REACTION RATES

Chemical kinetics &

Reactor Design

Course Code: Ch. E-847

Credit Hours: 3-0

Recommended Books

Aris R., Elementary Chemical Reactor

Analysis, Prentice-Hall 1969.

Foggler, H. S., Elements of Chemical

Reaction Engineering, Prentice Hall of

India, 1994.

Fromment G.F. and Bischoff K.B.,

Chemical Reactor Analysis and Design,

John Wiley 1994.

Schimdt L., The Engineering of Chemical

Reactions, Oxford, 2005

W

hat

is Chemical kinetics& Reactor

Design?

•

Chemical kinetics and reactor design

is the field that studies the rates and

mechanisms of chemical reactions

and the design of the reactors in

which they take place.

Fundamentals of Chemical

Reaction Kinetics and Design

•

Classification of chemical reactions

•

Rate Law

•

Out put

•

Kinetics and Mechanisms of reaction

•

Reactors and Design

•

Fundamentals/Introduction

•

Homogenous and Non-homogenous reactions

•

Elementary and Non-elementary reactions

•

Reaction Mechanisms (chain reaction

mechanism, Non chain, intermediate formation,

Ion, radicals,

Classification of Reactions

In CRE the most useful scheme is the breakdown according to the number and types of phases involved homogeneous and heterogeneous systems. A reaction is homogeneous if it take place in one phase alone.

A reaction is heterogeneous if it requires the presence of at least two phases to proceed.

It is immaterial whether the reaction takes place in one, two, or more phases; at an interface; or whether the reactants and products are distributed among the phases or are all contained within a single phase.

All that counts is that at least two species are necessary for the reaction to proceed as it does.

10

Variables Affecting the Rate of

Reaction

In homogeneous systems the temperature,

pressure, and composition are obvious

variables.

In heterogeneous systems more than one

phase is involved; hence, the problem

becomes more complex. Material may have

to move from phase to phase during

reaction; hence,

rate of mass transfer

rate of heat transfer

Chemical Identity

A chemical species is said to have reacted when it has lost its chemical identity.

The identity of a chemical species is determined by the kind, number, and configuration of that species’ atoms. 1. Decomposition 2. Combinatio n 3. Isomerization

Rate of Chemical Reaction

The rate of reaction tells us how fast number of moles of one chemical species are being consumed to form another chemical species. The term chemical species refers to any chemical component or element with a given identity.

OR

The reaction rate is the rate at which a species looses its chemical identity per unit volume.

The rate of a reaction (mol/dm3/s) can be expressed

as either,

The rate of Disappearance: -rA or as

Reaction Rate

Consider the isomerization A B

r_A = the rate of formation of species A per unit volume

-r_A = the rate of a disappearance of species A

per unit volume

r_B = the rate of formation of species B per unit volume

EXAMPLE: A B

If Species B is being formed at a rate of

0.2 moles per decimeter cubed per second, ie,

Single & Multiple

Reactions

Series Reactions

Elementary &

Reaction Rate

•

For a catalytic reaction, we refer to -rA', which is

the rate of disappearance of species A on a per mass of catalyst basis.

Reaction Rate

Consider species j:

r

is the rate of formation of species j per

unit volume [e.g. mol/dm

/s]

r

is a function of concentration,

temperature, pressure, and the type of

catalyst (if any)

r

is independent of the type of reaction

system (batch, plug flow, etc.)

r

is an algebraic equation, not a

Parameters affecting rates

of reaction:

Rate law

The rate law does not depends upon the type of reactor used

Reaction Rate

r

is the rate of formation of species j per

unit volume [e.g. mol/dm

/s]

r

is a function of concentration,

temperature, pressure, and the type of

catalyst (if any)

r

is independent of the type of reaction

system (batch, plug flow, etc.)

r

is an algebraic equation, not a

Parameters affecting rates of

reaction:

Rate law

Molecularity & Order of reactions

Molecularity means the number of

molecules involved in chemical reaction.

Its an integer value and not a fraction.

Its usually associated with the elementary

reactions.

Order of a reaction is the power to which

concentrations are raised.

Order of reaction could be a fraction.

They are not necessarily related to the

stoichiometric coefficients.

Rate Equation:

Rate of reaction is influenced by the

concentrations and energy of the

Representation of an

Elementary reaction

Representation of a

non-elementary reaction

Free radicals

Ions and polar substances

Molecules

Non chain reaction mechanism

Reaction Mechanisms and

Rate Expression

Reaction Mechanism

RM means detail description of a chemical reaction outlining each separate step or stage.

Mechanism of reaction include stable and unstable intermediates so needs to be audited continuously.

Reaction steps are sometimes very complex that needs to include thermodynamics of reaction.

For a reaction energy must be provided to reactants to start the reaction and breaking of bonds.

Reactant molecules becomes activated due to higher energy contents leading to unstable activated state or transition complex.

Activation energy is the amount of energy required to raise the reactant molecules to this state.

This energy also helps to find out the rate of reaction.

Catalyst enables the reactants to convert into products at low energy states by affecting the reaction rate. Therefore a catalyzed reaction has lower activation energy then an un-catalyzed reaction.

Reactants will absorb energy to cross this peak and the energy will be released back when stable products will form. This is called as heat of reaction.

Temperature

Dependence of Rate

Constants

The order of each reactant depends on the detailed reaction mechanism.

Chemical reaction

speed up when the

temperature is increased. － molecules must collide to react － _{an increase in} temperature increases the frequency of intermolecular collisions.

T(K) and

k

Ae

k

factor

p: steric

uency

ision freq

z:the coll

zpe

k





ln(A)

)

T

1

(

R

E

ln(k)







Plot ln(k) vs.

