Page Chemical Kieics Chaper O decomposiio i a isec O decomposiio caalyzed by MO Chemical Kieics I is o eough o udersad he soichiomery ad hermodyamics of a reacio; we also mus udersad he facors ha gover he rae of he reacio. We ca use hermodyamics o ell if a reacio is produc or reaca favored. Bu his gives us o ifo o OW FAST reacio goes from reacas o producs. KINETICS he sudy of REACTION RATES ad heir relaio o he way he reacio proceeds, i.e., is MECANISM. The reacio mechaism is our goal! Reacio Raes So, if chemical kieics is he sudy of reacio raes, i migh be a good idea o udersad wha reacios raes are. We defie he reacio rae as he chage i coceraio of a reaca or produc per ui ime. coceraio of A a ime coceraio of A a ime Rae Where A is he reaca or produc beig cosidered. 3 Dye Coc Deermiig a Reacio Rae Time Blue dye is oxidized wih bleach. Is coceraio decreases wih ime. The rae he chage i dye coc wih ime ca be deermied from he plo. 4 Usig he followig reacio we will explorer he world of reacio raes. NO (g) NO(g) + O (g) 5 Coceraio Daa We have he follow se of daa. Wha mehod of visualizig daa migh be useful o use here? 6
Page NO 7 (g) NO(g) + O (g) 8 A graph ca help you visualize wha is goig o a lo easier ha lookig a a able of daa. Usig a combiaio of he graph ad he able we ca sar deermiig some raes. Average Rae You kow he defiiio of a rae is as follows. Therefore o deermie he average rae a which he coceraio of NO chages over he firs 5 secods you would? Rae Rae.79 M. M 4. M/sec 5 sec sec We ca see ha he rae of he reacio is o cosa, bu chages wih ime. 9 Isaaeous Rae Someimes i is impora o kow wha he rae of a reacio is a a cerai ime. This is kow as a isaaeous rae. Isaaeous raes ca be deermied by he slope of a age lie a a cerai poi o he curvaure. For example: if we waed o kow he isaaeous rae a sec. of NO. Draw a age lie a he poi o he curve. Deermie he slope of ha age lie chage i y Slope chage i x NO (g) NO(g) + O (g). Wha is he chage i y? -.6 M. Wha is he chage i x? sec. 3. Wha is he slope? -.6 M / sec..4-5 M/sec 4. Wha happeed o he egaive sig? I is cusomary o work wih posiive reacio raes. NO (g) NO(g) + O (g) Wha else ca you see? If you look a he balaced chemical reacio ad he graph you should be able o oice ha he rae a which NO is used up is equal o he rae ha NO is produced. Lookig a O you ca oice ha he reacio rae is half of ha of NO or NO. Rae Laws: Iroducio Fac: All chemical reacios are reversible. So le us examie he decomposiio of NO NO (g) NO(g) + O (g) {Forward Reacio} If all reacios are reversible a some poi i ime he reverse reacio will be come impora. (Thik of a closed coaier.) NO(g) + O (g) NO (g) {Reverse Reacio} As you ca probably already see his makes life a lile more complicaed. So, we avoid his by sudyig he reacio whe he reverse reacio makes oly a egligible coribuio. Wha is i called whe he forward ad reverse reacio raes are equal? (C3)
Page 3 Rae Laws: Iroducio A wha poi i ime is he reverse reacio egligible? A a poi soo afer he reacas are mixed. Therefore he reacio rae will oly deped o he coceraio of he reacas. Rae k[no ] k rae cosa rae order (ca be a ieger icludig zero or a fracio) Impora Pois. The coceraio of he producs do o appear i he rae law. Why?. The value of he expoe mus be deermied by experime; i CANNOT be wrie from he balaced equaio. 3 Rae Laws: Iroducio We defied a rae as a chage i coceraio per ui ime. owever, which reaca or produc coceraio do we choose i defiig he rae? We could use ay of he hree species. NO (g) NO(g) + O (g) [ NO] Rae k[ NO] T [ O] Rae' k'[ NO] T Rae Rae' k[ NO ] k'[ NO ] k k' {Forward Reacio} 4 Because NO molecules are cosumed for every O molecule produced. 