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CHAPTER 10

CHAPTER 10. Properties of Gases. Evaporating gaseous globules emerging from pillars of molecular hydrogen gas in the Eagle Nebula (Hubble Space Telescope, 1995). http:// www.pangeaprogress.com/1/category/cosmos/1.html. States of matter. Solid Fixed shape Regardless of container shape

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CHAPTER 10

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  1. CHAPTER 10 Properties of Gases Evaporating gaseous globules emerging from pillars of molecular hydrogen gas in the Eagle Nebula (Hubble Space Telescope, 1995) http://www.pangeaprogress.com/1/category/cosmos/1.html

  2. States of matter • Solid • Fixed shape • Regardless of container shape • Liquid • Fixed volume • Conforms to container shape • Gas • Molecules move freely • Fills container • What else do you know about gases?

  3. Pressure • Pressure (P) = Force/Area • Pinternal & Pexternal are caused by gas molecules pushing on the walls of the container • In general, what if . . . • Pinternal = Pexternal • Pinternal < Pexternal • Pinternal > Pexternal

  4. Units of pressure SI unit? • Pa • atm • torr • bar • psi 1 atm = 760 torr = 101325 Pa = 1.013 bar =14.7 psi • Practice: If PO2 = 26.7 kPa, calculate this pressure in atm, torr, and psi = N/m2 = (kg•m/s2)/m2 = average atmospheric pressure at sea level = 1mm Hg = 105 Pa = lb/in2

  5. Barometer: measuring atmospheric gas pressure ∆h Patm

  6. Manometer: measuring experimental gas pressure “Closed” “Open”

  7. Gas laws • Variables: P, T, V, n • Any one can be determined by the other three • Hold two variables constant • Change one variable • Measure one variable • Three Laws • Boyle’s (P & V) • Charles’ (T & V) • Avogadro’s (n & V) Ideal gas law (P,T,V,n)

  8. Constant: T, n Change: P Measure: V Boyle’s Law • At constant temperature (T), the volume (V) occupied by a fixed amount of gas (n) is inversely proportional to the external pressure (P)

  9. Boyle’s Law • V  1/P • PV = constant • P1V1 = P2V2 http://www.grc.nasa.gov

  10. At constant: P, n Change: T Measure: V Charles’ Law • At constant pressure (P), the volume (V) occupied by a fixed amount of gas (n) is directly proportional to it absolute temperature in Kelvin (T)

  11. Charles’ Law • V  T • V/T = constant • V1/T1 = V2/T2 http://www.grc.nasa.gov

  12. At constant: T, P Change: n Measure: V Avogadro’s Principle • At fixed temperature in Kelvin (T), and pressure (P), equal volumes of any ideal gas contain equal numbers of moles (n) . . . or the volume of a gas is directly proportional to its number of moles. • V  n • V/n = constant • V1/n1 = V2/n2

  13. Ideal Gas Law PV = nRT • Combine • Boyle’s: PV = constant • Charles’: V/T = constant • Avogadro’s: V/n = constant • Therefore . . . PV/nT = constant • R is the universal gas constant • Solve for R using STP conditions • 1 atm • 22.4 L • 273 K • 1 mole • 6.02  1023 gas particles

  14. Using the Ideal Gas Law A weather balloon was measured at a pressure of 0.950 atm at 293 K, and its volume was 35.0 L. How many moles of an ideal gas are contained in the balloon? PV = nRT

  15. P1V1 P2V2 n1T1 n2T2 P1V1 n1T1 P2V2 n2T2 = = R = R More Ideal Gas Law • If . . . • And . . . • Then . . . PV = nRT

  16. Tips for solving gas law problems • Identify what variables are held constant • Identify what variables are changing • Ensure units are consistent (use Kelvin) • Rearrange ideal gas law to solve for missing variable • Predict change (/) and solve

  17. P1V1 P2V2 n1T1 n2T2 = Solving gas law problems Air trapped in a J-tube occupies 24.8 cm3 at 1.12 atm. By adding mercury to the tube, the pressure is increased to 2.64 atm. Assuming constant temperature, what is the new volume of air (in L)? PV = nRT 1atm = 1.01325x105 Pa

