CHM 8304 CHM 8304 Physical Organic Chemistry Kinetic analyses Scientific method • proposal of a hypothesis • conduct experiments to test this hypothesis – confirmation – refutation • the trait of refutability is what distinguishes a good scientific hypothesis from a pseudo-hypothesis (see Karl Popper) 2 Kinetic analyses 1 CHM 8304 “Proof” of a mechanism • a mechanism can never really be ‘proven’ – inter alia, it is not directly observable! • one can propose a hypothetical mechanism • one can conduct experiments designed to refute certain hypotheses • one can retain mechanisms that are not refuted • a mechanism can thus become “generally accepted” 3 Mechanistic studies • allow a better comprehension of a reaction, its scope and its utility • require kinetic experiments – rate of disappearance of reactants – rate of appearance of products • kinetic studies are therefore one of the most important disciplines in experimental chemistry 4 Kinetic analyses 2 CHM 8304 Outline: Energy surfaces • based on section 7.1 of A&D – energy surfaces – energy profiles – the nature of a transition state – rates and rate constants – reaction order and rate laws 5 Energy profiles and surfaces • tools for the visualisation of the change of energy as a function of chemical transformations – profiles: • two dimensions • often, energy as a function of ‘reaction coordinate’ – surfaces: • three dimensions • energy as a function of two reaction coordinates 6 Kinetic analyses 3 CHM 8304 Example: SN2 energy profile • one step passing by a single transition state δ- δ- X---Y---Z transition state activation ΔG‡ energy X:- + Y-Z reactants Free energy ΔG° X-Y + :Z- products Reaction co-ordinate 7 Reminder: activated complex • ethereal complex formed at the transition state of the reaction – partially formed bonds -13 – partially broken bonds very unstable; <10 s H H δ− δ− H HO + C Cl HO C Cl HO C + Cl HH HH H H not isolable partial transition state bonds 8 Kinetic analyses 4 CHM 8304 Free energy profiles vs surfaces • a reaction profile gives the impression that only one reaction pathway can lead to the formation of products • however, in reality, reactant molecules are free to ‘explore’ all available reaction pathways – the pathway with the lowest energy is the one that determines the predominant mechanism • free energy surfaces are in 3D, and take account of more than one event that must take place during a reaction (e.g. bond cleavage and formation) – allow the consideration off ‘off-pathway’ interactions – allow the visualisation of mechanistic promiscuity 9 Energy surfaces • allow the visualisation of several reaction pathways, or even several reactions that may take place activated complex for A activated complex for B product A product B reactant chem.wayne.edu 10 Kinetic analyses 5 CHM 8304 More-O’Ferrall and Jencks • Rory More-O’Ferrall – University College, Dublin – mechanisms et catalysis • William P. Jencks (1927-2007) – Biochemistry, Brandeis University – a father of modern physical organic chemistry and biological chemistry – author of classic textbook – laureate of several awards 11 Profile to surface δ- δ- X---Y---Z 2D: TS rxn. coord. & energy X:- + Y-Z X-Y + :Z- Free energy reactants products Reaction co-ordinate - X:- + Y+ + :Z- X: + Y-Z Cleavage of Y-Z bond reactants unstable intermediates ‡ 2D: 2 rxn. coord. - X-Y -Z 3D: unstable bond Formation of X-Y X-Y + :Z- 2 rxn. coord. & energy intermediate products 12 Kinetic analyses 6 CHM 8304 Mountain terminology summit (Mt. Robson) summit (Helmet Pk.) Helmet/Robson col 13 ‘Summit’ vs ‘col’ • the predominant mechanism follows the reaction pathway of lowest activation energy • the ‘summit’ (TS) of this pathway is often a ‘col’ between peaks of even higher energy Free energy Free Rxn. co-ord. 14 Kinetic analyses 7 CHM 8304 Exercise: Diagram to mechanism • Draw the reaction profile that corresponds to the lowest energy reaction pathway on the MOFJ diagram below. Draw the corresponding mechanism including its transition state(s). R GLGP + Nuc Cleavage of C-LG bond bond Nuc Formation of C- + GP REt LG + Nuc Nuc - H 3 C RCH 2 GLGP Free energy Rxn. Co-ord. R Nuc + GLGP 15 Multi-step reactions • when a reaction takes place via several elementary chemical steps, one of these steps will limit the global rate of transformation – named the rate determining step (rds) or rate limiting step (rls) • the rate limiting step is always the step having the highest energy transition state – even if this step does not have the largest microscopic activation barrier! 