5 6 Rae Laws: Types There are wo ypes of rae laws.. The differeial rae law (ofe called simply he rae law) shows how he rae of a reacio depeds o coceraios.. The iegraed rae law shows how he coceraios of species i he reacio deped o ime. Because we ypically cosider reacios oly uder codiios where he reverse reacio is uimpora, ou rae laws will ivolve oly coceraios of reacas. Because he differeial ad iegraed rae laws for a give reacio are relaed i a well-defied way, he experimeal deermiaio of eiher of he raes laws is sufficie. Experimeal coveiece usually dicaes which ype of rae law is deermied experimeally. Kowig he rae law for a reacio is impora maily because we ca usually ifer he idividual seps ivolved i he reacio from he specific form of he rae law. Deermiig he Form of he Rae Law (Wha is?) We eed o be able o deermie more ha jus he rae equaio. We eed o be able o deermie he value of ad also he value of k. The mehod we use is called he Mehod of Iiial Raes Le us cosider he followig reacio. N 4+ (aq) + NO - (aq) N (g) + O(l) 7 8 Order Deermiaio + [ N 4 ] + m Rae k[ N 4 ] [ NO ]. Look a he daa ad deermie he differeces You doubled he coceraio of NO - from experime o, bu kep he coceraio of N 4+ he same. This leads o a doublig of he iiial rae. You doubled he coceraio of N 4+ from experime o 3, bu kep he coceraio of NO - he same. This leads o a doublig of he iiial rae. Rae.35 Rae.7 Rae.7 Rae.35 m M s k(. M) (.5 M) M s k(. M) (. M) M s k(. M) (. M) M s k(. M) (.5 M) Rae 3 5.4 M s (. M). Rae.7 M s (. M) m m m m.
Page 4 9 Rae Orders ad Raios Therefore we kow he rae law is firs order i erms o N 4+ ad NO -. Rae k[n 4+ ][NO - ] We ca he calculae k from he daa. Rae k[n.35 k.7 ][NO M sec k(. M)(.5 M) -4 + 4 M sec - ] ow he iiial rae chages whe he coceraio is doubled No chage Rae Doubles Rae Quadruples Rae Order Overall Reacio Order Sum of he order of each compoe i he rae law. rae k[ SeO 3 ][ + ] [I ] 3 The overall reacio order is + + 3 6. Ge i? OVER-ALLS Deermie he rae law ad rae cosa for he followig daa Rae k[bro 3- ][Br - ][ + ] 8. 4 M sec k(. M)(. M)(. M) k 8. M 3 sec Wha is he overall reacio order? Iegraed Rae Law Up uil ow we have bee alkig abou differeial rae laws. I is also useful o be able o express he reaca coceraios as a fucio of ime. The Iegraed Rae Law To sar we will look a reacios ivolvig a sigle reaca aa producs Rae k where,, (zero, firs, ad secod order) 3 or e Firs Order Rae Law From he differeial forma we ca rewrie he equaio as follows d Rae - k (firs order) d d k(d) d -k k(d) l- l -k l k + l 4
Page 5 Firs Order Iegraed Rae Law l -k + l The equaio shows how he coceraio of A depeds o ime. If he iiial coceraio of A ad he rae cosa k are kow, he coceraio of A a ay ime ca be calculaed. The equaio ca also ake he form ymx+b. yl x m-k bl So, we have discovered a way o es if he reacio is firs order. If we plo l vs ime ad ge a sraigh lie we kow he reacio is firs order. 5 [N O 5 ] (M) Time (sec)..77 5.5.5.5 3.65 4 N O 5 (g) 4NO (g) + O (g). Verify ha he rae law is firs order.. Calculae he rae cosa. Well, we have o iformaio o he iiial raes; so, we sar hikig abou he iegraed rae laws If i is firs order we eed o be able o plo l [N O 5 ] vs. ime So, we cosruc a ew able ad plo he daa. 6 l [N O 5 ] Time (sec) -.33 -.649 5 -.996-3.689-4.38 3-5.75 4 The plo proves i is a sraigh lie ad so i is a firs order reacio. N O 5 (g) 4NO (g) + O (g) 7 l [N O 5 ] Time (sec) -.33 -.649 5 -.996-3.689-4.38 3-5.75 4 N O 5 (g) 4NO (g) + O (g) Sice i is a firs order reacio, we kow ha i he firs order iegraed rae law ha k is equal o he -slope of he lie. Y (l[no5]) Slope X - 5.75 - (-.33).77 3 Slope 6.93 s 4 4 3 k ( slope) 6.93 s 8 alf-life of a Firs-Order Reacio We ca also deermie wha is kow as a half-life. alf-life is defied as he ime required for a reaca o reach half of is origial coceraio. / 693. k / half-life of he reacio k rae cosa For a firs-order reacio, he half-life does o deped o coceraio. See pages 57 57 for mahemaical proof. 