Rates ad Mechaisms f Chemical Reactis Why sme rxs prceed very fast ad thers require days, mths r eve years t prduce a detectable amt f prduct? H (g) + F (g) HF (g) (very fast) 3 H (g) + N (g) NH 3 (g) (very slw) Hw d catalysts icrease the rates f chemical rxs? What des a study f the rate f a chemical rx tell us abut the way i which reactats cmbie t frm prducts? Chemical Kietics is the study f reacti rates Reacti rates: the chages i ccetrati f reactats r prducts as a fucti f time Uder a specific set f cditis, every reacti has its w characteristic rate, which depeds up the chemical ature f the reactats Fur factrs ifluece reacti rates:. Ccetrati - mlecules must cllide t react. Physical state - mlecules must mix t cllide 3. Temperature - mlecules must cllide with eugh eergy t react 4. The use f a catalyst Ccetrati f reactats Mlecules must cllide i rder t react. The mre mlecules preset at the ctaier the mre frequet they cllide ad the mre fte a rx betwee them ccurs Rate cllisi frequecy ccetrati Physical state Mlecules must mix t cllide queus sls: radm thermal mti brigs them it ctact. t differet phases ctact ccurs ly at the iterface (vigrus stirrig ad gridig may be eeded). The mre fiely divided a slid r liquid reactat, the greater its surface area per uit vlume, the mre ctact it maes with the ther reactat ad the faster the reacti ccurs
Temperature Rate cllisi eergy temperature Expressig the reacti rate Reacti rate - chages i the ccetratis f reactats r prducts per uit f time. Reactat ccetratis decrease while prduct ccetratis icrease. verage reacti rate: (chage i cc. f reactats r prducts) / chage i time It has uits: ml L - s - NO (g) + CO (g) NO (g) + CO (g) csumed prduced rate NO NO t f f NO t i i rate CO t CO f f CO t i i rate NO f NO t f NO t ( - b/c it is csumed) i i Geeral reacti, B rate B verage, Istataeus ad Iitial Reacti Rates Csider the reacti, C H 4 (g) + O 3 (g) C H 4 O (g) + O (g) (ivlved i phtchemical smg) CH 4 O3 rate The rate ver the etire 60 s f ur data 5 5 O3 (.0x0 mll 3.0x0 mll ) 7 rate 3.50x0 mll s 60.0s 0.0s This calculati gives us the average rate But it des t tell us hw fast the ze cc. is decreasig at ay give istace ad it des t shw that the rate is chagig.
Nw let s calculate the rate betwee the startig time ad 0.0 s. rate 7.80x0 mll s 0.0s 0.0s 5 5 O3 (.4x0 mll 3.0x0 mll ) 7 d w calculate betwee 50.0 ad 60.0 s 5 5 O (.0x0 mll.3x0 mll ) 7 3 rate.30x0 mll s 60.0s 50.0s The earlier rate is six times as fast as the later rate rate decreases durig the curse f the reacti the slpe f the straight lie cectig ay tw pits gives the average rate the slpe f the lie taget t the curve at a particular pit gives the istataeus rate the slpe f taget t the curve at t 0 gives the iitial rate We use the term reacti rate t mea the istataeus rate Plts f C H 4 ad O vs. time Measurig reactat C H 4 ad prduct O ver time we get curves f idetical shape but chagig i ppsite directis. The steep upward (psitive) slpe f O early i the reacti mirrrs the steep dwward (egative) slpe f C H 4 because the faster the C H 4 is used the faster the O is frmed. The curve shapes are idetical i this case b/c the equati cefficiets are idetical 3
