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Understanding Gases: Characteristics, Pressure, and Laws

Learn the properties, measurement methods, and laws governing gases. Explore Boyle's, Charles', and Avogadro's laws, as well as the ideal gas law. Understand gas mixtures, partial pressures, and more. Partner activities included.

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Understanding Gases: Characteristics, Pressure, and Laws

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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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