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CBSEClass–12SubjectChemistry

NCERTSolutions

Chapter–04

ChemicalsKinetics

In-textquestion

1.Forthereaction ,theconcentrationofareactantchangesfrom0.03Mto0.02

M in 25 minutes. Calculate the average rate of reaction using units of time both in

minutesandseconds.

Ans.Averagerateofreaction

2.Inareaction, Products,theconcentrationofAdecreasesfrom to

in10minutes.Calculatetherateduringthisinterval?

Ans.Averagerate

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=0.005molL-1min-1

=5×10-3Mmin-1

3.Forareaction, ’Product;theratelawisgivenby, .Whatis

theorderofthereaction?

Ans.Theorderofthereaction

=2.5

4.TheconversionofmoleculesXtoYfollowssecondorderkinetics.Ifconcentrationof

XisincreasedtothreetimeshowwillitaffecttherateofformationofY?

Ans.Thereaction followssecondorderkinetics.

Therefore,therateequationforthisreactionwillbe:

Rate= (1)

Let[X]=A ,thenequation(1)canbewrittenas:

Rate=

IftheconcentrationofXisincreasedtothreetimes,then[X]=3AmolL-1

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Now,therateequationwillbe:

Rate=K[3A]2

=9K[A]2

Hence,therateofformationwillincreaseby9times.

5.Afirstorderreactionhasarateconstant1.15x10-3.Howlongwill5gofthisreactant

taketoreduceto3g?

Ans.Fromthequestion,wecanwritedownthefollowinginformation:

Initialamount=5g

Finalconcentration=3g

Rateconstant=1.15x10-3

Weknowthatfora1storderreaction,

=444.38s

=444s(approx.)

6.Timerequiredtodecompose tohalfofitsinitialamountis60minutes.Ifthe

decompositionisafirstorderreaction,calculatetherateconstantofthereaction.

Ans.Weknowthatfora1storderreaction,

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Itisgiventhat

7.Whatwillbetheeffectoftemperatureonrateconstant?

Ans. The rate constant of a reaction is nearly doubled with a rise in temperature.

However,theexactdependenceoftherateofachemicalreactionontemperatureisgivenby

Arrheniusequation,

Where,

AistheArrheniusfactororthefrequencyfactor

Tisthetemperature

Risthegasconstant

istheactivationenergy.

8. The rate of the chemical reaction doubles for an increase of 10 K in absolute

temperaturefrom298K.Calculate .

Ans.Itisgiventhat =298K

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Therefore,

=308K

Wealsoknowthattherateofthereactiondoubleswhentemperatureisincreasedby .

Therefore,letustakethevalueof andthatof

Also,

Now,substitutingthesevaluesintheequation:

Weget:

9.Theactivationenergyfor thereaction is at581

K.Calculate the fractionofmolecules of reactantshaving energy equal to or greater

thanactivationenergy?

Ans.Inthegivencase:

T=581K

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Now,thefractionofmoleculesofreactantshavingenergyequaltoorgreaterthanactivation

energyisgivenas:

In

Now,x=Antilog(18.8323)

=Antilog

Class–XIIChemistry

Chapter–04ChemicalsKinetics

ChapterEndquestion

Part-1

1. From the rate expression for the following reactions, determine their order of

reactionandthedimensionsoftherateconstants.

(i)

(ii)

(iii)

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(iv)

Ans.(i)Givenrate=

Therefore,orderofthereaction=2

Dimensionof

(ii)Givenrate=


Dimensionof

(iii)Givenrate=

Therefore,orderofreaction=

Dimensionof

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(iv)Givenrate=


Dimensionof

2.Forthereaction: therate=

with . Calculate the initial rate of the reaction when

, .Calculatetherateofreactionafter[A]isreduced

to .

Ans.Theinitialrateofthereactionis

Rate=

When [A] is reduced from to , the concentration of A reacted =

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Therefore,concentrationofBreacted

Then,concentrationofBavailable,

After[A]isreducedto ,therateofthereactionisgivenby,

Rate=

3.Thedecompositionof onplatinumsurfaceiszeroorderreaction.Whatarethe

ratesofproductionof and if ?