Expressig rate i terms f reactat ad prduct ccetratis a + bb cc + dd rate a b B C c d D These relatis hld true prvided that there are trasiet itermediate species r if there itermediates their ccetratis are idepedet f time fr mst f the perid. Example Because it has a pllutig prduct (water vapr), hydrge gas is used fr fuel abard the space shuttle ad i prttype cars with Earth-bud egies: H (g) + O (g) H O(g) a) Express the rate i terms f chages i H, O, ad H O with time. H O H O rate b) Whe O is decreasig at 0.3 ml L - s -, at what rate is H O icreasig? O H O rate ( 0.3mlL s H O 46 x0.3mll s 0. mll s The rate law ad its cmpets Rate law (rate equati): ceterpiece f ay ietic study It depeds ccetrati f reactats ad temperature (Fr w we fcus ly the effects f ccetrati the rate law at fixed temperature) ) a + bb + cc + dd +.. rate m B. is the rate cstat (specific fr a give rx at a give temp., chage as rx prceeds m, are reacti rders (hw the rate is affected by reactat ccetrati If rate x as dubles, ad m 4
If rate x4 as B dubles, B ad If rate remais uchaged as dubles, 0 ad m 0 Keep i mid: the stichimetric cefficiets ( a, b, ) are t related t the rders (m,, ) The cmpets f the rate law (rate, reacti rders ad rate cstats) must fud by experimet. They are t deduced frm the reacti stichimetry. Chemists determie these cmpets experimetally. a) usig ccetrati measuremets t fid the iitial rate b) usig iitial rates frm several experimets t fid the reacti rders c) usig these values t calculate the rate cstats May experimetal techiques have bee develped t accmplish the three metied steps Reacti-Order termilgy reacti is havig a idividual rder w/r/t r w/r/i each reactat as well ad a verall rder rate - st rder: rate directly prprtial t rate d rder: rate directly prprtial t rate 0 () - 0th rder: rate is idepedet f Example Fr each f the fllwig reactis, use the give rate law t determie the reacti rder with respect t each reactat ad the verall rder: a) NO (g) + O (g) NO (g); rate NO O The reacti is d rder i NO, st rder i O, ad 3rd rder verall b) CH 3 CHO (g) CH 4 (g) + CO (g); rate CH 3 CHO 3/ The reacti is 3/ rder i CH 3 CHO ad 3/ rder verall. c) H O (aq) + 3 I (aq) + H + (aq) I 3 (aq) + H O (l); rate H O I 5
The reacti is st rder i H O, st rder i I, zer rder i H +, ad d rder verall. Determiig reacti rates O (g) + NO (g) NO (g) rate O m NO et rate frward rate reverse rate We ru a series f experimets startig each e with a differet set f reactat ccetratis ad btaiig a iitial rate i each case Cmpare tw experimets i which the ccetrati f e reactat varies ad the ccetrati f the ther reactat(s) remais cstat. rate rate O O m m NO NO 6.40x0 3.x0 3 3 (.0x0 (.0x0 mll mll ) ) m m (.30x0 (.30x0 mll mll.99 (.00) m m m, rx is st rder w/r/t O, whe O dubles the rate dubles. T fid the rder w/r/t NO we cmpare experimets 3 ad i which O is held cstat. m 3 m rate3 O NO.8x0 (.0x0 mll ) (.60x0 mll ) m 3 m rate O NO 3.x0 (.0x0 mll ) (.30x0 mll 0 3.99 (.00) 4, rx is d rder w/r/t NO, whe NO dubles the rate quadruples. S, rate O NO Nw we have t determie ) 0 6
