kinetics of homogeneous reaction

7/28/2019 Kinetics of Homogeneous reaction

1/56

1


2/56

IDEAL REACTORDEAL REACTORTYPESYPESa c

Plug flow

Steady-state flow

Mixed flow


3/56

Ideal Batch Reactor

It has neither inflow nor outflow of

being carried out.

Uniform com osition ever

where in the

reactor (perfectly mixed)

No variation in the rate of reactionroug ou e reac or vo ume


4/56

Batch Reactor

All reactants are supplied to the reactor at the outset. Thereactor is sealed and the reaction is performed. No addition

of reactants or removal of products during the reaction.

Vessel is ke t erfectl mixed. This means that there willbe uniform concentrations. Composition changes with time.

reactor - however, it may change with time.

Generally used for small scale processes.

Low ca ital cost. But hi h labour costs.

Multipurpose, therefore allowing variable product.


5/56

Glass Batch Reactor


6/56

Typical Commercial Batch Reactor


7/56

Ideal Mixed Flow Reactor Normally run at steady state.

everywhere within the reactor and at the exit.

enera y mo e e as avng no spa avariations in concentration, temperature, or

reaction rate throughout the vessel

CONTINUOUS STIRRED TANK REACTOR (CSTR)


8/56

Backmixed Well mixed or CSTR

sua y emp oye or

liquid phase

FA0(CA0)

reactions.FA

Use for gas phaseACA CA

for kinetic studies.CA

Assumption: Perfect mixing occurs.


9/56

Characteristics

Perfect mixing: the properties of the reaction mixture areuniform in all parts of the vessel and identical to the

properties of the reaction mixture in the exit stream (i.e.

CA, outlet = CA, tank) The inlet stream instantaneously mixes with the bulk of

the reactor volume.

reac or s assume o reac s ea y s a e.Therefore reaction rate is the same at every point, and.

What reactor volume, Vr , do we take?

r .

Gas phase: Vr = reactor volume = volume contents

r


10/56

CSTR/ Batch


11/56

Ideal Plug Flow Reactor

orma y opera e a s ea y s a e Fluid asses throu h the reactor with no mixin

of earlier and later entering fluid

Referred to as a plug-flow reactor

The reactants are continuously consumed as.

PLUG FLOW REACTOR (PFR), TUBULAR REACTOR


12/56

All fluid element have same residence time.

Used for either gas phase or liquid phase reactions.

The plug flow assumptions tend to hold when there isgoo ra a m x ng ac eve a g ow ra es e

>104) and when axial mixing may be neglected (when

(approx.))


13/56

Selection of Reactors

Batch Small scale . . High labor costs per batch

Diff icult for large-scale production CSTR : most homogeneous l iquid-phase flow reactors

When intense agitation is required

The conversion of reactant per volume of reactor is the smallestof the flow reactors - very large reactors are necessary to obtainhigh conversions

PFR : most homogeneous gas-phase flow reactors

Usually produces the highest conversion per reactor volume of

Difficult to control temperature within the reactor Hot spots can occur


14/56

The Rate Equation

uppose a s nge-p ase reac on

The most useful measure of reaction rate for reactant A is then:

In addition the rates of reaction of all materials are related b :


15/56

Experience shows that the rate of reaction is influenced by the

.By energy we mean the temperature (random kinetic energy ofthe molecules the li ht intensit within the s stem this maaffect the bond energy between atoms), the magnetic field

intensity, etc.Ordinarily we only need to conside the temperature, so let usfocus on this factor. Thus, we can write


16/56

Rate constant, k

.

In gas-phase reactions It depends on catalysts and may be a function of total pressure.

n qu system It can be a function of total pressure. may epen on onc s reng an c oce o so ven .

ere, we cons er e emperaure ony.


17/56

Rate of reaction and temperature

Empirical Observations.

ItwastheSwedishchemistSvanteArrheniuswhofirst suggeste that

the temperature dependenceof the specific reaction rate constant,k,

Ee

constantratereact on Arrhenius Equation

Where:

=E=Activationenergy, J/mol or cal/molR=Gasconstant, 8.314J/mol K (or 1.987cal/mol K)

T=Absolutetemperature, K


18/56

Arrhenius equation has been verified empirically to give thetem erature behaviour of most reaction rate constants (within

experimental accuracy)over fairy largeexperimental ranges.

reactionat several temperatures. After taking thenatural logarithmof

theArrheniusequation:

ln k -E/R TRAk lnln

1/T


19/56

Example 3-1(Fogler) Calculate the activation energy for the first-order decom osition reaction of benzene diazoniumchloride to

give chlorobenzene and nitrogen:

ln kA

1/T

A

E 1lnk lnA

E/RTk T Ae


20/56

14017

T

kJ kJE (14017K)R (14017K) 8.314 116.5

mol K mol

16 1.

