Reaction Mechanisms: Complex Reaction Mechanisms Chapter 36 Reaction mechanism is a collection o elementary (one step) reactions that would add up to result in the overall reaction. Generally elementary (simple) reactions are bimolecular and unimolecular, rarely are termolecular. Experimentally determined rate law does not conorm with the stoichiometric coeicients o reactions, in general; unless the mechanism itsel is simple. Therein lies the need to propose a mechanism or the reaction. A valid reaction mechanism must be consistent with the experimental rate law. For example; Proposed mechanism: Rate Law is o the orm ; R k[ N2O5] The orm o the rate law signals that the reaction involves multiple steps (a complex mechanism). Mechanisms involve many single step reactions (sum o them is the overall reaction), creation o intermediates (allowing use o steady state approximation) and equilibria. Reaction rate law can be written as; - 1
Invoking SSA or NO and NO 3. [NO] = Pre-equilibrium Approximation: A useul concept or reactions that can proceed via an equilibrium involving an intermediate I. (1) and rate= Viola!! (2) Upon rearrangement Substituting or [I] in rate expression 2
Reaction Mechanism: Pre-equilibrium Decay o intermediate Experiment R = Lindeman Theory Unimolecular Reactions: The energy necessary to overcome the activation energy is achieved by collisions with any molecule (M) and M can very well be A itsel. Two steps involved. In gas phase the reaction constants are concentration, (i.e. pressure (total)) dependent. In solution it is not concentration dependent, due to the act that the particle concentration is nearly constant in solution phase. Lindeman Theory Unimolecular Reactions: Lindeman Theory Uni-molecular Reactions: The energy necessary to overcome the activation energy is achieved by collisions with any molecule M and M can very well be an A. Two steps are involved, ormation o A * (activated reactant not an activated complex) and decomposition o A * to orm products. In general (solutions/ gases); For M=A The preequilibrium step. 3
Reaction rate = Applying SSA to A *. For k -1 [A]>>k 2 For k -1 [A]<<k 2 uni bi True or [A] large. Reaction rate = For the general case - Lindeman Theory : Reactions in solutions or gases at high pressure - k -1 [A] >>. uni [A] large with [M] ~ constant k app = k uni is not simplistic. 4
Upon rearrangement; k uni Catalysis Reaction progress: Energy diagram Increasing reaction rates amounts to increasing reaction Part o E a energy required to overcome repulsive orces among electron rate constants. clouds o reacting molecules. [M] E a E a >E a <E a Low T One strategy would be to lower E a. Thereby increase the raction o molecules with energy > E a. Catalysis a mechanism Reactant = S S-C complex Reaction rate; Applying SSA to SC; Catalyst remain unchanged ater the reaction, it changes the reaction mechanism by combining with reactant(s)/ intermediates and thereore changes the reaction coordinate. 5
Determining reaction parameters k 2 and K m ; Intial rate method. Substituting or [S] and [C] in and rearranging ; [SC] = Substituting or [SC]; Conservation o matter: @ t =, where R = R Simpliies to; yields; yields; Starting with; (1) For [C] << [S] For [S] >> [C] experimental conditions (a) and also i [S] < K m (b) and also i [S] > K m R k [ C] [ S] 2 Km [R] linear to [S]. At large [S], R =k 2 [C] 6
alternatively Again, (1) For [C] << [S] invert (b) i [S] >> K m Reciprocal plot [R] reaches a limiting value and zero order w.r.t. [S]. Michaelis-Menten Enzyme Kinetics using; (2) For [C] >> [S] (a) i [C] < K m R k [ C] [ S] 2 Km [R] linear to [C] & [S]. (b) i [C] > K m R k [ S] 2 [R] linear to [S]. enzyme substrate 7
Michaelis-Menten Enzyme Kinetics Enzymes are reaction speciic catalysts. Michaelis-Menten rate law For [E] << [S] ; Rate = K m = Michaelis-Menten constant and also i [S] >> K m above equation simpliies to, Mechanism The reaction rate plateau is at k 2 [E] C Lineweaver-Burk Equation Determination o K m With R max known, evaluate R max /2 substitute in invert K m? 8
Determination o K m With R max known, evaluate R max /2 substitute in k[s][e] 2 Rmax[S] R [S] Km [S] Km R R max max [S]@Rmax /2 2 [S]@Rmax/2 Km [S]@Rmax/2 Km 2[S] @Rmax/2 K [S] m @Rmax/2 Photochemistry physical processes Photochemistry deals with the chemical and physical changes o molecules ollowing absorption o photons in the visible/uv region. Following the absorption o photons molecules undergo electronic and vibrational and rotational (rotational in gas phase ) excitation (photoexcitation). h A A * A( radiatively) A( non radiatively) Photoproducts A* =excited molecule physical processes Photo-excitation; h A P I I 1 l [ A ] Rate o A undergoing photo excitation; d[a] = -k[a] dt Monochromatic beam I P I I I abs 1 l [ A ] I 1 l [ A ] h = molar absorptivity A 9
Setting [A] low, Iabs 1 1 l [ I A ] ( ) d[ A] I dt Keeping I a constant and l = 1, substitute or I abs ; abs d[ A] I( 233. ) [ A] dt First order loss d[ A] I( 233. ) [ A] dt Jablonski Diagram 7 2 (2 ) 4 In terms o number o molecules; A = # molecules o A, k a (paths) 12 (2 ) 3 F 12456 P 4, 8 ISC T S 9 1 3 8 5 6 A = absorption cross section. 7 IC S 1 S 2, 5, 9 VR 1
Jablonski Diagram shows the electronic states o a molecule and the photo-physical transormations between them in an energy diagram. The energy states are grouped horizontally by their spin multiplicity. Non-radiative transitions are shown by wavy arrows and radiative transitions by straight arrows. The vibrational ground state o each electronic state is indicated by heavy lines. Kinetics o photo-physical processes * Quenching: Excited molecules can lose its energy by way o collisions with other molecules (quenchers) and thereby relax non-radiatively. This must be considered another kinetic process. * Kasha s rule: Photon emission (luorescence or phosphorescence) occurs only rom the lowest-energy excited electronic state o a molecule. 11
[S 1 ] = [P] quencher q introduced Applying SSA to S 1. k q d[ S1 ] S ka[ S] ( k kic k k Q isc q[ ])[ S1] dt Deine [S ] = [A] SSA Fluorescence yield: k k ic Parallel reactions (elementary) S 1 k isc k q [Q] Florescence 12
Fluorescence yield: 1. invert 2. substitute # photons emitted as luorescence # photons absorbed 1 1 1 1 k kic k [ isc kq Q ] I k [S] k k [S] k a a Stern-Volmer Plot I k k and k ic isc with no quenching, we get pure lourescence I 1 1 I ka[s] I k [S] a k slope k q :Q present and k dominating 13
Measurement o Excite molecules with a short pulse o photons, monitor decay aterwards. [S 1 ] time Creates S 1 species, with excitation turned o monitor the luorescence decay o S 1. For S 1 ; time ln[ S ] ln[ S ] 1 t ln[ I ] ln[ I ] 1 t 1 1 I conditions are such that k kicand kisc Plot 1 1 k k k k [ Q] k k [ Q] slope kq ic isc q q intercept k k SVE slope k q 14