16 Kinetic analyses 8 CHM 8304 Rate-limiting step on a reaction profile • the rate-limiting step is the one with the highest energy transition state with respect to the ground state activation energy TS2 TS2 of global reaction; step 2 is rls TS1 ‡ TS1 ΔG2 int. int. products products ‡ ‡ ‡ ‡ ΔG Free energy Free energy ΔG1 ΔG1 > ΔG2 so step 1 is rls? reactants NO!! reactants Rxn. Co-ord. Rxn. Co-ord. 17 Rate-limiting step on a reaction profile • the rate-limiting step is the one with the highest energy transition state with respect to the ground state – see A&D, Figure 7.3 G‡ Δ ΔG‡ ΔG‡ Free energy Free energy Free energy Rxn. co-ord. Rxn. co-ord. Rxn. co-ord. ‡ ΔG ‡ ΔG‡ ΔG Free energy Free energy Free energy Rxn. co-ord. Rxn. co-ord. Rxn. co-ord. 18 Kinetic analyses 9 CHM 8304 Rate vs rate constant • the reaction rate depends on the activation barrier of the global reaction and the concentration of reactants, according to rate law for the reaction – e.g. v = k[A] • the proportionality constant, k, is called the rate constant 19 Rate vs rate constant • reaction rate at a given moment is the instantaneous slope of [P] vs time • a rate constant derives from the integration of the rate law 100 90 different 80 concentrations 70 of reactants; 60 different 50 [Produit] 40 end points different 30 initial 20 rates 10 0 0 5 10 15 20 Temps same half-lives; same rate constants 20 Kinetic analyses 10 CHM 8304 Rate law and molecularity • each reactant may or may not affect the reaction rate, according to the rate law for a given reaction • a rate law is an empirical observation of the variation of reaction rate as a function of the concentration of each reactant – procedure for determining a rate law: • measure the initial rate (<10% conversion) • vary the concentration of each reactant, one after the other • determine the order of the variation of rate as a function of the concentration of each reactant • e.g. v ∝ [A][B]2 • the order of each reactant in the rate law indicates the stoichiometry of its involvement in the transition state of the rate-determining step 21 Integers in rate laws • integers indicate the number of equivalents of each reactant that are found in the activated complex at the rae-limiting transition state – e.g.: • reaction: A + B à P – mechanism: A combines with B to form P • rate law: v ∝ [A][B] – one equivalent of each of A and B are present at the TS of the rds 22 Kinetic analyses 11 CHM 8304 Fractions in rate laws • fractions signify the dissociation of a complex of reactants, leading up to the rds: – e.g. : • elementary reactions: A à B + B; B + C à P – mechanism: reactant A exists in the form of a dimer that must dissociate before reacting with C to form P • rate law: v ∝ [A]½[C] – true rate law is v ∝ [B][C], but B comes from the dissociation of dimer A – observed rate law, written in terms of reactants A and C, reflects the dissociation of A – it is therefore very important to know the nature of reactants in solution! 23 Negative integers in rate laws • negative integers indicate the presence of an equilibrium that provides a reactive species: – e.g. : • elementary reactions: A B + C; B + D à P – mechanism: A dissociates to give B and C, before B reacts with D to give P • rate law: v ∝ [A][C]-1[D] – true rate law is v ∝ [B][D], but B comes from the dissociation of A – observed rate law, written in terms of reactants A and D, reflects the dissociation of A – apparent inhibition by C reflects the displacement of the initial equilibrium 24 Kinetic analyses 12 CHM 8304 Outline: Transition State Theory • based on section 7.2 of A&D – Arrhenius approach – Eyring approach – temperature effects – interpretation of thermodynamic parameters 25 Arrhenius • Svante Arrhenius (1859-1927) – Swedish physicist and chemist (Stockholm) – solution chemistry, activation energy – also: panspermia, universal language, greenhouse effect, racial biology – one of the founders of the Nobel Institute – Nobel Prize (1903) for the electrolytic theory of of dissociation 26 Kinetic analyses 13 CHM 8304 Arrhenius equation • in 1889, Arrhenius noted that the rate constant of a given reaction increases exponentially with temperature : E d lnk a Ea = 2 lnk = − + lnA dT RT RT • the activation energy, Ea, was defined as the energy necessary to convert reactants into “high energy species” • however, this energy is not expressed in terms of thermodynamic parameters – for this, it was necessary to develop the transition state theory 27 Arrhenius plot Graphique d'Arrhenius ln A E lnk = − a + lnA RT slopepente = - Ea / R obs k ln 1 / T (K-1) 28 Kinetic analyses 14 CHM 8304 Eyring • Henry Eyring (Sr.) (1901-1981) – American professor of theoretical chemistry and reaction rates (Princeton, Utah) – laureate of several prizes: Wolf Prize, Priestley Medal et National Medal of Science 29 Transition State Theory (TST) • developed by Eyring to explain observed reaction rates in terms of standard thermodynamic parameters • in their transformation into products, reactants must attain a