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CHEMICAL KINETICS

Objectives

Order andmolecularity

Kinetics ofrst andsecond orderreaction

Pseudo unimolecularreaction

Arrhenius equation

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1.1 ChemicalKinetics

Chemical kineticsis thebranch ofph ysicalchemistry whichdeals withastudyof the speed ofchemical reactions.Such studiesalso enableus tounderstand themechanism by whichthe reactionoccurs. Thus,in chemicalkinetics wecan alsodetermine therate of chemicalreaction. From thekinetic standpoint thereactions areclassified intotw ogroups: a) homogeneousreactions whichoccur entirelyin onephase b)heterogeneous reactions where thetransformation takes placeonthesurf aceof acatalyst orthe wallsofa con- tainer.

1.2 Rateof reaction

The rateof reactioni.e. thev elocityof areaction istheamountof achemical change occurring perunit time. The rateis generallye xpressedas thedecreaseinconcentration ofa reactantor asthe increase inconcentration ofthe product.If Cthe concentrationof areactant atan ytime t is,the rateis dC dtor ifthe concentration ofaproductbe xat anytimet, therate would bedx dt. The timeis usuallye xpressedin seconds.Theratewill hav eunits ofconcentration dividedby time. The concentrationsare taken ingm-moles/litre,hencerate ismoles/litre/second.

Factorsinuencing therate ofreaction

Rate ofa chemicalreaction isinfluenced bythe following factors (i) Temperature(ii)Concentration ofthe reactants(iii) Natureof reactants (iv) Catalysts (v) Radiation (i) Temperature In mostcases, therate ofa reactionin ahomogeneous reactionis approximatelydoubled or tripledby anincrease intemperature ofonly 100C. Insome casesthe risein reaction rates aree venhigher. (ii) Concentrationof thereactants At afix edtemperatureandin theabsence ofcatalyst, therate ofgi ven reactionincreases with increasedconcentration ofreactants. With increasingconcentration ofthereactant 4 the numberof moleculesper unitv olumeis increased,thus thecollisionfrequency is increased, whichultimately causesincreased reactionrate. (iii) Natureof reactants to theproduct. Oldbonds arebrok enand new bondsareformed.Consequently ,the na- ture andthe strengthof thebonds inreactant moleculesgreatly influencet herate ofits transformation intoproducts. Thereaction inwhich inv olve lesserbond rearrangement proceeds muchf asterthanthosewhich inv olve larger bondrearrangement. (iv) Catalysts The rateof achemical reactionis increasedin presenceof acatalyst whichultimately enhanced thespeed ofa chemicalreaction. (v) Radiation The rateof anumber ofchemical reactionsincreases whenradiations ofspecific wa ve length areabsorbedby thereacting molecules.Such reactionsare calledphotochemical reactions. Fore xample,chlorinemaybe mixed safelywith hydrogen indark,since thereaction between thetw oisvery slow .Howev erwhenthemixtureise xposedtolight,thereaction is explosive.

H2+Cl2hn!2HCl+188KJ

SKILL TEST

1.What doyou meanby chemicalkinetics?

2.What doyou meanby rateof areaction?

3.What isspecific reactionrate orv elocityconstant (k)?

4.What arethe factors thatcan changethevalue ofK?

5Chemistry-I

1.3 Orderof reaction

The orderis thenumber ofconcentration termson whichreaction ratesdepends. Thus, if therate ofa reactiondepends onthe firstpo werof theconcentration ofreactant, i.e.

Rate=KC1

Thus thereaction issaid tobe ofthe first order.When therate isproportional tot he product oftw oreactantconcentrationsor thesquare ofthe concentrationof areactant, the reactionis ofthe second order.

Fore xample,thedecompositionof hydroiodic acid

Rate=K C2HI

Rate=K C2HI

and theh ydrogen-iodinereaction

H2+I2!2H I

Rate =KC H2CI2

Here bothare second orderreactions.

If thereaction rateis experimentally foundto berepresentedby dC dt=KCn

The orderof thereaction isn.

If severalreactantsA,B, C,. .. .. ..etc areinvolvedanditisobservedexperimentally that therate ofthe processis giv enby , dc dt=KCaACb BCg

C:::::::

Then theorder ofthe reactionw ouldbe n=a+b+g+::::::: The reactionis saidto beathorder withrespect toA, bthorder withrespect toB etc. But thereare reactionsin whichthe orderis fractionali.e. n=1 2;3

2etc:. Forexample,

the ortho- parah ydrogencon version,itsrate isexpressedbyd[H2] dt=K C3/2H2 6

1.4 Molecularityof ar eaction

The molecularityof areaction isdefined asthe numberof moleculesor atomswhich takepart inthe processof achemical change. The reactionis saidto beunimolecular,bimolecular ,termolecularaccording toone, two,or threemolecules arein volv edin theprocessofachemicalchange. The termunimolecular was usedforallfirst orderreactions, theterm bimolecularfor

2nd orderreactions etc.

SKILL TEST

1.What doyou meanby theorder ofa reaction?

2.What isthe molecularityof areaction?

3.Can orderof areaction befractional?

4.Is itpossible fora reactionto hav eidentical values formolecularity andorder?

1.5 ZeroOrderKinetics

A chemicalreaction whoserate doesnot dependon concentrationof reactantsis called a zeroorder chemicalreaction.

The rateof thereaction canbe writtenas

dx dt= Constant )dx dt= K or,dx=Kdt

On integration,Rdx=KRdt

or,x=Kt+Z(IntegrationConstant).

Whent=0;x=0 henceZ=0

So,x=Kt

Or,K=x

t A plotof xversustshould giveastraightline passingthrough theorigin assho wnin the figure andthe slopeof thisstraight lineis K. Example: Photochemicalcombination ofH2andCl2to formHCl.

