Complex Reactions and Mechanisms (continued)

Transcription

1 5.60 Spring 2005 Lecture #29 page 1 Cmplex Reactins and Mechanisms (cntinued) Sme cmments abut analyzing kinetic data A) Reactins with ne reactant: A prducts a) Plt r analyze [A vs. t ln[a vs. t 1/[A vs. t andfindwhich givesa straight line. b) Half-lifemethd: measuret 1/2 vs. [A 1 st rder t 1/2 [A 0 2 nd rder t 1/2 [A -1 etc. c) Multiple lifetimes (t 3/4 and t 1/2 )(at t 3/4, [A=[A /4 ) t 1 st 3/4 rder t 3/4 =(2ln2)/k = 2 t 1/2 t 2 nd 3/ 4 rder t 3/4 =3/([A k) = 3 t 1/2 B) Reactins with mre than ne reactant: e.g. A + B + C prducts a) Initial Rate Methd

2 5.60 Spring 2005 Lecture #29 page 2 Fr [A [A t t= 0 = R k[a [B [C / [A / / / Fr [A = R k[a [B [C t t=0 Experimentally determine R = [A / / R [A If 2 [A / =[A then, if if if if R / R = 1 = 0 R = 2 = 1/2 R / R = 2 = 1 R / R = 4 = 2 R / VI) Chain Reactins In chain reactins, a prduct frm a step in the mechanism is a reactant fr a previus step (i.e. the reactin feeds itself). a) Statinary r stable chain reactins. he cncentratin f reactive intermediates is cnstant in time r slwly decreasing. Example:

3 5.60 Spring 2005 Lecture #29 page 3 CH 3 CHO CH 4 + CO Experimental bservatins: Small amunts f C 2 H 6 and H 2 are als prduced, and the Rate f Reactin [CH 3 CHO 3/2. (hese are signatures f a chain reactin mechanism) Prpsed mechanism fr this reactin (Rice Herzfeld mechanism) : [he means a free radical, i.e., a mlecular fragment with an unpaired electrn k 1 Initiatin: CH 3 CHO CH 3 + CHO k 2 Prpagatin: CH 3 + CH 3 CHO CH 3 CO + CH 4 CH 3 CO k 3 CH 3 + CO k 4 erminatin: 2 CH3 C 2 H 6 k 5 Side Reactins: CHO + M CO + H + M k 6 H +CH 3 CHO H 2 + CH 3 CO

4 5.60 Spring 2005 Lecture #29 page 4 Kinetic Equatins: dch [ 4 = k2 [CH 3 [CH 3 CHO d[ch 3 = k1 [CH 3 CHO k 2 [CH 3 [CH 3 CHO+ k 3 [ CH 3 CO 2k 4 [CH 3 2 d[ CH 3 CO = k2 [CH 3 [CH 3 CHO k 3 [ CH 3 CO We can als write kinetic equatins fr [HCO, [H Assume Steady State apprximatin fr all free radical species ([R is small, d[r / 0) [ 3 d[ CH 3 CO dch = = 0 Steady State Apprximatin [ CH 3 CO ss = (k 2 /k 3 ) [CH 3 [CH 3 CHO [CH 3 SS = 2 k 1/2 1 [CH 3 CHO 1/2 k4 1/2 d[ch 4 k 1 3/2 S = k 2 [CH 3 CHO 2k 4 Nte: in agreement with bserved rate law; "phenmenlgical" rate cefficient is cmpsite f three elementary reactin rate cnstants

5 5.60 Spring 2005 Lecture #29 page 5 Chain Length: he # f prpagatin steps per initiatin step befre a terminatin step kills the free radical Chain length rate f prduct frmatin = rate f initial radical frmatin Fr acetaldehyde decmpsitin, = 1/2 k 1 [CH 3/2 3CHO 2k k 1 [CH 3 CHO k 2 4 k 1/2 2 = [CH 3 CHO 2k 1 k 4 (experimentally 300 at typical pressures) b) Nn-statinary r unstable chain reactins: he prpagatin includes a branching step, which increases the cncentratin f reactive intermediates. ne type f EXPLOSION!! Example: the cmbustin f hydrgen t frm water 2H 2 + O 2 2H 2 O Mechanism: R I Initiatin: H 2 2H

6 5.60 Spring 2005 Lecture #29 page 6 k 1 Branching: H + O 2 OH + O (O in 3 P atmic state) O + H 2 k 2 OH + H k 3 Prpagatin: OH + H 2 H + H 2 O k 4 erminatin: H H wall H 2, eventually H + O 2 + M Kinetic Equatins k 5 HO 2 + M d[h = RI k 1 [H[O 2 + k 2 [O[H 2 + k 3 [OH[H 2 k 4 [H k 5 [H[O 2 [M d[o = k1 [H[O 2 k 2 [O[H 2 d[oh = k1 [H[O 2 + k 2 [O[H 2 k 3 [OH[H 2 Assume S. S. Apprximatin ([Intermediates=small, d[int./~0) ** If S.S. App. Fails EXPLOSION (because nt true) ** Slve fr [Int. SS [O SS = k 1 [H[O 2 k 2 [H 2 [OH SS = k 1[H[O 2 + k 2 [O SS [H 2 = 2k 1 [H [O 2 k 3 [H 2 k 3 [H 2

7 5.60 Spring 2005 Lecture #29 page 7 d[h SS = R I + {2k 1 [O 2 (k 4 [H SS + k 5 [H SS [O 2 [M)}[H SS = 0? R I S [H SS = k4 + k 5 [O 2 [M 2k 1 [O 2 Limiting Cases i) Lw Pressure (k 1 [O 2, k 5 [O 2 [M) << k 4 Wall cllisins dminate ver branching S.S. app. is valid N explsin ii) Medium Pressure 2k 1 [O 2 ~ k 4 + k 5 [O 2 [M Branching is imprtant, [H SS is large! S.S. is NO valid! EXPLOSION!! iii) Higher Pressure k 5 [O 2 [M > 2 k 1 [O 2 erminatin dminates ver branching S.S. is valid N explsin iv) Very High Pressure

8 5.60 Spring 2005 Lecture #29 page 8 HO 2 + H 2 H 2 O + OH becmes imprtant his increases OH EXPLOSION!! S we have a stability diagram fr hydrgen cmbustin, Pressure Stable Reactin Explsin emperature Branching chain reactins als ccur in nuclear reactins. Fr example, in fissin reactins f 235 U, 3 neutrns are prduced fr each neutrn absrbed by a uranium nucleus. In a nuclear pwer reactr, cntrl rds that absrb neutrns terminate the chain and mderate the reactin (usually). Anther example f a free radical chain reactin is the frmatin and destructin f zne in the Earth's stratsphere. We will cnsider this mechanism in detail in a subsequent lecture.