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# Phys Chem Life Sci CHE 107B

UCD

GPA 3.76

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This 27 page Class Notes was uploaded by Mr. Cornell Weimann on Wednesday September 9, 2015. The Class Notes belongs to CHE 107B at University of California - Davis taught by James Ames in Fall. Since its upload, it has received 34 views. For similar materials see /class/191940/che-107b-university-of-california-davis in Chemistry at University of California - Davis.

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Date Created: 09/09/15

Thermodynamics vs Kinetics Chemical Reaction or Biological Process Keq BJA kkrev Thermo 107A kf A gt B kf forward rate constant Kinetics 1073 k rev Thermodynamics predicts how far a rxn proceeds Keq depends on stability between final amp initial state AG B Kinetics measures how fast kf in seconds or millenia g Rate depends on barrier height Ea o A A l B Time krev Keq BA oc expAG RT kf 0c expEaRT 104 Csdiamond Cscoal 23 1000 yrs Free Energy Glycolysis glucose gt pyruvate NADH Protein phosphorylation R ATP gt RP ADP Dephosphorylation RP H20 gt R Pi Rxn coordinate Kinetic Theory of Gases Ch 2629 Ch 2 Homework Problems 52 54 56 58 62 64 68 78 85 98 100 Thermal random energy motion Why study gases Gas properties Press Vol Temp relate to speed and energy of moving molecules hence kinetics Gas properties are easy to measure PV nRT Gas reaction kinetics modeled by molecular collisions A gt B rate oc of collisions amp collision speed Kinetics of ideal gas generalize to kinetics of biological reactions in dilute solution ie ideal soln lt1O393 M Ideal Gas Properties and States Pressure P Forcearea collisionsarea Pa or atm Volume V length Width height m3 or 0 Gas 4 A Temp T oc thermal energy Kelvin or K nz lmol n number of gas molecules moles P1atm R ideal gas constant 8314 J K397 mol397 T298 K 1 1 H4 3 9 008206 L atm K mol PV nRT Ideal gas law m4 I39800 A n lmol V002 39 P nRT V nRT a V P 395 D 8 E of gas molecules N in 1liter n PV 1 alm1 L RT 008206 L atm K 1 mol1 298 K 23 N 25 molecules N nNA 004 moles 246 x1022 molecules V 246gtlt10 7 m0 6 004 moles Kinetic Theory of Gases Question How do we describe macroscopic properties of a gas eg press vol or temp in terms of molecular motion ie speed and energy of individual molecules Work Energy PV nRT PV ac Energy ie motion of gas molecules Model Gas consists of large number of molecules far apart on average 1023 in 1liter Molecules have small size compared to distance from neighbor 200fold Collisions between molecules are elastic and random thermal energy kBT No interactions between molecules no attraction or repulsion Goal Derive an expression for Pressure and Temp in terms of average speed of individual molecules Velocity of a Molecule Velocity vector v Figure 31 Molecule moving in three dimensions Speed c is length of velocity vector 7 Velocity v of a molecule AdistanceAtime Projection of velocity v in the xy plane OA calculated using a2 b2 c2 2 2 2 OA 2 vx vy Length of velocity vector squared v2 2 v2 0A 1222 2 2 2 vxvyvz l2 2 2 c vxvyvz Gas Pressure vs Velocity Pressure P is Force per area P25 with AF A V V I 4 43 L Force F amp mimenAtum p of a molecule V After Before FmamEf p my Change of momentum due to collision 1 Appbefore Pa a ltva ltm vx Molecule moving along X hits wall Pressure P oc collision velocity vx Force and Velocity of a Gas Force mass X acceleration Time between collisions At dv mass x distance x time392 mass x velocity x time7 I l j 21 At tb e 7 7 7 momentum AP 2mvx efm a vx V time At At 1 equency ofcollisions is E E 7 vx Vx Force momentum divided by time ApAt F 2 2mvx mvi w 4 w a At 21 1 After Before vx 5 Force by N moleculeS39 vayg 4 2 gt lt I NFT PVwork amp Temp vs Velocity vai ms 91 2 E Z 1 Z vai Z vai After Before A 13 V f 2 K t TEE PV my f A N IdeaIGas Law NA Temperature T is a measure of molecular velocity vx 1 Velocity of a Gas in 3D Velocity vector v N Molecules of gas each have different velocities Average is MEANSQARE VELOCITY v2 ltv2gt 2 v12v3v32v2V v N 7 Isotropic 2 2 2 Vx Vy 2V2 2 motion PVwork vs Energy Pressure in 1D Isotropic gas in 3D 2 2 PV vax PV 2 vi 2 v 3 3 N 7 2N 1 2N PV mv mV2 Z Etrans 3 3 2 3 1 2 PV ENEtranS Elrans Emv 3 Average translational kinetic energy Kinetic Energy vs Temperature Ideal Gas Law PV nRT Kinetic