Arrhenius Equation16Ak (T) 1.32 10 exp

T


21/56

Homo eneous Hetero eneous

Elementary Non-elementary

Single Multiple

Chemical Bio-chemicalClassification

Reversible Irreversible

Exothermic Endothermic

-


22/56

When a single stoichiometric equation and single rate equation,

single reaction.

When more than one stoichiometric equation is chosen to

represent the observed changes, then more than one kineticexpress on s nee e o o ow e c angng compos on o a ereaction components, and we have multiple reactions.

series reactions:

parallel reactions, which are of two types:


23/56

and more complicated schemes, an example of which is

Here, reaction roceeds in arallel with res ect to B, but in serieswith respect to A, R, and S.


24/56

Order of reaction

One of the mostgeneral forms: a b dA B Dr kC C ....C

where k = velocity constant or specific rate constant.

A, B , .

a , b = reaction order with respect to CA , CB .

a + b + ... +d = overall order (this treatment is only applicableto simple reactions).

Reaction order

Power to which concentration is raised to make ratero ortional to it.

It can only be determined experimentally.


25/56

Elementaryreaction Elementaryreactionisonethatevolvesasinglestep.

reactionareidenticaltothepowersintheratelaw: OHOCHOHCHO 33 OHCHOOO CCkr 3

Anelementaryreactionhasanelementaryratelaw.

anelementaryreaction.2

2ONONONO

CCkr 2 22NO O 2NO

HIIH 222

2222

IHHHr


26/56


27/56


28/56


29/56

Molecularity

This is the number of atoms, ions, or molecules involved(colliding) in a reaction.

Examples:

i Bimolecula reaction since two s ecies22 are involved in the reaction step.

(ii)Unimolecular

42

23490

23892 HeThU

urianium-238 heliumthorium


30/56

Representation of an Elementary Reaction

n express ng a ra e we may use any measure equva en oconcentration (for example, partial pressure), in which case:

,it will affect the rate constant k.

,

equation showing both the molecularity and the rate constant. Forexam le

re resents a biomolecula irreversible reaction with second-order

12A 2R

rate constant k1, implying that the rate of reaction is

f


31/56


It would not be ro er to write mentioned e uation as:

1kA R

for this would imply that the rate expression is:

Thus, we mustbe careful to distinguish between the one particular

possible representations of the stoichiometry.

R t ti f El t R ti


32/56


R t ti f N l t R ti


33/56

Representation of a Nonelementary Reaction

match its kinetics.

Ki ti M d l f N l t R ti


34/56

Kinetic Models for Nonelementary Reactions

If the kinetics of the reaction:

Indicates that the reaction is nonelementary, we may postulate aseries of elementary steps to explain the kinetics, such as

Ki ti M d l f N l t R ti


35/56

Kinetic Models for Nonelementary Reactions

Free radicals

Ions and polar substances

Molecules

Transit ion complexes


36/56

Nonchain Reactions


37/56

var ous n s


38/56

Free radicalschain reaction mechanism

1k

2k

221

1 BrH CCk

22 BrHBrf

CCk

This is not a bimolecular reaction.


39/56

Because the reaction occurs as follows:

2 n a on HHBrH

2

Br

rrH BHBB 2 Propagation

rHH BHBr

2rBr2 B Termination

Each step has a molecularity, which mustbe an integer.us, or e an mo ecuar y are no necessar y

identical for a given reaction.


40/56

Molecular intermediatesnonchain mechanism

The general class of enzyme catalyzed fermentation reactions:

with ex erimental rate

is viewed to proceed with intermediate (A. enzyme)* as follows:


41/56

Transition complexnonchain mechanism

The spontaneous decomposition of azomethane


42/56

h th i th i t f ith f t t f


43/56

we hypothesize the existence of either of two types of.

.

present at very small concentration

This is called the steady-state approximation.

