(BQ) Part 2 book An introduction to chemical kinetics has contents: Complex reactions in the gas phase, reactions in solution, examples of reactions in solution. (BQ) Part 2 book An introduction to chemical kinetics has contents: Complex reactions in the gas phase, reactions in solution, examples of reactions in solution. (BQ) Part 2 book An introduction to chemical kinetics has contents: Complex reactions in the gas phase, reactions in solution, examples of reactions in solution.
6 Complex Reactions in the Gas Phase Aims This chapter discusses complex reactions and focuses on the chemical mechanism By the end of this chapter you should be able to recognize and classify the large variety of complex reactions distinguish between chain and non-chain mechanisms deduce mechanisms from experimental observations apply the steady state treatment recognize that there can be kinetically equivalent mechanisms recognize the distinctions between steady state and pre-equilibrium treatments quote the characteristics of chain reactions and their kinetic features appreciate the significance of third bodies in complex mechanisms understand the special features of surface termination be aware of the features of branched chain reactions and the relation between branched chains and explosions, and be aware of the features of degenerate branching and the relation between degenerate branching and mild explosions An Introduction to Chemical Kinetics Margaret Robson Wright # 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09058-8 (hbk) 0-470-09059-6 (pbk) 184 COMPLEX REACTIONS IN THE GAS PHASE 6.1 Elementary and Complex Reactions Elementary reactions occur via a single chemical step If reaction occurs mechanistically as A ỵ B ! products with mechanistic rate ẳ kẵAẵB 6:1ị then the reaction is bimolecular and second order There are only a few elementary bimolecular reactions in the gas phase, e.g the reaction NO ỵ O3 ! NO2 ỵ O2 is believed to occur in one step involving the simultaneous coming together of NO and O3 to form an activated complex, which changes configuration to give NO2 and O2 with 6:2ị rate ẳ kẵNOẵO3 Many of the bimolecular reactions for which extensive data are available occur as individual steps in reactions involving radicals, e.g CH3 ỵ C2 H6 ! CH4 ỵ C2 H5 C2 H5 ỵ C2 H5 ! C4 H10 Reactions between light molecules have been extensively studied in the last two decades, generally by molecular beam techniques (see Chapter 4, Section 4.2), and these have allowed detailed testing of the predictions made from calculated potential energy surfaces There are three typical mechanisms for gas phase reactions The stripping reactions showing forward scattering and large cross sections are typified by reactions such as Na ỵ Cl2 ! NaCl ỵ Cl Na ỵ PCl3 ! NaCl ỵ PCl2 The rebound mechanism showing backward scattering and small cross sections is typified by Br ỵ HCl ! HBr ỵ Cl K ỵ CH3 I ! KI ỵ CH3 Reactions involving collision complexes are sometimes found Here an intermediate is produced, which lasts long enough for it to perform several rotations, and this results in symmetrical scattering Typical reactions are Cs ỵ SF6 ! CsF ỵ SF5 CHBr ! CH2 CHCl ỵ Br Cl ỵ CH2 185 ELEMENTARY AND COMPLEX REACTIONS Ionmolecule reactions have also proved fertile ground for both theoretical studies and experiment Here there are mainly two typical ionmolecule mechanisms: stripping reactions such as ỵ Nỵ ỵ H2 ! N2 H ỵ H ỵ Nỵ ỵ CH4 ! N2 H ỵ CH3 and collision complexes for the more complex ionmolecule reactions such as ỵ C2 Hỵ ỵ C2 H4 ! C3 H5 ỵ CH3 Reaction can also be a simple breakdown of one molecule as A ! products with mechanistic rate ẳ kẵA 6:3ị Such reactions are typified by the unimolecular decomposition of cyclopropane to give propene, where one molecule of reactant moves into the critical configuration and thence to products, with rate ẳ kẵC3 H6 6:4ị Like the bimolecular reactions, unimolecular reactions are often found as individual steps in complex reactions These include the unimolecular breakdown of molecules into radicals often found as first initiation steps and propagation steps in chain reactions, e.g C2 H6 ! CH3 ỵ CH3 CH3 CO ! CH3 ỵ CO Complex reactions proceed in several elementary chemical steps, and have a variety of mechanisms But each elementary step in every mechanism also involves a common physical mechanism, with steps of activation and deactivation by binary collisions followed by the reaction step (Chapter and Section 4.5) This can be important when discussing individual steps in, e.g., chain reactions, Section 6.9 This physical mechanism is k1 A ỵ A ! A ỵ A k1 A ỵ A!A ỵ A k2 A ỵ b A ! products activation by collision deactivation by collision reaction step b ẳ 0; reaction is unimolecular; b ẳ 1; reaction is bimolecular; b ẳ 2; reaction is termolecular: 186 COMPLEX REACTIONS IN THE GAS PHASE 6.2 Intermediates in Complex Reactions Complex reactions invariably involve intermediates which are formed in some steps, removed in others, and have a wide range of lifetimes Longer lifetimes can result in build-up to significant intermediate concentrations during reaction, but these intermediates must also be sufficiently reactive to allow the subsequent reactions to occur Intermediates can also be so short lived that they are removed almost as soon as they are formed, resulting in very, very low steady state concentrations The lifetimes of intermediates and their concentrations have profound effects on the analysis of the kinetics of the reactions in which they occur Reminder When steady state conditions prevail, the intermediates are highly reactive, and the total rate of their production is virtually balanced by their total rate of removal by reaction They are present in very, very small and steady concentrations, and dẵIss =dt ẳ Reactions involving intermediates are classified as non-chain or chain A chain reaction is a special type of complex reaction where the distinguishing