POC4SOC Introduction to Kinetics II NJB POC4SOC Transition State Theory standard molar Gibbs energy reaction coordinate NJB POC4SOC Transition State Theory equilibrium constant ΔG ‡o k T − k=B e ⋅ RT h standard molar Gibbs energy reaction coordinate term related with crossing barrier NJB POC4SOC Eyring Plot ⎛ ⎞ o≠ o≠ ⎜ k⋅ h ⎟ ΔH ΔS Linear Regression for Data1_B: ln = − + Y = A + B * X ⎜ 3- 1−n ⎟ RT⋅ R ⎝kB⋅mol T ⋅() dm ⎠ Parameter Value Error -36 ------------------------------------------------------------ A -21.53946 0.46944 B -5.1717 0.15165 ------------------------------------------------------------ -37 RSDNP ------------------------------------------------------------ )} T -0.99914 0.04994 4 8.588E-4 B ------------------------------------------------------------ k )/( -38 k h ln{( ΔHø≠ = 42 kJ mol-1 ø≠ -1 -1 -39 ΔS = -179 J K mol 2.9 3.0 3.1 3.2 3.3 3.4 3 -1 -1 10 T / K NJB POC4SOC Activation parameters • Use as ‘reality checks’ – compare with theoretical estimates (at various levels of “theory”) NJB POC4SOC Kinetic isotope effects what is the standard molar Gibbs energy and how can it depend on isotopes? standard molar Gibbs energy reaction coordinate NJB POC4SOC Zero point energy differences narrow potential -1 wells increase the difference in / kJ mol / kJ G zero point (vibrational) energy – note link with IR frequencies NJB POC4SOC Typical KIE standard molar Gibbs energy reaction coordinate NJB POC4SOC • This is fine for single-step reactions, but what if we are studying a multi-step reaction? • How does one determine the rate- determining step? • Is the rate-determining step always the rate-determining step? • How do additional steps affect the observed kinetics? NJB POC4SOC Transition State Theory The standard molar Gibbs energy of activation ΔGø≠ is the change in the Gibbs energy of the system associated with the hypothetical formation of 1 mole of activated complex from standard molar Gibbs energy reactant(s) at constant temperature with all reaction coordinate species being in the standard state (normally 1 mol dm-3). NJB POC4SOC A multistep reaction A (+B)→TST (+B)→I + B→TST→P 40 standard state 1 mol dm-3 20 [B] = 1 mol dm-3 0 [B] = 0.1 mol dm-3 [B] = 0.01 mol dm-3 molar Gibbs energy -3 -20 [B] = 0.001 mol dm reaction coordinate For 2 (or more) consecutive steps, the rds can depend on relative concentrations. At low [B], step 1 becomes an equilibrium NJB Determining a pH-rate profile – POC4SOC specific acid/base catalysis 4 6 2 ) -1 4 obs k / s obs k log( 0 2 -2 0 0 5 10 15 0.0 0.1 0.2 0.3 0.4 0.5 pH [buffer] / mol dm-3 tot As an alternative to using buffer, effects at high and low pH, - + where OH and H3O are in large excess (pseudo first order conditions), can sometimes be determined directly using - + different [OH ] and [H3O ]. NJB Determining a pH-rate profile – POC4SOC general acid/base catalysis 15 4 2 10 ) -1 obs k / s / obs log( 0 k 5 -2 0 0 5 10 15 0.0 0.1 0.2 0.3 0.4 0.5 pH [buffer] / mol dm-3 tot The slopes of kobs vs [buffer]tot give kgb when buffer ratio is corrected for. Alternatively, kobs is plotted as a function of [buffer]basic which should give parallel lines NJB g) base catalysedand acidcatalys catalysed e)base catalysedwithsatura catalysed, uncatalysed base catal and a) acidcatalysed anduncatalysed b) basecatalysedanduncatalysed c) acid log(k ) log(k ) obs obs ef ab cd pH pH log(k ) log(k ) pH rateprofiles obs obs pH pH ed with changeinrds uncatalysed h) NJB ysed d)acidcatalysed, andbase log(k ) tion f)acidcatalysed withsaturation obs log(k ) obs pH pH g log(k ) obs log(k ) obs pH pH h POC4SOC POC4SOC catalysis by acids and bases Specific acid catalysis + kobs= k o + k + HO[ ⋅3 ] HO3 General acid (ga) catalysis + k=obs k + o k + HO ⋅[ 3 ] +kga, i[ga ⋅] i HO3 ∑ i Specific base catalysis − k k k− OH obs= o +OH [ ⋅ ] General base (gb) catalysis − k= k + k− ⋅OH +k gb ⋅ obs o OH [ ] ∑ gb, i[ ] i i NJB POC4SOC Specific acid catalysis rate law • Rapid protonation resulting in a pre-equilibrium • The pre-equilibrium is followed, at some stage, by the rate determining step • The rate determining step does not involve proton transfer • Deviations from linearity will be found for reactions where increasing extent of protonation (with increasing concentration of acid) leads to saturation, i.e. full protonation of the substrate. NJB POC4SOC Specific acid catalysis molar Gibbs energy NJB POC4SOC Rapid pre-equilibrium protonation H OCH -1 OCH 3 fast, Ka,2 3 slow, k1 + OCH3 +H3O OCH3 +H2O H -C3OH H H 12 OCH 3 fast H O H 2 These equations are true even for 3 protonation reaching saturation. However, for such systems, the d[] P =k1 [] ⋅2 rate law is better expressed in dt terms of a total reactant -1 + concentration of [1]+[2]. 2[]=Ka,2 ][ ⋅ 1HO[ ⋅ 3 ] d[] P =k ⋅ K- ⋅1 []1 HO ⋅[ + ] k =[]1 HO ⋅[ ⋅ + ] dt 1 a,2 3 obs 3 NJB POC4SOC Rapid protonation vs catalysis • Kinetic models analogous to specific acid catalysis are used for all reactions involving a rapid equilibrium preceding the rds – e.g. other catalytic species • kobs contains “contributions” of all steps up to and including the rds NJB POC4SOC General acid catalysis • Mechanisms giving rise to general acid catalysis: – Rate determining proton transfer – Rapid protonation of the substrate in a pre-equilibrium followed by rate determining deprotonation at a different site by any base – Rate determining acid assisted nucleophilic attack NJB POC4SOC Rate determining proton transfer d[] P + =k ⋅obs []1 ={ k + HO ⋅[ 3 ] k +AH []AH ⋅} []1 ⋅ dt HO3 + −3 2 . 08 Hk=obs O ⋅[ 13 .] + 78 ⋅ 10[ ⋅3 2 CH] CO H NJB J. Chem. Soc. B, 1967, 53-57 POC4SOC rate-determining H-transfer & KIE standard molar Gibbs energy NJB POC4SOC Solvent kinetic isotope effects + + “D3O is a stronger acid than H3O because the O-H bond in + H3O is the floppiest heavy-atom-to-proton bond in H2O- + solutions and the same is true for D3O in D2O-solutions. This means that the isotope effect on all other heavy-atom-to-proton + bonds is larger than that on the O-H and O-D bonds in H3O + and D3O , respectively. As a result, for protonation, equilibria in D2O (for identical strong acid concentration, i.e. when pD=pH) lie further towards protonated substrate: pKa(D2O)>pKa(H2O)” NJB POC4SOC Solvent kinetic isotope effects Empirically, potential wells for X-L bonds are typically narrower + than the potential well for the O-L bond in L3O -1 / kJ mol G This contradicts intuition which suggests that potential wells should be narrower for stronger (bond energy) bonds. NJB POC4SOC SKIE and specific acid catalysis molar Gibbs energy NJB POC4SOC Solvent kinetic isotope effects • In the case of general acid and general base catalysis, proton transfer in the rds is accompanied by a normal isotope effect: kH2O>kD2O. + SKIE kH2O/kD2O = 2.95, H3O as general acid (J.Chem.Soc.B, 1967,53-57) • In specific acid and base catalysis, the proton transfer step is not the rds; one needs to know the effect of isotopic exchange on equilibrium constants. H OCH -1 OCH 3 fast, Ka,2 3 + OCH3 +H3O OCH3 +H2O H H 12 SKIE kD2O/kH2O ~ 3 (Chem.Rev., 74, 581-603) NJB POC4SOC Summary • Eyring plot yields activation parameters; support (or not) proposed mechanisms • Kinetic isotope effects provide information on rds and/or equilibrium protonation • The rds of a reaction can depend on conditions NJB POC4SOC • Many of these aspects may seem difficult to take into account when designing experiment. In fact, one often gets things “wrong” the first (and second …) time around; this is why POC typically involves a series of experiments to check mechanistic predictions and often involves an “evolution” of a mechanistic description with increasing availability of data. NJB.