Type 2


44/56

Type 2.

a homogeneous catalyst of initial concentration Co

,

free catalyst C

intermediate X

Example 2.1 SEARCH FOR THE REACTION MECHANISM


45/56

The irreversible reaction

=

has been studied kineticall and the rate of formation of roducthas been found to be well correlated by the following rateequation:

2AB A Br kC independentof C

What reaction mechanism is suggested by this rate expression if

the chemistry of the reaction suggests that the intermediateconsists of an association of reactant molecules and that a chainreaction does not occur?


46/56

If this were an elementary reaction, the rate would be given by

AB A Br kC C k[A][B]

Model 1 12

k *

2k2A A

3

4

k*

2 kA B A AB

w c rea y nvo ves our e emen ary reac ons

1k *

22A A

2k*

2A 2A

3k*

2A B A AB

4k *

2A AB A B


47/56

* AB 3 2 4

2 * *1*2

1 2 2 3 2 4A 2

*2A

11 4

*2 2[A ]

21 1 3 2 4AB

2rk k B

21k k [A] [B] k k [A][AB]


48/56

2

1 3 2 4k k [A] [B] k k [A][AB]

AB2 3r k k [B]

if k2, is very small, this expression reduces to

11 3 2 4

AB2r

2 3

21AB 1

2

if k2, is very small, this expression reduces to2

1 3 2(k k 2k )[A] [B]r 3 2


49/56

1k *

2B B B

3

4

k*

2 kA B A AB

Example 2.2 SEARCH FOR A MECHANISM FOR THEENZYMESUBSTRATE REACTION


50/56

ENZYMESUBSTRATE REACTION

Here, a reactant, called the substrate, is converted to product bythe action of an enzyme, a high molecular weight (MW >10000)protein-like substance. An enzyme is highly specific, catalyzingone particular reaction, or one group of reactions. Thus,

EnzymeA R

Many of these reactions exhibit the following behavio :1. A rate proportional to the concentration of enzyme

0 .

2. At low reactant concentration the rate is proportional to the

reac an concen ra on, .

3. At high reactant concentration the rate levels off andecomes n epen en o reac an concen ra on.

Propose a mechanismto account for this behavior.

Michaelis and Menten (1913) were the first to solve this puzzle.


51/56

( ) p

1

They guessed that the reaction proceeded as follows:

2

3

X R E

with the two assumptions

E =E +X

d[X]0

dt

d[R] 3dt

d X1 2 3

dt

k [A][E ] 3d[R]

k [X]dt


52/56

1 0k [A][E ] dt

2 3 1(k k ) k [A]

1 3 0 3 0

2 3 1 2 3 1

k k [A][E ] k [A][E ]d[R]

dt (k k ) k [A] (k k ) k [A]

3 0k [A][E ]d[R]

dt [M] [A]

0[E ]

[A] when [A] [M]dt dt

TEMPERATURE-DEPENDENT TERM OF A RATE


53/56

EQUATIONQUATIONTemperature Dependency from Arrhenius' Law

i 1 2r f (temperature) f (composition)

2k f (composition)

E RT0e

where k is called the fre uenc or re-ex onential factor and Eis called the activation energy of the reaction

2 2

1 1 1 2

rln lnr k R T T

provided that E stays constant.

TEMPERATURE-DEPENDENT TERM OF A RATE


54/56

EQUATIONQUATIONComparison of Theories with Arrhenius' Law

m E RT

0

k k T e 0 m 1

summarizes the predictions of the simpler versions of the collisionand transition state theories for the temperature dependency oft e rate constant.

For more complicated versions m can be as great as 3 or 4. Now,

sensitive than the pre-exponential term, the variation of the latter

with tem erature is effectivel masked, thus

E RTk k e


55/56

From Arrhenius' law a plot of ln k vs 1/T gives a straight line, withReactions with high activation energies are very temperature-Any given reaction is much more temperature-sensitive at a lowFrom the Arrhenius law, the value of the frequenc facto k, doeslarge slope for large E and small slope for small E.sensitive; reactions with low activation energies are relatively

temperature-insensitive.

temperature than ata high temperature.notaffect the temperature sensitivity.

Example 2.3 SEARCH FOR THE ACTIVATION ENERGY OF APASTEURIZATION PROCESS


56/56

PASTEURIZATION PROCESS

Milk is pasteurized if it is heated to 63C for 30 min, but if it isheated to 74C it only needs 15 s for the same result. Find theactivation energy of this sterilization process.

assuming anArrhenius temperature dependency

2 1

1 2 1 2

ln lnr t R T T

1t30 E 1 1ln ln

E=422000 J/mol20.25 t 8.314 336 347

kinetics of homogeneous reaction

Documents