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Kinetics

161

Dferen cemca reacons occur a dferen raes

(.e. speeds). Some, suc as e neurasaon o a

srong acd by a srong base n aqueous souon, ake pace

very rapdy ws oers, suc as e rusng o ron, ake

pace ar more sowy. Raes o reacons soud no be

conused w ow ar a reacon goes - s s deermned

by equbrum.

he rate of a chemical reaction s a measure o e speed

a wc producs are ormed, measured as e cange n

concenraon dvded by e cange n me, so reacon

rae as uns o mo dm–3 s–1. hs s equa o e rae a

wc e reacans are consumed, so or a reacon:

R P, rae = ∆[ P ] ____ ∆t

= –∆[ R ] _____ ∆t

Figure 601 An explosion is a quick reaction

Figure 602 Corrosion is a slow reaction

6.1.1 Define the term rate of reaction.

6.1.2 Describe suitable experimental

procedures for measuring rates of

reactions.

6.1.3 Analyse data from rate experiments.

© IBO 2007

6.1 Rates of Reaction

Kinetics6.1 Rates of reaction

6.2 Collision theory

16.1 Rate Expression (AHL)

16.2 Reaction mechanism (AHL)

16.3 Activation energy (AHL)

6

070809 Chem Chap 6-3 for correct161 161 7/12/2007



CHAPTER 6

162

P r o p

e r t y

Time

P r o p

e r t y

Time

Gradient = – initial rate

Gradient = – rate at time t = x

Gradient = initial rate

Gradient = rate at time t = x

Product formation Reactant consumption

x x

Figure 603 The variation of reaction rate with time

c o R e

Noe e mnus sgn or e reacans, wc s necessary

as e concenraons o reacans decreases w me

wereas e concenraons o producs ncreases. Rae s

aways posve.

he numerca vaue w vary accordng o e amoun o

e subsance nvoved n e socomerc equaon, so

a n e reacon:

MnO4

–(aq) + 8 H+

(aq) + 5 Fe2+ (aq) Mn2+ (aq) + 4 H

2O () + 5 Fe3+ (aq)

he rae o appearance o Fe3+ s ve mes as grea as

e rae a wc MnO4

– s consumed. he rae s usuay

consdered o appy o a produc a as a coeicen o

one as e equaon s usuay wren:

Rae = –∆[ MnO

4 – ] ________

∆t = 1 _ 5 ∆[ Fe3+ ] ______

∆t

Or more smpy or a reacon: a A b B, en

Rae = 1 __ b

∆[ B ] _____ ∆t

= –1 __ a ∆[ A ] _____ ∆t

Any propery a dfers beween e reacans and e

producs can be used o measure e rae o e reacon.

Refer to Secton 6.2. Wcever propery s cosen, a

grap s drawn o a propery agans me and e rae

o reacon s proporona o e graden o e curve or

ne gnorng e sgn. Canges n e graden o smar

graps usrae e efec o cangng condons on e

rae o reacon, wou e need o conver e uns o

mo dm–3 s–1.

In mos cases e rae o reacon decreases w me

because e concenraon o e reacans decreases w

me and e reacon rae usuay depends on e reacan

concenraon. I s mos common o compare na

raes, a s, e graden o e angen o e curve a

t = 0. A s me e concenraons o e reagens are

accuraey known, as s e emperaure o e sysem. I

s aso eases o draw angens a s me as s secon

o e curve s e mos near. Typca curves obaned or

e consumpon o a reagen and ormaon o a produc

are sown n Fgure 603.

Exercise 6.1

1. he equaon or a reacon s:

4 NO2

(g) + 2 H2O (g) + O

2(g) 4 HNO

3(g)

Wc one o e oowng s no numercay equao e oers?

A – 1 __ 2

∆[ NO

2 ] _______

∆t

B – 1 __ 2

∆[ O2

] _____ ∆t

C –∆[ H2

O ] _______ ∆t

D 1 __ 2

∆[ HNO

3 ] ________

∆t

2. Wc o e curves on e oowng grap sows

e greaes na reacon rae?




Kinetics

163

A

B

C

D C o n c e n t r a t i o n

Time

3. Iodae(V) ons oxdse odde ons n acdc souon

o orm odne and waer accordng o e equaon

IO3

– (aq) + 5 I– (aq) + 6 H+(aq)3 I

2 (aq) + 3 H

2O ()

I e number o moes o eac reacan consumed

ater one mnue was measured, wc woud ave

been consumed eas?

A IO3

–

B I–

C H+

D hey woud a ave been consumed o

e same exen.

4. he rae o reacon beween ydrogen peroxde and

e odde ons was measured by monorng e

absorpon o bue g by e odne. I e equaon

or e reacon s

H2O2 (aq) + 2 I–(aq) + 2 H+(aq) I2 (aq) + 2 H2O ()

a) I 0.005 mo dm-3 o odne s produced n

e rs 2 mnues, wa s e na reacon

rae n mo dm-3 s-1?

b) Wa s e rae a wc

ydrogen peroxde s consumed?

odde ons are consumed?

Expan wy ese are dferen.

5. he rae o reacon beween znc and suurc acd

s measured by wegng a znc pae, wc s en

paced no a beaker o e acd. Every 10 mnues

s removed, rnsed, dred and reweged. hs s

connued un a o e acd s consumed.

a) Skec e grap you woud expec or e

mass o e znc pae agans me n e acd.

b) A wa pon s e reacon rae e

greaes? How can you e?

c) Sugges anoer way a e rae o s

reacon coud ave been measured.

here are a varey o ecnques a can be used o

measure e rae o a cemca reacon and some o e

more common are descrbed beow. Any propery a

canges beween e sar and end o e reacon can n

prncpe be used. I s owever bes s canges by a

arge amoun compared o e ms o accuracy o s

measuremen. I s aso smper o use quanavey e

caracersc s drecy proporona o e concenraon

o one or more componens. For ese reasons monorng

e rae o reacon by observng a pH cange s generay

no o be recommended, because e pH, beng a

ogarmc scae, w ony cange by 0.30 or a cange o

[H+] by a acor o 2.

In some ecnques e me aken or a parcuar even

o occur may be used o measure e reacon rae (e.g. e

me aken or a pece o magnesum rbbon o dssove

n a due acd). In ese ecnques s mporan o

remember a e greaer e me e smaer e rae o

reacon, .e. e rae o reacon s nversey proporona

o e me aken:

Rae ∝ 1 _____ Tme

I e purpose o e nvesgaon s smpy o observe

e efec o some varabe, suc as e concenraon

o a parcuar speces, on e rae o reacon, en agrap o e propery proporona o concenraon

agans me, w suice. I owever e reacon rae s

requred n sandard uns (mo dm–3 s–1) en w be

necessary o cabrae e sysem so as o produce graps

o concenraon agans me.

Wcever ecnque s beng used, s mporan o keep

e reacon mxure a a consan emperaure durng e

reacon, because emperaure as a grea efec on e

rae o reacon. For s reason s usua o mmerse e

reacon vesse n a waer ba a e requred emperaure.