Theory N 2 PVnRT RTNkBT PVZ NEtrcms NA 3 2 PV ENEfFClnS Efrans Kinetic Energy of ideal gas depends on kBT thermal energy Mean Velocity of Gas 3 1 Etrans EkBT 5171122 2 Temp is a measure of molecular velocity v m 2 3k T 3RT whereRNAkB andMmNA B V Vrms m M R 8314 J mol1 K1 M molar mass kgmol T temperature K RootMeanSquare Velocity of Air N2 The average rootmeansquare velocity of N2 molecule in air 1 R Ideal Gas constant J K391 mol39l v 2 My 2 PIC ET PIE kB RNA m m M M molar mass kgmol mNA T temperature K N2 gas molecules 28 gmol in air are moving at gt1000 miles per hour at T298K 3RT 2 3 8314J 4 1 1 298K 2 v X39 I Imo X 515msll46mph quotquotS MN2 002802kgmoz 2 1 J 1 kg 2 SCC 12 12 3k T 23 1 Vrms B 3xl38gtlt1026 K x298K ZSISmS21146mph m 465 x 10 cgmolecule N2 Molecular Velocity and Energy Large of molecules N 1023 in 1literat 298 K and 1 atm How do we calculate statistics for velocity and energy Statistics of Speed c and Energy E Maxwell Distribution Boltzmann Distribution fc a c2 eXp 21 0 exP kET C B C B 9 9 5 5 U U i i Speed C Energy E Probability c1 lt c lt c2 Probability E gt Ea 3 13 Id gtd E C C a d Ea fE dE explt kBT Mean Speed ltcgt Mean Energy ltEgt c E j cfcdc E E j EfEdE Maxwell Distribution of Speed 1 Fraction of molecules dNIN with speeds c to cdc 3 2 300 K g m dN 02 47rcz m e ZkBTdc J J fcdc N 271k N 01 Maxwell 3 quotml Distribution 5 16 m fc 47zv2 7 6 ET 272k Wm WM L i V o 2gtlt10a 4x103 6x103 8x103 1 Z Z Z cm ic1vxvyvz V y Mean Speed ltcgt mm 1 a w v velocity has a direction vector ltcgt 0 1 cfcdc 0 c speed no direction scalar Average Molecular Speed Eorcgt 2 ltCgt E Z I cf 6616 f C 47rcz2 ZT 3 mcz 3 m 2 3 4 m 2 1 6 4 27rkBT fee dc t k 2 m 2 I 2kBT 2 1 3 From Integral table 8036 e ax dx22 2 a In ourcase 612 andthus E 8kBT 8RT V 72m V 7Z39M where R NAkB and M mNA Root Mean Squared Speed crms 2 lt62gtI2CrmsIczfltcgtdc 2 fltcgt4 cf m 27rkBT 12 3 ch m E 00 4 2kBT crms 4n mj 0 c 6 dc 2 3 7 From integral table I80x4e X 01ng 5 a m In ourcase a ZkBT C 3kBT 3RT rms m M where R NAkB and M mNA Most Probable Speed c The most probable speed cm is determined by setting dfcdc O and solving for c mp 3 E mcz dfc O f c 4723962 m e ZkBT dc 27rkBT 3 dfc 47r m A26 H163 emc BT 0 dc 27rkBT kB T 2kBT 2RT Cmp most probable speed m M Maxwell Distribution of Molecular Speeds quotF RB314JK mol T 293 K 0 M 0032 kglmol 2 0ms 1171kg39m z 5 2 sec Calculate cmwzand arms for 02 0032 kglmol at 298 K 2X8 314x298K 8X8 314XZ9SK 7444 988 h cw Donkg 7393m57875mph c Moonkg m 5 mp 52gt w481ms1072mph 0032kg Square of Mean ltcgtz a Mean Squared 8 Maxwell Distribution f ltcgt 2 Igfcdc 3RT E 2 z lt52gtIowczf0dcV Mniacuiur Swan 2 SRT 3RT c 5 lt02 7 7 M M Per mole N 6022 x1023 Per molecule R 8314 J K391mol39i kE RINA 138 X 103923 J Kquot Tlemperaiure K Tlemperaiure K m molecular mass kgmolecule M molar mass kgmoi Kinetic Theory of Gases Summary 1 Molecular velocity vs Pressure Volume and Temperature 2 PVsz T R N k PV Nmltv gt gt2 3kBT PV R NM 3 m n NA6X1023mo391 kB 138 X 103923 J K391 2 Translational kinetic energy vs Temperature thermal energy kBT Etrans 3 PV 2 Etrans 3 Average molecular speed c SRT 3RT ZRT R 8314 J mol391 K1 c Crms Cmp T Temp K 7Z39M M M M molar mass kgmol 1J1kgm23392 Rate Depends on Collision Frequency ZAB and Boltzmann Factor eEaRT i Irlie Product Iquot P Rate of rxn of collisions per second X of collisions having E gt Ea ZAB oc area C density eXP39EaRT E 8RT mv2 7rM 2 2 2 2 2 cv 1vx vy vZ Molecular Collisions Chemical reactions can only take place if molecules collide v P 51 How often do gas molecules collide One molecule red moves through cylinder ndz I All other molecules are COH39Slon quot39 assumed stationary Molecule in motion Area quotle2 Collision Frequency Z1 Z1 depends on average speed E and density Collision Frequency Z1 Volume of cylinder X density of molecules For one molecule Z1 Time area X length 2 N 246gtlt1022 Volume of cylinder 7rd Xltcgttgt Number densn y V T 5 Z collisions 5391 Just 1N t V 7 4 21 7z4x10 10m25x102ms246x1025m 3 Collisiontube Z1 k 6 X109S1 at 298K Miss Molecule in motion I 109 Collisions by a single molecule in one second Relative Speed of Colliding Molecules What matters during binary collision is the relative speed of the two molecules ltCrel gt 90 collision is most likely Erelatz39ve 272 24ij 7T 21 xEZ1 J Endigj

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