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- 1. General Reaction:aA + bB k cC + dD where k is a the Wait!! k is contant? NOT TRUE!!! “rate constant” Obviously k = f(T) General Rate Equations: 1) Separate variables 2) Apply approximations if necessary 3) Integrate over relevant limits ([A]o, ([B]o) 4) Algebreically solve for variable of interest ([A](t))Upadhyay
- 2. Jacobus Henricus van’t Hoff Svante August Arrhenius Proposed in 1884: Proposed in 1889: where A is the “pre-exponential factor” (A(T)) and Ea is the energy of activation. Awarded Nobel Prize in Chemistry in Awarded Nobel Prize in Chemistry in 1901: “in recognition of the 1903: "in recognition of the extraordinary services he has rendered by extraordinary services he has rendered to the discovery of the laws of chemical the advancement of chemistry by his dynamics and osmotic pressure in electrolytic theory of dissociation". solutions".Nobelprize.org
- 3. Max Trautz (1916)William Lewis (1918)Objective:To develop a model describing how the rate constant of a reaction varies withchanging temperature considering energetic collisions.General Assumptions:1) Molecules are hard spheres in temperature dependent translation.2) The molecules undergo collisions, and any collision with sufficient energy (E*) will result in a reaction.3) Concentration affects reaction rate due to it’s effects on collision rate.
- 4. b = “impact parameter” Impact Parameter:bmax = r1 + r2 Distance of closest possible approach of the center of the species involved in a collision. Reactant A -There exists some maximum impact parameter b above which a collision will not occur (bmax). Ie: r2 b > bmax no collision no reaction bmax r1 Reactant B b < bmax collision occurs reaction may occur if sufficient energy is transferred
- 5. Area of collision = π b2max = “hard-sphere cross section” v V (bmax, Δt) = (vΔt)π-Collision frequency (Z) per unit time and volume is given by: Z = π b2max<v>n1n2where n1 and n2 are proportional to the number of collision partners present (concetration).-Reactive cross section(σ) is the sum of the hard sphere cross sections of collision over timeand depends on the probability of a reaction having sufficient energy for a reaction to occur.
- 6. Maxium Energy Transfer in Collisionb=0 vb > bmax v No Energy Transfer in Collision
- 7. -The energy transfer of a collision (Et) depends v on the velocity of approach relative to the line of α centers of the collisional partners. b bmax vlc α -Relationships allow determination of vlc:The energy along the line of centers is given by (KE=1/2mv2): where μ is the reduced mass of the system.
- 8. -The energy transfer of a collision (Et) depends v on the velocity of approach relative to the line of α centers of the collisional partners. b bmax vlc α -Relationships allow determination of vlc:The energy along the line of centers is given by (KE=1/2mv2): where μ is the reduced mass of the system.
- 9. db Solve b Physical limits provide limits of integration P(Et,b) = 1 > E*Elc > E* Elc < E* REACTION! P(Et,b) = 0
- 10. The Maxwell-Boltzmann energy distribution: Reaction rate = k(Et)n1n2 where k(Et) = σ(Et)vt Mathematical relationship: and vt = (2Et/μ)1/2 Integrate & solve for k
- 11. -Rates predicted by collision theory trend higherthan experimental evidence indicates Non-reactive approach zoneAt least partially due to the “steric factor”:compensated for by introducing a constant (p): Reactive approach zone-Also, what about reaction order? Reactive 2 3 4 n Species: Possible 1 3 6 Collisions: Rate ≈ Z = π b2max<v>n1n2
- 12. Three Steps to Reaction: Activation: Dectivation: Decomposition: k1 k -1 k2 A+A A + A* A + A* A+A A* P Apply steady state conditions with respect to [A*] and then solve for rate of reaction: Reduce based on two pressurek -1 [A] >> k 2 limits.k 2 >> k -1 [A]
- 13. Four Steps to Reaction: Activation/Deacivation: k1 A+A A + A* k -1 Decomposition 1& 2: k2 A* A≠ A≠ P Adapted from R. A. Marcus, J. Chem. Phys. 43, 2658 (1965)AwardedNobel Prize in Fraction of molecules with energy between E andChemistry in E+dE is given by1956: "for [his]researches intothe mechanism Consider multiple internal degrees ofof chemical freedom (s):reactions.” Cyril N. Hinshelwood