3 rate 3.x0 mll s Frm experimet : O NO (.0x0 mll )(.30x0 mll ).73x0 3 L ml - s - Example Fr the reacti 4 (g) + 3B (g) C (g) the fllwig data were btaied at cstat temperature Experimet (ru) Iitial (ml L - ) Iitial B (ml L - ) Iitial rate (ml L - mi - ) 0.00 0.00 5.00 0.300 0.00 45.0 3 0.00 0.00 0.0 4 0.300 0.00 90.0 a) Fid the rder with respect t each reactat Use experimets ad (r 3 ad 4 wuld wr) t fid the rder with respect t. m rate exp exp rate exp exp m 45.0 ml/l mi 0.300 ml/l 5.00 ml/l mi 0.00 ml/l 9.00 (3.00) m lg (9.00) m lg (3.00) m Usig experimets 3 ad 4 als gives d rder with respect t. Use experimets ad 3 with 0.00 M r ad 4 with 0.300 M t fid rder with respect t B. rate exp B exp rate exp B exp 0.0 ml/l mi 0.00 ml/l 5.00 ml/l mi 0.00 ml/l.00 (.00) lg (.00) lg (.00) The reacti is first rder with respect t B. 7
b) Write the rate law rate B. c) Calculate usig the data frm experimet (ru)? rate B 5.00 ml/l mi 0.00 ml/l 0.00 ml/l 5.00 x 0 3 L /ml mi 8
PROBLEM: May gaseus reactis ccur i a car egie ad exhaust systems. Oe f these is NO (g) + CO(g) NO(g) + CO (g) rate NO m CO Use the fllwig data t determie the idividual ad verall reacti rders: Experimet 3 Iitial Rate (ml/l s) Iitial NO (ml/l) Iitial CO (ml/l) 0.0050 0.0 0.0 0.080 0.40 0.0 0.0050 0.0 0.0 PLN: Slve fr the rder with respect t each reactat usig the geeral rate law usig the methd described previusly. SOLUTION: rate NO m CO rate NO m CO NO NO m CO NO 0.080 0.0050 First, chse tw experimets i which CO remais cstat ad the NO varies. 0.40 0.0 m 6 4.0 m ad m.0 The reacti is d rder i NO. rate 3 rate 0.0050 0.0050 0.0 0.0 NO 3CO 3 NO CO CO 3 CO.0 ad 0 The reacti is zer rder i CO. rate NO CO 0 NO The reacti is secd rder verall. 9
Ccetrati chages ver time: itegrated rate laws We wuld lie t aswer questis f the type: hw lg will it tae fr x mles per liter f t be used up? Or, What is the ccetrati f after y miutes f reacti? Let us csider the reacti: N O 5 (g) NO (g) + ½ O (g) N O5 The rate is r N O 5 Origial value f N O 5 (g) ccetrati: N O 5 We see a mathematical expressi that gives us the ruig ccetrati f N O 5 i terms f elapsed time, t, ad N O 5 Calculus will help us t N O5 N O e l N O5 l N O5 t 5 t I geeral, e l l t l t l t + l st rder reactis y mx + b slpe - itercept l imprtat t we pay lts f atteti is t / which is called t half-life ad it is the time required fr l 0.693 l l t / l t/ t/ s, t / 0. 693 0
Graphical determiati f the reacti rder fr the decmpsiti f N O 5 plt f N O 5 vs. time fr three half-lives
d Order Reactis a Prducts t a r We defie a ad althugh t shwig all the steps this differetial rate law ca be itegrated as t + y mx + b slpe itercept d rder half-life ad t t t / / / + Nte: Remember that a ad a is the stichimetric cefficiet Zer-rder reactis r 0 t t + y mx + b slpe - itercept Half-life: ad t t / / + Third-rder reactis gai as i the d rder reactis a Prducts t a r We defie a ad althugh t shwig all the steps this differetial rate law ca be itegrated as t + I geeral fr th-rder reactis t ) ( + fr ad t / ) ( fr
Itegrated rate laws ad reacti rders.rate l t -t + l 0 / t t + / 0 t -t + Example Cyclprpae is the smallest cyclic hydrcarb. Because its 60 bd agles reduce rbital verlap, its bds are wea. s a result, it is thermally ustable ad rearrages t prpee at 000 C via the fllwig first-rder reacti: The rate cstat is 9. s -. (a) What is the half-life f the reacti? 0 / 693 t / 0.693 t/ 0. 075s 9.s 3
