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Lecture+2+-+Chemical+Kinetics

# Lecture+2+-+Chemical+Kinetics - Rate Depends on Collision...

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A + B Product E a Rate = (# of collisions per second) X (fraction collisions having E > E a ) exp(-E a /RT) Rate Depends on Collision Frequency (Z 11 ) and Boltzmann Factor (e -Ea/RT ) P Rate = { Z 11 (10 8 M s -1 ) } X { exp(-0/RT) } = 10 8 M/s 2 2 11 2 2 = V N c d Z π If every collision produces product, then Rate = 10 8 M/s (upper limit). Fastest reaction rate in solution is ~10 10 M/s for H + + OH - H 2 O

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Kinetic Theory of Gases Summary 3. Molecular Binary Collision Frequency (Z 11 or Z AB ) : 4. Rate of Gas Phase Reaction: ( ) 1 3 35 3 25 9 1 11 10 10 5 . 2 2 / 10 2 = × = = s m collisions m s collisions V N Z Z 1 8 11 10 s M Z Rate = (# of collisions per second, Z 11 ) X (exp(- E a /RT) Fastest rate = Z 11 X exp(-0/RT) = 10 8 M s -1 2. Average molecular speed (c) determined by Maxwell Distribution: M RT c rms 3 = M RT c mp 2 = R = 8.314 J mol -1 K -1 T = Temp (K) M = molar mass (kg/mol) 1 J = 1 kg m 2 s -2 = V N d c Z 2 1 2 π Mean free path ( λ ) = <c>/Z 1 = 640 Ǻ M RT c π 8 = 475 m/s 515 m/s 421 m/s 1. Molecular velocity and energy vs Pressure, Volume and Temp: 3 2 v Nm PV = 3 2 trans E N PV = T k E B trans 2 3 =