- 14. Differentiate forIntegrate over limits range of energies between E and E + dE Replace to get expression of equilibrium proportion of molecules with energy between E and E + dE
- 15. 4 1 H-H eqEnergy (eV) 2 H-H (Å) 1 1.5 2.0 D-H (Å) 2 2 D-Heq 1Houston 2
- 16. Henry Eyring and John Polanyi (1931) Objective: To develop a model describing how the rate constant of a reaction varies with changing temperature considering unstable transition states.General Assumptions: John Polanyi1) An eqillibrium exists between the reactants “activated state (“transition state”) of a Awarded Nobel Prize in chemical reaction. Chemistry in 1986: for2) The difference in energy (Eact)between these his contributions two states must be supplied for the to the concerning the dynamics reaction for the it to form. of chemical elementary3) A certain vibrational degree of freedom processes“. exists that is necessarily active for the transition state to dissociate
- 17. General Reaction: X≠ C+D1 K≠ through A+B X≠ C+D [X≠] = K≠ [A][B] 3 vibrational mode v with Evib=hv=kbT. Gibb’s-Helmholtz Standard Relation: Enthalpy Change: ∆G∘ = ∆H∘ - T∆S∘ RT lnK = -∆G∘ 2 ∆H∘ = Eact
- 18. 2 Run the Reaction1 Preparation of select vibrational mode(s) Simple Infrared Excitation Stimulated Raman Excitation Infrared Multiphoton Excitation 3 Detection of Mode Vibrational Overtone Excitation Specific Products Stimulated Emission Pumping Photoacoustic Spectroscopy Resonance Enhanced Multiphoton Imaging (REMPI)
- 19. The selection rule for rotational state transitions is given by: ∆J = ±1The different energies of the allowed transitions lead to elaborate vibrational spectrum: Wiki
- 20. 1 2 Laser pulses shoot sample with infrared or near-ir frequency Sample heats up from radiation. the radiation, which activates modes of vibration and rotation. This in turn creates Photoacoustic pressure waves Spectrum in the air. 3 The pressure waves Fourier are detected as sound by a microphone. Transformhttp://www.shimadzu.com/an/ftir/support/ftirtalk/talk7/intro.html
- 21. Gas Flow Cell Window Microphone Buffer Gas Semipermiable Resonating Volumes Mirrors ChamberBraz. J. Phys. vol.32 no.2b São Paulo June 2002 Wiki PAS
- 22. Path A Length = LWiki
- 23. CalculatedTwo Endothermicity 1Possible CH3 + DCl 2200 cm-1Abstraction CH3D + Cl CH2D + HCl 1800 cm-1Pathways 2 Pathway 1 H Pathway 2 Cl D H Cl H
- 24. Calculated Potentials: In the thermal reaction, what would we expect the product distribution to be? “Primary Kinetic Isotope Effect” F r E e n q e u r e g n y c yG. D. Boone, F. Agyin, D. J. Robichaud, F.-M. Tao, and On these considerations, we expect theS. A. Hewitt, J.Phys. Chem. A 105, 1456 ~2001 major product to be CH2D in the absence of state specific vibrational excitation.
- 25. 1) A molecular beam was created using a 1:1:4 mixture of CH3D, Cl2, and He with a 660 torr backing pressure.2) Deuteromethane was vibrationally excited with 2.3 μm (4300 cm-1) laser pulses (excitation laser).3) Molecular chlorine was dissociated with a 355 nm laser pulse (dissociation laser).4) After a 200-250 ns delay, a 2+1 REMPI produces ions from either the CH2D or CH3 product (probe laser).5) Time-of-flight mass spectrometry detects products.Simultaneously, the laser beam is directed through a cell containing15 torr CH3D for collection of absorbtion spectrum tocomputationally verify vibrational assignments.
- 26. Action Spectra Monitors the generation of a product of a specific product over a range of vibrational excitation laser wavelengths. Provides information similar to photoacoustic spectroscopy. Allows determination of degree of generation of a specific product with respect to individual vibrational modes. REMPI Excitation Spectra Monitors the generation of multiple products through mass resolved spectrometric detection after REMPI. Allow determination of product distributions from vibrational mode specific reactants.
- 27. 6x Stronger Signal REMPI spectrum: J. Chem. Phys., Vol. 119, No. 9, 1 September 2003 6xWeaker Signal
- 28. 2v2 2v2 A1 E Symmetry Symmetry Parallel Transition Perpendicular TransitionJ. Chem. Phys., Vol. 119, No. 9, 1 September 2003
- 29. 1Houston 2

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