(b) Hw lg des it tae fr the ccetrati f cyclprpae t reach e-quarter f the iitial value? This is half-lives r 0.075 x 0.5 s Example t 000 C cyclbutae (C 4 H 8 ) decmpses it a first-rder reacti with the very high rate cstat f 87 s - t tw mlecules f ethylee, C H 4. a) If the iitial ccetrati f C 4 H 8 is.0 M what is the ccetrati after 0.00 s? C H 4 8 t C H C H l l 4 8 (0.87s )(0.00s) 0. 87 4 8.0 l C H8 l(.00) 0.87 0.768 C 4 H 8 0.84 ml L - 4 b) What fracti f C 4 H 8 has decmpsed i this time? C H8 C 4 C H 4 0 4 8 8 Reacti Mechaisms H.0 0.84.0 0.58, r 58% Mst rxs prceed thrugh a series f tw r mre steps ( elemetary steps) I elemetary steps there are direct cllisis f atms, mlecules r is The umber f reactig species i a elemetary step is called mlecularity f the step. Elemetary steps ivlvig 4 r mre mlecules are t bserved ad eve termlecular are very rare. Reacti mechaism: a sequece f simple rx steps that sum up t the verall reacti. 4
Example The fllwig tw reactis are prpsed as elemetary steps i the mechaism f a verall reacti: () NO Cl (g) NO (g) + Cl (g) () NO Cl (g) + Cl (g) NO (g) + Cl (g) a) Write the verall balaced equati b) Determie the mlecularity f each step c) Write the rate law fr each step a) The verall equati is the sum f the steps: NO Cl (g) NO (g) + Cl (g) b) uimlecular c) Rate NO Cl NO Cl (g) + Cl (g) NO (g) + Cl (g) b) bimlecular c) Rate NO ClCl ---------------------------------------------- NO Cl (g) NO (g) + Cl (g) verall reacti I this example we bserve that Cl (g) des t appear i the verall reacti. It is a itermediate. Itermediates d t appear i the verall reacti but are essetial fr the rx t ccur. Usually they are ustable cmpared t reactats ad prducts. They have rmal bds ad smetimes are stable t be islated. Chemists prpse a rx mechaism i rder t shw hw a reacti ccurs ad the they test the mechaism. The verall rate f a reacti is related t the rate f the slwest step, which is the ratedetermiig step The priciple f detailed balace states that, Frward rate at equilibrium reverse rate at equilibrium There is a cecti betwee the equilibrium cstat f a reacti that taes place i a sequece f steps ad the rate cstats i each step. Csider, + B I C + D Suppse it prceeds as: + r + B C + D r B Nw C + D + B r - CD + r - The first tw are the frward reactis ad the last tw are the reverse reactis. 5
S, eq -,eq, eq B eq - C eq D eq, eq eq ad K K C, eq, eq D B eq eq C D, eq eq eq K KK eq Beq, eq C B eq eq D eq, eq Crrelatig the Mechaism with the Rate Law. The elemetary steps must add up t the verall balaced equati. The elemetary steps must be physically reasable 3. The mechaism must crrelate with the rate law EXMPLES Reacti Mechaisms. chemist prpses the fllwig mechaism fr the sythesis f NOBr (g) itrsyl brmide: NO (g) + Br (g) NOBr(g) NO (g) + Br (g) NOBr (g) fast NOBr (g) + NO (g) NOBr (g) slw If the rate law is r NO Br, is the prpsed mechaism valid? I rder fr the mechaism t be valid three criteria have t be satisfied: i) elemetary steps must add t verall equati; ii) elemetary steps are physically reasable; iii) derived rate law frm mechaism equals the w rate law The reactis sum t the equati NO (g) + Br (g) NOBr(g) Criteri (i) is met Bth elemetary steps are bimlecular. Criteri (ii) is met The slw step i the mechaism is the secd step with rate law: rate NOBr NO Sice NOBr is a itermediate, it must be replaced by usig the first step. Fr a equilibrium lie Step, rate frward rx rate reverse rx 6