9.693 k ( s order alf-life) A cerai firs-order reacio has a half-life of. miues.. Calculae k for he reacio. ow much ime is required for his reacio o be 75 % complee? /.693 k 3.47.mi mi If he reacio is 75% complee ha meas here is 5% of he reaca lef. l - k + l If we assume ha he origal a 75% compleio is.5. l.5 -k + l - - l.5 - l ( 3.47 mi ) - - -.3863 -(3.47 mi ) 39.95 mi 4 mi 3 coceraio ishe he coceraio
Page 6 Secod-Order Rae Law We will skip he calculus lesso ad jus give you he secod-order iegraed rae law. For aa producs i a secod-order reacio, Rae Iegraed rae law is A k A + k A A o Therefore A plo of / vs. ime wih produce a sraigh lie wih he slope equal o k 3 alf-life of a Secod-Order Reacio / k A o / half-life of he reacio k rae cosa A o iiial coceraio of A The half-life is depede upo he iiial coceraio. 3 C 4 6 (g) C 8 (g) Wih he followig daa deermie:. Is he reacio firs of secod order?. Wha is he value of he rae cosa for he reacio? 3. Wha is he half-life for he reacio uder he codiios of his experime [C 4 6 ] (M) Time (sec)..65.476 8.37 8.33 36.7 44.4 5.8 6 Sice we kow ha firs order reacios creae a sraigh lie whe you plo l vs. ime ad secod order reacios creae a sraigh lie whe you plo / vs. ime. We ca creae a ew able ad graphs. 33 (s) /[C 4 6 ] l[c 4 4 ] -4.65 6-5.75 8-5.348 8 7-5.599 36 3-5.767 44 37-5.95 5 45-6.8 6 48-6.75 If we plo his daa we will obai he followig wo graphs. From he graphs we will be able o ascerai wha order he reacio is. So, wha order is he reacio? 34 From he previous daa you ca do some calculaios ad obai he followig able. Sice we kow ha he reacio is secod order we ca use he secod order iegraed rae-law o deermie k. [C 4 6 ] (M) Time (sec)..65.476 8.37 8.33 36.7 44.4 5.8 6.8 48 k(6) + 38 6 k + k(6) + k 6.4. M sec 35 We ca do he same hig o calculae he half life or use he secodorder half life equaio..5 (6.4 / k + (6.4 M M sec)( 68.66 sec.63 sec)( / 3 ) sec / ) +. 36
Page 7 We ca do he same hig o calculae he half life or use he secodorder half life equaio. / k 37 Zero-Order Rae Laws Mos reacios ivolvig a sigle reaca show eiher firs or secod order kieics. owever, here ca be zero-order reacios. The rae is cosa. I does o chage wih coceraio. Rae k k() k 38 / / (6.4 M 68.66 sec.63 sec)(. M) 3 sec k + / k : The followig reacio akes place o a ho plaium surface. N O(g) N (g) + O (g) The plaium surface is compleely covered wih N O molecules. If we icrease he coceraio, i has o effec o he rae. Sice oly hose N O molecules o he surface ca reac. A of a zero-order reacio. 39 A Summary Simplificaio: Codiios are se such ha oly forward reacio is impora. Two ypes:» differeial rae law» iegraed rae law Which ype? Depeds o he ype of daa colleced - differeial ad iegraed forms ca be iercovered. Mos commo: mehod of iiial raes. Coceraio v. ime: used o deermie iegraed rae law, ofe graphically. For several reacas: choose codiios uder which oly oe reaca varies sigificaly (pseudo firs-order codiios). 4 4 4 Reacio Mechaisms The sequece of eves a he molecular level ha corol he speed ad oucome of a reacio. A chemical equaio does o ell us how reacas become producs - i is a summary of he overall process. Br from biomass burig desroys sraospheric ozoe. (See R.J. Ciceroe, Sciece, volume 63, page 43, 994.) Sep : Br + O 3 ---> BrO + O Sep : Cl + O 3 ---> ClO + O Sep 3: BrO + ClO + ligh ---> Br + Cl + O NET: O 3 ---> 3 O The reacio has may seps i he reacio mechaism.
