Modified Kinetics Lecture

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CHEMICAL KINETICS


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INTRODUCTION

Rate is a measure of how fast or slowa reaction occurs

Rate is the change in concentrationper unit time.

Units of rate are mol dm-3 s-1mol dm-3

min-1and mol dm-3 h-1


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The Decomposition of Nitrogen Dioxide


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Types of Rates

Initial Rates Rates measured at the beginning of the reaction,

which is dependent on the initial concentrations of

reactants. Instantaneous Rates

Rates measured at any point during the reaction.

Average Rates An overall rate measured over a period or timeinterval.


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Instantaneous Rate

alue of the rateat a particular

time.

!an be obtained

by computing the

slope of a line

tangent to the

curve at that point.


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REACTION RATE

/

The rate of a chemical reaction isde0ned as the change inconcentration of a reactant in a

particular time inter+al.


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The Decomposition of Nitrogen Dioxide

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Reaction Rates and "toichiometric Relationships

!onsider the reaction#

$N$%&'N%$ ( %$

Rate of disappearance of N$%&) Rate of formation of N%$)

Rate of formation of %$)

"toichiometric relationships of these rates


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'n general

4or a reaction

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Rate law

An e6pression which shows how the reaction rate is related to concentration ofreactants 7catalyst8 is called the rate law or rate e9uation.

4or a reaction

The rate law generally has the form

# rate constant, proportionality constant

temperature dependent

:alue and unit obtained from the rate law

and are small whole numbers called the order of reaction

Rate law is determined from e6perimental dataThe reaction rate with respect to A or ; is determined by +aryingconcentration of one reactant, keeping that of the other constant.

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Rate law

$ompare 6periments 1 and ,?@ doubles, the initial rate doubles.

The date below is for the e6periment

1owe+er, for some elementary reactions thepowers in the rate law may correspond tocoeBcient in the chemical e9uation.

*(t (s(all+ the powers of o!e!trat"o! "!

the rate law are #"$ere!t from oe%"e!t.Thus for the reaction 78 abo+e, the rate is found

to be proportional to =>


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%rder of a reaction

Also called rate order

't is the powersCe6ponents of the concentration terms in therate e9uation 7law8

$onsider the rate law

The reaction order with respect to a gi+en reactant speciese9uals the e6ponent of the concentration of that species inthe rate law, as determined e6perimentally.

and are reaction orders with respect to A and ; respecti+ely

The o+erall order of a reaction e9uals the sum of the ordersof the reactant species in the rate law

is the o+erall order

$an ha+e integral or half integral +alues

1/


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%rder of a reaction

Reaction %bser+ed Rate

law

%rder

with

respect

to

Reactant

1

%rder

with

respect

to

Reactant


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$omple6 Reaction

A comple6 reaction is that which occurs in two ormore steps.

*or example, the overall reaction#

$A ( + ! ( D

may involve the following elementary stepsin its mechanism#

"tep-# A ( +/

"tep$# ( A0/

"tep1# 0! ( D

%verall reaction# $A ( +! ( D/

and 0 are called reactive intermediates


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!ultistep !echanisms

'n a multistep process, one of the steps will beslower than all others.

The o+erall reaction cannot occur faster than this

slowest, 't is the rate-determining step.


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(low 'nitial (tep

A proposed mechanism for this reaction is

(tep 1# &%


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4ast 'nitial (tep

The rate law for this reaction is found

7e6perimentally8 to be

;ecause termolecular 7 trimolecular8processes are rare, this rate lawsuggests a two-step mechanism.

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4ast 'nitial (tep

A proposed mechanism is

Step 1 is an equilibrium-

it includes the forward and reverse reactions.

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4ast 'nitial (tep

The rate of the o+erall reaction

depends upon the rate of the slowstep.

The rate law for that step would be

;ut how can we 0nd =&%;r


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4ast 'nitial (tep

&%;r


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4ast 'nitial (tep

;ecause Ratef Rater ,

k1=&%@ =;r


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4ast 'nitial (tep

(ubstituting this e6pression for

=&%;r


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Mea!"!0 of the Rate Express"o!

Example1 It has been determined e6perimentally thatthe se9uence of steps for a chemical reaction is as

follows#A ? ; $ 7slow8

$ ? ; J 7fast8

Hhat is the rate e9uation and the o+erall chemical

e9uationGSol(t"o!# The o+erall chemical e9uation will beobtained by adding the abo+e e9uations i.e.

A ? ; $ 7slow8

$ ? ; J 7fast8A 2 3* D 4slow5

(ince the rate of reaction is controlled by the slowstep, the rate e9uation will be

Rate k=A@=;@


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MOLECULARIT/ 6ERSUS ORDER OF REACTION

The term molecularity is not the same asorder of reaction.

The total number of molecules or atoms

which take part in a reaction asrepresented by the chemical e9uation isknown as the mole(lar"t+ of reat"o!.