Rate (frward) NOBr Rate (reverse) NOBr NOBr NOBr NOBr ( / )NOBr NOBr K NOBr Rate (frward) NOBr NO Substitute the expressi fr NOBr it slw step rate equati Rate (frward) K NOBr NO Cmbie the separate cstats it e cstat: K Rate NO Br Criteri (iii) is met. prpsed mechaism fr the gas-phase reacti betwee chlrie ad itrge dixide is: Cl (g) + NO (g) NO Cl(g) rate Cl NO Cl (g) + NO (g) Cl (g) +NO Cl (g) slw Cl (g) + NO (g) NO Cl (g) fast r Cl NO a) What is the verall reacti equati? The verall reacti ca be btaied by addig the tw steps tgether: Cl (g) + NO (g) Cl(g) + NO Cl(g) Cl(g) + NO (g) NO Cl(g) Cl (g) + NO (g) + Cl(g) + NO (g) Cl(g) + NO Cl(g) + NO Cl(g) Overall reacti: Cl (g) + NO (g) NO Cl(g) b) Idetify the itermediates, if ay. Itermediates appear i the mechaism first as prducts, the as reactats. Cl is a itermediate. c) What are the mlecularity ad the rate law fr each step. Step Mlecularity Rate law Cl (g) + NO (g) Cl(g) + NO Cl(g) bimlecular r Cl NO Cl(g) + NO (g) NO Cl(g) bimlecular r ClNO 7
d) Is the mechaism csistet with the actual rate law? The slw step i the mechaism is the first step with the rate law: rate Cl NO. This rate law is the same as the actual rate law. 3. Csider the mechaism fr the reacti, ClO (aq) + I (aq) Cl (aq) + IO (aq), Rate I HClO () ClO (aq) + H O(l) HClO(aq) + OH (aq) fast () I (aq) + HClO(aq) HIO(aq) + Cl (aq) slw (3) OH (aq) + HIO(aq) H O(l) + IO (aq) fase a) What is the verall equati? (verall) ClO (aq) + I (aq) Cl (aq) + IO (aq) b) Idetify the itermediates, if ay HClO(aq), OH (aq), ad HIO(aq) c) What are the mlecularity ad the rate law fr each step? () Bimlecular; Rate ClO H O () Bimlecular; Rate I HClO (3) Bimlecular; Rate 3 3 OH HIO d) Is the mechaism csistet with the experimetal rate law, Rate ClO I? Fr the slw step: Rate I HClO Hwever, HClO is a itermediate, ad shuld be replaced. Frm step (), leavig ut the water, HClO (K ClO )/ OH Replacig HClO i the slw step rate law gives: Rate I ClO / OH This is t the bserved rate law. Therefre the mechaism is t csistet with the experimetal rate law. 8
Chai Reactis. Iitiati ( r 3 reactive itermediates are geerated). Prpagati (reactive itermediates react t give prducts ad they furish ew supplies f reactive itermediates) 3. Termiati ( reactive itermediates cmbie t give a stable prduct) Example CH 4 (g) + F (g) CH 3 F (g) + HF (g) Mechaism CH 4 (g) + F (g) CH 3 (g) + HF (g) + F (g) (iitiati) CH 3 (g) + F (g) CH 3 F (g) + F (g) (prpagati) CH 4 (g) + F (g) CH 3 (g) + HF (g) (prpagati) CH 3 (g) + F (g) + M (g) CH 3 F (g) + M (g) (termiati) CH 3 ad F are radicals (e r mre upaired valece electrs) If the umber f itermediates icreases durig the prpagati steps the we have a brachig chai reacti. Effect f temperature reacti rates e E a RT - rrheius equati Where is the ietic rate cstat at T, E a is the activati eergy (miimum eergy the mlecules must have t react), R is the uiversal gas cstat, T is the Kelvi temperature, is the cllisi frequecy factr. Higher T larger icreased rate Ea l l R T y b + m x 9
