Reaction Mechanism A detailed sequence of steps for a reaction Reasonable mechanism: 1. Elementary steps sum to the overall reaction 2. Elementary steps are physically reasonable 3. Mechanism is consistent with rate law and other experimental observations (generally found from rate limiting (slow) step(s) A mechanism can be supported but never proven NO2 + CO NO + CO2 2 Observed rate = k [NO2] Deduce a possible and reasonable mechanism NO2 + NO2 NO3 + NO slow NO3 + CO NO2 + CO2 fast Overall, NO2 + CO NO + CO2 Is the rate law for this sequence consistent with observation? Yes Does this prove that this must be what is actually happening? No! NO2 + CO NO + CO2 2 Observed rate = k [NO2] Deduce a possible and reasonable mechanism NO2 + NO2 NO3 + NO slow NO3 + CO NO2 + CO2 fast Overall, NO2 + CO NO + CO2 Is the rate law for this sequence consistent with observation? Yes Does this prove that this must be what is actually happening? No! Note the NO3 intermediate product! Arrhenius Equation Temperature dependence of k kAe E/RTa A = pre-exponential factor Ea= activation energy Now let’s look at the NO2 + CO reaction pathway* (1D). Just what IS a reaction coordinate? NO2 + CO NO + CO2 High barrier TS for step 1 Reactants: Lower barrier TS for step 2 NO2 +NO2 +CO Products Products Bottleneck NO +CO2 NO +CO2 Potential Energy Step 1 Step 2 Reaction Coordinate NO2 + CO NO + CO2 NO22 NO NO 3 NO NO CO NO CO 222In this two-step reaction, there are two barriers, one for each elementary step. The well between the two transition states holds a reactive intermediate. Potential Energy A reactive intermediate is a compound formed transiently, but Reaction Coordinate absent in the overall reaction. We need to do better than just using a 1-D energy slice, namely a multidimensional potential energy surface! Different Types of Composite Reactions Simultaneous: Opposing: A Y and A Z A + B Z Y or A z Consecutive: Consecutive with opposition: A X Y A X Y In order for the system to be at complete equilibrium, the time derivative of all species concentrations must be zero! Reaction with Three Simultaneous Pathways x 100 k1 [A] k “Branching ratio” A 2 y k [x] : [y] : [z] = k1 : k2 : k3 3 Rate law: z 0 dA time kA kA kA dt 123 Now look at products (k k k ) A dx (k k k )t 123 kA kA e123 dt 11 0 (k k k )t 123 k (k k k )t AAe xA1et 1 123 0 0 kkk123 k xA 1 At long times, 0 kkk123 Kinetic vs Thermodynamic control x k1 X K1 Kinetic Control k Y Z K2 K3 A 2 y k3 z Thermodynamic Control? Proportions of various products are determined using ΔGrxn of all possible reactions. Reaction with Three Simultaneous Pathways PChem Lab: Quenching of Electronically Excited Naphthalene, A* A* can relax by radiative, non-radiative or collisional quenching decay A* A + hv (Radiative) A* A + heat (Non-Radiative) A* + Q A + Q (Collisional Quenching) Kinetics for Simple Consecutive Reactions k1 k2 AXZ kk AX12 and X Z What are the differential rate equations for A, X and Z? What are the integrated rate equations for A, X and Z? Kinetics for a Simple Consecutive Reaction kk AX12 and X Z What are the differential rate equations for [A], [X] and [Z]? dA kA1 (1) Let [A] = [A] dt t=0 0 We can solve (1) directly and [X]t=0 = [Z]t=0 = 0 kt AAe 1 0 Now [X] and [Z] dX kX kA (2) dt 21 dZ kX (3) dt 2 Kinetics for a Simple Consecutive Reaction kk kt1 12AAe AX and X Zwith 0 dX kX kA (2) dt 21 becomes dX kt kX kAe 1 dt 21 0 dX kt kX kAe 1 a "standard form" o.d.e. with solution dt 21 0 k kt kt XeeA2 12 0 and kk21 kt kt ke21 ke ZA AXA 1 12 00 kk 21 Variation of Concentrations for Consecutive Reactions A X Z Kinetics for a Simple Consecutive Reaction kk AX12 and X Z kt kt 21 kt1 ke ke AAe ZA 1 12 0 0 kk 21 k1 >> k2 k2 >> k1 One More Case: k1 = 10 k2 kk AX12 and X Z k1t Quasi-Steady State Approximation A Quasi Rationale kk AX12 Z We see that, whenever, k1 > k2, [X] has an initial growth period, but after that, [X] tends to track [A]. This leads one to imagine that we might find a condition where [X] is in a quasi steady state, namely its sources and sinks cancel out each other, and d[X]/dt=0. Try it!.