Ans. The decomposition of on platinum surface is represented by the following

equation.

Therefore,

However,itisgiventhatthereactionisofzeroorder.

Therefore,

Therefore,therateofproductionof is

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And,therateofproductionof is

4.Thedecompositionofdimethyletherleadstotheformationof , andCOand

thereactionrateisgivenbyRate= .Therateofreactionisfollowedby

increaseinpressureinaclosedvessel,sotheratecanalsobeexpressedintermsofthe

partial pressure of dimethyl ether, i.e., If the pressure is

measured in bar and time in minutes, then what are the units of rate and rate

constants?

Ans.Ifpressureismeasuredinbarandtimeinminutes,then

Unitofrate=

Therefore,unitofrateconstants

5.Mentionthefactorsthataffecttherateofachemicalreaction.

Ans.Thefactorsthataffecttherateofareactionareasfollows.

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(i)Concentrationofreactants(pressureincaseofgases)

(ii)Temperature

(iii)Presenceofacatalyst

6. A reaction is second order with respect to a reactant. How is the rate of reaction

affectediftheconcentrationofthereactantis

(i)doubled

(ii)reducedtohalf?

Ans.Lettheconcentrationofthereactantbe[A]=a

Rateofreaction,

(i)Iftheconcentrationofthereactantisdoubled,i.e.[A]=2a,thentherateofthereaction

wouldbe

=4R

Therefore,therateofthereactionwouldincreaseby4times.

(ii)Iftheconcentrationofthereactantisreducedtohalf,i.e. ,thentherateofthe

reactionwouldbe

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Therefore,therateofthereactionwouldbereducedto

7.What is theeffectof temperatureon therateconstantofareaction?Howcan this

temperatureeffectonrateconstantberepresentedquantitatively?

Ans.Therateconstant isnearlydoubledwitharise in temperatureby for a chemical

reaction.

ThetemperatureeffectontherateconstantcanberepresentedquantitativelybyArrhenius

equation,

where,kistherateconstant,

AistheArrheniusfactororthefrequencyfactor,

Risthegasconstant,

Tisthetemperature,and

istheenergyofactivationforthereaction.

8. In a pseudo first order hydrolysis of ester in water, the following results were

obtained:

(i)Calculatetheaveragerateofreactionbetweenthetimeinterval30to60seconds.

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(ii)Calculatethepseudofirstorderrateconstantforthehydrolysisofester.

Ans.(i)Averagerateofreactionbetweenthetimeinterval,30to60seconds,

(ii)Forapseudofirstorderreaction,

Fort=30s,

Fort=60s,

Fort=90s,

Then,averagerateconstant,

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9.AreactionisfirstorderinAandsecondorderinB.

(i)Writethedifferentialrateequation.

(ii)HowistherateaffectedonincreasingtheconcentrationofBthreetimes?

(iii)HowistherateaffectedwhentheconcentrationsofbothAandBaredoubled?

Ans.(i)Thedifferentialrateequationwillbe

(ii)IftheconcentrationofBisincreasedthreetimes,then

Therefore,therateofreactionwillincrease9times.

(iii)WhentheconcentrationsofbothAandBaredoubled,

Therefore,therateofreactionwillincrease8times.

10. In a reactionbetweenA andB, the initial rate of reaction wasmeasured for

differentinitialconcentrationsofAandBasgivenbelow:

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WhatistheorderofthereactionwithrespecttoAandB?

Ans.LettheorderofthereactionwithrespecttoAbexandwithrespecttoBbey.

Therefore, ]

Dividingequation(i)by(ii),weobtain

y=0

Dividingequation(iii)by(ii),weobtain

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=1.496

=1.5(approximately)

Hence,theorderofthereactionwithrespecttoAis1.5andwithrespecttoBiszero.

11.Thefollowingresultshavebeenobtainedduringthekineticstudiesofthereaction:

Determinetheratelawandtherateconstantforthereaction.

