Lecture+1+-+Kinetic+Theory+of+Gases

Lecture+1+-+Kinetic+Theory+of+Gases - Thermodynamics vs...

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Thermodynamics vs Kinetics Chemical Reaction or Biological Process: K eq = [B]/[A] = k f /k rev (Thermo, 107A) k f = forward rate constant (Kinetics, 107B) Thermo predicts how far a rxn proceeds (K eq ). State function depends on difference Δ G°). Kinetics measures how fast (k f in seconds or millenia). Rate depends on barrier and details of pathway . K eq = [B]/[A] exp(- Δ Gº/RT) k f exp(-E a /RT) C(s) diamond C(s) coal B A Time Conc Rxn coordinate Free Energy A B Δ E a A B k f k rev K eq ~ 10 4 1/k f ~ 1000 yrs A B k f k rev Glycolysis (glucose pyruvate + NADH) Protein phosphorylation (R + ATP R-P + ADP) Dephosphorylation (R-P + H 2 O R + P i )
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Kinetic Theory of Gases (Ch 2.6-2.9) Why study gases? Gas properties (pressure or volume) relate to speed of moving molecules (hence, kinetics). Gas properties are easy to measure (PV = nRT). Gas reaction kinetics modeled by molecular collisions: A B rate Kinetics of ideal gas generalize to kinetics of biological reactions in dilute solution (i.e. ideal soln: <10 -3 M). Ch 2 Homework Problems : 52, 54, 56, 58, 62, 64, 68, 78, 98, 100
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Ideal Gas Properties and States Pressure (P) = Force/area (collisions/area, Pa or atm) Volume (V) = length* width* height (m 3 or ) Temp (T) average speed of gas molecules n = number of gas molecules (moles) R = ideal gas constant = 8.314 J K -1 mol -1 = 0.08206 L atm K -1 mol -1 PV = nRT (Ideal gas law) Pressure V o l u m e P = nRT V V = nRT P n=1mol P=1 atm T=298 K V=24 ~800 Ǻ 4 Ǻ # of gas molecules (N) in 1-liter: moles K mol K atm L L atm RT PV n 04 . 0 ) 298 )( 08206 . 0 ( ) 1 )( 1 ( 1 1 = = = molecules mole moles nN N A 22 23 10 46 . 2 1 10 022 . 6 ) 04 . 0 ( × = × = = Liq (V=0.02 )
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Kinetic Theory of Gases Model: Gas consists of large number of molecules far apart on average (~10 23 in 1-liter). Molecules have small size compared to distance from neighbor (~1000-fold). Collisions between molecules are elastic and random (thermal energy = k B T). No interactions between molecules (no attraction or repulsion). Question: How do we describe macroscopic properties of a gas (e.g. press, vol or temp) in terms of molecular motion (i.e. speed and energy of individual molecules)? PV = nRT PV Energy (i.e. motion) of gas molecules Goal: Derive an expression for Pressure and Temp in terms of average speed of individual molecules. Work Energy
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Velocity of a Molecule 2 2 2 OA y x v v + = 2 2 2 2 2 2 z y x z v v v v OA v + + = + = Projection of velocity (v) in the xy plane (OA) calculated using a 2 = b 2 + c 2 : Length of velocity vector squared (v 2 ): Molecule moving in three dimensions Speed (c) is length of velocity vector ( v ): 2 2 2 z y x v v v c + + = Velocity (v) of a molecule = Δ distance/ Δ time
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This note was uploaded on 08/07/2011 for the course CHE 107B taught by Professor Ames during the Summer '11 term at UC Davis.

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Lecture+1+-+Kinetic+Theory+of+Gases - Thermodynamics vs...

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