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Derivation

Units. A.P. Chem. Ch. 5. mm, torr, atm, Pa, kPa, N/cm 2. Gases. Pressure: Force Area. C a P tot = P a. Dalton’s Law P tot = P a + P b…. Boyle’s Law PV=k. Charles’ Law V/T=k. Avog. Law V/n=k. Graham’s Law R a /R b = (MM b /MM a ) 1/2. Stoich. Devices. Barometer.

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Derivation

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  1. Units A.P. Chem. Ch. 5 mm, torr, atm, Pa, kPa, N/cm2 Gases Pressure: Force Area CaPtot= Pa Dalton’s Law Ptot= Pa+ Pb… Boyle’s Law PV=k Charles’ Law V/T=k Avog. Law V/n=k Graham’s Law Ra/Rb = (MMb/MMa)1/2 Stoich. Devices Barometer At STP 0.0821 L atm/mol K 8.31 J/ mol K Manometer 22.4 L = 1 mole PV= nRT The way we choose to view it Non- STP P = dRT/MM Due to Avogadro’s Hypothesis.` Derivation KMT P = 2 nNA1/2mu2 3V urms= (3RT/MM)1/2 P = 2 nKEper mol Dimensionless Pts. 3V The Way It Really Is. KEper mol = (3/2)RT In constant motion Colliding 100% elast. Particle interactions Creating pressure P= nRT – a(n/V)2 w/o influence In such a way that Temp is dir. Prop. To average KE. V-nb Volumes of particles

  2. Format of the Test • Option 1 – The marathon problem (1 system; many parts) 70 points • Option 2 – The regular test (single parts; many systems) 70 points • 13 multiple choice [~20 minutes] • 2 free response [~25 minutes] Problems to emphasize in your HW: 43, 61, 67, 83, 85

  3. The average kinetic energy of the gas molecules is • greatest in container A • greatest in container B • greatest in container C • the same for all three containers How would you calculate the average KE per mole of gas? Avg. KEmol = 1.5 (8.31 J/mol K) 300.K Avg. KEmol = 3740 J/mol

  4. The average velocity of the gas molecules is • greatest in container A • greatest in container B • greatest in container C • the same for all three containers How would you calculate the velocity of the methane gas? urms = [3(8.31J/mol K)(300. K)/0.016 kg]½ urms = 680 m/s

  5. The number of gas molecules is • greatest in container A • greatest in container B • greatest in container C • the same for all three containers How would you calculate the number of particles of ethane? n = (4.0 atm)(3.0L) (0.0821 L atm/mol K)(300. K) n = 0.49 mol

  6. The density of the gas is • greatest in container A • greatest in container B • greatest in container C • the same for all three containers How would you calculate the density of the ethane gas? d = (4.0 atm)(30. g/mol) (0.0821 L atm/mol K)(300. K) d = 4.9 g/L

  7. If the containers were opened simultaneously the diffusion rates of the gas molecules out of the containers through air would be • greatest in container A • greatest in container B • greatest in container C • the same for all three containers Calculate how much faster the methane diffuses compared to the ethane. (ratemeth/rateeth) = (30.g/mol/16g/mol)½ (ratemeth/rateeth) = 1.4 (times faster)

  8. Consider the production of water at 450. K and 1.00 atm: 2 H2(g) + O2(g) --- > 2 H2O(g) If 300.0 mL of hydrogen is mixed with 550.0 mL of oxygen, determine the volume of the reaction mixture when the reaction is complete. You Have: 300.0 mL of H2 550.0 mL of O2 You Need: Twice as many milliliters of H2 than O2 (from balanced reaction equation) Consequence: H2 is the L.R. Since H2 is the L.R. then 300.0 mL of it is used and only 150 mL of the O2 is used. (2:1 mole ratio can be viewed as 2:1 volume ration as well due to Gay-Lussac’s Law) Also, 300.0 mL of H2O will be produced. The reaction mixture remaining will be 700 mL in volume from the 300.0mL of water made and the 400.0 mL of O2 unused.

  9. amount H2/timeH2 √ UH2 MMI2 RateH2 timeI2 = = = UI2 MMH2 RateI2 timeH2 amount I2/timeI2 √ 52 s 253.8g = timeH2= 4.6 s timeH2 2.02 g

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