feature is the presence of propagation steps Here one step removes an intermediate or chain carrier to form a second intermediate, also a chain carrier This second chain carrier reacts to regenerate the first chain carrier and the characteristic cycle of a chain is set up, and continues until all the reactant is used up (see Section 6.9) Although complex reactions can be classified as non-chain and chain, the type of experimental data collected and the manner in which it is analysed is common to both The ultimate aim is to produce a mechanism, to determine the rate expression and to find the rate constants, activation energies and A-factors for all of the individual steps The following problem illustrates the variety of types of reaction which can occur Worked Problem 6.1 Question Classify the following reactions in terms of the type of mechanism, i.e elementary, complex etc: (a) slow ICl ỵ H2 ! HI ỵ HCl fast HI ỵ ICl ! HCl ỵ I2 (b) cyclo-C4 H8 ! C2 H4 (c) 238 U ! 234 Th ỵ 234 Th ! 234 Pa ỵ 234 Pa ! 234 U ỵ 234 U ! INTERMEDIATES IN COMPLEX REACTIONS (d) ỵ Oỵ ỵ NO ! O2 ỵ NO (e) N2 O4 ! NO2 (f) O3 ỵ M ! O2 ỵ O ỵ M O2 ỵ O ỵ M ! O3 ỵ M O3 ỵ O ! O2 (g) cis-di-deuterocyclopropane ! trans-di-deuterocyclopropane cis-di-deuterocyclopropane ! di-deuteropropenes (h) C2 H6 ! CH3 (i) CH3 ị3 COOCCH3 ị3 ! 2CH3 ị3 CO CH3 ị3 CO ! CH3 COCH3 ỵ CH3 CH3 ỵ CH3 ! C2 H6 (j) k1 NO ỵ O2 !NO3 k1 NO3 !NO ỵ O2 k2 NO3 ỵ NO!2 NO2 (k) N2 O5 ! NO2 ỵ NO3 NO2 ỵ NO3 ! NO2 ỵ O2 ỵ NO NO ỵ N2 O5 ! NO2 (l) (m) C2 H5 ỵ CH3 COCH3 ! C2 H6 ỵ CH2 COCH3 Br2 ỵ M ! Br ỵ M Br ỵ CH4 ! CH3 ỵ HBr CH3 ỵ Br2 ! CH3 Br ỵ Br HBr ỵ CH3 ! CH4 ỵ Br Br ỵ M ! Br2 ỵ M (n) Krỵ ỵ H2 ! KrHỵ ỵ H Answer (a) Two step consecutive (b) One step elementary (c) Many step consecutive (d) One step elementary (e) Reversible reaction 187 188 COMPLEX REACTIONS IN THE GAS PHASE (f) Three step complex with the second step being the reverse of the first (g) Two step parallel (h) Elementary step in a complex reaction (i) Three step complex (j) Three step complex with the second step being the reverse of the first (k) Four step complex with the second step being the reverse of the first (l) Elementary step in a complex reaction (m) Five step complex with two reversible steps, i.e steps and are the reverse of each other, likewise for steps and This is a chain reaction Br and CH3 are recycled (n) Elementary reaction 6.3 Experimental Data The following is a summary of the type of data involved in the study of complex reactions Kinetic and non-kinetic information is required Detection of products and intermediates is essential, and determination of their concentration throughout reaction allows products and intermediates to be classified as present in major, minor, trace or very trace amounts This is relatively easy for products Though easily detected, the very low concentrations of highly reactive intermediates can be difficult to determine accurately (Sections 2.1.4 and 2.1.5) Nonetheless, it is still possible to distinguish between very low steady state concentration intermediates and higher non-steady state concentrations This has important consequences when unravelling the kinetics Photochemically initiated reactions and quantum yields can yield vital clues in finding the mechanism; see Section 6.8 Thermochemical data, and the effect of temperature on relative yields can also help in determining mechanism Kinetic studies, often from initial rates, give orders, experimental rate expressions, rate constants and activation parameters MECHANISTIC ANALYSIS OF COMPLEX NON-CHAIN REACTIONS 189 The proposed mechanism must fit all the experimental facts, and the mechanistic rate expression must fit the experimental one If these fit, the proposed mechanism is a possible or highly plausible one, but this does not prove the mechanism to be the correct one Sometimes more than one mechanism can fit, called kinetically equivalent, and a distinction between them can only be made on non-kinetic evidence (see Section 6.6) The derivation of the mechanistic rate expression is considerably simplified if the steady state treatment can be used (Sections 3.19, 3.19.1 and 3.20) When intermediate concentrations are not sufficiently low and constant, the steady state approximation is no longer valid Numerical integration by computer of the differential equations involved in the analysis, or computer simulation, may have to be used 6.4 Mechanistic Analysis of Complex Non-chain Reactions The methods and techniques described above will be illustrated by the following worked examples Worked Problem 6.2 This problem illustrates how to deduce a mechanism from basically non-kinetic data Question The following results were obtained from a study of the photochemical decomposition of propanone, CH3COCH3: CH3 COCH3 ! C2 H6 ỵ CO The quantum yield of CO is unity above 120 C, but is less than unity below 120 C The major products are C2H6 and CO, but CH4 is also found in substantial amounts CH3COCOCH3 is also formed below 120 C The minor products are CH3COCH2CH3, CH3COCH2CH2COCH3 and CH2CO Spectroscopy, esr and mass spectrometry detect CH3 , CH3 COCH2 and CH3 CO Addition of O2 and NO reduces yields of CH4 and C2H6 to zero Deduce a mechanism that fits these observations 190 COMPLEX REACTIONS IN THE GAS PHASE Answer Type of process Detection of CH3 , CH3 COCH2 and CH3 CO demonstrates a free radical process, while the quantum yield of the product CO indicates a nonchain mechanism (see Section 6.8) Possible primary steps A rule of thumb suggests that CC bonds break more readily than CO bonds, which in turn break more easily than CH bonds, suggesting two possible first steps This rule of thumb is a summary of a vast amount of experimental data, including kinetic studies and bond dissociation measurements Aị CH3 COCH3 ! CH3 ỵ CO CH3 COCH3 ! CH3 ỵ CH3 CO Bị CH3 COCOCH3 is formed from recombination of two CH3 CO radicals, and is only found below 120 C, suggesting step (B) as a possible