7Chemistry-I

Figure 1.1:Plot ofconcentration against tfor areaction

H2+Cl2hn!2HCl

The rateof thisreaction doesnot dependon concentration.

1.6 FirstOrder Kinetics

A reactionof thefirst orderis representedas

X!Y where Xis thereactant andY theproduct. Therate ofthe reactionwill bedirectly proportional tothe concentrationi.e., (1.1)dc dt=KC in whichC isthe concentrationof thereactant atan ytime tand Kis aconstant, called the velocityconstantor specificreaction rate.

Thusdc

C=Kdt

On integrationRdc

C=KRdt

8 lnc=kt+Z(IntegrationConstant). If atthe startof thereaction theinitial concentrationof thereactant isCothen weha ve att=0;C=Co

SubstitutinglnCo=Z

lnC=KtlnCo lnCo C=Kt OrC

Co=eKtOr

(1.2)C=CoeKt The concentrationC thereforediminishes exponentially withtime.

Wemay alsowrite

(1.3) CoC=Co(1eKt) The rateequation mayalso becon veniently expressed inanalternativeform, byex- pressing therate interms ofthe product.When xmoles perunit volume ofproductY is formedfrom thereactant, theconcentration ofthe reactantis (ax), whereais the initial concentrationof thereactants. So d dt(ax) =K(ax) dx dt=K(ax) dx ax=K dt

On integrationRdx

ax=KRdt or,ln(ax) =Kt+Z0(IntegrationConstant)

Whent=0;x=0;hencelna=Z

0

9Chemistry-I

ln(ax) =Ktlna lna ax=Kt (1.4)K=1 tlna (ax) (1.5)x=a(1eKt)

The fractionale xtentofthereaction atan ytime tis

(1.6)x a= (1eKt) When theinitial concentrationais notkno wnbutthe concentrationsattwo intervals t1andt2are known,therate equationcan bederi ved. Ifx1andx2are theconcentrations of productat timet1andt2, thecorresponding concentrationsof reactantsw ouldbe (a x1)and(ax2). So

Kt1=lna

ax1and Kt2=lna ax2 (1.7)K(t2t1) =lnax1 ax2

Characteristics

1) Ina firstorder reactionC=CoeKt, thereaction cannot becomplete becauseC would

become zeroat infinitetime.

2) Thequantity a

(ax)or CoC is aratio ofconcentrations, so,its value willbe thesame what everunitsareemplo yedto express theconcentrationse.g.moles/litre, gms/c.cetc.

It showsthatthe velocity constant K=1

tlna ax will havethedimensionof reciprocal time,Sec1: 10

3) Theequation isln (ax) =Kt+lna

log(ax) = K 2:303 t+loga If log(ax)is plottedgraphically against time,itwould giv ea straightline.Sowhen a plotconstructed frome xperimentalv aluesoflog(ax)and tis foundto belinear ,the reaction isof thefirst order .The slopeofthelineisK

2:303from whichthe velocity

constant Kcan bedetermined.

Figure 1.2:Plot oflog (ax)againstt fora reaction

4) Thetime requiredfor halfthe reactantto changecan beeasily ev aluated.Let t1/2be

the timerequired whenx=a 2.

Thent1/2=1

Klna aa/2 =1 Klna a 2 =2:303 log2

K=0:693

K The periodof halfdecomposition isthus constantfor agi ven reactionand isindependent of initialconcentration. Thetime requiredis calledhalf value periodor halflife incase of radioactivechanges. The timenecessary tocomplete any definitefraction (j)of thereaction isindependent of theinitial concentrationin firstorder kinetics,for tf=2:303 Kloga aaf =2:303 Klog1

1j=constant.

11Chemistry-I

1.7 SecondOrder Kinetics

A reactionwill beof thesecond orderwhen thereaction ratew oulddepend uponthe product oftw oconcentrations.

Second orderreactions areof two types

(i) Therate isproportional tothe squareof thesame reactantconcentration (ii) Therate isproportional tothe productof thetw oreactant concentration (i) Ther ateisproportional tothe squareofthe samer eactantconcentr ation

Let say,2A!Products

(ax) If thetw osubstanceshav ethe sameinitialconcentration(a)and ifx denotesthe concen- tration ofthe reactantswhich disappearsin timet, thenthe ratewill be dx dt=K(ax)2 dx (ax)2=Kdt

On integration,

Zdx (ax)2=K Z dt 1 (ax)=Kt+Z(Integrationconstant)

Whent=0;x=0)1

a=Z

Substituting thev alueofZ

(1.8)1 (ax)1 a=Kt

Thus thev elocityconstant

(1.9)K=x at(ax) Hence atan ytimet,the fractionale xtentof thereaction would be 12 x a=11 1+Kta In asecond orderreaction, wherethe two initialconcentrations arethe samethenfrom

1.9 thehalf value periodisgiv enby

t1/2=x ak(aa 2)= a 2 a:k:a 2 =1 ak i.e. thetime requiredfor halfthe amountof reactantto undergo thechange isin versely proportional toinitial concentrationa, whereas inrst orderreaction t1/2is constant. (ii) Ther ateisproportional tothe productofthe twor eactantconcentr ation

Let sayanother typeof reaction

A+B!Product

(ax) (bx) When theinitial concentrationsof thetw osubstances participatingare different,saya and b,then therate isgi ven by, dx dt=K(ax)(bx) wherexis theamount ofan yreactant transformedintimet dx (ax)(bx)=K dt 1 (ab)quotesdbs_dbs10.pdfusesText_16

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