I s aso preerabe o mmerse e reacans n e waer

ba, o aow em o reac e requred emperaure

beore mxng. One reason or preerng ‘na rae’ daa

s a e efec o an endo- or exoermc reacon on e

emperaure o e sysem s mnmsed.

some techniques foR measuRing

Rates




CHAPTER 6

164

c o R e

tr

hs nvoves removng sma sampes rom e reacon

mxure a dferen mes and en rang e sampe o

deermne e concenraon o eer one o e reacans

or one o e producs a s me. he resus can en be

used drecy o generae a grap o concenraon agans

me. In s smpes orm s s ony reay suabe or

que sow reacons, n wc e me aken o rae

e mxure s nsgncan compared o e oa me

aken or e reacon. One common varan a eps

o overcome s dicuy s o quenc e reacon

beore carryng ou e raon. hs means aerng e

condons so as o vruay sop e reacon. hs can

be done by rapdy coong e reacon mxure o a very

ow emperaure or by addng an excess o a compound

a rapdy reacs w one o e reacans. I or exampe

e reacon was a o a aogenoakane w an aka,

coud be quenced by runnng e reacon mxure

no an excess o a srong acd. hs means a e me awc e sampe o e reacon mxure was quenced s

muc easer o deermne.

Anoer exampe o a reacon a can be ready measured

by s ecnque s e rae o reacon o ydrogen

peroxde w odde ons n acdc souon o produce

odne and waer. he amoun o odne produced can be

measured by rang e mxure w aqueous sodum

osuae. he reacon mxure can be quenced by

addng excess o an nsoube sod base, suc as powdered

cacum carbonae, o neurase e acd requred or

reacon.

H2O2 (aq) + 2 H+ (aq) + 2 I– (aq) 2 H2O () + I2 (aq)

cll ld /r rr

he gas produced n e reacon s coeced eer n a gas

syrnge, or n a graduaed vesse over waer. he voume

o gas coeced a dferen mes can be recorded. hs

ecnque s obvousy med o reacons a produce a

gas. In addon, e gas s o be coeced over waer, s

gas mus no be waer soube. An aernave ecnque s

o carry ou e reacon n a vesse o xed voume and

monor e ncrease n e gas pressure. hese ecnques

woud be suabe or measurng e rae o reacon

beween a moderaey reacve mea (suc as znc) and an

acd (suc as ydrocorc acd), or reacon o a carbonae

w acd:

Zn (s) + 2 H+ (aq) Zn2+ (aq) + H2 (g)

Na2CO

3 (s) + 2 HC (aq)

2 NaC (aq) + CO2 (g) + H

2O ()

TOK The empirical nature of chemistry

I used to think all magpies were black and white.

In both England and New Zealand (my two “home”

countries – whatever that concept implies) the

magpie (very different species in both countries

– the New Zealand version is a lot heavier and

doesn’t have the long tail) are black and white birds.

Then there’s the magpie robin, a much smaller bird,

and the magpie goose - both also black and white.

Indeed in England Newcastle United football club

are nicknamed ‘the magpies’ because of their black

and white shirts. My simple world was turned on its

head when I arrived in Hong Kong and encountered

the blue magpie. Definitely a magpie shape, but

with bright blue as the dominant colour (along with

black and white) and a gorgeous long tail. I’m afraid

I was another victim of the fundamental problem of

inductive logic - you can never be sure. However, incase you’re thinking you will just rely on deductive

techniques, reflect for a few seconds on how you

establish your premises.

All empirical science suffers in the same way - it is

quite easy to prove a theory wrong, but it is never

possible to prove it correct. Tomorrow somebody

might come up with a piece of evidence that

contradicts your theory and then it’s back to the

drawing boards. Falsification is so fundamental to

science that the Austrian philosopher, Karl Popper ,

said that if you could not think of an experiment

that would disprove your theory, then it was not ascientific theory.

In kinetics, the balanced equation tells us nothing

about how changing the concentrations will

affect the rate and we have to do experiments to

determine the rate equation. We can then postulate

mechanisms that would account for the empirical rate

equation and certainly we can rule out some possible

mechanisms, but even if we have a mechanism that

explains the rate equation (and sometimes there can

be more than one mechanism that does this, read

this chapter) we can never be sure that tomorrow

somebody will not come up with an alternative.




Kinetics

165

mr r r

he oa mass o e reacon mxure w ony vary a

gas s evoved. To be reay efecve, e gas beng evoved

soud ave a g moar mass (.e. no ydrogen), so

a ere s a sgncan cange n mass, aso e gas

soud no be sgncany soube n e soven used.

hs ecnque woud be suabe or measurng e rae

o reacon beween a mea carbonae (suc as cacum

carbonae, marbe cps) and an acd (suc as ydrocorc

acd), by measurng e rae o mass oss resung rom

e evouon o carbon doxde.

CaCO3 (s) + 2 H+

(aq) Ca2+(aq) + H

2O () + CO

2 (g)

L br

I a reacon produces a precpae, en e me aken

or e precpae o obscure a mark made on a pece o

paper under e reacon vesse can be used as a measure

o reacon rae. For smpe work comparson o e mes,

keepng e dep o e qud consan w suice; e.g.

e me aken doubes en e reacon rae s aved.

A reacon a s oten suded by s ecnque s e

reacon beween aqueous osuae ons and a due

acd wc gves suur doxde, waer and a ney dvded

precpae o suur.

S2O

32– (aq) + 2 H+ (aq) H

2O () + SO

2 (g) + S (s)

A convenen way o oow s reacon s o pace a back

cross/mark on a we pece o paper under e reacon

mxure and o measure e me aken or e ney

suspended yeow suur o obscure e cross.

I e reacon nvoves a cooured reacan or produc,

en e nensy o e coour can be used o monor

e concenraon o a speces. In s smpes orm

s can be done by comparng e coour by eye agans

a se o sandard souons o known concenraon.

he ecnque s ar more precse an nsrumen a

measures e absorbance (wc s drecy proporona

o concenraon – reer o e Beer–Lamber aw n

Secon A8.6, Caper 12) suc as a coormeer or

specropoomeer s avaabe. I a coormeer s used

en a er o e compemenary coour o a o e

cooured speces soud be cosen – an aqueous souon o

a copper(II) sa s bue because absorbs red g, so a

s e nensy o ransmed red g no bue g a

w vary w s concenraon. I a specropoomeer s

used, en a waveeng near o e absorpon maxmum

o e cooured speces soud be seeced.

A reacon a s oten suded by s ecnque s

e reacon beween propanone and odne o orm

odopropanone. he yeow–brown odne s e ony

cooured speces nvoved and so e nensy o bue g

(or g o waveeng ≈450 nm a specropoomeer s

used) passng roug e souon w ncrease w me

as e concenraon o e odne as. Mos nsrumens,

owever, gve a drec readng o absorbance wc as

an nverse reaonsp o e ransmed g, so a

absorbance decreases w me.

CH3COCH

3 (aq) + I

2 (aq)

CH3COCH

2I (aq) + H+ (aq) + I– (aq)

elrl d

he presence o ons aows a souon o conduc, so

ere s a sgncan cange n e concenraon o ons(especay ydrogen and ydroxde ons wc ave

an unusuay g conducvy) durng e course o

a reacon, en e reacon rae may be ound rom

e cange n conducvy. hs s usuay ound by

measurng e A.C. ressance beween wo eecrodes

w a xed geomery, mmersed n e souon. A

reacon a s suabe or s ecnque woud be e

ydroyss o posporus(III) corde a produces

dydrogenpospae(III) ons, ydrogen ons and

corde ons rom non–onc reacans.