primary step for these temperatures This is consistent with the fact that CH3 CO is relatively stable below 120 C and can undergo reactions other than decomposition to CO and CH3 , i.e recombination can occur At higher temperatures butane-2,3-dione, CH3COCOCH3, is no longer produced, and this is consistent with the known very rapid decomposition of the radical, CH3CO , above 120 C, CH3 CO ! CH3 ỵ CO which suggests that (A) is the dominant primary process above 120 C These inferences are also consistent with the observed quantum yields (a) Above 120 C a quantum yield of unity for CO fits CH3 COCH3 ! CH3 ỵ CO Aị CH3 COCH3 ! CH3 ỵ CH3 CO Bị But it also fits since the very rapid decomposition of CH3 CO also results in one molecule of CO produced per molecule of CH3 COCH3 decomposed (b) Below 120 C the quantum yield of CO decreases, consistent with the emergence of the competitive reaction CH3 CO ỵ CH3 CO ! CH3 COCOCH3 becoming possible, which will reduce the yield of CO per given amount of CH3COCH3 decomposing 421 CHAPTER Since the units of kobs are time1, kobs is a pseudo-first order rate constant, which implies that L4Co(NHR2)X2ỵ, or OH, is being held in excess The fact that [OH]total, and not ẵL4 CoNHR2 ịX2ỵ total , appears in the expression for kobs given in the question indicates that the observed rate expression has to be first order in L4Co(NHR2)X2ỵ and zero order in OH This can only be achieved by having OH held in excess, so that ẵOH actual ẳ ẵOH total ; rate of reaction ẳ k2 ẵL4 CoNHR2 ịX2ỵ total K1 ẵOH total ỵ K1 ẵOH total Observed rate of reaction ẳ kẵL4 CoNHR2 ịX2ỵ total ẵOH total ẳ kobs ẵL4 CoNHR2 ịX2ỵ total where kobs is a pseudo-first order rate constant ẳ kẵOH total ; kobs ẵL4 CoNHR2 ịX2ỵ total ẳ ; kobs ẳ k2 ẵL4 CoNHR2 ịX2ỵ total K1 ẵOH total ỵ K1 ẵOH total k2 K1 ẵOH total ỵ K1 ẵOH total If the pre-equilibrium is set up rapidly and maintained throughout the reaction, then step will be the rate-determining step Rate of reaction ẳ k2 ẵMLactual ẵX ẵMLactual K1 ẳ ẵMactual ẵLactual equil ẵMtotal ẳ ẵMactual ỵ ẵMLactual and ẵMactual ẳ ẵMLactual K1 ẵLactual Need to get ẵMLactual in terms of ẵMtotal and K1 ẵMLactual ỵ ẵMLactual K1 ẵLactual ẳ ẵMLactual ỵ1 K1 ẵLactual ỵ K1 ẵLactual ẳ ẵMLactual K1 ẵLactual ; ẵMtotal ẳ 422 ANSWERS TO PROBLEMS ẵMLactual ẳ ẵMtotal K1 ẵLactual ỵ K1 ẵLactual ; rate ẳ k2 ẵMtotal K1 ẵLactual ẵX ỵ K1 ẵLactual observed rate ẳ kẵMtotal ẵLẵX This is third order, but the quoted observed rate constants are given in terms of a second order rate constant, as indicated by the units, mol1 dm3 s1 The standard procedure in reactions of the type being considered is to hold the ligand in excess That this is the case is confirmed by the question asking what would happen at high and low concentrations of ligand ; observed rate ẳ kobs ẵMtotal ẵX where kobs is a pseudo-second order rate constant ẳ kẵLtotal L is held in excess, ; ẵLactual ẳ ẵLtotal ; kobs ẳ k2 K1 ẵLactual k2 K1 ẵLtotal ẳ ỵ K1 ẵLactual ỵ K1 ẵLtotal At very high values of the excess L, K1 ẵLtotal ) 1, and ; kobs ẳ k2 , and the reaction is zero order in ligand At low values of the excess ligand: K1 ẵLtotal ( 1, and ; kobs ẳ k2 K1 ẵLtotal , and the reaction is now first order in ligand To find k2 and K1 , kobs ỵ K1 ẵLtotal k2 K1 ẵLtotal 1 ẳ ỵ k2 K1 ẵLtotal k2 ẳ A plot of 1=kobs versus 1/[L]total should be linear with intercept ẳ 1=k2 and slope ẳ 1=k2 K1 ẵL moldm3 ẵL=moldm3 104 kobs mol1 dm3 s1 104 kobs =mol1 dm3 s1 0:00856 0:0192 0:0301 0:0423 0:0654 0:0988 116:8 52:1 33:2 23:6 15:3 10:1 0:83 1:28 1:51 1:67 1:84 1:96 1:205 0:781 0:662 0:599 0:543 0:510 423 CHAPTER The graph is linear confirming the kinetic analysis: intercept ẳ 1=k2 ẳ 0:43 104 mol dm3 s ; k2 ẳ 2:33 104 mol1 dm3 s1 k2 0:66 102 ẳ 65 mol1 dm3 slope ẳ 1=k2 K1 ẳ 0:66 102 mol2 dm6 s ; K1 ẳ (a) rate of reaction ẳ k2 ẵML5 actual ẵL actual ẵML6 total ẳ ẵML6 actual ỵ ẵML5 actual ẵML5 actual ẵLactual ẵML5 actual ẵLactual K1 ẳ and ẵML6 actual ẳ ẵML6 actual K1 We need to find ẵML5 actual in terms of ẵML6 total and K1 ẵML5 actual ẵLactual ỵ ẵML5 actual K1 & ' ẵLactual ỵ K1 ẳ ẵML5 actual K1 & ' K1 ẳ ẵML6 total ẵLactual ỵ K1 ẵML6 total ẳ ẵML5 actual ; rate of reaction ẳ k2 ẵML5 actual ẵL actual ẳ k2 K1 ẵML6 total ẵL actual ẵLactual ỵ K1 Since L is held in excess, then the amount removed by reaction is very small compared with ẵL total , ; ẵL actual % ẵL total ; rate ẳ k2 K1 ẵML6 total ẵL total ẵLactual ỵ K1 observed rate ẳ kobs ẵML6 total ẵL total kobs ẳ k2 K1 ẵLactual ỵ K1 Note: kobs here is a true second order rate constant Usually, with an equation having a denominator which is a sum or difference, the reciprocal of both sides is taken: kobs ẳ K1 ỵ ẵLactual ẵL ẳ ỵ actual k2 k K1 k K1 The standard graph would be a plot of 1=kobs versus [L]actual This is not possible since L is the product of the pre-equilibrium, which is not removed by further reaction, and so builds up continuously throughout the reaction 424 ANSWERS TO PROBLEMS (b) If L is held in excess by adding a known large excess, then ẵLactual ẳ ẵLtotal , and values of kobs could be found for several experiments where a different value of excess L is used for each A plot of 1=kobs versus [L]total would then be linear with intercept ẳ 1=k2 and slope ẳ 1=k2 K1 From these k2 and k1 can be found individually (a) Since the equilibrium is set up rapidly and is maintained throughout reaction, the slow step is step 2, and rate of reaction ẳ k2 ẵadductactual ẵBr2 actual K1 ẳ ẵadductactual ẵadductactual and ẵalkeneactual ẳ ẵalkeneactual ẵBr2 actual K1 ẵBr2 actual ẵalkenetotal ẳ ẵalkeneactual ỵ ẵadductactual ẵadductactual ẳ ỵ ẵadductactual K1 ẵBr2 actual & ' ỵ K1 ẵBr2 actual ẳ ẵadductactual K1 ẵBr2 actual & ' K1 ẵBr2 actual ẵadductactual ẳ ẵalkenetotal ỵ K1 ẵBr2 actual rate ẳ k2 K1 ẵBr2 2actual ẵalkenetotal ỵ K1 ẵBr2 actual observed rate ẳ kobs ẵalkenetotal ẵBr2 2total Note: the observed rate is second order in Br2, since the reaction involves, in effect, one molecule of alkene