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Reaction Kinetics in Organic Reactions

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Autumn 2004 Reaction Kinetics in Organic Reactions Why are kinetic analyses important? • Consider two classic examples in asymmetric catalysis: geraniol epoxidation 5-10% Ti(O-i-C3H7)4 O DET OH * * OH + TBHP CH2Cl2 3A mol sieve OH COOH5C2 L-(+)-DET = OH COOH5C2 * OH geraniol hydrogenation OH 0.1% Ru(II)-BINAP + H2 CH3OH P(C6H5)2 (S)-BINAP = P(C6 H5)2 • In both cases, high enantioselectivities may be achieved. However, there are fundamental differences between these two reactions which kinetics can inform us about. 1 Autumn 2004 Kinetics of Asymmetric Catalytic Reactions geraniol epoxidation: • enantioselectivity is controlled primarily by the preferred mode of initial binding of the prochiral substrate and, therefore, the relative stability of intermediate species. The transition state resembles the intermediate species. Finn and Sharpless in Asymmetric Synthesis, Morrison, J.D., ed., Academic Press: New York, 1986, v. 5, p. 247. geraniol hydrogenation: • enantioselectivity may be dictated by the relative reactivity rather than the stability of the intermediate species. The transition state may not resemble the intermediate species. for example, hydrogenation of enamides using Rh+(dipamp) studied by Landis and Halpern (JACS, 1987, 109,1746) 2 Autumn 2004 Kinetics of Asymmetric Catalytic Reactions “Asymmetric catalysis is four-dimensional chemistry. Simple stereochemical scrutiny of the substrate or reagent is not enough. The high efficiency that these reactions provide can only be achieved through a combination of both an ideal three-dimensional structure (x,y,z) and suitable kinetics (t).” R. Noyori, Asymmetric Catalysis in Organic Synthesis,Wiley-Interscience: New York, 1994, p.3. “Studying the photograph of a racehorse cannot tell you how fast it can run.” J. Knowles, Angew. Chemie Int. Ed. Eng. 1977. 3 Autumn 2004 Transition State Theory kinetics • Intermediate species are energy wells; they tell us about stability highest TS The more stable an intermediate species, the higher its concentration energy this tells us nothing about how fast it energy reacts! intermediate • Transition states are energy maxima; thermodynamics they tell us about reactivity The lower in energy a transition state, • The rate of the overall reaction is determined by the energy difference between that of the the faster the reaction highest transition state and that of the reactant. this tells us nothing about the ! population of intermediate species! !G ! = standard free energy of activation 4 Autumn 2004 Reaction Rate Consider the reaction: A + B !! " C + D How do we define the rate of the reaction? First, we define something called the extent of the reaction: Subscript i refer to the reactants and products ni " ni 0 ! = extent of reaction = (A, B, C, and D) # i ni0 means the number of moles of species i initially present #i means the stoichiometric coefficient of species i (-1,-1,1, and 1) Reaction rate is defined as the 1 d" 1 1 dn instantaneous change in the extent rate = ! = ! i V dt V dt of reaction per unit reaction volume: #i 5 Autumn 2004 Reaction Rate 1 d" 1 1 dn 1 dC rate = ! = ! i = ! i V dt V dt dt #i #i • For reactions in the liquid phase, the volume doesn’t change very much over the course of the reaction: V " constant. We can use the instantaneous change in species concentration as the variable we measure. Concentration (Ci = ni/V) is given in units of molarity (moles/liter). • This definition of reaction rate is the overall or global reaction rate, and it doesn’t depend on which species i we choose. • We can also define the reaction rate of a particular species i as follows: dCi rate of reaction of species i = rate!"i = dt 6 Autumn 2004 Reaction Rate 1 dC rate = i ! dt i dCi rate of reaction of species i = rate!"i = dt • Consider the following example: NO2 NH2 + 2 H2O + 3 H2 • How do we measure rate? – By FTIR monitoring of PhNO2 disappearance – By hydrogen pressure uptake – By monitoring production of water • We get a different “species rate” for each of these. 