PC3 (aq) + 3 H

2O ()

H2PO3– (aq) + 4 H+ (aq) + 3 C– (aq)

clk

here are some reacons n wc e produc can

be consumed by urer reacon w anoer added

subsance. Wen a o s subsance s consumed en

an observabe cange w occur. he me aken or s

corresponds o e me or a ceran amoun o produc

o ave been ormed and so s nversey proporona o

e rae o reacon. he cassc reacon suded n s

way s e reacon beween ydrogen peroxde and odde

ons, n e presence o acd, o orm odne and waer.

hosuae ons are added o e sysem and ese nay

reac rapdy w e odne produced. Wen a o e

osuae as been consumed, ree odne s beraed

and s coours e souon yeow, or more commony

bue–back roug e addon o sarc souon (wc

orms an nensey cooured compex w odne) o e

sysem.




CHAPTER 6

166

c o R e

he bue coour o e odne-sarc compex suddeny appears wen a o e osuae

as been consumed. he me aken or s o occur s nversey proporona o e rae.

Exercise 6.1

1. he rae o a cemca reacon can somemes be

deermned by measurng e cange n mass o e

reacon lask and s conens w me. For wco e oowng reacons woud s ecnque be

mos successu?

A Magnesum oxde and

due suurc acd.

B Aqueous sodum corde and

aqueous sver nrae.

C Copper(II) carbonae and

due ydrocorc acd.

D Znc and

aqueous copper(II) suae.

2. You ws o carry ou an nvesgaon a nvovese use o a conducvy meer o monor e rae

o a cemca reacon. Wc o e reacons beow

woud be e eas suabe or s?

A H2O

2 (aq) + 2 H+ (aq) + 2 I–

(aq)

2 H2O () + I

2 (aq)

B Ba2+ (aq) + SO4

2– (aq) BaSO4 (s)

C POC3 () + 3 H

2O ()

4 H+ (aq) + 3 C– (aq) + H2PO

4– (aq)

D 2 H2O

2 (aq) 2 H

2O () + O

2 (g)

3. For wc one o e oowng reacons woud a

coormeer be mos suabe or monorng e

reacon rae?

A he reacon o acded permanganae

ons (manganae(VII)) ons w

eanedoc acd (oxac acd) o orm

carbon doxde, manganese(II) ons andwaer.

B he reacon o magnesum carbonae

w a due acd o orm a soube

magnesum sa, carbon doxde and

waer.

C he reacon o bromobuane w

aqueous sodum ydroxde o orm

buano and aqueous sodum bromde.

D he reacon o um w waer o

orm aqueous um ydroxde and

ydrogen.

4. You ws o measure e rae o reacon o acdeddcromae(VI) ons w aqueous suur doxde o

produce aqueous cromum(III) ons and aqueous

suae ons a 35 °C. hs reacon nvoves a coour

cange rom orange o green. Dscuss ow you mg

go abou dong s, e measuremens you woud

need o ake and e precauons requred.

5. Durng your sudy o cemsry you w mos key

ave suded e way n wc aerng ceran

varabes afeced e rae o a cemca reacon.

a) Wa reacon dd you sudy?

b) Wa ecnque dd you use o sudy e

rae o s reacon? Wy do you nk s

meod was approprae?

c) Wa varabe dd you cange? How was s

carred ou?

d) How coud you mody e nvesgaon o

sudy anoer varabe. Sae wc varabe

you are now gong o sudy and oune ow

you woud carry s ou aong w any

precauons you woud ake.

H2O

2 () + 2 H+ (aq) + 2 I– (aq) 2 H

2O () + I

2 (aq)

2 S2O32– (aq) + I2 (aq) S4O6

2– (aq) + 2 I– (aq)




Kinetics

167

Collisions are va or cemca cange, bo o provde

e energy requred or a parce o cange (or exampe, a

bond o break), and o brng e reacans no conac.

As parces approac eac oer ere s repuson beween

e eecron couds o e parces. In order or reacon

o occur, e coson mus ave suicen kinetic energy

o overcome s repuson. Frequeny energy s aso

requred o break some o e bonds n e parces beore

a reacon can ake pace. Hence no a cosons ead o

a reacon. hs mnmum amoun o energy requred or

reacon s known as e activation energy (Ea) or e

reacon (uns o Ea: kJ mo–1). hs s usraed, or an

exoermc reacon, n Fgure 605.

Reactants

Products

A c t i v a t i o n

E n e r g y ( E

a )

P o t e n

t i a l E n e r g y

Figure 605 The principle of activation energy

he acvaon energy nvoved vares remendousy rom

reacon o reacon. In some cases (suc as e reacon

o e ydrogen on and ydroxde on) s so ow a

reacon occurs on amos every coson even a ow

emperaures. In oer cases (suc as sugar and oxygen)

s so g a reacon a room emperaure s neggbe.

In order o reac, e wo parces nvoved mus:

code w eac oer

e coson mus be energec enoug o overcome

e acvaon energy o e reacon, (.e. e

coson mus ave E > Ea)

e coson mus occur w e correc geomerca

agnmen, a s mus brng e reacve pars o

e moecue no conac n e correc way

hs na acor, oten caed e steric factor, s parcuary

mporan w regard o reacons nvovng arge organcmoecues.

I anyng ncreases e collision rate, en e rae o

reacon ncreases. Smary anyng a ncreases e

proporon o e cosons a ave an energy equa o

or greaer an e acvaon energy w ncrease e rae

o reacon. hese acors are summarsed n Fgure 606.

Facors many afecng e coson

rae

Facors many afecng e

proporon w

requred Ea

Concenraon/pressure Temperaure

Surace area Caays

Figure 606 Factors affecting the rate of reaction (table)

•

•

•

6.2 coLLisiontheoRy

6.2.1 Describe the kinetic theory in terms

of the movement of particles whose

average energy is proportional to

temperature in kelvins.

6.2.2 Define activation energy, E a.

6.2.3 Describe the collision theory.

6.2.4 Predict and explain, using collision

theory, the qualitative effects of particle

size, temperature, concentration and

pressure on the rate of a reaction.

6.2.5 Sketch and explain qualitativelythe Maxwell–Boltzmann energy

distribution curve for a fixed amount

of gas at different temperatures and its

consequences for changes in reaction

rate.

6.2.6 Describe the effect of a catalyst on a

chemical reaction.

6.2.7 Sketch and explain Maxwell–Boltzmann

curves for reactions with and without

catalysts.

© IBO 2007




CHAPTER 6

168

c o R e

the effect of concentRationhe rae a wc parces code s ncreased by ncreasng

e concenraon o e reacans. hus marbe cps

reac aser w concenraed ydrocorc acd an ey

do w e due acd. For reacng gases, ncreasng e

pressure s equvaen o ncreasng e concenraon. he

efec o concenraon on rae s usraed n Fgure 607.

Figure 607 The effect of concentration

the effect of suRface aReaI e reacon nvoves subsances n pases a do no

mx (e.g. a sod and a qud, or a qud and a gas) en

an ncrease n e surace area n conac w ncrease e

coson rae. As a resu powdered cacum carbonae

reacs aser w ydrocorc acd an umps o e sod

w e same mass. hs s usraed n Fgure 608.