and two molecules of Br2 Since Br2 is in excess, ẵBr2 actual % ẵBr2 total k2 K1 ẵBr2 2total ẵalkenetotal ỵ K1 ẵBr2 total k K1 ẳ ỵ K1 ẵBr2 total rate ẳ ; kobs (b) If the Br2 excess is small, then K1 ẵBr2 total ( 1, and rate % k2 K1 ẵalkenetotal ẵBr2 2total , and reaction is second order in Br2 If the Br2 excess is large, then K1 ẵBr2 total ) 1, and rate % k2 ẵalkenetotal ẵBr2 total , and reaction is first order in Br2 (c) k K1 ỵ K1 ẵBr2 total 1 ỵ K1 ẵBr2 total ẳ k K1 kobs ẵBr2 total ẳ ỵ k2 K1 k2 kobs ẳ 425 CHAPTER A plot of 1=kobs versus ẵBr2 total should be linear with intercept ẳ 1=k2 K1 ị and slope ẳ 1=k2 Hence k2 and K1 can be found (d) If K1 is very small, then K1 ẵBr2 total ( 1, and kobs ẳ k2 K1 Unless K1 is known independently, k2 cannot be found dẵH2 Atotal ẳ kuncat ẵH2 Atotal ỵ kcat ẵZnAactual dt dẵH2 Atotal ẳ kobs ẵH2 Atotal dt ẵZnAactual kobs ẳ kuncat ỵ kcat ẵH2 Atotal 2ỵ ẵZn actual ẵA2 actual ẳ kuncat ỵ kcat K ẵH2 Atotal since Kẳ ẵZnAactual ẵZn actual ẵA2 actual 2ỵ The reaction is carried out at constant pH and so the fraction of the acid ionized to the dianion, , is constant throughout the experiment Since the Zn2ỵ is in excess then ẵZnzỵ actual % ẵZnzỵ total , giving kobs ẳ kuncat ỵ kcat K ẵZn2ỵ total where ẳ ẵA2 actual ẵH2 Atotal If the mechanism is correct and the approximations justified, a plot of kobs versus [Zn2ỵ]total should be linear with slope ẳ kcat K and intercept ẳ kuncat The graph is linear with intercept ẳ kuncat ẳ 0:725 104 s1 and slope ẳ kcat K ẳ 1:475 102 mol1 dm3 s1 Since K ẳ 1580 mol1 dm3 and ẳ ẵA2 actual =ẵH2 Atotal ẳ 105 =0:03 ẳ 0:002 00; then 1:475 102 mol1 dm3 s1 1580 mol1 dm3 0:002 00 ẳ 4:67 103 s1 kcat ẳ Index Bold type indicates definitions A factor 93, 104, 108109, 136137, 138140, 140, 143144, 265267, 289, 293, 294, 295, 297, 298, 299, 300, 339 determination of 104, 108, 349 Absorbance 8, 813, 20, 29 Absorption coefficient, molar 8, 11 Absorption of radiation 2, 7, 89, 13, 14, 15, 19, 20, 204206 Absorption of sound 3538 Accelerated flow 29 Acid catalysed hydrolysis 26, 75, 331336 Acidbase catalysis 359, 365 Activated complex 4, 100, 125127, 129, 130, 131, 132, 224 degrees of freedom 135, 137139, 143145 in unimolecular theory 155, 158159, 160161 thermodynamic aspects 140142, 143145 with respect to PE surfaces 165168, 169, 171180 statistical mechanical aspects 132139 reactions in solution 265, 267, 269272, 281, 284, 289, 292, 293, 294, 296297, 297300, 303304, 305, 306, 308309, 310313, 329, 331332, 335336 structure, reactions in solution 331332, 335336 Activated intermediate 129130, 132 Activated molecule 23, 122, 129, 147148, 152, 153, 154, 155, 156, 158, 159, 160161, 196, 223 Activating collision 3, 153 Activation 2, 3, 4, 8789, 122, 135, 147, 148 in unimolecular reactions 152153, 153154, 155, 157, 158160 in complex gas reactions 185, 196198, 222223, 224, 227229, 235 in reactions in solution 293, 296, 297300, 302, 303304, 304, 308309, 310313 Activation energy 2, 9295, 103, 104108, 134, 136, 156158, 224, 227, 238239, 255257, 267268, 303304 determination of 9295 calculations using 104108 see also critical energy Activity 270271, 342 Activity coefficient 270271, 271272 Actual and total concentration 8990, 284285, 321328, 330331, 332336, 336339, 340341, 341342, 342343, 344346, 346351, 352356, 356358, 360363, 363365, 365368 Actual ionic strength 284285 Adsorption at surface 240243 Angle of scattering 110112, 112122 Angular velocity 103 Anharmonicity 124125, 161, 228 Anion catalysis 317, 334, 334336 Approach to equilibrium 66, 90 Arrhenius Arrhenius equation 9295, 100, 103, 104106, 108109, 136, 154159, 161, 279280, 339 Association 264, 281, 284285, 289, 313 An Introduction to Chemical Kinetics Margaret Robson Wright # 2004 John Wiley & Sons, Ltd ISBNs: 0-470-09058-8 (hbk) 0-470-09059-6 (pbk) 432 Associative mechanism 292, 300301, 301, 310313 Atomatom recombination 160, 214, 228229, 240, 243 Atomic mechanism, H2/I2 reaction, 206208 Atoms degrees of freedom 137140 light and heavy 170, 172177, 178 H2/I2 reaction 206208 Attractive forces 110, 172, 265, 327328 Attractive interaction 119, 123 Attractive surface 167168, 170172, 177, 178 Autocatalysis 85, 244 Average rate 45 Back reaction 87, 91, 127128, 170, 214, 215, 255257, 360363 Backward scattering 111, 112, 114, 174, 184 see also rebound Barrier 130, 131, 165168, 169, 170179 Base hydrolysis 51, 318320, 321325, 325 328, 328331, 331, 336339, 344346 Basin 178180 Beers Law, 89, 913 Bimolecular 3, 8789, 185, 206, 213, 222 Bimolecular activation 3, 159160 Bimolecular deactivation Bimolecular reaction 3, 8789, 102, 104, 152, 185, 206, 213 Br2-stat 2627 Branched chain 244 Branched chain explosions 247252 Branched chain reaction 244252, 252259 Branching coefficient 244 Brownian motion 265 Build-up to explosion 243, 244246, 247249, 253254, 257259 to steady state 14, 8284, 85, 186, 209210, 219, 234, 244 Catalysis 18, 329331, 331, 332336, 344346 see also Acid/base catalysis, Metal ion catalysis, Anion catalysis, Enzyme catalysis Chain carriers 208209, 210211, 211213, 213218, 219, 221, 223224, 224227, 230, 234, 236 Chain length 221, see also Chain reactions INDEX Chain reactions 47, 87, 183, 186, 188, 204, 205206, 208209, 209239 with branching 244252 with degenerate branching 252259 with surface termination 240243 Charge 109110, 263268, 270, 271272, 272274, 296297 effect of on thermodynamic quantities, 301313 in reactions of charged species 271299, 300301, 302, 306308, 310, 310313, 317365 Charge separation 264, 265, 296297, 299300, 309, 310313 Charge/solvent interactions 282 Charged activated complex/transition state 264, 265 Charge-distribution 293, 297, 299 Charge-separated activated complexes 265, 293, 303, 309, 310, 311 Charge-separated species 264, 265, 271, 274, 297, 299 Chelation 285 Chemical potential 270 Chemiluminescence 100, 165, 170, 177 Christiansen Chromatographic techniques/methods 6, 7, 15, 16, 27, 29, 30 Collision complex 119121, 178180, 184 Collision frequency 102 