CHEMICAL KINETICS Rate Order Rate law Rate constant Half-life Molecularity Elementary. Complex Temperature dependence, Steady-state Approximation
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1 CHEMICL KINETICS Rae Order Rae law Rae consan Half-life Moleculariy Elemenary Complex Temperaure dependence, Seady-sae pproximaion
2 Chemical Reacions Kineics Chemical ineics is he sudy of ime dependence of he change in he concenraion of reacans and producs. Chemical Reacion involve he forming and breaing of chemical bonds Reacan Molecules (H, I ) approach one anoher and collide and inerac wih appropriae energy and orienaion. Bonds are sreched, broen, and formed and finally produc molecules (HI) move away from one anoher. How can we describe he rae a which such a chemical ransformaion aes place?
3 Chemical Reacion Kineics H (g) + I (g) HI(g) Reacans producs Thermodynamics ell us all abou he energeic feasibiliy of a reacion: we measure he Gibbs energy G for he chemical reacion. Thermodynamics does no ell us how quicly he reacion will proceed: i does no provide ineic informaion. 3
4 Basic Ideas in Reacion Kineics Chemical reacion ineics deals wih he rae of velociy of chemical reacions. We wish o quanify: The velociy a which reacans are ransformed o producs The deailed molecular pahway by which a reacion proceed (he reacion mechanism) 4
5 Basic Ideas in Reacion Kineics Chemical reacions are said o be acivaed processes: energy (usually hermal (hea) energy) mus be inroduced ino he sysem so ha chemical ransformaion occur more rapidly when emperaure of he sysem is increased. In simple erms an acivaion energy barrier mus be overcome before reacans can be ransformed ino producs. 5
6 Rae of reacion Wha do we mean by erm reacion rae? The erm rae implies ha somehing changes wih respec o somehing else. How many reacion raes can be deermined? The reacion rae is quanified in erms of he change in concenraion of a reacan or produc species wih respec o ime. This requires an experimenal measuremen of he manner in which he concenraion changes wih ime of reacion. We can monior eiher he concenraion change direcly, or monior changes in some physical quaniy which is direcly proporional o he concenraion. 6
7 Rae of reacion The reacan concenraion decreases wih increasing ime, and he produc concenraion increases wih increasing ime. The rae of a chemical reacion depends on he concenraion of each of he paricipaing reacan species. The manner in which he rae changes in magniude wih changes in he magniude of each of paricipaing reacans is ermed he reacion order. 7
8 Rae of reacion Symbol: R, n Soichiomeric equaion: m + n B p X + q Y Rae: R m d d n db d p dx d q dy d 8
9 Unis of, rae consan concenraion ime d R m B m d (concenraion) m no reacion coeff. n (concenraion) n Rae Law Order Unis of R = R = R = R= B in, B overall R = / / R m B (concenraion) ime n mn
10 Facors Tha ffec Reacion Raes Concenraion of Reacans s he concenraion of reacans increases, so does he lielihood ha reacan molecules will collide. Temperaure higher emperaures, reacan molecules have more ineic energy, move faser, and collide more ofen and wih greaer energy. Caalyss Speed rxn by changing mechanism.
11 Rae Law How does he rae depend upon s? Find ou by experimen The Rae Law equaion R = a B b (for many reacions) order, n = a + b + (dimensionless) rae consan, (unis depend on rxn rder) Rae = when each conc = uniy
12 Rae laws can be complicaed ) H (g) + I (g) HI (g) R HI ) H (g) + Br (g) HBr (g) R H Br HBrBr / These rae laws sugges ha hese wo reacions occur via differen mechanisms (ses of individual seps). The firs may be a elemenary reacion (one sep) whereas he laer is cerainly a mulisep process. We will soon explore how o obain complicaed rae laws from suggesed mechanisms.