Figure 608 The effect of surface area

the effect of tempeRatuReNo a parces ave e same energy so ere s a

dsrbuon o knec energy, and ence veocy,

amongs e parces o e gas, known as e Maxwell-

Boltzmann distribution, sown n Fgure 609. As w

cars on a reeway, some are movng more rapdy and

oers more sowy. he mean speed o e parces s

proporona o e absoue emperaure bu, because e

curve s asymmerc, s does no concde w e mos

probabe speed. he area under e curve represens e

oa number o parces and ence, n a cosed sysem,

s area mus reman consan.

P r o b a b i l i t y

o f t h i s

e n e r g y

Energy

Low temperature

High temperature

E awith catalyst

E aun-catalysed

Figure 609 The effects of temperature and catalyst

As prevousy saed, a coson mus ave a ceran

mnmum energy, e acvaon energy, beore reacon

can occur. As can be seen n Fgure 609, e number o

moecues w e requred acvaon energy s mucgreaer a a ger emperaure an a a ower one. hs

means a marbe cps reac more rapdy w warm

ydrocorc acd an w cod ydrocorc acd.

Increasng e emperaure aso as a very sg efec on

e coson rae, bu n mos cases s s nsgncan

compared o s efec on e proporon o cosons w

e requred acvaon energy. For many reacons an

ncrease n emperaure o 10 °C w approxmaey doube

e rae o reacon (a crude generazaon), bu e ncrease

n e coson rae a s rse n emperaure causes

s ony ≈2%. To summarse, ncreasng e emperaure

ncreases e requency o cosons bu, more mporan

s e ncrease n e proporon o moecues w E > Ea.

he efec o emperaure on reacon rae s dscussed n

muc more dea n Caper 6.6.




Kinetics

169

Reactants

Products

E n t

h a l p y U

n c a t a l y s e d

E a

C a t a l y s e d

E a

With catalyst

Without catalyst

∆H

Figure 610 The effect of a catalyst

the effect of cataLystA caays s a subsance a s usuay requred n sma

amouns and can ncrease e rae o a cemca reacon

wou undergong any overa cange. Caayss speed up

a reacon by provdng an aernave reacon mecansm

or paway (ke a mounan pass) w a ower acvaon

energy by wc e reacon can ake pace. hs meansa a greaer proporon o cosons w ave e

requred energy o reac by e new mecansm and so

e reacon rae ncreases. Typcay, e eicency o a

caays decreases w me as becomes nacve due o

mpures n e reacon mxure, sde reacons, or s

surace becomes coaed and unavaabe or acvy.

he way s afecs e suaon n erms o e Maxwe-

Bozmann dsrbuon and e energy dagram s sown

n Fgures 609 & 610.

the effect of LightSome cemca reacons are broug abou by exposure

o g. Exampes woud be e darkenng o sver ades

wen exposed o sung (e bass o back and we

poograpy) and e reacon o akanes w corne

or bromne (or exampe, e reacon o meane and

corne). hs s because reacan parces absorb g

energy and s brngs abou eer e excaon o one

o e reacans (as s e case w e sver ades) or

e breakng o a bond (suc as e aogen—aogen

bond n e aogenaon o e akanes) wc naes

e reacon. I s or s reason a many cemcas are

sored n brown gass conaners.

Exercise 6.2

1. Wc one o e oowng acors does no afec

e rae o a cemca reacon?

A he amouns o e reagens.

B he concenraon o e reagens.

C he emperaure o e reagens.

D he presence o a caays.

2. In mos cemca reacons, e rae o reacon

decreases as e reacon proceeds. he usua reason

or s s a

A he energy or e reacon s runnng

ou.

B he concenraons o e reacans are

becomng ower.

C he emperaure s ang as e

reacon proceeds.

D he acvaon energy becomes greaer.

3. In wc o e oowng suaons woud you

expec e rae o reacon beween marbe (cacum

carbonae) and nrc acd o be e greaes?

A Powdered marbe and 2 mo dm–3 acd

a 40 °C.

B Powdered marbe and 0.5 mo dm–3 acd

a 40 °C.

C Powdered marbe and 2 mo dm–3 acd

a 20 °C.

B Marbe cps and 0.5 mo dm–3 acd a

40 °C.




CHAPTER 6

170

a h L

4. In wc one o e oowng reacons woud surace

area no be a acor afecng e rae?

A Znc and suurc acd.

B Carbon doxde gas w mewaer

(aqueous cacum ydroxde).

C Vegeabe o and aqueous sodum

ydroxde.

D Aqueous eanedoc (oxac) acd and

aqueous poassum permanganae.

5. Wc one o e oowng reacons mus occur by

more an one reacon sep?

A H+ (aq) + OH– (aq) H2O ()

B 2 H2O

2 (aq) 2 H

2O () + O

2 (g)

C 2 H2 (g) + O

2 (g) 2 H

2O ()

D H2 (g) + O

3 (g) H

2O () + O

2(g)

6. Expan brely wy:

a) Increasng e concenraon o e reagens

usuay ncreases e rae o a cemca

reacon.

b) A reacon does no occur every me e

reacng speces code.

c) Increasng e emperaure ncreases e rae

o reacon.

7. he rae o decomposon o an aqueous souon o ydrogen peroxde can be oowed by recordng e

voume o gas coeced over waer n a measurng

cynder, agans me.

a) Skec e grap o voume agans me you

woud expec or e compee decomposon

o a sampe o ydrogen peroxde.

b) On e same axes, use a doed ne o skec

e curve a you woud expec o nd e

expermen were repeaed usng a smaer

voume o a more concenraed souon o

ydrogen peroxde so a e amoun o

ydrogen peroxde remans consan.

c) Wen ead(IV) oxde s added, e rae a wc

oxygen s evoved suddeny ncreases, even

oug a e end o e reacon, e ead(IV)

oxde remans uncanged. Expan s.

d) In wa way, apar rom aerng e

concenraon or addng anoer subsance,

coud e rae a wc e ydrogen

peroxde decomposes be ncreased?

Aerng e concenraon o e reacans usuay afecs

e rae o e reacon, bu e way n wc e rae s

afeced s no e same or a subsances, nor can be

predced rom e baanced equaon or e reacon.

he rate expression, wc s a maemaca uncon

expressng e dependence o e rae on e concenraons

o e reacans, mus be deermned expermenay. hs

s usuay done by measurng e reacon rae ws varyng e concenraon o one speces bu odng

ose o e oer speces consan. Consder a reacon

nvovng reacans A, B, ec. he rae expresson or s

reacon akes e orm:

Rae o reacon = – d [ A ] ____ dt

= k[ A ] m [ B ] n ec

he order of reaction s sad o be ‘m’ n subsance A, ‘n’

n subsance B ec. he overa order o e reacon s e

sum o ese powers, .e. m + n ec. he consan ‘k’ n e

rae expresson s known as e rae consan.

Noe a ‘k’ does no vary w concenraon, bu vares

greay w emperaure, so s mporan o aways sae

e emperaure a wc e rae consan was measured.

Noe a were a sod s nvoved n a reacon, ‘k´

mus aso vary w parce sze (snce or exampe n

e reacon o acd w cacum carbonae a e same

concenraon o acd and emperaure, e rae canges as

parce sze canges).