Ans.LettheorderofthereactionwithrespecttoAbexandwithrespecttoBbey.

Therefore,rateofthereactionisgivenby,

Accordingtothequestion,

Dividingequation(iv)by(i),weobtain

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x=1

Dividingequation(iii)by(ii),weobtain

y=2

Therefore,theratelawis

FromexperimentI,weobtain

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FromexperimentII,weobtain,

FromexperimentIII,weobtain

FromexperimentIV,weobtain

Therefore,rateconstant,k=

12.ThereactionbetweenAandBisfirstorderwithrespecttoAandzeroorderwith

respecttoB.Fillintheblanksinthefollowingtable:

Ans.ThegivenreactionisofthefirstorderwithrespecttoAandofzeroorderwithrespect

toB.

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Therefore,therateofthereactionisgivenby,

Rate=k[A]

FromexperimentI,weobtain

FromexperimentII,weobtain

FromexperimentIII,weobtain

FromexperimentIV,weobtain

13. Calculate the half-life of a first order reaction from their rate constants given

below:

(i)

(ii)

(iii)4

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Ans.(i)Half-life,

(approximately)

(ii)Half-life,

=0.35min(approximately)

(iii)Half-life,

=0.173years(approximately)

14. Thehalf-life for radioactivedecay of 14C is 5730 years.Anarchaeological artifact

woodhadonly80%ofthe14Cfoundinalivingtree.Estimatetheageofthesample.

Ans.Here,

Itisknownthat,

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=1845years(approximately)

Hence,theageofthesampleis1845years.

15.Theexperimentaldata fordecompositionof in gas

phaseat318Karegivenbelow:

(i)Plot againstt.

(ii)Findthehalf-lifeperiodforthereaction.

(iii)Drawagraphbetweenlog andt.

(iv)Whatistheratelaw?

(v)Calculatetherateconstant.

(vi)Calculatethehalf-lifeperiodfromkandcompareitwith(ii).

Ans.

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(ii)Timecorrespondingtotheconcentration, isthehalf-

life.Fromthegraph,thehalf-lifeisobtainedas1450s.

(iii)

(iv) The given reaction is of the first order as the plot, v/st, is a straight line.

Therefore,theratelawofthereactionis

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(v)Fromtheplot, v/st,weobtain

Again,slopeofthelineoftheplot v/stisgivenby Therefore,weobtain,

Class–XIIChemistry

Chapter–04ChemicalsKinetics

ChapterEndquestion

Part-2

16.Therateconstantforafirstorderreactionis60s-1.Howmuchtimewillittaketo

reducetheinitialconcentrationofthereactanttoits1/16thvalue?

Ans.Itisknownthat,

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Hence,therequiredtimeis .

17.Duringnuclearexplosion,oneoftheproductsis withhalf-lifeof28.1years.If

of wasabsorbed in thebonesofanewlybornbaby insteadof calcium,how

muchofitwillremainafter10yearsand60yearsifitisnotlostmetabolically.

Ans.Here,

Itisknownthat,

Therefore, of willremainafter10years.

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Again,

Therefore, of willremainafter60years.

18.Forafirstorderreaction,showthattimerequiredfor99%completionistwicethe

timerequiredforthecompletionof90%ofreaction.

Ans.Forafirstorderreaction,thetimerequiredfor99%completionis

Forafirstorderreaction,thetimerequiredfor90%completionis

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Therefore,

Hence, the time required for 99% completion of a first order reaction is twice the time

requiredforthecompletionof90%ofthereaction.

19.Afirstorderreactiontakes40minfor30%decomposition.Calculate .

Ans.Forafirstorderreaction,

Therefore, ofthedecompositionreactionis

=77.7min(approximately)

20. For the decomposition of azoisopropane to hexane and nitrogen at 543 K, the

followingdataareobtained.

Calculatetherateconstant.

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Ans.Thedecompositionofazoisopropanetohexaneandnitrogenat543Kisrepresentedby

thefollowingequation.