13 Finding rae laws experimenally There are wo common mehods for deermining rae laws: Mehod of isolaion Se up reacion so one reacan is in excess. ny change in rae will be due o changes in oher reacan. Repea for oher reacan. R B n where m Mehod of iniial raes Measure concenraion change as a funcion of ime, ~v(), for a series of experimenal condiions. (Condiions mus include ses where he reacan has he same iniial concenraion bu B changes and vice versa).
14 Inegraion of rae laws Order of reacion For a reacion a producs he rae law is: d R a d d a d defining a d R d or jus wrien as : d R d n n n n rae of change in he concenraion of 4
15 5 Firs-order reacion ) ( ) ln( d d d d d d R
16 Firs-order reacion ln ln ( ) ln ln plo of ln versus gives a sraigh line of slope - if r = 6
17 7 e e ln ) ( ln ln Firs-order reacion Firs order reacions decay exponenially.
18 Firs-order reacion: example Ozone decays via firs order ineics O ( g) O ( g) O( g) 3 O e 3 O3 =.78-5 s - a 3 K O ln O 3 3 Wha is slope?
19 Wha happens as increases? e ln =.5 s - =.5 s - =.5 s - =. s -
20 Firs-order reacion: example Consider he process in which mehyl isonirile is convered o aceonirile. CH 3 NC CH 3 CN How do we now his is a firs order rxn?
21 Firs-order reacion: example CH 3 NC CH 3 CN This daa was colleced for his reacion a 98.9 C. Does rae=ch 3 NC for all ime inervals?
22 Firs-order reacion When ln P is ploed as a funcion of ime, a sraigh line resuls. The process is firs-order. is he negaive slope: s -.
23 Half life: firs-order reacion The ime aen for o drop o half is original value is called he reacion s half-life, /. Seing = ½ and = / in: ln ln / 3
24 Half life: firs-order reacion ln / / or / 4
25 When is a reacion over? = e - Technically = only afer infinie ime 5
26 Second-order reacion Similarly, inegraing he rae law for a process ha is second-order in reacan : R d d d d d d 6
27 7 ) ( plo of / versus gives a sraigh line of slope if r = Second-order reacion also in he form y = mx + b
28 Deermining rxn order The decomposiion of NO a 3 C is described by he equaion NO (g) NO (g) + / O (g) and yields hese daa: Time (s) NO, M
29 Deermining rxn order Graphing ln NO vs. yields: The plo is no a sraigh line, so he process is no firsorder in. Time (s) NO, M ln NO Does no fi:
30 Second-Order Processes graph of /NO vs. gives his plo. Time (s) NO, M /NO This is a sraigh line. Therefore, he process is secondorder in NO.
31 Half-Life Half-life is defined as he ime required for one-half of a reacan o reac. Because a / is one-half of he original, =.5.
32 Half life: second-order reacion For a second-order process, se =.5 in nd order equaion. o / or / / 3
33 Ouline: Kineics Rae Laws Inegraed Rae Laws Firs order Second order Second order (Bimoleculer) complicaed (discussed laer) Half-life Complicaed (discussed laer)
34 Problems: Define/derive Inegraed Rae Laws and Half-life of 3 rd -order and n h -order reacions whose rae laws are given below: 3 R B where R n 34
35 Ouline: Kineics Third order n h -order Rae Laws Inegraed Rae Laws Half-life 3 R n R n n n ) ( ) ( ) ( n n o n () 3 o
36 Rae law for elemenary reacion Law of Mass cion applies: rae of rxn produc of acive masses of reacans acive mass molar concenraion raised o power of number of species Examples: P + Q rae = + B C + D rae = B + B E + F + G rae = 3 B 36
37 Moleculariy of elemenary reacions? Unimolecular (decay) P d d Bimolecular (collision) + B P d B d Termolecular (collision) + B + C P d 3 B C d No oher are feasible! Saisically highly unliely. 37
38 Oher order reacions Second order reacion: producs B producs Second order rae: R d d R d d B Inegraed rae law: B ln B B Zero order reacion: producs Zero order rae: R d d Inegraed rae law:
39 Pseudo-firs order reacions You can overload he oher reacans o deermine he order wih respec o one individual reacan (mehod of isolaion). For B producs, wha happens if B >>? R d d B
40 Reversible reacions (small r G) B d d B - ssume firs order, elemenary rxn in boh direcions B d d Rae: B B B B Conservaion of Mass: B B ) ( ln Inegrae:
41 equilibrium equilibrium - B d d d d Wha is he equilibrium consan for his reacion? In erms of rae consans? K eq B B eq The forward rae equals he reverse a equilibrium. K eq eq B eq eq
42 Temperaure dependence? C H 5 Cl C H 4 + HCl /s - T/K Conclusion: very sensiive o emperaure Rule of humb: rae doubles for a K rise 4
43 Hood = exp{ -B/T } Deails of T dependence rrhenius = exp{ - E / RT } -facor or pre-exponenial facor a T E acivaion energy Rae of rxn (energy barrier) J mol - or J mol - R gas consan. Temperaure 43
44 rrhenius eqn. = exp{-e/rt} Useful linear form: ln = -(E/R)(/T) + ln Plo ln along Y-axis vs (/T) along X-axis Slope is negaive -(E/R); inercep = ln Experimenal Es range from o +4 J mol - Examples: H + HCl H + Cl 9 J mol - H + HF H + F 39 J mol - C H 5 I C H 4 + HI 9 J mol - C H 6 CH J mol - 44
45 ln /(dm 3 mol - s - ) Pracical rrhenius plo, origin no included 8 6 Inercep = 7.6 fromwhich =. x dm 3 mol - s - 4 Slope = -,55 fromwhich E = 88 J/mol K / T 45
46 46 Rae consan expression RT E exp ln exp ) ( ) ( exp T T R E T T R E RT E RT E ln mol J E E E E
47 Temperaure Dependence of The rae consan can vary in differen ways wih T. Svane rrhenius Winner of he 3 rd Nobel Prize in Chemisry Differenial form of he rrhenius Equaion: d ln dt E RT a
48 Inegraed forms of rrhenius equaion: ln ln Ea RT rrhenius Parameers e E a / RT E a is he acivaion energy. This is he energy required o ge over a barrier (a he acivaed or ransiion sae) beween he reacans and producs. E a has unis of energy and is T independen. civaed (or ransiion) sae is he pre-exponenial or rrhenius facor and is T dependen. is a measure of rae a which collisions occur (and aes los of hings ino acc such as orienaion, molecular size, number of molecules per volume, molecular velociy, ec). HI(g) I (g) + H (g)
49 BT h e K Transiion-Sae Theory Eyring Equaion (ey o ransiion-sae heory) From CEq: So e G / RT B is he ransiion sae (or acivaed complex.) G / RT G H TS Transiion sae heory assumes ha he ransiion sae and reacans are in equilibrium wih each oher, and uses conceps from chemical equilibrium and saisical mechanics o find ineic info such as rae consans! BT h e BT h K Change in Gibbs energy from reacans o TS Enropy of acivaion C S / R H / RT e Enhalpy of acivaion
50 Necessary Pieces Relaing E a o hermodynamics! rrhenius Equaion: Differeniae wr T: ln d ln dt Ea ln RT Ea RT or E a RT d ln dt From Eyring Equaion: d ln dt T d ln K dt C van Hoff Equaion (for K c ): d ln KC U dt RT Puing i all ogeher E a RT T d ln K dt C or E a RT U
51 E a Wha abou, he pre-exponenial? RT U and U H RT n g so E a RT H RT n Unimolecular Gas Phase Reacion Producs BT h e Bimolecular Gas Phase Reacion +BB Producs e e e T h so S / R H / RT BT h so E a B S / R E e e RT S / R E H E a H RT e e / RT a / RT Wha is? Same for reacions in soluion
52 EX-CK3 Transiion Sae Theory and NMR H Lab In he NMR/N,N-DM Paper, Gasparro e al. found an acivaion energy of 7.3 J/mol and a pre-facor of.87 s -. Using hese values, and a emperaure of 98 K, find S G Why is TST imporan?. Provides deails of a reacion on he molecular scale.. Connecs quanum mechanics and ineics. 3. Currenly used for many compuaional sudies on reacion raes.