16.1 RateexpRession (ahL)

16.1.1 Distinguish between the terms rate

constant, overall order of reaction and

order of reaction with respect to a

particular reactant.

16.1.2 Deduce the rate expression for a reaction

from experimental data.

16.1.3 Solve problems involving the rate

expression.

16.1.4 Sketch, identify and analyse graphicalrepresentations for zero-, first- and

second-order reactions.

© IBO 2007

higheR LeveL




Kinetics

171

Figure 611 The effect of concentration changes on the rate of a reaction

Expermen[A]

mo dm–33

[B]

mo dm–33

[C]

mo dm–33

Ina rae

mo dm–33 s–11

1 0.400 1.600 0.0600 4.86 × 10–3

2 0.800 1.600 0.0600 9.72 × 10–3

3 0.400 0.800 0.0600 4.86 × 10–3

4 0.800 1.600 0.1800 87.5 × 10–3

I doubng e concenraon o one speces (say A), ws

e oer condons are ed consan, as no efec on

e na rae o reacon, en e reacon s zero order

w respec o A (as 20 = 1). I doubng e concenraon

o A doubes e rae, en e reacon s rs order w

respec o A (as 21 = 2). I ncreases by a acor o our

s second order w respec o A (as 22 = 4), by a acor

o eg en rd order w respec o A (as 23

= 8) ec.Smar consderaons appy o aerng e concenraons

by oer acors (or exampe e concenraon was

decreased by a acor o 3, en e rae woud aso decrease

by a acor o 3 e reacon was rs order w respec

o s reagen).

Fgure 611 gves some daa abou e efec o varyng

concenraons upon e rae o a cemca reacon

nvovng ree speces – A, B and C:

Comparng expermens 1 and 2, e ony cange s a e

concenraon o A as been doubed. he daa n e abe

ndcae a e rae as been doubed, so e reacon srs order w respec o A. Comparng 1 and 3, e ony

cange s a e concenraon o B as been aved, bu

ere s no efec on e reacon rae, ndcang a e

reacon s zero order w respec o B ( rs order

woud be ½ e rae n 1, second order, en ¼ o e rae

n 1). Comparng 2 and 4 e ony dference s a e

concenraon o C as been ncreased by a acor o ree.

he rae as ncreased by a acor o nne, so e reacon s

second order n C (as 32 = 9 – ad been rs order n C,

e rae woud ony ave ncreased by a acor o 3.). hs

means a e rae expresson or s reacon s:

Rae = k.[A]1[B]0[C]2

or more smpy

Rae = k.[A][C]2

Hence e reacon s rd order (1 + 2) overa.

he rae consan or a reacon may be cacuaed provded

a e rae o reacon as been measured n sandard

uns o mo dm–3 s–1, or known concenraons o e

reagens. Consder e daa n Fgure 611 above. he rae

consan can be cacuaed by subsung any se o daa

n e rae expresson. For exampe usng e daa rom

expermen 1:

Rae = k.[ A][C]2

4.86 × 10–3 = k[0.400][0.06]2

k = 4.86 × 10–3 ___________ 0.400 × 0.062

= 3.375 mo–2 dm6 s–1

and usng e daa rom expermen 2:

Rae = k.[ A][C]2

9.72 × 10–3 = k[0.800][0.06]2

k = 9.72 × 10–3

___________ 0.800 × 0.062

= 3.375 mo–2 dm6 s–1

Noe e uns or e rae consan. hese ony od

or a reacon a s rd order overa and oer order

reacons w ave rae consans w dferen uns.

he uns can be cacuaed rememberng a e uns or

raes are mo dm–3 s–1 and e uns or concenraons are

mo dm–3. Hence e uns o e rae consan are:

Zero order overa mo dm–3 s–1

Frs order overa s–1

Second order overa mo–1 dm3 s–1

hrd order overa mo–2 dm6 s–1

In genera (mo dm–3)q–1 s–1 were q s e overa order

he order o reacon can aso be ound rom a grap

sowng e way n wc e na rae vares w e

na concenraon o e reacan, a oer acors beng

equa. hs s usraed n Fgure 612.




CHAPTER 6

172

0

25

50

100

75

1 2 3 4 5 Time

C o n c e

n t r a t i o n

Constant half–life = t1/2

t1/2

First order

t1/2t1/2

0

25

50

100

75

1 2 3 4 5 Time

C o n c

e n t r a t i o n

0

25

50

100

75

1 2 3 4 5 Time

C o n c

e n t r a t i o n

redrodnoceSredrooreZ

Each t1/2 is half preceding t1/2 Each t1/2 is double preceding t1/2

Gradient constant Gradient after first half life = ¼ initial gradient

Figure 613 a, b and c. Graphs showing the variation of concentration with time for reactions of different orders

a h L

I n i t

i a l R a t e

Initial Concentration

Zero order

First order

Second order

Figure 612 The effect of concentration on rate

he order o a reacon can aso be ound rom a grap o

concenraon agans me, wc sows e efec o e

reacans beng used up on e rae o reacon. he graden

o e grap a any pon gves e rae o reacon. I s sconsan (.e. e grap s a srag ne) en e reacon

mus be zero order n e reacans wose concenraons

are undergong sgncan cange, because e decrease n

concenraon s no afecng e rae o reacon (wc

we know rom e consan graden). I e reacon rae

(e graden o e ne) s aved wen e concenraon

s aved, en e reacon s irst order. I avng e

concenraon causes e rae (graden) o decrease by a

acor o 4, e reacon s second order (½)2 = ¼ ec. To

be reay useu, suc expermens soud ave a bu one

reagen n arge excess, so a e order n e mng

reagen s wa causes e reacon rae o cange.

hs s n ac e bass or a very poweru ecnque o

smpy e rae equaon. Consder a reacon a s

second order overa n wc e na concenraon o

A s 0.02 mo dm–3 and e na concenraon o B s

2 mo dm–3. Wen e reacon s compee (assumng

e socomery s 1 moe o A reacs w 1 moe o

B), e na concenraon o A s zero and a o B s

1.98 mo dm–3, .e. e concenraon o B remans vruay

uncanged, ence:

Rae = k.[A].[B] ≈ k´.[A] (were k´ = k.[B])

A reacon o s ype s caed a “pseudo irst-orderreacton” because obeys a rs order rae aw, bu

e observed rae consan (k´) w depend on e

concenraon o anoer speces ( [B] s doubed en

e reacon rae w doube and e a-e w decrease

o a o s na vaue). he same ecnque (makng

e concenraon o one reagen muc ess an a o e




Kinetics

173

R a t e

Concentration

R a t e

Concentration

R a t e

Concentration

R a t e

Concentration

A B C D

oers) can be used o vary e observed order o reacons

w oer rae expressons.