7 Autumn 2004 Elementary Reactions • an elementary reaction is one which occurs on a molecular level exactly as it is written – this means that the rate expression for an elementary reaction may be written on inspection • the number of chemical species involved as reactants is referred to as the molecularity of the reaction – almost all elementary reactions are either unimolecular or bimolecular • a reaction which is unimolecular in one direction may be bimolecular in the other direction! k1 Unimolecular reaction: A !! " B + C r = k1 #CA Bimolecular reaction: k2 M + N ! !" P r = k2 #CM #CN 8 Autumn 2004 Empirical Kinetic Methods • Experimental observations show that chemical reactions often depend on the concentrations of reactants. • Empirical methods have been developed with the aim to determine the mathematical dependence of each substrate’s concentration. • This mathematical relationship between rate and concentration is known as a reaction rate equation or reaction rate law. • The most common approach is to look for a “power law” form of the rate law: x y reaction rate = f concentration = k !CACB ( ) 9 Autumn 2004 Initial Rate Methods • Holding the concentration of one substrate constant, we measure the change in concentration of second substrate over a brief period of time at the beginning of the reaction. • If the change is concentration of the substrate is not too large, then we can say that !CA/!t approximates the instantaneous change dCA/dt at that value of CA. • We repeat this experiment using different initial concentrations of substrate A (still holding substrate B constant). 0,754 • From this set of experiments, we can 0,752 build a plot of rate (!C /!t) vs. C . !C A A 0,75 initial rate = A !t (M) A 0,748 • Then we carry out the same C 0,746 procedure again, this time holding CB 0,744 constant and varying CA. 0,742 0,74 0 0,5 1 1,5 2 2,5 3 time (min) 10 Autumn 2004 Initial Rate Methods • Consider these nucleophilic substitution reactions of alkyl halides: k t-BuBr + NaOH !k!1 "t-BuOH + NaBr MeI + NaSMe !!2 " MeSMe + NaI Monitor rate at: Monitor rate at: constant [NaOH] constant [t-BuBr] constant [NaSMe] constant [MeI] first order in [t-BuBr] zero order in [NaOH] first order in [NaSMe] first order in [MeI] SN1 SN2 11 Autumn 2004 Methods for Non-Integer Order • If we don’t get a straight line plotting rate vs. CA, we can plot the data differently to determine the reaction order in species A. • The orderin substrate A may be obtained by plotting a different relationship to obtain a straight line: 0,4 x y rate = k !C C 0,2 A B x = 0.48 x y log rate log k C C 0 ( ) = ( ! A B ) y x (rate) -0,2 log k C log C log = ( ! B ) + ( A ) -0,4 -0,6 log rate log k C y x log C ( ) = ( ! B ) + ! ( A ) -0,8 -2,5 -2 -1,5 -1 -0,5 0 log(C ) A constant reaction order in CA (y-intercept) (slope) 12 Autumn 2004 IntegraTed Rate Equations • Mathematical characterization of simple cases (for example, where x and y are 0, 1, or 2). dCA x y reaction rate = ! = k "CACB dt We can integrate these equations analytically: !dCA C C k t r = = k A = A0 ! " dt !dC r = A = kC ln C = ln C ! k "t dt A ( A) ( A0 ) 1 1 !dC 2 = + k "t r = A = kC C C dt A A A0 # C & # C & !dC B Bo A ln% ( = ln% ( + CAo)B ! CBo)A kt r = = kCACB C C ( ) dt $ A ' $ Ao ' # C & # C & ln B = ln Bo + C !C kt when ) ,) = !1 % C ( % C ( ( Bo Ao) A B $ A ' $ Ao ' 13 Autumn 2004 Following reactions as a function of time Zero order First order 30 2 25 r ate = !k 0 k = 0.24/min A of 20 -2 15 -4 ln(CA/CAo) 10 -6 Concentration 5 zero-order kinetic fit: -8 rate = !kC k = 3.4 mmolel/mmmole/min/liter/min A R=0.997 0 -10 0 1 2 3 4 5 6 7 8 0 2 4 6 8 10 12 Time (min) time (min) Second order Type I Second order Type II 0,5 4 2 3,5 rate = !kC C A B 0,4 rate = !kCA 3 2nd order Type II kinetic fit: A k= 0.09 l/mole/min 2,5 0,3 2nd order Type I kinetic fit: /C B k= 0.007 l/mmole/min C 2 ln (liter/mmole) 0,2 1,5 1/CA 1 0,1 0,5 0 0 0 1 2 3 4 5 6 7 8 0 1 2 3 4 5 6 7 8 time (min) time (min) 14 Autumn 2004 Limitations of Empirical Methods • These mathematical descriptions are simply and solely mathematical constructs to help reveal trends in the experimental data • The reaction order obtained with any of these methods may have no physical meaning or relationship to the intrinsic reaction processes occurring on the molecular level • These methods may be useful for thinking about reactions for which not much is known about the reaction mechanism the more we know about how the reaction proceeds on the molecular level, the better we will be able to model its behavior so that we may carry it out under any conditions of scale, temperature and composition ! REACTION MECHANISM! 15 Autumn 2004 Reaction Mechanisms • a reaction mechanism is a series of elementary steps through which it is proposed that a reaction proceeds • a mechanism is a hypothetical construct and cannot be proven! At best, it may be said that a proposed reaction mechanism is consistent with the experimental evidence • elementary steps in a proposed reaction mechanism often contain intermediate species which may be impossible to isolate or even to detect • the reaction mechanism must represent the overall observed reaction stoichiometry via a linear combination of the proposed elementary steps (this just means that we add up the steps we need to get the overall rate expression) • any intermediates produced in the elementary steps in the mechanism must be eliminated to obtain the final rate expression • a postulated mechanism for a reaction in the forward direction must also hold for the
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