Page 8 Ofe Used Terms 43 44 Iermediae: formed i oe sep ad used up i a subseque sep ad so is ever see as a produc. Moleculariy: he umber of species ha mus collide o produce he reacio idicaed by ha sep. Elemeary Sep: A reacio whose rae law ca be wrie from is moleculariy. ui, bi ad ermolecular NO (g) + CO(g) NO(g) + CO (g) ere is a basic reacio. Rae k[no ] Bu he mechaism is hough o ivolve he followig seps. k NO(g) + NO(g) NO3(g) + NO(g) k NO3(g) + CO(g) NO(g) + CO(g) 45 The sum of he elemeary seps mus give he overall balaced equaio for he reacio. NO (g) + NO (g) NO 3 (g) + NO(g) NO 3 (g) + CO(g) NO (g) + CO (g) --------------------------------------------------- NO (g) + CO(g) NO(g) + CO (g) 46 Rae-Deermiig Sep 47 The mechaism mus agree wih he experimeally deermied rae law. 48 I a mulisep reacio, i is he slowes sep. I herefore deermies he rae of reacio. NO (g) + NO (g) NO 3 (g) + NO(g) NO 3 (g) + CO(g) NO (g) + CO (g) Rae of formaio of Overall rae slow fas [NO3 ] NO3 k[no ] k [NO ] Which agrees wih he experimeally deermied rae law.
Page 9 5 Collisio Model We will discuss a model ha accous for he observed characerisics of reacio raes, he collisio model. The basic idea of he model is ha i order for molecules o reac, hey mus collide. 49 6 Coceraio Wha is a easy way o icrease he umber of collisios? Icrease he coceraio If we have a higher coceraio, he we will have more molecules, which i ur gives us more collisios per ui ime. If we have more collisios, he he reacio rae mus icrease. 5 Coceraio ca affec he rae of a chemical reacio Facors Affecig Raes Coceraios 5 Rae wih.3 M Cl Rae wih 6. M Cl 7 Temperaure Aoher way o chage he umber of collisios is o chage he emperaure. Le us cosider emperaure of a gas: If we icrease he emperaure:. We icrease he molecular velociy. Which would icrease he frequecy of collisios bewee molecules 3. Which icreases he reacio rae Temperaure ca affec he rae of a chemical reacio 5 Facors Affecig Raes Temperaure Bleach a 54 C Bleach a C 53 8 of Chage i Temperaure ad Coceraio As he "emperaure" icreases, he spheres hi he edges more frequely. Whe more spheres are added, he ierparicle collisios are more freque. 54 hp://chemed.chem.purdue.edu/demos/mai_pages/4.4.hml
Page Facors Affecig Raes 55 Problems wih Collisio Model 56 Physical sae of reacas I has bee show ha he reacio rae is much smaller ha he calculaed collisio frequecy. I oher words, oly a small fracio of all collisios produces a reacio. 57 58 Svae Arrheius I he 88 s, his problem was firs addressed by Svae Arrheius. e proposed ha here is a hreshold eergy which mus be overcome i order for he chemical reacio o ake place. This hreshold eergy is called he acivaio eergy. of Acivaio Eergy Le us look a a example of acivaio eergy. We will use he decomposiio of BrNO(g) as a example: BrNO(g) NO(g) + Br (g) I his reacio, wo Br-N bods eed o be broke ad oe Br-Br bod eeds o form. The eergy required o break a Br-N bod is cosiderable (43 kj/mol). This eergy mus be supplied from somewhere, bu from where? of Acivaio Eergy (co d) Based upo he collisio model, he eergy comes from he kieic eergy of he molecules. Oce he molecules collide, he kieic eergy is chaged io poeial eergy which breaks he bods ad rearrages he aoms. 59 Svae Arrheius Arrheius posulaed ha he umber of collisios havig he acivaio eergy is a fracio of he oal umber of collisios. 6 Where do you hik he Acivaio producs would be Eergy if he reacio was edohermic? Reacas Trasiio Sae Because he producs are lower i eergy ha he reacas, his chemical reacio is exohermic Producs(i produces hea). Number of collisios wih he acivaio eergy (oal umber of collisios) e -Ea/RT Ea is he acivaio eergy R is he uiversal gas cosa T is he emperaure i Kelvi e Ea/RT is he fracio of collisios wih eergy Ea or greaer a emperaure T
