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Ch 10: Gases

Ch 10: Gases. Brown, LeMay AP Chemistry Monta Vista High School. Problem Set #8, 13, 18, 19, 24, 36, 42, 45, 58, 71, 73; Recommended #5, 16, 22, 60, 61, 83. 10.1: Characteristics of Gases. Particles in a gas are very far apart, and have almost no interaction.

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Ch 10: Gases

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  1. Ch 10: Gases Brown, LeMay AP Chemistry Monta Vista High School Problem Set #8, 13, 18, 19, 24, 36, 42, 45, 58, 71, 73; Recommended #5, 16, 22, 60, 61, 83

  2. 10.1: Characteristics of Gases • Particles in a gas are very far apart, and have almost no interaction. • Ex: In a sample of air, only 0.1% of the total volume actually consists of matter. • Gases expand spontaneously to fill their container (have indefinite volume and shape.) • http://chemconnections.org/Java/molecules/index.html • http://zonalandeducation.com/mstm/physics/mechanics/energy/heatAndTemperature/gasMoleculeMotion/gasMoleculeMotion.html

  3. 10.2: Pressure (P) • A force that acts on a given area • Atmospheric pressure:the result of the bombardment of air molecules upon all surfaces • 1 atm = 760 mm Hg = 760 torr = 101.3 kPa = 14.7 PSI 100 km

  4. Measuring pressure (using Hg) Barometer: measures atmospheric P compared to a vacuum • * Invented by Torricelli in 1643 • Liquid Hg is pushed up the closed glass tube by air pressure Evangelista Torricelli(1608-1647)

  5. Manometers: measure P of a gas • Closed-end:difference in Hg levels (Dh) shows P of gas in container compared to a vacuum http://www.chm.davidson.edu/ChemistryApplets/GasLaws/Pressure.html closed

  6. 2. Open-end: • Difference in Hg levels (Dh) shows P of gas in container compared to Patm

  7. 10.3: The Gas Laws Amadeo Avogadro (1776 - 1856) Robert Boyle(1627-1691) Jacques Charles (1746-1823) John Dalton (1766-1844) Joseph Louis Gay-Lussac(1778-1850) Thomas Graham(1805-1869)

  8. V V P 1/P 10.3: The Gas Laws • Boyle’s law:the volume (V) of a fixed quantity (n) of a gas is inversely proportional to the pressure at constant temperature (T). Ex: A sample of gas is sealed in a chamber with a movable piston. If the piston applies twice the pressure on the sample, the volume of the gas will be . If the volume of the sample is tripled, the pressure of the gas will be halved reduced to 1/3 Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aboyle.html

  9. V T Charles’ law • V of a fixed quantity of a gas is directly proportional to its absolute T at constant P. Extrapolation to V = 0 is the basis for absolute zero.  Ex: A 10.0 L sample of gas is sealed in a chamber with a movable piston. If the temperature of the gas increases from 50.0 ºC to 100.0 ºC, what will be the new volume of the sample? V = 11.5 L Animation: http://www.grc.nasa.gov/WWW/K-12/airplane/aglussac.html

  10. P T “Gay-Lussac’s law” • Seen as derivative of C’s and B’s laws • P of a fixed quantity of a gas is directly proportional to its absolute T at constant V. http://www.youtube.com/watch?v=Mytvt0wlZK8&feature=related

  11. V n Avogadro’s hypothesis • Equal volumes of gases at the same T & P contain equal numbers of molecules

  12. Combined gas law • Ex: A 10.0 L sample of gas at 100.0ºC and 2.0 atm is sealed in a chamber. If the temperature of the gas increases to 300.0ºC and the pressure decreases to 0.25 atm, what will be the new volume of the sample? V2 =120 L

  13. 10.4: The ideal gas lawhttp://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=25.msg167#msg167 • Used for calculations for an ideal (hypothetical) gas whose P, V and T behavior are completely predictable. R = 0.0821 L•atm/mol•K = 8.31 J/mol•K • Ex: How many moles of an ideal gas have a volume of 200.0 mL at 200.0ºC and 450 mm Hg? n = 3.0 x 10-3 mol