Collision number 102 Collision rate 2, 88, 100, 102108, 109110, 265268 Collision theory 2, 4, 99110, 110122, 280, 294 comparison with transition state theory 136137, 142143 for reactions in solution 265268, 280, 294 Collision theory modified 4, 99, 110122 Collision theory simple 99110, 136137, 142143 Complex equilibria 35, 36 see also Ultrasonics Complex kinetics 7984, 8586, 8789, 89 90, 147152, 195204, 206208, 213 224, 225227, 229232, 233238, 238239, 241243, 247249, 317368 Complex mechanism see Complex reactions and Complex kinetics Complex mixtures, analysis of 67 INDEX Complex model (unimolecular), 155159 Complex reactions/mechanisms 3, 67, 1314, 1516, 8586, 189192, 192 195, 195198, 198201, 202204, 206208, 209, 210, 210211, 211213, 213218, 219220, 225227, 229232, 233238, 238239, 241243, 247249, 249250, 254255, 318320, 320321, 321325, 325328, 330331, 332336, 336339, 339342, 342343, 344346, 346358, 360363, 363365, 365368 Complexes, complexing 264, 285, 320321, 344, 351 Complex kinetic schemes 7981 Complexity of structure in unimolecular reactions 159160, 223 H 6ẳ for solution reactions 302 V 6ẳ for reactions in solution 310 and p factors and S6ẳ 140, 143, 292295, 300301, 312313 Composite rate definition 209210 Computer analysis 36, 58 Computer simulation 81, 189 Concurrent reactions 317321, 321328, 328331, 332336, 336339, 339343, 344346 Conductance methods use in measuring rates 2425, 29 Configuration geometrical 3, 122123, 123131, 133135, 135, 147, 152, 155, 158159, 160161, 165, 167, 171, 172, 173, 176, 178, 184, 185, 263, 271 Consecutive reactions 35, 186187 Continuous flow 2728, 29, 33 Continuum, solvent as 281 Conventional methods for rate measurement 5, 2027 Conventional radiation 13, 204206 use for H2/I2 reaction 206208 Conventional rates 1718, 19 Conventional source of radiation 8, 13, 19 Cool flames 255259 Critical configuration 3, 4, 125, 129, 131, 133, 135, 147, 152, 158, 160, 165, 171, 172, 173, 174, 178, 185, 271 see also Activated complex and Transition state Critical energy 23, 19, 99100, 102, 104, 122, 125131, 133, 151154, 155160 433 see also Activation energy Cross section 101, 103, 111, 112113, 117, 119, 120, 172, 175, 177 Cutting the corner trajectory 172174, 175177 Cycle in chain reactions 186, 208209, 211, 221, 257 Deactivation 2, 3, 4, 8789, 122, 147148, 148, 151, 153, 155, 158, 185, 222223, 227229 DebyeHuă ckel constant 270, 272 DebyeHuă ckel equation (law) 270, 272 DebyeHuă ckel theory 270279 Decarboxylation reactions 339343 Decomposition unimolecular 145161, 185, 195, 196198, 204, 227229 Decomposition specific examples of 21, 2324, 64, 8586, 189192, 193195, 195198, 210211, 211213, 219220, 222, 233238, 238239 Deflection 100, 110112, 112122, 177, 179180 Degenerate branching 244, 252259 Degree of orientation of solvent 297300, 303304, 308309 Degrees of freedom 123125, 135, 137139, 144145, 224, 228229, 235 internal for reactions in solution 292, 294, 295, 298, 299, 300301, 302, 306, 310312 Degrees of freedom non-linear activated complex 137139, 144145 Degrees of freedom, linear activated complex 137139 Degrees of freedom, linear molecule 135, 137139, 144145, 153 Degrees of freedom, non-linear molecule 135, 137139, 144145, 153, 229 Dependence of rate constant on pressure, reactions in solution 141142, 304309 Dependence of rate on temperature 92, 9295, 250252 see Arrhenius equation Derivative 5859, 141142 Detection of species 5, 617, 2829, 30, 188 Determination of concentrations 5, 617, 30, 7778, 188 Diatomic molecule, degrees of freedom 123125, 137139, 228229 434 Diatomic molecule, Morse curve 123125 Dielectric 263 Differential rate equation 59, 62, 66, 68, 71, 7377, 7981, 84, 8990, 186, 189, and Tables 3.2, 3.4 see also Steady state equations Differential rate methods 5258 Diffusion 8, 240, 241, 243, 251252, 265 Dilatometry 27 Dipole moment 295 Dipole/dipolar 263, 264, 282, 285, 295, 296, 297, 298, 299301, 308, 312313 Displacement from equilibrium 30, 31, 3335 see Relaxation methods and Approach to Equilibrium Disproportionation 209 Dissociation energy 123125 Dissociation limit 124 Dissociative mechanism 292, 301, 305306, 310313 Dissociative step 292, 305306, 310313 Distribution of velocities in products 112114 Early barrier 167168, 170172, 178 Effect of solvent 280283, 293296, 302303, 308 see also Solvation pattern Electric field 33, 264 Electric field jump 3335 Electron spin resonance esr 15, 38, 189 Electron withdrawing 339340, 341, 344 Electronic distribution 264 Electronic properties 264 Electronic states 7, 100, 132, 253, 257 Electrostatic energy of interaction 264, 266268, 280281 Electrostatic interactions 264, 266268, 269, 274, 280282, 284, 293, 295, 299, 302 Electrostatically modified collision theory 265268 Electrostatically modified transition state theory 263, 269272, 279284, 289313 Elementary reaction 3, 8789, 122, 147148, 168170, 184185, 186188, 201 Elementary step 185, 186188, 204208, 222 Emf methods 2627 Emission of radiation 2, 7, 9, 100, 205 INDEX see Chemiluminescence, Fluorescence, Laser induced fluorescence Emission spectra Endothermic 127128, 177178, 255257 Energised molecules, see Activated molecules, Excited molecules Energy disposal on reaction 172173, 173177, 177178, 179180 Energy of activation, see Activation energy, Critical energy Energy transfer 2, 4, 3538, 122, 147148, 151, 152153, 155, 158159, 159160, 161, 196197, 222223, 227229 Enhancement of rate 172, 174, 175176 Enthalpy of activation, H 6ẳ , 141143, 224, 264, 279, 282, 290292, 301304, 311313 Entrance valley 125, 131, 165168, 171172, 174, 178 Entropy of activation, S6ẳ , 142144, 144 145, 224, 264, 279, 282, 289301, 303, 308309, 310311, 312313 Enzyme kinetics 359, 365368 Equilibrium constant in transition state theory 132, 134, 141, 269272 Equilibrium internuclear distance in transition state theory 123, 125, 173, 173174, 178 Equilibrium position 30, 31, 3334, 8990 Equilibrium statistical mechanics 132, 133, 134 Excitation 9, 13, 1920, 100, 152, 204 