If we w the rate cstats at tw differet temperatures the l Ea R T T Ifrmati sequece t determie the ietic parameters f a reacti Explaiig the effects f ccetrati ad temperature Cllisi thery: basis f the rate law Reactats (atms, is, r mlecules) must cllide with each ther i rder t react. The umber f cllisis per uit time prvides a upper limit f hw fast a reacti ca ccur Why ccetratis are multiplied i the rate law? Hwever, cllisi frequecy cat be the ly factr that affects rate. I fact, i the vast majrity f cllisis the mlecules rebud withut reactig. rrheius prpsed that every reacti has a eergy threshld that the cllidig mlecules shuld exceed i rder t react. This is the activati eergy, E a. Oly cllisis with eugh eergy t exceed E a ca lead t reacti. t a give temperature, T, the fracti f cllisis, f, with eugh eergy t exceed E a is f e E a RT 0
Therefre, Smaller E a (r higher T) larger icreased rate Larger E a (r lwer T smaller decreased rate Hw mlecular structure affects rate? Effective cllisis are the cllisis that lead it prducts Mlecules must cllide s that the reactig atms mae ctact. Therefre, a effective cllisi must have eugh eergy ad a particular mlecular rietati. The effect f this particular mlecular rietati is ctaied i the term i the rrheius equati. p Z (p is the rietati prbability factr, Z is the cllisi frequecy) ad is called preexpetial factr, r frequecy factr. The frward reacti is exthermic because the reactats have mre eergy tha the prducts. The imprtace f mlecular rietati t a effective cllisi. NO + NO 3 NO
Cllisi thery has shrtcmigs b/c it cat prvide a isight abut a) why E a is eeded b) b) hw the activated mlecules l T uderstad these items we tur t TRNSITION STTE THEORY Nature f the trasiti state i the reacti betwee CH 3 Br ad OH - The reacti eergy diagram Reacti crdiate r extet f reacti H rx Ea, frward Ea, reverse
Example NOCl (g) NO (g) + Cl (g) NO (g) + O 3 (g) NO (g) + O (g) Example ey reacti i the upper atmsphere is: O 3 (g) + O (g) O (g). The E a (fwd) is 9 J, ad the H rx fr the reacti is -39 J. Draw a reacti eergy diagram fr this reacti, pstulate a trasiti state, ad calculate E a (rev). Csider the relatiships amg the reactats, prducts, ad trasiti state. The reactats are at a higher eergy level tha the prducts ad the trasiti state is slightly higher tha the reactats. H rx Ea frward Ea reverse Ea reverse 9 ( 39) 4J,,, 3
Reacti eergy diagram fr the tw-step reacti f NO ad F NO (g)+ F (g) NO F (g) Mechaism () NO (g) + F (g) NO F (g) + F (g) (slw) () NO (g) + F (g) NO F (g) (fast) CTLYSIS Each catalyst has its w specific way f fuctiig. I geeral, a catalyst lwers the eergy f activati. Lwerig the Ea icreases the rate cstat,, ad thereby icreases the rate f the reacti. catalyst icreases the rate f the frward ad reverse reactis. catalyzed reacti yields the prducts mre quicly, but des t yield mre prduct tha the ucatalyzed reacti. 4
catalyst lwers Ea by prvidig a differet mechaism, fr the reacti thrugh a ew, lwer eergy pathway. Reacti eergy diagram fr a catalyzed ad a ucatalyzed prcess Nature is the master desiger f catalysts ( ezymes) speed up cellular rxs Hmgeeus ad hetergeeus catalysts The metal-catalyzed hydrgeati f ethylee: H C CH (g) + H (g) H 3 C CH 3 (g) 5