REACTION RATES

Chemical kinetics & Reactor Design Course Code: Ch. E-847 Credit Hours: 3-0 Course 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 •

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Classification of chemical reactions Rate Law Out put Kinetics and Mechanisms of reaction Reactors and Design Product distribution and Selectivity

Fundamentals/Introduction •

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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.

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 10

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/dm 3/s) can be expressed as either, The rate of Disappearance: -rA or as The rate of Formation (Generation): rA

Reaction Rate Consider the isomerization

AB

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: AB 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 & NonElementary 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 nonelementary reaction

Free radicals

Ions and polar substances Molecules Chain reaction mechanism

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.

Exothermic Reactions

Endothermic Reactions

Unstable intermediate Reactions

Temperature Dependence of Rate The order ofConstants 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.

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Ea RT

k  zpe z:the collision freq uency p: steric factor k  Ae

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Ea RT

Ea 1 ln(k)   ( )  ln(A) R T

T(K) and k

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” –

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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: -Ea/RT

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 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.

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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 •

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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.

- 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

Cl .

Cl .

Cl .

B r B r H H

H

Desired rxn cannot occur. Desired rxn cannot occur.

B r

Desired rxn can occur.

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)

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the minimum energy the reactants must have for a reaction to occur the energy difference between the reactants and the transition state •

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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 reactionenergy diagram. –

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Collision theory

Comparison

Chain Reaction Mechanism

Rice Herzfeld reaction mechanism

Gas Phase Decomposition of Acetaldehyde

Decomposition of Ethane

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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

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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

GAS-SOLID CATALYTIC REACTIONS •

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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.

Ideal reactor types •

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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 •

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Integral method of analysis Differential method of analysis

General Mole Balance

Batch Reactor Mole Balance

CSTR Mole Balance

Plug Flow Reactor

Plug Flow Reactor Mole Balance PFR:

The integral form is:

dF A FA 0 rA

V

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 FA0  FA 

 r dW  A

The integral form to find the catalyst weight is:

dNA dt

dFA FA 0 r A

W

FA

Reactor Mole Balance Summary