Page More Deails Experimes have show ha he observed reacio rae is cosiderably smaller ha he rae of collisios wih eough eergy o surmou he barrier. I oher words, here are eough collisios wih eough eergy o cause he reacio, bu he reacio does o occur. Why (does chemisry have o be so difficul)? 6 Molecular Orieaio I has o do wih molecular orieaio. Whe molecules collide, hey mus be lied up a cerai way for he reacio o proceed. Lie up so ha he wo Br aoms ca reac wih each oher ad NO(g) ca be ejeced. Remember his is he decomposiio reacio BrNO(g) NO(g) + Br (g) 6 The Br aoms are o lied up o allow for he reacio o efficiely occur. Mai Pois For a reacio o occur: The collisio mus ivolve eough eergy o produce he reacio or he collisio eergy mus be equal or greaer ha he acivaio eergy. The relaive orieaio of he reacas mus allow efficie formaio of ay ew bods ecessary o produce he producs. We ca represe hese facors as a rae cosa (k) wih oe equaio called he Arrheius Equaio. k A e -Ea/RT A is he frequecy facor ha is made up of he collisio frequecy ad he seric facor (molecular orieaio). 63 Facors So Far ha Affec he Rae of a Chemical Reacio We have see ad reviewed differe facors ha affec he rae of a chemical reacio. Coceraio (he more molecules, he more collisios). Temperaure (if we speed up he moveme of he molecules, his will help he reacio o occur ad speed i up). Molecular orieaio (molecules mus be properly orieaed i order o reac) Acivaio eergy (mus provide eough eergy o ge over he hill) If we cosider he Arrheius Equaio, we ca easily see how emperaure affecs he rae of a chemical reacio. Wha oher facors could here be? Ca we chage he acivaio eergy? k A e -Ea/RT Temperaure ca chage 64 65 Yes, We Ca Chage he Acivaio Eergy. This is doe hrough he use of a caalys. A caalys is a subsace ha speeds up a reacio wihou beig cosumed. I does his by providig a ew reacio pahway ha has a lower acivaio eergy. Two differe classificaios of caalyss: omogeous eerogeeous Poeial Eergy Reacio Progress Figure.8: The exhaus gases from a auomobile egie are passed hrough a caalyic coverer o miimize eviromeal damage. 66
Page Facors Affecig Raes Caalyss: caalyzed decomp of O O --> O + O 67 eerogeeous Caalys (hydrogeaio of ehylee) C C (g) + (g) A heerogeeous caalys is oe ha exiss i a differe phase relaive o he reacas, usually a solid. eerogeeous caalyic reacios ypically ivolves four seps:. Adsorpio of he reacas. Migraio of he adsorbed reacas o he surface 3. Reacio of he adsorbed subsaces 4. Escape, or desorpio, of he producs C C (g) 68 omogeeous Caalys A homogeeous caalys is oe ha exiss i he same phase as he reacig molecules. A example of his is he breakdow of ozoe (O 3 ). Chlorie aoms are released from CCl F (Freo-) whe i reacs wih ligh. These chlorie aoms he go o o break dow ozoe. Cl(g) + O 3 (g) ClO(g) + O (g) O(g) + ClO(g) Cl(g) + O (g) O(g) + O 3 (g) O (g) Therefore, he chlorie gas is he homogeeous caalys. 69 The Take OME Message There are five major facors ha ifluece a chemical reacio.. Coceraio of Reacas. Temperaure 3. Acivaio Eergy 4. Molecular Orieaio 5. Use of Caalys The Arrheius equaio (k A e Ea/RT ) describes how some of hese facors affec he reacio rae (k). A caalys lowers he acivaio eergy ad is o cosumed. 7