L21S07_KineticTheory 03-07-07

L21S07_KineticTheory 03-07-07 - Chem1A L21:...

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Unformatted text preview: Chem1A L21: "Kinetic Theory of Gases" Ideal Gas, Boyle, Constant T P Isothermal Compression, Expansion P C Previously PV=const PV= T2 T1 P const P= V T2 Compressibility =- 1 V V P B A C A B A L19-6 T1 V A.Pines,M.Kubinec,UCB V L14-2 UC Regents 1 A V Effect of T, Charles, Gay-Lussac GayV PV=nRT piV=niRT Gas 2 Gas 1 The Constants and Variables PV=nRT PV=nRT PV=nRT PV=nRT V=nRT PV=nR P = pressure in atmospheres Vm(STP)=22.4L V = volume in liters n = number of moles R = 0.08206 atm L K-1 mol-1 (8.314 J K-1 mol-1) T = absolute temperature in Kelvins UC Regents L19-10 T(K) = T(C ) + 273.15 STP = 1 atm, 273 K atm, T L14-5 A.Pines,M.Kubinec,UCB The Constants and Variables PV=nR PV=nRT PV=nRT PV=nRT PV=nRT V=nRT P = pressure in atmospheres Vm(STP)=22.4L V = volume in liters n = number of moles R = 0.08206 atm L K-1 mol-1 (8.314 J K-1 mol-1) T = absolute temperature in Kelvins 2001 A.Pines,M.Kubinec,UCB L21-2 Examples of T (K), Approach to Absolute Zero Sun Interior Sun Surface W Melt Point ~108 LN2 Boil Point ~104 LH2 Boil Point ~103 LHe Boil Point ~77 ~20 ~4 H2O Boil Point ~373 Dilution Fridge ~10-3 H2O Melt Point ~273 Laser Cooling ~10-6 CO2 Sublime Point ~195 Spin Temperature ~10-9 2001 A.Pines,M.Kubinec,UCB L21-3 A.Pines,M.Kubinec,UCB 1 Chem1A L21: "Kinetic Theory of Gases" ChemQuiz 20.2 An ideal gas in a 1 L balloon is heated from 100C to 200C 100 200 at 1 atm. What is the final atm. volume of the balloon? balloon? 1) < 2 L 2001 A.Pines,M.Kubinec,UCB 1L 1 atm 100C 100 2) 2 L 3) > 2 L L21-4 ChemQuiz 20.3 CH4 (g) + 2 O2 (g) CO2 (g) + 2 H2O (g) A mixture of 1.0 atm of CH4, and 2.0 atm O2 react in a 1 L flask at constant high T. What happens to the total pressure ? 1) increases 2001 A.Pines,M.Kubinec,UCB CH4 O2 2) same 3) decreases L21-6 Kinetic Theory of Gases Pressure,Energy and Temperature PV= 3 N0mv2 -- Ek T P(V, No, m, v) ~ Summary ~mv Average over v2 Momentum Transfer of collisions * Number unit t,A per ~ N0v V (frequency) -- N (mv2) = RT = 3 0 2 Ek -- N0mv2 3V Ek = 3 2 ek RT ek = 3 2 kBT UC Regents --=mean square speed v2 P= Per mole Per molecule L20-6 kB=R/N0 UC Regents L20-7 Root-Mean-Square Speed Root- Meanvrms= -- v2 = 3kBT = m 3RT 3RT M Distribution of Speeds vrms F(v) vrms Maxwell-Boltzmann MaxwellHigh T Low T Low m High m R=8.31 J/K mol kB=1.381 x 10-23 J/K UC Regents vrms~ T M L20-10 v UC Regents L20-14 A.Pines,M.Kubinec,UCB 2 Chem1A L21: "Kinetic Theory of Gases" Kinetic Theory of Gases gas consists of identical wellwellseparated particles (low number density) moving in random direction with a distribution of speeds move in straight lines between collisions collisions between particles or walls are elastic conservation of energy 2001 A.Pines,M.Kubinec,UCB L21-9 Kinetic Theory of Gases One Mole Ideal gas: P(V, N0, m, v) Momentum Transfer ~mv 2001 A.Pines,M.Kubinec,UCB L21-10 Kinetic Theory of Gases One mole ideal gas: P(V, No, m, v) Momentum Transfer ~mv 2001 A.Pines,M.Kubinec,UCB L21-11 A.Pines,M.Kubinec,UCB 3 Chem1A L21: "Kinetic Theory of Gases" Kinetic Theory of Gases One mole ideal gas: P(V, No, m, v) Momentum Transfer ~mv 2001 A.Pines,M.Kubinec,UCB L21-12 Kinetic Theory of Gases P(V, No, m, v) ~ Momentum Transfer of * Numberunitcollisions per t, A ~mv ~ N0v V (frequency) Average over v2 --=mean square speed v2 P= -- N0mv2 3V 2001 A.Pines,M.Kubinec,UCB L21-13 Pressure, Energy and Temperature PV= N0mv2 3 -- Ek T = Ek 2 3 N0 (mv2) -- = RT ek RT ek = 3 2 Ek = 3 2 kBT Per mole Per molecule kB=R/N0 2001 A.Pines,M.Kubinec,UCB L21-14 A.Pines,M.Kubinec,UCB 4 Chem1A L21: "Kinetic Theory of Gases" ChemQuiz 21.1 One mole each of Br2 and H2 are placed in a balloon. What are the relative kinetic energies ? Molar Mass H Br 1 80 Br2, H2 1) Br2 > H2 2001 A.Pines,M.Kubinec,UCB 2) Br2 = H2 3) Br2 < H2 L21-15 Root-Mean-Square Speed vrms= -- v2 = 3kBT = m 3RT 3RT M R=8.31 J/K mol kB=1.381 x 10-23 J/K 2001 A.Pines,M.Kubinec,UCB vrms~ T M L21-17 Distribution of Speeds vrms F(v) vrms Maxwell-Boltzmann MaxwellHigh T Low T F(v) proportional v2 e F(v) Low m High m -E/kBT E/k v (ms-1) 2001 A.Pines,M.Kubinec,UCB L21-18 A.Pines,M.Kubinec,UCB 5 Chem1A L21: "Kinetic Theory of Gases" ChemQuiz 21.2 What is the vrms (m/s) for Br2 at 300 K? K? 1) ~ 1 2001 A.Pines,M.Kubinec,UCB 2) ~ 10 3) ~ 100 L21-19 ChemQuiz 21.3 If y is vrms, what quantity is plotted on the x axis ? vrms x 1) T2 2001 A.Pines,M.Kubinec,UCB 2) T 3) T L21-21 ChemQuiz 21.4 Shown is the MB F(v) distribution at ~300 K for Br2 and X. What is X? Br2 vrms X vrms v Molar Mass Ne Ar Br Kr 20 40 80 83 1) Ne 2001 A.Pines,M.Kubinec,UCB 2) Ar 3) Kr L21-23 A.Pines,M.Kubinec,UCB 6 Chem1A L21: "Kinetic Theory of Gases" Lecture Complete 2001 A.Pines,M.Kubinec,UCB L21-25 A.Pines,M.Kubinec,UCB 7 ...
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