I s easy o recognse a rs order reacon rom

graps o concenraon (or someng proporona

o concenraon) agans me. hs s because e

concenraon sows an exponena decrease, a s e

me or e concenraon o a rom s na vaue o

a s na vaue, s equa o e me requred or o

a rom a o one quarer o s na vaue and rom

one quarer o one eg ec. hs me s known as e

half-life t ½

o e reacon and s usraed n Fgure

613 wc sows a e successve a ves o reacons

o oer orders vary n caracersc ways.

he rs order exponena decay s e same as a ound

n radioactive decay . Because remans consan, e

a-e s an mporan quany or ese sysems and

can be ound rom an approprae grap (suc as a

above) or may be ound rom e rae consan (k) by subsung n e equaon:

t 1 _ 2 =n2 ___

k

For exampe, e rae consan o a rs order reacon s

0.005 s-1, en e a-e w be n2 ____ 0.005 = 139 s.

hs resus rom e negraon o e rs order

rae expresson. I e a-e s known, say rom a

concenraon-me grap, en s equaon may be

rearranged o nd e rae consan. For exampe e

a-e or a rs order reacon s 4 mnues:

k = n2 _______ ( 4 × 60 ) = 0.0289 s-1

Exercise 16.1

Quesons 1 o 4 reer o e rae expresson or a cemca

reacon gven beow:

Rae = k[A][B]2[H+]

1. Wc one o e oowng saemens s no rue

abou s reacon?

A I s rs order n A.

B I s second order n B.

C I s rs order n H+.

D I s rd order overa.

2. he uns o e rae consan (k) w be:

A mo dm–3

s–1

B mo s–1

C dm3 mo–1 s–1

D dm9 mo–3 s–1

3. I e concenraons o A and B are bo doubed,

bu e concenraon o H+ remans consan, e

rae woud ncrease by a acor o:

A 2

B 4

C 8

D 16

4. Wc one o e oowng woud ead o e greaes

ncrease n reacon rae?

A Doubng e concenraon o A ony.

B Doubng e concenraon o B ony.

C Doubng e concenraon o A and H+

ony.

D Doubng e concenraon o B and H+

ony.

5. Wc one o e graps sown woud ndcae

a a reacon was zero order n e reacan wose

concenraon was beng vared?




CHAPTER 6

174

a h L

6. he oowng daa reers o e acd caaysed odnaon o propanone

CH3—CO—CH

3 (aq) + I

2 (aq) CH

3—CO—CH

2—I (aq) + H+ (aq) + I– (aq)

Souon[CH

3—CO—CH

3]

mo dm–33

[I2]

mo dm–3

[H+]

mo dm–3

Ina Rae

mo dm–3 s–1

1 0.2 0.008 1 4 × 10–6

2 0.4 0.008 1 8 × 10–6

3 0.6 0.008 1 1.2 × 10–5

4 0.4 0.004 1 8 × 10–6

5 0.4 0.002 1 8 × 10–6

6 0.2 0.008 2 8 × 10–6

7 0.2 0.008 4 1.6 × 10× 1010–55

a) From e daa n e abe derve e rae expresson or e reacon, expanng

e evdence or e dependency on eac o e speces.

b) Gve e order w respec o CH3—CO—CH

3, I

2and H+, and e overa

order.

c) Use e daa rom Souon 1 o cacuae e vaue o e rae consan.

7. he daa gven beow reer o e ydroyss o a 0.002 mo dm–3 souon o an eser by

0.2 mo dm–3 aqueous sodum ydroxde.

Tme (s) 60 120 180 240 300 360 420 480

[eser] (mmo dm–3

) 1.48 1.10 0.81 0.60 0.45 0.33 0.24 0.18

a) Po a suabe grap o deermne e order o e reacon w respec o e

eser, expanng your meod.

b) Use your grap o deermne e a-e o e reacon and ence deermne a

vaue or e apparen rae consan, gvng approprae uns.

c) Wy does s grap gve no ndcaon o e order w respec o e

ydroxde on?

d) How woud you mody e expermen o deermne e dependence on

ydroxde on?

e) Assumng a s aso rs order n ydroxde on, wre a new rae

expresson.

Use s o cacuae a vaue or e rae consan, gvng approprae uns.

Wy does s dfer rom e vaue ound n b) and ow are e wo reaed?




Kinetics

175

he cance o more an wo parces codng

smuaneousy w e correc geomery and mnmum

energy s very sma. hs means a ere are more

an wo reacans, e reacon mus occur by a numbero smper reacon seps. In addon, many reacons a

ave appareny smpe equaons do no occur n s

manner, bu are e resu o a number o seps. hese

seps nvove speces a are e produc o an earer

sep and are en compeey consumed n a aer sep (so

ey do no appear n e socomerc equaon). hese

speces are known as “intermediates”. he smpe sages

by wc a cemca reacon occurs are known as e

mecansm o e reacon. he sum o e varous seps

o e mecansm mus equa e baanced equaon or

e reacon.

he varous seps n e reacon mecansm w ave epoena o occur a dferen raes. he producs canno

owever be ormed aser an e sowes o ese seps

and so s s known as e rae deermnng sep (rds). An

anaogy woud be a peope can come of a ran a e

rae o 20 per second, can rave up e escaaor a a rae

o 10 per second, and can pass roug e cke barrer

no e sree a a rae o 50 per second, en ey w

s ony reac e sree a a rae o 10 peope per second.

Makng arger doors on e ran or pung n an exra

cke barrer w no make s any aser, ony a cange

afecng e escaaor, e sowes sep, w ncrease e

rae.

In summary, a mecansm s a mode o ow a reacon

occurs. he rae o overa reacon s e rae o e sowes

sep. hs sowes sep s caed e rate determining step.

Speces produced n earer seps o e mecansm a

are consumed n aer seps are caed nermedaes. A

mecansm mus accoun or e overa socomery

o e reacon, e observed rae expresson and any

oer avaabe evdence (suc as e efec o g or a

caays).

here are ony wo knds o undamena process a can

occur o brng abou a cemca reacon. Frsy, a specescan break up or undergo nerna rearrangemen o orm

producs, wc s known as a unimolecular process.

As s ony nvoves one speces, a unmoecuar sep s

rs order n a speces. Radoacve decay, or exampe,

s unmoecuar. Secondy, wo speces can code and

nerac o orm e produc(s) and s s known as a

bimolecular process. As s nvoves e coson o e

wo speces en doubng e concenraon o eer w

doube e coson rae. Hence, s rs order n eac and

second order overa. Bo unmoecuar and bmoecuar

processes can be eer reversbe (ead o equbrum) or

rreversbe (ead o compee reacon) dependng on e

reave saby o e reacans and producs. Weera parcuar reacon sep s unmoecuar or bmoecuar,

s known as e molecularity o a reacon sep. In a

bmoecuar process, e speces code o nay gve a

ranson sae (or acvaed compex), wc en breaks

down o eer orm e producs or reorm e reacans.

16.2 Reactionmechanism (ahL)

16.2.1 Explain that reactions can occur by more

than one step and that the slowest step

determines the rate of reaction (rate-

determining step).

16.2.2 Describe the relationship between

reaction mechanism, order of reaction

and rate-determining step.

© IBO 2007

A Unmoecuar sep A Bmoecuar sep

A unmoecuar sep nvoves a snge speces as a reacan. A bmoecuar seps nvoves coson o wo speces (a

orm a ranson sae or an acvaed compex a can

no be soaed).