53 Reacion Mechanisms
54 lways remember. One can never prove a reacion mechanism, alhough evidence may disprove a mechanism. Verifying proposed mechanisms requires exensive experimenal verificaion of each proposed sep!
55 Le s examine a reacion obs P Reacion could progress in muliple ways How can we disinguish? Case : One elemenary sep Case : Two sep reacion P I I P
56 le s focus on he inermediae I P How do and relae in case a? in case b? (a) I forms quicly bu decays slowly is fas relaive o. (b) I builds up o a consan, nearly negligible, concenraion unil near end of reacion. is slow relaive o. d I d Seady sae approximaion... Valid only if >.
57 Rae Laws do no yield unique mechanisms n empirically deermined rae law does no imply a unique reacion mechanism! Consider reacion: obs NO( g) O( g) NO( g) Experimenally, i was deermined ha he rae is given by: v( ) NO O obs Researchers proposed wo possible mechanisms. They need o deermine if one of hem is correc. So how would researchers disinguish beween he mechanisms?
58 Remember he Chain Rxn from CK-6? H (g) + Br (g) HBr (g) Proposed Mechanism Iniiaion: v H Br / ( ) HBrBr Br ( g) M( g) Br ( g) M( g) Propagaion: Inhibiion: Terminaion: Br H ( g) H( g) HBr( g) H ( g) 3 ( g) Br ( g) HBr( g) Br ( g) ( ) ( ) HBr g H g Br ( g) H( g ) Br ( g) M( g) Br ( g) M( g )
59 reacion: CO + Cl COCl...?? Expal rae law: d CO d CO Cl Conclusion?: reacion does no proceed as wrien Elemenary reacions; rxns. ha proceed as wrien a he molecular level. Cl Cl + Cl () Decay Cl + CO COCl () Collisional COCl + Cl COCl + Cl (3) Collisional Cl + Cl Cl (4) Collisional Seps hrough 4 comprise he mechanism of he reacion. 59
60 d CO d CO Cl 6 If seps & 3 are slow in comparison o & 4....hen, Cl Cl or K = Cl / Cl So Cl = K Cl / Hence: d CO d. CO. Cl Predic ha: observed = K Therefore mechanism confirmed (?)
61 H + I HI Predic: + (/) (dhi/d) = H I Bu if via: I I I + I + H HI rae = I H I + I I ssume, as before, ha & 3 are fas cf. o Then: I I or K = I / I Rae = I H = K I H (idenical) Chec? I + hn I (ligh of 578 nm) 6
62 Problem In he decomposiion of azomehane,, a a pressure of.8 Pa & a emperaure of 576 K he following concenraions were recorded as a funcion of ime, : Time, /mins / mmol dm Show ha he reacion is s order in azomehane & deermine he rae consan a his emperaure. 6
63 63 Recognise ha his is a rae law quesion dealing wih he inegral mehod. - (d/d) =? = Re-arrange & inegrae Tes: ln = - + ln Complee able: Time, /mins ln Plo ln along y-axis; along x-axis Is i linear? Yes. Conclusion follows. Calc. slope as: so = min -
64 More recen quesions Wrie down he rae of rxn for he rxn: C 3 H O = 3 CO + 4 H O for boh producs & reacans 8 mars For a nd order rxn he rae law can be wrien: - (d/d) = Wha are he unis of? 5 mars Why is he elemenary rxn NO + NO N O 4 referred o as a bimolecular rxn? 3 mars 64
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