see also Activation Excited molecules 9, 1920, 100, 151, 191, 204208, 228229 see also Activated molecules, Energised molecules Excited states 7, 9, 1920, 38, 100, 172, 253, 257 Exit valley 125, 131, 165, 167, 171, 172, 173, 176, 178 Exothermic 100, 118, 127128, 170177, 178, 227229, 244, 255257, 257259 Exothermicity 228229 Explosion 210, 243259 Explosion limits 249252, 258259 Fast reactions 4, 5, 14, 1718, 25, 2738, 8284, 210 Field strength see Electric field 435 INDEX Fine structure First order integrated rate equation 6266, Tables 3.3 and 3.4 First order rate constant, meaning of 4849 First order, meaning of 48, 48, 49 Flash photolysis 7, 13, 14, 3132, 33 Flow methods 13, 2730, 33 see Accelerated flow, Continuous flow, Stopped flow Flow of energy around molecule 158, 159, 161, 227229 Flow rate 28, 29 Fluorescence 9, 13, 1415, 83, 100, 205 Forces 110, 117, 119, 172, 264, 265, 327 Forward reaction 127129, 170, 255257 Forward scattering 117118, 172, 185 see Stripping Fractional life-time 6466 see also Half-life, Table 3.3 Free energy 269270 Free energy of activation, G6ẳ , 141142, 280281, 282, 290, 292, 293, 295, 302, 304, 307308 Free radical reactions, see radical reactions Free radical, see Radicals Free translation (internal) 130, 134135, 137139, 142, 144145, 269271 Frequency 7, 9, 13, 14, 15, 3538, 132, 138 see also Vibration Gas phase termination (distinct from surface termination) 240243, 247249, 249, 251252, 255, 257 see also Termination and Straight chains General acid catalysis 334 General base catalysis 327, 334 Geometrical configuration, see Configuration Grazing 117118 see Stripping H abstraction 191, 212, 237, 238, 239, 255 Half-life 1718, 18, 31, 32, 43, 5962, 6364, 6466, 67 68, 70, Tables 3.3 and 3.4 Harmonic oscillator/vibration 103, 123124, 135, 161 Heavy atom 170, 172, 175177 Herzfeld see RiceHerzfeld High pressures (unimolecular reactions) 2, 3, 8789, 145147, 148149, 149151, 154155, 155157, 159160, 161, 222223, 227229 High temperature explosion limit 259 Hinshelwood Theory 155158 Hydrogen bonding 264 Hydrolysis 75, 285289, 318320, 321328, 328331, 331336, 336339, 344346 Ideality 268, 270 Identification 617, 36, 204 Impact parameter 101102, 111112, 117118, 118119, 172, 175, 177 Incident intensity Individual rate constants in complex kinetics, determination of 217218, 218220, 233, 237238 see also Reactions in solutions 317368 Induction period 210, 253 Infra red 8, 13, 14, 16 Inhibition 18, 191, 209, 213214, 214216, 221 Initial rate 4647, 58, 188, 215, 216, 319, 365, 367368 Initiation methods of 1920, 27 see also Photochemical initiation and Thermal initiation Initiation step see Chain reactions Initiator 229 Inorganic chain mechanisms 213218 Instantaneous rate 4546 Integrated rate equation/expression 35, 43, 5873, 7984, 8990 Integrated rate methods 5873 Intensity of radiation 79, 1315, 20, 3132, 205, 208, 214, 216, 218 see also Flash photolysis, Lasers Interaction 117, 119, 123, 125, 177, 179 see Electrostatic interaction, Interionic interaction, Intermolecular interaction Interchange mechanism 301, 310, 311, 312313 Interchange step 306 Interionic interactions 264, 268, 270, 277, 281, 284 see Electrostatic interaction Intermediates 6, 7, 1314, 15, 31, 8187, 186, 188, 192201, 205, 208209, 211, 222, 229232, 264, 346365, 365368 436 see Steady state and Chain carriers Intermolecular interactions 100, 110, 111 Internal degrees of freedom see Degrees of freedom Internal free translation see Free translation Internal modes for reactions in solution 310, 311 see also Degrees of freedom Internal motions 137, 138, 292, 299, 302, 306 see also Free translation Internal states 7, 9, 100 Internal structure 110, 137, 294, 296, 298, 299 Inverse first order 50, 202204 Ion pair 264, 284285, 285289, 328331 Iondipole reactions 295 Ionic strength 19, 270, 271279, 281, 284289, 293, 329, 332, 342 Ionion reactions 7, 265268, 269272, 273279, 279289, 293294, 296298, 300301, 302304, 306307, 308309, 310313 Ionmolecule reactions 7, 185, 271, 274, 280, 295, 296, 298299, 302303, 308, 309, 310313 Kassel Theory 158160, 161 Kinetic analysis 5, 31, 4395, 346358 Kinetic energy 102103, 104, 123 see also Rotation, Translation, Vibration Kinetic theory 102, 131, 133 Kinetically equivalent mechanisms 183, 189, 198201, 206208, 317, 328331, 332336, 363365 Large perturbation 3133 Laser photolysis 14, 19, 31, 32, 204 Laser-induced fluorescence 9, 100 Lasers 4, 9, 13, 1314, 15, 19, 20, 31, 32, 33, 83, 100, 204 Late barrier 165, 167, 167169, 172177, 178 Life time 186 Light atoms 170, 172175, 176 Like charge/sign 109110, 268, 281, 293294, 297298, 300, 302, 304307, 310, 311, 312 Lindemann Mechanism 3, 153155 Line broadening 38 Line width 7, 38 INDEX Linear activated complex degrees of freedom see Degrees of Freedom, linear activated complex Linear approach/linear recession 123 Linear configuration 123 Linear molecule degrees of freedom see Degrees of freedom, linear molecule Long chains approximation 215, 217, 220, 221, 229232, 234, 236 Low pressure unimolecular reactions 23, 88, 145147, 148, 150, 159160, 196198, 222223, 227228, 229, 235 Low pressure surface termination 240, 251252, 254 Lower explosion limit 251252 Luminescence 252, 257, 258 Major intermediate 188 Major products 188, 189, 211, 211212 Mass 102, 130, 132, 138, 170 Mass/charge ratio Mass spectrometry MS 67, 17, 27, 29, 30, 189 Mass type 170, 172177 see also Heavy atom, Light atom Master mechanism 3, 8789, 147148, 151160, 185, 222223 Mathematically complex schemes 81 Maximum rate 47 Maximum scattering 113114 MaxwellBoltzmann distribution 2, 102 103, 125, 154, 155156, 157158 Mechanism 2, 3, 5, see Complex reactions Medium 264, 282 Metal ion catalysis 317, 329, 331, 334, 344346 Metal ion complexes 344, 345 Michaelis constant 368 MichaelisMenten equation 368 Microscopic 4, 122, 281, 283, 289 Microscopically inhomogeneous 283 Microwave 7, 8, 13, 15 Mild explosions 252, 253, 254 see also Cool flames Minimum energy path 4, 165, 