A / Producs A + B / Producs

Is rae aw s ereore 1s order w respec a reacan.

rae ∝ [A]

Is rae aw s 1s order w respec o eac o e codng

speces and s ereore 2nd order overa.

rae ∝ [A][B]

Figure 617 Comparing uni- and bi-molecular steps




CHAPTER 6

176

MecansmRae

expresson

I

A + B X + C; Sow rds

A + X D; Fas

(A + B + A + X X + C + D

= 2 A + B C + D overa)

Rae∝ [A] [B]

II

A + B X; Fas

A + X C + D; Sow rds

(A + B + A + X X + C + D

= 2 A + B C + D overa)

Rae∝[A]2[B]

IIIA + A A

2; Fas

A2

+ B C + D; Sow rdsRae∝[A]2[B]

IVA + A A2; Sow rds

A2

+ B C + D; FasRae∝ [A]2

V

B X; Sow rds

X + A Y + C; Fas

Y + A D; Fas

Rae∝ [B]

Figure 618 Some possible mechanisms for the reaction;

2 A + B C + D

a h L

A transition state s an unsabe arrangemen n wc

e bonds are n e process o beng broken and ormed.

I ereore occurs a e maxmum pon on a poena

energy dagram and canno be soaed.

As ouned above, many cemca reacons occur by a

seres o smpe seps known as e mecansm o e

reacon. I s possbe o wre a number o mecansms

(a s a seres o undamena processes by wc e

reacon coud occur) or any reacon and s ony possbe

o sugges wc s e correc one by sudyng e knecs

o e reacon. Ony speces a are nvoved n e rae

deermnng sep, or n an equbrum precedng , can

afec e overa rae o reacon. Hence, deermnng e

rae expresson or a reacon w ep o deny e rae

deermnng sep and s w emnae many possbe

mecansms or e reacon.

Consder or exampe a reacon

2 A + B C + D

as an usraon o ow e rae expresson w depend

upon e mecansm and upon wc sep n e

mecansm s e rae deermnng sep.

here are ree parces nvoved n e reacon, so

s mos unkey a s occurs as a snge sep. Many

mecansms or e reacon coud be wren and ese

woud produce a varey o rae expressons. Some exampes

are gven n Fgure 618. Noe a addng ogeer e

dferen seps aways eads o e same overa equaon

as sown or e rs wo possbe mecansms n Fgure618.

Some o ese mecansms nvove equbra, a opc a

s dea w n greaer dea n Caper 7. For e presen

purposes s enoug o know a or e equbrum,

A + B X, e [X] w depend on bo e [A] and [B].

Smary n e equbrum, A + A A2, e [A

2] w

be proporona o [A]2. Noe aso a e concenraon o

e nermedae (X) never appears n e rae expresson.

In I, e rs bmoecuar sep s rae deermnng so a

e rae w depend on e rae o cosons beween A

and B, ence e rae w be proporona o [A].[B]. In

II e second bmoecuar sep s rae deermnng so a

e rae w depend on e rae o cosons beween A

and X, ence e rae w be proporona o [A] [X],

bu [X] w depend on bo [A] and [B], so a akng

s no accoun e rae depends on [A]2 [B]. In V e

rae depends on e unmoecuar converson o B o an

nermedae X, so e rae ony depends upon [B].

Noe a III and IV ony dfer n wc o e wo sepss e rae deermnng sep. hs s no necessary xed,

or exampe a very ow [B] e second sep coud be e

rae deermnng sep (mecansm III), bu a very g

[B] e second sep w become muc aser so a now

e rs sep mg be rae deermnng (mecansm IV).

Because A2

w reac w B as soon as s ormed, e

rs sep s now no onger an equbrum. Noe aso a

bo mecansm II and mecansm III ead o e same

rae expresson and so some oer means (suc as ryng

o ge some normaon abou e nermedae X) woud

ave o be used o decde wc ( eer.) was operang.

Consder as anoer exampe e reacon beween

propanone and odne:

CH3COCH3 (aq) + I2 (aq) CH

3COCH

2I (aq) + H+ (aq) + I– (aq)

hs woud appear o be a smpe bmoecuar process,

bu s were e case, en e rae o reacon woud

be expeced o depend on e concenraons o bo e




Kinetics

177

E n t h a

l p y

A 1

A 2

A 3

CH3COCH3

CH3C(OH+)CH3

CH2=C(OH)CH3

CH3COCH2 I

Intermediates

∆H

Figure 619 P.E. diagram for the iodination of propanone

propanone and e odne ence e rae expresson woud

be:

Rae = k [CH3COCH

3] [I

2]

In pracce s ound a e reacon s caaysed by acdsand a e rae s ndependen o e concenraon o

odne ence e reacon s rs order n bo propanone

and ydrogen ons, bu zero order n odne. Hence e

rae expresson s:

Rae = k [CH3COCH

3] [H+]

hs means a one moecue o propanone and one

ydrogen on mus be nvoved n e rae deermnng

sep, or n equbra occurrng beore s. he commony

acceped mecansm or s reacon s:

CH3COCH3 + H+ CH3C(OH+)CH3 Fas equbrum

CH3C(OH+)CH

3CH

2=C(OH)CH

3+ H+

Sow – rae deermnng sep

CH2=

C(OH)CH3

+ I2

CH3COCH

2I + H+ + I–

Fas (does no afec rae)

hs mecansm agrees w e expermenay

deermned rae expresson. he rae expresson can never

prove a a parcuar mecansm s correc, bu can

provde evdence a oer possbe mecansms are

wrong.

(Good TOK pont – an example of a dculty that besets all

processes of nductve logc.)

he speces CH3C(OH+)CH

3and CH

2=C(OH)CH

3are

nermedaes; ey ave a ne e and occur a a poena

energy mnmum on e reacon dagram. In s reacon

mecansm ere woud be a number o ranson saes,

rsy (A1) beween CH

3COCH

3and H+ beore ormng

CH3C(OH+

)CH3 secondy (A2) wen CH3C(OH+

)CH3 sars o break up o orm CH2=C(OH)CH

3and H+ and

nay (A3) n e reacon o s w odne. hese do

no ave a ne e and occur a poena energy maxma

on e reacon dagram. hs s usraed n Fgure 619

and e dferences beween nermedaes and ranson

saes (acvaed compexes) are summarsed n Fgure

620.

Inermedaes Transon Saes

Exs or a ne meHave ony a ransen

exsence

Occur a a P.E. mnmum Occur a a P.E. maxmum

Formed n one sep o a

reacon and consumed n

a subsequen sep

Exs par way roug

every sep o a reacon

Figure 620 Differences between intermediates and

transition states

he dferences beween nermedaes and ranson

saes can aso be usraed by e SN

1 and SN

2

mecansms or e nuceopc subsuon reacons o

aogenoakanes.




CHAPTER 6

178

a h L

1. Wc one o ese seps s unmoecuar?

A NH3

+ H+ NH4

+

B H+ + OH– H2O

C N2O

42 NO

2

D H• + C• HC

2. Wc one o e oowng s not a dference

beween an acvaed compex and an nermedae?

A An acvaed compex occurs a a

poena energy maxmum and an

nermedae a a mnmum.

B An acvaed compex canno ake

par n bmoecuar reacons, bu an

nermedae can.C An acvaed compex does no exs or

a ne me bu an nermedae does.

D An acvaed compex can reorm e

reacans, bu an nermedae canno.

3. he rae deermnng sep o a mecansm s e one

wc

A occurs mos rapdy.

