9b - Michael Polanyi 1891-1976 Henry Eyring 1901-1981...

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1 Dudley R. Herschbach 1932- Yuan T. Lee 1936- John C. Polanyi 1929- Henry Eyring 1901-1981 Michael Polanyi 1891-1976 Eugene Wigner 1902-1995 Hendrik Kramers 1894-1952 Rudolph A. Marcus (1923- ) What happens on a molecular scale when a chemical reaction takes place?
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2 An elementary bimolecular reaction in the gas phase The simplest possible chemical reaction: BB AA HH +→ B A R B A R () B A VR The atomic configuration can be described in terms of one coordinate (the internuclear distance). Hence, the potential energy can be described on a 2D plot. The next simplest possible chemical reaction: A CC A H H H H +→+ B A R C B R C A R General collision geometry The atomic configuration can be described in terms of three independent coordinates (the internuclear distances). Hence, the potential energy can be described on a 4D plot, which is hard to visualize… B A R C B R B B RR R = + Colinear collision geometry The atomic configuration can be described in terms of two independent coordinate. Hence, the potential energy can be described on a 3D plot, which can be visualized!
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3 The potential surface for the co linear reaction A CC BB A H H H H HH + →+ B A C H H H + Reaction coordinate Potential energy 1 36.8 kJ mol B A C H H H + 1 432 kJ mol C A B H H H + + B A C H H H Reaction dynamics (bimolecular gas phase reactions) A collision between the reacting molecules is necessary, but not sufficient , for a reaction to take place. Only a small fraction of collisions is reactive. Reactive collisions must involve sufficient (relative) kinetic energy for overcoming the activation energy barrier involved in forming the transition state from reactants to products. ( ) () e x p / aA P EE ER T >≈ Arrhenius law: exp / A kA T
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4 [] [] 2 1 2 Goal: To find an explicit expre Consider the simple bimolecular el ssion for the rate constant . Str ementary re ategy: Employ the kinetic theory of gas P Rate es AA action: + law: . d Ak A dt k =− 22 2 AA The total number of binary Assume that molecule can be des - collisions per unit time cribed as a h per unit volu ard sphere me: 8 Z of di 2 2 ameter . 2 BB kT NN N dv d d Vm V A d mV ππ π ⎛⎞ == = ⎜⎟ ⎝⎠ () r2 AA AA 2 The total number of reactive c is the molecular mass of A ollisions per unit time per / is the number of m unit volume: Z olecules per uni Z exp( / ) 2 exp( / t volume . B B A A aa A A B m k N T Ek T A dE k V m −= = 2 ) A N T V [] 2 A 2 2 The reaction rate constant A Two A molecules are consumed per reactive collision: 1 Z2 e x 11 2e p( / ) 2 1 xp( 2 /) 2 B aB B Aa B A A A A A k A Nd N d E k T dN N A NV d t m dt V m V d d =⇒ = ⎝⎝ ±²²²²²³²²²²²´ 2 2 exp( / ) ; 2 ; B A A A a B N Z N d m E k A t = = = The expression we obtained for the rate constant has the form of Arrhenius law (proposed by Arrhenius in 1889 based on empirical evidence).
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9b - Michael Polanyi 1891-1976 Henry Eyring 1901-1981...

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