 s

for the same result. Find the activation energy of

this sterilization process.

EXAMPLE2.3


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t1= 30 min at T1= 336 K

t2= 15 s at T2= 347 K

Using Eq. 25:

E = 422,000 J/mol = 422 kJ/mol

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Chap 2 CRE.ppt