B occurs mos sowy.

C gves ou e mos energy.

D gves ou e eas energy.

4. Wc one o e oowng mecansms woud gve

a rs order dependence on A and zero order on B or

e reacon beow?

A + B C

A A + X Y (as) en

Y + B C + X (sow)

B B X (sow) en

X + A C (as)

C 2 A A2

(sow) en

A2

+ B C (as)

D A X (sow) en

X + B C (as)

5. A reacon nvoves wo reacans, A and B. he na

reacon rae was measured w dferen sarng

concenraons o A and B and e oowng resus

were obaned a 25 °C:

[A]

mo dm3[B]

mo dm3Ina rae

mo dm3 s1

0.2 0.2 3.2 × 104

0.4 0.4 1.3 × 103

0.4 0.8 1.3 × 103

a) Deduce e order o e reacon n A, n

B and e overa order. Hence wre a rae

expresson or e reacon.

b) Cacuae a vaue or e rae consan, gvng

suabe uns.

c) Wa na rae woud you expec e

na concenraons o bo reacans were

0.1 mo dm–3?

d) I e overa equaon or e reacon s

A + B C + D, wre a mecansm,

ndcang wc sep s e rae deermnng

sep, a s:

conssen w e rae expresson

ound.

nconssen w e rae expresson

ound.

Exercise 16.2




Kinetics

179

In a lud, ere s a dsrbuon o energy amongs e

parces known as e Maxwe–Bozmann dsrbuon

(see Secon 6.3). As e emperaure ncreases, e

number o parces w a g energy ncreases, ougere are s some parces w very e energy. he

resu s a laenng o e dsrbuon curve, because e

oa area under mus reman consan (refer to igure

609, reproduced agan as Fgure 622 for convenence).

P r o b

a b i l i t y

o f

t h i s

e n e r g y

E aCatalysed E aUncatalysed

Low T

High T

Kinetic Energy

Figure 622 The distribution of kinetic energy at two

different temperatures

A cemca reacons requre a ceran mnmum energy,

e acvaon energy (Ea), or e reacon o occur. As

can be seen rom Fgure 622, a e ger emperaure

a greaer proporon o e moecues ave an energy

greaer an e acvaon energy, .e. ere s a greaer

proporon o e oa area under e curve o e rg

o e Ea

ne (eer e caaysed or uncaaysed) on e

ger emperaure curve an on e ower emperaure

curve. hs s usuay e major reason wy reacons

occur more rapdy a ger emperaures.

For many reacons s ound a e efec o emperaure

on e rae consan or a reacon (k) s gven by e

expresson:

k = A e( – Ea ___ RT

)

were Ea

s e acvaon energy, T e absoue

emperaure (n Kevn), R e gas consan (8.314 J K–1

mo–1) and A s caed e Arrenus consan (or e

pre–exponena acor). I s dependen on coson rae

and serc acors, a s any requremens regardng e

geomery o e codng parces. hs equaon s known

as e Arrhenius equation ater e Sweds cems,

Svante August Arrhenus, wo rs proposed .

he expresson ndcaes a e rae consan k depends

exponenay on emperaure, wc s wy emperaure

as suc a arge efec on reacon rae. Raer sasyngy

e expresson or e area under e Maxwe–Bozmann

dsrbuon curve n excess o Ea

aso gves an exponena

dependence Ea>>RT . I we ake ogarms o e base

e (naura ogarms (n) - a maemaca procedure

you may possby no ave me) and en rearrange, eArrenus equaon s convered o:

nk = n A – ( Ea __ R

) 1 __ T

hs s e equaon o a srag ne so, as sown n Fgure

623 beow, a grap o n k agans 1 __ T

w be near w

graden–

Ea __

R

and an nercep on e y–axs o n A.

he acvaon energy or a reacon can ereore be ound

by measurng e rae o reacon a dferen emperaures,

w a e oer condons uncanged (so a rae ∝ k),

and en pong n(rae) agans 1 __

T

(Noe agan, T mus

be n Kevn, no oCesus).

1T --- (K

–1)

Intercept = ln A

Gradient =E aR

-----–

l n k

o r

l n ( r a t e )

Figure 623 Determining the activation energy

graphically

16.3 activationeneRgy (ahL)

16.3.1 Describe qualitatively the relationship

between the rate constant (k ) and

temperature (T ).

16.3.2 Determine activation energy (E a) values

from the Arrhenius equation by a

graphical method.

© IBO 2007




CHAPTER 6

180

a h L

Exercise 16.3

1. Wc one o e oowng s no rue abou e

acvaon energy o a reacon?

A I s reaed o e enapy cange (∆H )

o e reacon.

B I s decreased by e addon o a

caays.

C I s e mnmum amoun o energy

a e reacans mus ave n order o

orm e producs.

D he greaer e acvaon energy e

ower e rae o reacon.

2. he acvaon energy o a cemca reacon can be

deermned by measurng e efec on reacon rae

o varyng

A e emperaure.

B e concenraon o e reagens.

C e concenraon o e caays.

D e surace area n conac.

3. he emperaure a wc a reacon s carred ou

s ncreased rom 20 °C o 40 °C. I e a-e o

e reacon was nay , e a-e a e ger

emperaure w be:

A 2

B ½ C 2

D I woud depend on e sze o e

acvaon energy.

4. he acvaon energy or e reacon beow s

112 kJ mo–1 and ∆H s +57 kJ mo–1.

2 NO2 (g) 2 NO(g) + O

2 (g)

a) Draw an energy eve dagram usrang

e energy canges or s reacon. Ceary

mark and abe e acvaon energy Ea

and

e enapy cange (∆H ).

b) On e same dagram, usng doed nes,

sow e efec o a panum caays, ceary

abeng e cange ‘W caays’. Woud

e panum be acng as a omogeneous or

eerogeneous caays?

c) Is e reacon exoermc or endoermc?

Wen occurs w e conaner become

oer, or cooer?

d) I e emperaure was ncreased, ow woud

s afec e rae o reacon? Expan s n

erms o e coson eory o reacons (a

dagram mg ep).

e) Wa oer acor (.e. not emperaure or

caays) coud be canged o ncrease e

rae o reacon – be precse, rememberng

a ese are a gases.

) Nrogen doxde s a brown gas, wereas

nrogen monoxde s coouress. Sugges

ow you mg be abe o measure e rae o

reacon.

5. Wen aqueous souons o benzenedazonum

corde decompose, ey evove nrogen gas. he

abe beow gves e voume o gas obaned a

dferen mes or suc a decomposon a 70 °C.

Tme

mn

Voume

cm3

1 5

2 9

3 13

4 17

5 21

7 28

9 33

12 40

16 48

20 54

a) I, wen decomposon was compee, e

oa voume o gas reeased was 70 cm3,

grapcay deermne e order o e

reacon. Wa urer daa, any, woud

you need o cacuae a vaue or e rae

consan?

b) Draw e apparaus you coud use o oban

suc daa and sae wa precauons you

woud ake.

c) I you waned o deermne e acvaon

energy or s reacon, wa urer

expermens woud you carry ou? How

woud you use e daa rom ese o

deermne e acvaon energy?

070809 Ch Ch 6 3 f t180 180 7/12/2007

chapter 06 kinetics

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