Aftertime,t,totalpressure,

Therefore,

Forafirstorderreaction,

Whent=360s,

Whent=720s,

Hence,theaveragevalueofrateconstantis

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21.Thefollowingdatawereobtainedduringthefirstorderthermaldecompositionof

ataconstantvolume.

Calculatetherateofthereactionwhentotalpressureis0.65atm.

Ans. The thermal decomposition of at a constant volume is represented by the

followingequation.

Aftertime,t,totalpressure,

Therefore,

Forafirstorderreaction,

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Whent=100s,

When ,

=0.65–0.5

=0.15atm

Therefore,whenthetotalpressureis0.65atm,pressureof is

=0.5–0.15

=0.35atm

Therefore,therateofequation,whentotalpressureis0.65atm,isgivenby,

22.Therateconstantforthedecompositionof atvarioustemperaturesisgiven

below:

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Drawagraphbetweenlnkand1/Tandcalculate thevaluesofAand .Predict the

rateconstantat and .

Ans.Fromthegivendata,weobtain

Slopeoftheline,

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AccordingtoArrheniusequation,

Slope=

=

Again,

WhenT=273K

Ink=–7.147

Then,InA=

=37.911

Therefore,A=

When,T=30+273K=303K

Then,at ,

Ink=–2.8

Therefore,k=

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Again,whenT=50+273K=323K

1/T=3.09x10-3

lnk=-0.6

k=0.5488s-1

23.Therateconstantforthedecompositionofhydrocarbonsis at546K.

If the energy of activation is 179.9 kJ/mol, what will be the value of pre-exponential

factor.

Ans.

T=546K

AccordingtotheArrheniusequation,

=(0.3835-5)+17.2082

=12.5917

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Therefore,A=antilog(12.5917)

= (approximately)

24. Consider a certain reaction A Products with . Calculate the

concentrationofAremainingafter100siftheinitialconcentrationofAis .

Ans.

T=100s

Sincetheunitofkis ,thegivenreactionisafirstorderreaction.

Therefore,

= (approximately)

Hence,theremainingconcentrationofAis .

25.Sucrosedecomposesinacidsolutionintoglucoseandfructoseaccordingtothefirst

orderratelaw,with .Whatfractionofsampleofsucroseremainsafter

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8hours?


Itisgiventhat,

Therefore,

=

Then,

(approx)

=0.158

Hence,thefractionofsampleofsucrosethatremainsafter8hoursis0.158.

26. The decomposition of hydrocarbon follows the equation

.

Calculate .

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Ans.Thegivenequationis ……………..(i)

Arrheniusequationisgivenby,

……………….(ii)

Fromequation(i)and(ii),weobtain

27. The rate constant for the first order decomposition of is given by the

followingequation: Calculate forthisreactionand

atwhattemperaturewillitshalf-periodbe256minutes?

Ans.Arrheniusequationisgivenby,

Thegivenequationis

……………………..(ii)

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Fromequation(i)and(ii),weobtain

(approximately)

Also,when

Itisalsogiventhat,

=668.95K

=669K(approximately)

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28. The decomposition of A into product has value of k as at and

energyofactivation .Atwhattemperaturewouldkbe ?

Ans.FromArrheniusequation,weobtain

Also,

=273+10=283K

Then,

=297K

=

Hence,kwouldbe at .

29.Thetimerequiredfor10%completionofafirstorderreactionat298Kisequalto

thatrequiredforits25%completionat308K.IfthevalueofAis .Calculatek

at318Kand .


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At298K,

At308K,

Accordingtothequestion,t=t’

FromArrheniusequation,weobtain

Tocalculatekat318K,

Itisgiventhat,

Again,fromArrheniusequation,weobtain

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=(0.6021+10)–12.5876

=–1.9855

Therefore,k=Antilog(–1.9855)

=

30.Therateofareactionquadrupleswhenthetemperaturechangesfrom293Kto313

K.Calculatetheenergyofactivationof thereactionassumingthat itdoesnotchange

withtemperature.

Ans.FromArrheniusequation,weobtain

Itisgiventhat,

Therefore,

Hence,therequiredenergyofactivationis .

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