1/T

Arrhenius Equation for Rate

of Reaction and Collision

Arrhenius Equation

•

Reaction rate increases with

temperature because:

–

molecules have more kinetic energy

–

more collisions occur

–

greater number of collisions occur with

enough energy to “get over the hill”

•

Arrhenius Equation

The Arrhenius Equation relates the value of the rate

constant to Ea and the temperature:

k = Ae

where k = rate constant

Ea = activation energy

R = gas constant (8.314 J/mol. K)

T = temperature in Kelvin

A = frequency factor (a constant)

A is related to the frequency of collisions and the probability that the collisions are oriented favorably for reaction.

Arrhenius Equation

The activation energy of a reaction can be found by measuring the rate constant at various temperatures

and using another version of the Arrhenius equation

.

Example: At 189.7oC, the rate constant for the

rearrangement of methyl isonitrile to acetonitrile is 2.52 x 10-5 s-1. At 251.2oC, the rate constant for the

reaction is 3.16 x 10-3 s-1. Calculate the activation

Arrhenius Equation

Once you find the value for Ea, you can use the

Arrhenius Equation to find the frequency factor (A) for the reaction.

Once you have the value for Ea and A, you can

calculate the value for the rate constant at any temperature.

The following two examples illustrate this process.

Example: Using the activation energy obtained in

the previous example, calculate the value for the frequency factor using k = 2.52 x 10-5 s-1 at 189.7oC

Example: Use the value for the frequency factor (A)

and the activation energy obtained in the previous two examples to calculate the value of the rate constant at 25oC.

•

Plot of ln k vs 1/T is a straight line with large slope for large E and small slope for small E.

•

High E reactions are very temperature sensitive and low E reactions are less.

•

Any given reaction is more temperature

sensitive at a low T than at high temperature.

•

From Arrhenius law ,the value of frequency factor or constant does not affect the

The Collision Model

The reaction rate depends on:

collision frequency

a probability or orientation factor

activation energy (E

)

The reaction rate increases as the

number of collisions between reacting

species increase.

Concentration

temperature

Collisions Frequency and

Molecular orientations

•

Experiments show that the observed reaction rate is considerably smaller than the rate of collisions with enough energy to surmount the barrier.

•

The collision must involve enough energy to produce the reaction.

•

The relative orientation of the reactants must allow formation of any new bonds necessary to products.

The Collision Model

Collisions must occur in a particular orientation for reactions to occur. For the reaction: Cl. + H - Br H - Cl + Br .

Cl

.

B

r

H

Cl

B

r

H

Cl

B

r

H

- Reactions result when atoms/molecules collide with sufficient energy to break bonds

- Molecules must collide in an orientation that leads to productive bond cleavage and/or formation

BrNO

collision

The Collision Model

•

Collisions must occur with a specific

minimum amount of energy in order

for a reaction to take place.

–

Activation energy (E

)

•

the minimum energy the reactants must have for a reaction to occur

•

the energy difference between the reactants and the transition state

The Collision Model

•

Transition state:

–

a particular arrangement of atoms of

the reacting species in which bonds are

partially broken and partially formed

–

the state of highest energy between

reactants and products

–

a relative maximum on the

reaction-energy diagram.

Chain Reaction Mechanism

Gas Phase Decomposition of

Acetaldehyde

ENZYME CATALYZED

REACTIONS

•

Soluble enzyme–insoluble substrate

•

Insoluble enzyme–soluble substrate

•

Soluble enzyme–soluble substrate

The study of enzymes is important because every synthetic and degradation reaction in all living cells is controlled and catalyzed by specific enzymes.

Acid base catalysis

•A catalyst is defined as a substance that influences the rate or the •direction of a chemical reaction without being consumed.

•Homogeneous catalytic processes are where the catalyst is dissolved in a liquid reaction medium.

•The varieties of chemical species that may act as homogeneous catalysts include anions, cations, neutral species, enzymes, and association complexes. In acid-base catalysis, one step in the reaction mechanism consists of a proton transfer between the catalyst and the substrate.

•The protonated reactant species or intermediate further reacts with either another species in the solution or by a decomposition process.

Autocatalytic reactions

•

There are many reactions in which the products formed often act as catalysts for the reaction. The reaction rate accelerates as the reaction continues, and this process is referred to as autocatalysis.

•

The reaction rate is proportional to a product concentration raised to a

•

positive exponent for an autocatalytic reaction.

•

Examples of this type of reaction are the hydrolysis of several esters. This is because the acids formed by the reaction give rise to hydrogen ions that act as catalysts for subsequent reactions.

•

The fermentation reaction that involves the action of a micro-organism on an organic feedstock is a significant autocatalytic reaction. Normally, when a material reacts, its initial rate of disappearance is high and the rate decreases continuously as the reactant is consumed.

•

However, in autocatalytic reaction, the initial rate is relatively slow since little or no product is formed. The rate then increases to a maximum as the products are formed and then decreases to a low value as the reactants are consumed.

•

•

Consider a gaseous reactant flowing through a bed of

solid catalyst pellets. The physical steps involved are,

•

the transfer of the component gases up to the catalyst

surface, diffusion of reactants into the interior of the

pellet, diffusion of the products back to the exterior

surface, and finally the transfer of the products from

the exterior surface to the main stream.

GAS-SOLID CATALYTIC

REACTIONS

Ideal reactor types

•

Batch Reactors

•

To find rate equation from batch

reactor

•Usually operated isothermally and constant volume. •Good for small scale laboratory setup

•It needs little auxiliary equipments

Analysis of kinetic data

•

Integral method of analysis

•

Batch Reactor Mole

Balance

CSTR

Plug Flow Reactor Mole

Balance

Packed Bed Reactor

Mole Balance

Reactor Mole Balance

Summary