  14. = ( 1 . 000 atm ) V ( 1 . 000 mol )( 0 . 0821 )( 273 K ) • What is the V of 1.000 mol of an ideal gas at standard temperature and pressure (STP, 0.00°C and 1.000 atm) • V = 22.4 L (called the molar volume) • 22.4 L of an ideal gas at STP contains 6.022 x 1023 particles (Avogadro’s number)

  15. Do the following Partner Activity: • http://www.chm.davidson.edu/vce/GasLaws/GasConstant.html

  16. 10.5: More of the ideal gas law • Gas density (d): • Molar mass (M):

  17. 10.6: Gas Mixtures & Partial Pressures • Partial pressure: P exerted by a particular component in a mixture of gases • Dalton’s law of partial pressures:the total P of a mixture of gases is the sum of the partial pressures of each gas PTOTAL = PA + PB + PC + … (also, nTOTAL = nA + nB + nC + …)

  18. Ex: What are the partial pressures of a mixture of 0.60 mol H2 and 1.50 mol He in a 5.0 L container at 20ºC, and what is the total P? = + PH2 =(0.60)(0.0821)(293) / 5.0 = 2.9 atm PHe=(1.50)(0.0821)(293) / 5.0 = 7.2 atm PT = 2.9 + 7.2 = 10.1 atm

  19. Mole fraction (X): • Ratio of moles of one component to the total moles in the mixture (dimensionless, similar to a %) ∴ Ex: What are the mole fractions of H2 and He in the previous example?

  20. Collecting Gases “over Water”http://www.kentchemistry.com/moviesfiles/Units/GasLaws/gasoverwater.htm • When a gas is bubbled through water, the vapor pressure of the water (partial pressure of the water) must be subtracted from the pressure of the collected gas: PT = Pgas + PH2O ∴ Pgas = PT – PH2O • See Appendix B for vapor pressures of water at different temperatures.

  21. 10.7: Kinetic-Molecular Theory * Formulated by Bernoulli in 1738 Assumptions: • Gases consist of particles (atoms or molecules) that are point masses. No volume - just a mass. • Gas particles travel linearly until colliding ‘elastically’ (do not stick together). • Gas particles do not experience intermolecular forces. Daniel Bernoulli (1700-1782)

  22. 10.7: Kinetic-Molecular Theory • Two gases at the same T have the same kinetic energy • KE is proportional to absolute T urms = root-mean-square speedm = mass of gas particle (NOTE: in kg)k = Boltzmann’s constant, 1.38 x 10-23 J/K http://www.epa.gov/apti/bces/module1/kinetics/kinetics.htm#animate1 Ludwig Boltzmann (1844-1906)

  23. Maxwell-Boltzmann distribution graph http://intro.chem.okstate.edu/1314f00/laboratory/glp.htm James Clerk Maxwell (1831-1879)

  24. O2 at 273K O2 at 1000K H2 at 273K Number at speed, u Speed, u

  25. 10.8: Kinetic Energy and Gaseshttp://www.youtube.com/watch?NR=1&v=UNn_trajMFo • Since the average KE of a gas has a specific value at a given absolute T, then a gas composed of lighter particles will have a higher urms. m = mass (kg)M = molar mass (kg/mol)R = ideal gas law constant, 8.31 J/mol·K

  26. Effusion:escape of gas molecules through a tiny hole into an evacuated space • http://www.rkm.com.au/animations/GAS-effusion.html • Diffusion:spread of one substance throughout a space or throughout a second substance • http://sci-culture.com/advancedpoll/GCSE/diffusion%20simulator.html

  27. Graham’s lawhttp://www.youtube.com/watch?v=GRcZNCA9DxE • The effusion rate of a gas is inversely proportional to the square root of its molar mass r = u = rate (speed) of effusion t = time of effusion

  28. 10.9: Deviations from Ideal Behavior • Particles of a real gas: • Have measurable volumes • Interact with each other (experience intermolecular forces) • Van der Waal’s equation: a = correction for dec in P from intermolecular attractions (significant at high P, low T) b = correction for available free space from V of atoms (significant at high concentrations) Johannes van der Waals(1837-1923) or

  29. 10.9: Deviations from Ideal Behavior A gas deviates from ideal: • As the particles get larger (van der Waal’s “b”) • As the e- become more widely spread out (van der Waal’s “a”) The most nearly ideal gas is He.

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