172173, 176 see Reaction coordinate Minor product 6, 7, 188, 189, 191, 209, 211, 212, 221, 222 INDEX Modified solventsolvent interaction 268 Molar absorption coefficient 8, 11 Molar units 103, 139140, 157, 289 Molecular beam contour diagrams 112122, 180 Molecular beams 4, 13, 100, 110, 110122, 151, 170, 172, 174, 176177, 179180, 206 Molecular dynamics Molecular units 103, 139140, 157, 289 Molecularity 3, 292, 301, 305306 Moleculemolecule reactions in solution 296, 299300, 310312 Moment of inertia 138 Morse curve 123125 Most probable route 125, 172173, 176 see Minimum energy path, Reaction coordinate Most probable velocity in products 113116, 117, 119 Multi-step relaxation equilibria 35 Negative activation energy 240 Negative temperature coefficient/dependence 253, 254, 259 Non-chain complex reactions in gas phase 189192, 192195, 195198, 198201, 206208 Non-equilibrium position 30 see Relaxation methods Non-explosive region in branched chain reactions 247249, 250252, 258259 Non-ideality 263, 268, 269280, 280, 284, 334, 342 Non-linear activated complex degrees of freedom, see Degrees of freedom non-linear activated complex Non-linear molecule degrees of freedom, see Degrees of freedom non-linear molecule Non-radical intermediates in steady state treatments 202204, 359363 Non-reactive collision 100 Non-steady state 14, 188, 209210 see Build up, Explosions Normal mode in transition state theory 123, 132, 135, 144 437 in unimolecular theory 153, 155, 157, 158159, 159160, 160, 161 with reference to third bodies 224, 227229, 233, 235 Normal mode of vibration 123, 132, 135, 144, 153, 155, 157, 158159, 159160, 160161, 224, 227229, 233, 235 Nuclear magnetic resonance, nmr 15, 38 Nuclear spin states Numerical integration 81, 189 Observed activation energy in terms of EAs of individual steps 238239 Oppositely charged, see Unlike charge Order (entropy) 298 Order meaning of 4850 Order, determination of Differential methods 5258 Integrated methods 5884 Orientation of solvent 297300, 303304, 308309 Oscillate/oscillatory reaction 85, 255258 Oscillator 123124, 135, 161 see also Vibrational modes Overall order 48 Oxidation of hydrocarbons 229232 see also Cool flames p factor 108109, 109110, 136, 140, 142143, 145, 295, 296, 298 p factors, A, S6ẳ for gases 109110, 136, 140, 142143, 145 p factors, A, S6ẳ for solution reactions 265, 294, 295, 296, 298 Parallel reactions 186188 Partial derivative 141142 Partial pressure in stoichiometry 2324 Partition function 99, 132133, 134135, 135136, 137140, 142143, 265, 269, 271 Partition function per unit volume 133, 135 Path-length PE contour diagram see Potential energy contour diagram, Entrance valley, Exit valley PE maximum 4, 125 PE profile 126128, 129130, 133, 165180 Period of sound wave 35 Periodic (displacements) 30, 3538 438 Permittivity, see Relative permittivity Perturbation 30, 31, 3335, 66, 90 pH 26, 2627, 51, 319320, 323, 324, 325328, 331, 337339, 341, 342, 342343, 345 Photochemical equivalence, law of 205 Photochemical initiation 19, 214, 216 Photochemical rate 216, 218 see H2/I2 reaction 206208 Photochemistry (photochemical) 2, 19, 1920, 30, 3132, 33, 188, 189192, 204206, 206208, 210, 214, 216, 218, 237, 238 Photoelectron spectroscopy 1516 Photolysis 7, 13, 14, 19, 3132, 33, 204, 218 pH-stat 2627, 319, 331, 345 Physical mechanism 8789, 147148, 185, 222 see Master mechanism Physical methods 2127, 2738, 79 Polarisability 263264, 313 Polyatomic molecule or ion, degrees of freedom 137, 153, 228229, 294, 295 see also Degrees of freedom, linear molecule and non-linear molecule Polyatomic molecule PE surface 122 Position of equilibrium 33, 35, 255257, 322 Potential energy 3, 4, 103, 122131, 133, 134, 135, 154, 165180, 264, 271, 285 Potential energy barrier 130, 165168 Potential energy contour diagram 126, 129, 131, 165, 166, 167, 169, 171, 173, 174, 175, 176 Potential energy surface 3, 122131, 133, 134, 135, 142, 165180, 184, 271 Potential energy well 178179 Pre-equilibrium 92, 201, 202204, 346358, 359365 Pre-exponential factor, see A factor Pressure jump 3335 Pressure limits in explosions 250252, 254 Primary process, photochemical 204206 Product valley, see Exit valley Propagation 185, 186, 205206 Straight chains 208239 Branched chains, 244259 Pseudo order 66, 7477 INDEX Pseudo rate constant 7477, 245, 318, 320, 320321, 351, 354, 355, 358 Pulsed laser 14, 29, 32 Pulsed radiolysis 32 Quadrupole 282 Quantum (of radiation) in photochemistry 204206 Quantum mechanical calculations 2, 123, 165 Quantum mechanical tunnelling 129130 Quantum unimolecular theory 159, 161 Quantum yield 189192, 204206, 210 Quenching 20 Radiation 2, 715, 1516, 19, 1920, 29, 3133, 100, 204206, 208 Radicals detection and identification of 6, 7, 1317, 19, 3133, 204 generation of 1920, 3133, 204 in solution 264, 359 see also Chain reactions, Chain carriers Raman spectra 7, Rate constant meaning of 4850 determination, differential method 5258 determination, integral method 5884 Rate, meaning of 4447 determination of 1738 Rate equation Differential, see Differential rate equation Integrated, see Integrated rate equation Rate expression, meaning of 4850 Rate of activation in unimolecular reactions 147148, 151152, 153, 155, 157158, 158, 159160 Rate of branching 245246, 257, 258 Rate of change of configuration 130, 131 Rate of collision, see Collision rate Rate of deactivation in unimolecular reactions 147148, 151152, 153154, 155, 158, 159160 Rate of initiation, see Steady state, Explosions Rate of propagation, see Propagation, Steady state Rate of reaction step in unimolecular reactions 147148, 154, 155, 158, 159160 439 INDEX Rate of termination, see Steady state, Explosions Rate, dependence on temperature see Dependence of rate on temperature, Arrhenius equation Rate-determining step 8283, 8789, 92, 148, 154, 159160, 222, 227228, 235, 240, 243, 346347, 348, 352, 357 Reactant valley, see Entrance valley Reaction coordinate 4, 125, 126, 127, 129, 130, 133, 134, 135, 