The sum of the powers to which theconcentrations are raised in the rate lawis known as the or#er of reat"o!.


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DIFFERENCES *ET)EEN ORDER ANDMOLECULARIT/


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DETERMINATION OF ORDER OF REACTION

The rate e9uation of a reaction with a multi-stepmechanism cannot, in general, be deduced from the

stoichiometric coeBcients of the o+erall reactionK

it must be determined e6perimentally.

The e9uation may in+ol+e fractional e6ponentialcoeBcients, or it may depend on the concentrationof an intermediate species.

The rate e9uation is a diDerential e9uation, and itcan be integrated to obtain an integrated ratee9uation that links concentrations of reactants orproducts with time.


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DETERMINATION OF ORDER OF REACTION

D"$ere!t"al Rate Law 7Rate law8 - e6presses howthe rate depends on concentration.

I!te0rate# rate law - e6presses how the

concentration depends on time.

He can work backwards from the rate law to infer

the steps by which their reaction occurs.

!ost chemical reactions do not take place in a single

step but result from a series of se9uential steps.To understand a chemical reaction, we must learn

what these steps are.


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CONCE7T CHECK

LU(T'% The following tabulated datarefer to the hypothetical reaction

A ?


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6ample# The following tabulated data refer to

the hypothetical reaction

A ?


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The general e6pression for a rate law is

4rom 1 M < changed by a factor of

Ji+iding < by 1

Thus

'n a similar fashion

Hill yield

Thus the rate law is

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7b8 To calculate the rate constant, ,substitute any of the three sets ofdata into the rate law e6pression


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*or the reaction# "$

%2$,3a45

( 1I, 3a45

6$"%'$, 3a45

(I1, 3a45

The data below were obtained. 3a5 Determine the order of the reaction w.r.t. each reactant. 7rite the rate law

for the above reaction.

3b5 !alculate the rate constant, k, and give its appropriate units.

3c5 !alculate the reaction rate when each reactant concentration is 8.$8 M6pt.N

=(


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"olution# The rate lawhas the form Rate ) k9"$%2$:x9I:y,

herexandyare rate orders.

3a5 !alculation of rate order,x# we nee to use the e4uations with varying concentration of 9"$%2$:

Dividing gives

similarly

This reaction is first order w.r.t. 9"$%2$: and 9I:

Rate ) k9"$%2$:9I:

If , and


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Types of Rate ;aws

Differential Rate ;aw 3rate law5 < shows

how the rate of a reaction depends on

concentrations.

This is what we have been discussing so far

Integrated Rate ;aw < shows how the

concentrations of species in the reaction

depend on time. Graphical method to derive the rate law of

a reaction

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Oero order

'f the reaction A

=roducts is azeroorder reaction, then

which yields

And a plot ofversuswill yield a straight line

withslope)

2


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4irst order 'f the reaction A=roducts is afirst

order reaction, then

which yields

or And a plot of versuswill yield a straight line

withslope) and y-intercept)


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(econd order

'f the reaction A=roducts is asecondorder reaction, then

which yields

A plot of versuswill yield a straight line with

slope) k and y-intercept)

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INTEGRATED RATE FOR 6ARIOUSREACTION ORDERS

E l Th h d l i f th l


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Example1 The hydrolysis of ethylnitrobenFoate by a9eous sodium hydro6idewas followed at


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Sol(t"o!# 4or the second order reaction

Thealternati+e

methodA plot of 1C=A@t +ersus t

will gi+e astraight linewith

(lope ?k

HALF LIFE


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HALF8LIFE

>alf life of a reaction, t1Calf-life is a con+enient way to describe

how fast a reaction occurs, especially if itis a 0rst-order process. A fast reaction hasa short half-life.

(ubstituting this for =A@t in the integratedrate e9uation for any of the order gi+esthe half life e6pression.


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>alf-)ife4or a 0rst-order process, set =A@t5. =A@5 inintegrated rate e9uation#

NOT$% &or a first-orderprocess, the half-life

does not depend on ['(.


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>alf-)ife-


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COLLISION THEOR/ OF REACTION RATES

According to this theory, a chemical reactiontakes place only by collision between thereacting molecules.

;ut not all collisions are eDecti+e. %nly a smallfraction of collisions produce a reaction.

The two main conditions for a collisionbetween reacting molecules to be producti+e

areThe colliding molecules must posses suBcient

kinetic energy to cause a reaction.

The reacting molecules must collide with

proper orientation


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COLLISION THEOR/ OF REACTION RATES


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Acti+ation nergy

4or the rearrangement#


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Reaction $oordinate

Jiagrams 't shows the energy

of the reactants andproducts 7and,therefore, E8.

The high point on thediagram is thetransition state. The species present at the

transition state is called the

activated co)ple*.

The ener+ +ap etween thereactants and the activated

co)ple* is the activation ener+

arrier.

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the collision theoryFor the reaction#

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Modified Kinetics Lecture

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