( ) Reac%on Rates and Temperature N A. = exp ΔE /k N B. Boltzmann law: At higher temperatures, more molecules have enough energy to react.

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1 eac%on ates and Temperature Boltzmann law: B A ( ) = exp ΔE /k B T! B E A At higher temperatures, more molecules have enough energy to react. Thus, reac;on rates increase with temperature:

2 Arrhenius Equa%on The Arrhenius equa;on (1889) describes the ratetemperature rela;onship empirically:! k = A exp ( E /k T ) a B similar to Boltzmann distribu;on analagous to van t Hoff equa;on (1884), which describes equilibrium constants vs. temprerature: ΔG 0 = ΔH 0 TΔS 0 = T lnk lnk = ΔH0 T + ΔS0 K = exp ΔH0 T + ΔS0! See J. Chem. Educ. 1967, 44, 755 for more details on this deriva;on.

3 eac%on ates and Temperature ate does not increase exponen;ally, despite the appearance of this graph:! k = A exp ( E /k T ) a B rate approaches an asymptote of A graph merely looks exponen;al for small temperatures, which coincides with typical experimental condi;ons J. Chem. Educ. 1998, 75, 1186

4 Eyring Equa%on Eyring (1935) used transi;on state theory to describe rate vs. temperature: κ: transmission coefficient (normally 1) k =κ k T B! h exp ( ΔG /T ) decompose into enthalpy and entropy terms: k = k T B h! ΔH exp T + ΔS barriers for elementary reac;ons are always posi;ve (J. Chem. Educ. 2013, 90, 1024)

5 Determining Ac%va%on Parameters Kine;cists like straight lines, so the linearized Eyring equa;on is: ln k T = ΔH! PloZng ln k/t vs. 1/T will yield a straight line: 1 T + ΔS + ln k B h The slope is related to the entropy and the intercept is related to the enthalpy.

6 Determining Ac%va%on Parameters To get enthalpy and entropy directly: ln! kh k B T = ΔH 1 T + ΔS. H H enthalpy (slope): 29.5 kcal entropy (1000*intercept): eu

7 Error Analysis The intercept occurs when 1/T = 0 (i.e., infinite temperature). Because this amounts to a large extrapola;on, it might appear that the entropy is unreliable: ln! kh k B T = ΔH 1 T + ΔS intercept = entropy slope = enthalpy this is an ar;fact of lineariza;on (see Poe ew J. Chem. 2005, 29, 759) in reality, finding enthalpy and entropy mean determining curvature, not extrapola;ng

8 Error Analysis This graph shows the effect of a 1 eu uncertainty in the entropy, assuming the best fit enthalpy: -7.3 eu rate const. (s -1 ) best fit -8.3 eu -9.3 eu temperature (K) Clearly, the uncertainty in the entropy is much less than 1 eu.

9 Interpreta%on of Eyring Parameters bimolecular reactions unimolecular fragmentations H Et H H 26 eu H H H 6 eu H H H H H Me +4.5 eu Cl +10 eu H 3 C +11 eu C 2 Et unimolecular rearrangements Cl H 3 C 31 eu I PhS 17 eu 1.4 eu 7 eu H 45 eu 32 eu 14 eu 7 eu bimolecular reac;ons: ac;va;on entropy is nega;ve due to the loss of transla;onal entropy cost of bringing together two molecules: roughly 810 kcal/mol, or roughly 30 eu. (see J. Chem. Educ for the calcula;on) Anslyn and Dougherty, page 373 Houk J. Phys. Chem. A. 2003, 107,

10 Effec%ve Molarity What is the benefit of performing a reac;on intramolecularly?! Define the effec;ve molarity : EM = k intra s 1 k inter ( ) ( M 1 s 1 ) = M anhydride formation C 2 Me C 2 Me C 2 Me C 2 H C 2 H C 2 H 3 x 10 9 M 6 x M 4 x M lactonization H H H C2 H C 2 H C 2 H 4 x 10 4 M 7 x 10 6 M 2 x M etherification Ms Ms Ms 6.6 x 10 3 M 2.0 x 10 7 M 5.7 x 10 9 M Kirby Adv. Phys. rg. Chem

11 ing Closure Galli and Mandolini EJC , JACS , JACS H 3 C H 3 C Br k inter Br k intra ring closures are productlike, so the rate is controlled by ring strain and entropy small rings are disfavored due to restricted rotors medium rings are disfavored due to transannular interac;ons

12 ing Closure Galli and Mandolini EJC , JACS , JACS H 3 C H 3 C Br k inter Br k intra effec;ve molarity is highest for 4, 5, and 6membered rings, where entropy only par;ally compensates for unfavorable enthalpy rate of large ring forma;on is controlled mostly by chain entropy

13 Mechanis%c Fingerprints Sanford JACS intramolecular? XBz ionic reductive elimination Pd BzX Pd BzX intermolecular? XBz + XBz + Pd(II) X solvent effect: iden;cal rates in benzene (nonpolar) and acetone (polar) Hammeg (on benzoate): ρ = 1.36, indica;ng benzoate is a nucleophile cf. ρ = for C bond forma;on from Pt(IV) crossover: none no incorpora;on of exogenous acetate Eyring: S = +4.2 eu (DMS), 1.4 eu (chloroform) typical ionic reduc;ve elimina;ons: 13 to 49 eu (sensi;ve to solvent ordering) this mechanism is unlikely

14 Mechanis%c Fingerprints Pd BzX direct reductive elimination should not be affected Pd BzX + XBz X intramolecular Pd dissociation should be affected Pd BzX XBz X other mechanisms are kine;cally indis;nguishable Pd BzX Pd BzX increased rigidity of righthand complex should slow bogom mechanism, but not affect the top mechanism X X thus, bogom mechanism is proposed 4 75 C C

15 Ester Hydrolysis H (kcal) S (eu) S sie (eu) k H /k D (solvent) Stewart JACS H + H H + EtH H 3 C 2 H + ArH H + t-buh the similar parameters for the dinitro substrate reflect a compe;;on between the reduced reac;vity of vs. CF 3 and the increased reac;vity of the leaving group the tbutyl substrate hydrolyzes (in dilute acid) by expelling tbutyl ca;on, a unimolecular process (A AC 1) that is enthalpically unfavorable, but entropically favorable

16 Ester Hydrolysis H (kcal) S (eu) S sie (eu) k H /k D (solvent) Stewart JACS H + H H + EtH H 3 C 2 H + ArH H + t-buh in general, large solvent KIEs are interpreted enthalpically: proton transfer in the rds tbutyl case: small solvent KIE because nucleophilic addi;on is not the rds dinitro case: Eyring analysis shows a large entropic effect on the KIE from solvent ordering that lowers the apparent KIE