reaction rates

Chemical kinetics & Reactor Design

Course Code: Ch. E-847Credit Hours: 3-0Course Instructor: Dr. Erum Pervaiz

Recommended Books

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

What 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• Product distribution and Selectivity

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.

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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. Combination 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

The rate of Formation (Generation): rA

Reaction RateConsider the isomerization AB

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

-rA = the rate of a disappearance of species A per unit volume

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

EXAMPLE: AB If Species B is being formed at a rate

of 0.2 moles per decimeter cubed per

second, ie,

rB = 0.2 mole/dm3/s

Types of Reactions:

Single & Multiple Reactions

Series Reactions

Multiple or complex

Elementary & Non-Elementary Reactions:

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.

(mol/gcat/s)

Reaction Rate

Consider species j: • rj is the rate of formation of species j per

unit volume [e.g. mol/dm3/s]• rj is a function of concentration,

temperature, pressure, and the type of catalyst (if any)

• rj is independent of the type of reaction system (batch, plug flow, etc.)

• rj is an algebraic equation, not a differential equation

Reaction Rate

Parameters affecting rates of reaction:

Rate law

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

Rate Equation:

Reaction Rate• rj is the rate of formation of species j per

unit volume [e.g. mol/dm3/s] • rj is a function of concentration,

temperature, pressure, and the type of catalyst (if any)

• rj is independent of the type of reaction system (batch, plug flow, etc.)

• rj is an algebraic equation, not a differential equation

Parameters affecting rates of reaction:

Rate law

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

Rate Equation

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 material.

Representation of an Elementary reaction

Representation of a non-elementary reaction

Free radicals

Ions and polar substances

Molecules

Non chain reaction mechanism

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.

Exothermic Reactions

Endothermic Reactions

Unstable intermediate Reactions

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

Aek

factorp: steric

uencyision freqz:the coll

zpek

RT

E

RT

E

a

a

ln(A))T

1(

R

Eln(k) a

Plot ln(k) vs. 1/T

Arrhenius Equation for Rate of Reaction and Collision

Theory

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”•i.e. with energy greater than or equal to Ea

Arrhenius Equation• The Arrhenius Equation relates the value of the

rate constant to Ea and the temperature:

k = Aewhere k = rate constant

Ea = activation energy

R = gas constant (8.314 J/mol. K)T = temperature in KelvinA = frequency factor (a constant)

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

-Ea/RT

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 energy for this reaction.

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 temperature.

The Collision Model

• The reaction rate depends on:–collision frequency–a probability or orientation factor–activation energy (Ea)

• 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 .

Br

HDesired rxn cannot occur.

Cl .

Br

H

Cl .

BrH

Desired rxn cannot occur.

Desired rxn can occur.

- 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 (Ea)•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.

Collision theory

Comparison

Chain Reaction MechanismRice Herzfeld reaction mechanism

Gas Phase Decomposition of Acetaldehyde

Decomposition of Ethane

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.

Contd.

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 the following mechanism for an autocatalytic reaction

• 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• Flow Reactors

Batch Reactor

To find rate equation from batch reactor

•Usually operated isothermally and constant volume.•Good for small scale laboratory setup•It needs little auxiliary equipments•Usually used for obtaining homogenous kinetic data

Analysis of kinetic data

• Integral method of analysis• Differential method of analysis

General Mole Balance

Batch Reactor Mole Balance

CSTRMole Balance

Plug Flow Reactor

Plug Flow Reactor Mole Balance

PFR:

The integral form is:

V dFAr

AFA 0

FA

This is the volume necessary to reduce the entering molar flow rate (mol/s) from FA0 to the exit molar flow rate of FA.

Packed Bed Reactor Mole Balance

PBR

The integral form to find the catalyst weight is:

W dFA

r AFA 0

FA

FA0 FA r AdW dNA

dt

Reactor Mole Balance Summary