165, 172, 176, 178 Reaction unit/Reaction entity 122, 123, 125, 126, 130, 131, 133, 165, 171, 173, 174, 176, 178, 263 Reactions in solution 19, 20, 21, 38, 141142, 263368 Reactive collision 103, 111112 Rebound mechanism 118119, 174, 184 Recycle, see Regeneration Redistribution of energy 100, 155 Reduced mass 102, 105106, 133135 Regeneration of chain carriers 186, 188, 192, 193, 208, 209, 211, 212 Regeneration of catalyst 331, 332, 365 Relative permittivity 19, 263, 264, 265, 266, 267, 268, 269, 280283, 285, 293, 295, 296, 299, 302, 303, 306 307, 308 Relative translational motion 102, 104, 152 Relative velocity 100101 Relaxation methods 3032, 3238 Relaxation time 3536, 6466, Table 3.3 Repulsion 110, 119, 171, 178, 265 Repulsive barrier see Late barrier Reversible reactions 81, 8991, 92, 198201, 202204, 255257, 257258, 346358, 359368 RiceHerzfeld Mechanisms 221243 Rotation 7, 100, 103, 110, 119, 135, 137, 138139, 140, 144145, 153, 178179, 224, 292, 294, 306 Rotational degrees of freedom 135, 137, 138139, 144145, 153, 224, 292, 294, 306 Rotational mode 103, 135, 144145, 153 Rotational partition function 132, 135, 138139, 140 Rotational state 7, 100 Rotational symmetry number 132 Rotational energy 153 Rotational structure 100, 294 Saturation 354 see Swamping Scattered products 111, 111122, 172, 174175, 177, 178180, 184 Scattering 100, 110122, 172, 174175, 177, 178180, 184 Scattering diagram (long lived complex) 119120, 178180, 184 Second explosion limit 252 Second order meaning of 4749 Second order integrated rate equation 6668, 68, Table 3.4 Second order rate constant meaning of 4749 Secondary process, photochemical 204205 Self-heating 244, 252, 257258 Shock tube 7, 13, 31, 33, 34 Simple model (unimolecular) 153155, 157 Sine waves 161 Single impulse 30, 3335, 90 Slater Theory 160161 Small perturbation 30, 3335, 3538, 66 Solute/solute interactions 268 see also Ionic interactions Solute/solvent interactions 268 Solvation 263, 267, 268, 269, 281, 282, 283, 285, 296301, 303304, 308309, 310, 311, 312, 312313 Solvation pattern 263, 269, 281, 296301, 303304, 308309, 310, 311, 312, 312313 Solvent/solvent interactions 263, 268 Sound wave 3538 Specific base catalysis 329 Spectrophotometry 813, 14, 27, 29 Spectroscopic methods of analysis/ determination/estimation 6, 716, 19, 27, 29, 30, 3132, 38, 132, 170, 204206 Spectroscopic quantities used in statistical mechanics 132, 135, 271 Spin resonance 15, 38 Squared terms 102103, 154, 155156, 157158 Standard state 142, 307 Steady state conditions/region 8489, 246, 247249, 257 440 Steady state method/treatment/analysis 8489, 89, 147149, 186, 192195, 196198, 198201, 202204, 207 208, 213, 214218, 218221, 222, 225227, 229232, 233238, 238239, 241243, 246, 247249, 257, 359360, 360362, 362363, 363365, 365368 Stoichiometric arguments 2324, 7779 Stoichiometric concentration 284285 Stoichiometric ionic strength 284285, 289 Stopped flow 2829 Straight chain 208239, 240243 comparisons with Branched chain 244, 246, 247248, 249250, 254, 254255, 255257, 258259 Stripping 117118, 119, 120, 170172, 177 Structureless continuum 281 Substrate in enzyme kinetics 365 Successful collisions 103, 111112 Surface reactions 19, 210, 240243, 247249, 249, 251252, 255, 257 Surface termination 210, 240243, 247249, 249, 251252, 255, 257 Swamping 354 see Saturation Symmetrical PE barrier 131, 165167 Symmetrical PE contour diagram 131, 166 Symmetrical PE profile 131, 166167 Symmetrical scattering 119122 Symmetry number 132 Temperature effect of 1, 9295, 100, 104 108, 154155, 157, 159, 160, 161, 250 252, 254, 255257, 257259, 268, 339 see also Arrhenius equation Temperature, effect on relative permittivity 293 Temperature jump 3335 Temperature limit, cool flames 254, 258259 Termination 208239, 239243, 243259 Termolecular reaction 3, 87, 185, 199, 201 Thermal explosions 244 Thermal initiation 1920, 216 Thermal rate, see H2/I2 reaction 206208 Thermodynamic formulation of transition state theory 140145, 265, 269, 269272, 279313 INDEX Thermodynamic functions/quantities 140142 Thermoneutral 127128 Third bodies 183, 227229, 241, 243 Third explosion limit 252 Third order meaning of 48, Table 3.4 Three-halves (3/2) order 48, and Table 3.2 Time lag 3, 147, 154, 158, 159 Total energy in transition state theory 123, 125, 129 Total molecular partition function 134 Trace 6, 188, 211, 212, 253 Trajectory 172173, 176 Transition state 4, 125 see Activated complex Transition state theory 4, 99, 122145, 224, 237, 263, 265, 269272, 279284, 289313 Transition state theory expression 132, 136, 269 Translational degrees of freedom 135, 137, 138139, 144145, 224 Translational energy 118, 119, 120, 172, 174, 175177, 178, 179 Translational partition function 132, 134135, 137, 138139 Transmission coefficient 130, 133134, 269 Tunable laser 13 Tunnelling 129130 Ultrasonic relaxation techniques 3538, 66 Ultraviolet 7, 8, 13, 14, 16 Undeflected molecules 111, 172 Unimolecular 2, 3, 87, 185, 222 Unimolecular theories 2, 99, 145, 145161, 195 see Lindemann mechanism, Hinshelwood theory, Kassel theory, Slater theory Unimolecular reaction 2, 3, 19, 87, 99, 145161, 185, 195198, 222223, 227229, 233, 235, 240, 243, 292 Units 47, 4950, 53, 55, 7577, 95, 103, 107108, 109, 139140, 157158, 289, 305, 318, 332334, 354, 355, 358 Units of rate 47 Units of rate constants 4950, 53 of pseudo rate constants 7577, 318, 332334, 354, 355, 358 ... ẳ dt k1 ẵNO2 ; ẵN2 O2 ẳ k1 ỵ k2 ẵO2 dẵNO2 ẳ k2 ẵN2 O2 ẵO2 ỵ dt k1 k2 ẵNO2 ẵO2 ẳ k1 ỵ k2 ẵO2 ỵ 6:30ị 6:31ị 6: 32 6:33ị The factor of two is included, since two molecules of NO2 are formed... CH3 ! C2 H6 (j) k1 NO ỵ O2 !NO3 k1 NO3 !NO ỵ O2 k2 NO3 ỵ NO !2 NO2 (k) N2 O5 ! NO2 ỵ NO3 NO2 ỵ NO3 ! NO2 ỵ O2 ỵ NO NO ỵ N2 O5 ! NO2 (l) (m) C2 H5 ỵ CH3 COCH3 ! C2 H6 ỵ CH2 COCH3 Br2 ỵ M !... can be proposed Mechanism A k1 NO ! N2 O2 k1 N2 O2 ! NO k2 N2 O2 ỵ O2 ! NO2 199 KINETICALLY EQUIVALENT MECHANISMS Mechanism B k1 NO ỵ O2 ! NO3 k1 NO3 ! NO ỵ O2 k2 NO3 ỵ NO ! NO2 Assuming the steady