  18. Density • Mass / Volume • Gases are miscible, when thoroughly mixed • What does it look like if they are not mixed?

  19. More info on STP, density &molar volume 19

  20. How are density, molarity, molar mass & the ideal gas law related? • Density (m/V) • Rearrange PV = nRT • Molarity (n/V) • Rearrange PV = nRT • Molar mass (m/n) • Rearrange PV = nRT Lab 1: Molar mass of CO2

  21. Determining molar mass of a gas • As part of a rock analysis, a student added hydrochloric acid to a rock sample and observed a fizzing action, indicating a gas was being evolved. The student collected the sample of the gas in a 0.220 L bulb until its pressure reached 0.757 atm at a temperature of 25.0˚C. The sample weighed 0.299 g. What is the molar mass (and the possible identity) of the gas?

  22. Stoichiometry and gas law problems • Many chemical reactions consume or give off gases • The ideal gas law can be used to relate the volumes and amounts of substances in a given reaction • The next two slides contain pretty tough questions looking at this • Limiting reactant • Stoichiometry & fun dimensional analysis practice

  23. Reactions with gases(limiting reactant) • Ammonia and hydrogen chloride gases react to form solid ammonium chloride. A 10.0 L reaction flask contains ammonia at 0.452 atm and 22°C, and 155 mL of hydrogen chloride gas at 7.50 atm and 271 K is introduced. After the reaction occurs and the temperature returns to 22°C, what is the pressure inside the flask? • Note: neglect the volume of solid formed

  24. Reactions with gases(stoichiometry & dimensional analysis practice) • How many liters of molecular oxygen gas (measured at 740 mm Hg and 24°C) are consumed when burning 1.5 g of liquid octane, C8H18 (114.26 g/mol), to form carbon dioxide and water? • How many grams of octane (d = 703 g/L) does your car consume when you drive the speed limit on the freeway (60 mph) in 1.0 s, if you get 25 mpg and buy regular 87-grade gasoline? • Note: Assume 87-grade gasoline = 87 L octane per 100 L gasoline, 1 gallon = 3.79 L

  25. Gas mixtures • So far we have only discussed pure gases, now we are moving the discussion to gas mixtures? • All components occupy same volume • All components occupy same temperature • What about pressure?

  26. Dalton’s law of partial pressures • If we assume . . . • Homogenous mixture • Every gas behaves independently (i.e. no chemical interactions) • . . . then the total pressure of a mixture of gases is the sum of their individual partial pressures • Ptotal = PA + PB + . . .

  27. Partial pressure calculation • What is the total pressure of a gas mixture if PO2 = 159.12 torr, PN2 = 593.44 torr, and PAr = 7.10 torr

  28. Mole fraction • “Orange fraction” • The ratio of the number of a given component (oranges) to the total number of all components (fruit basket) • The ratio of the number of moles of a given component to the total number of moles of all components • At constant V & T:

  29. Gas movement • Diffusion: spontaneous movement of one gas through another (mixing) • Effusion: gradual movement of gas escaping through a hole in a vacuum • Rates are inversely proportional to the square roots of their molar masses (or densities)

  30. Kinetic molecular theory • Three postulates (assumptions) • Motion: particles travel in constant random straight-line motion except for collisions (i.e. no attraction/repulsion between particles) • Volume: particle size is tiny compared to the space between them, so their contribution to volume can be ignored • Collisions: particle collisions are elastic and are the cause of exerted pressure (no energy is lost by friction . . . Ek is constant and directly proportional to T)

  31. Real gases don’t always behave • Kinetic molecular theory is tends to be useful under “normal” conditions (i.e. room temperature and atmospheric pressure) • At extreme conditions, we may need to rethink our assumptions (e.g. high external pressure) • Motion: particles travel in constant random straight-line motion except for collisions (i.e. no attraction/repulsion between particles) • Volume: particle size is tiny compared to the space between them, so their contribution to volume can be ignored • Collisions: particle collisions are elastic and are the cause of exerted pressure (no energy is lost by friction . . . Ek is constant and directly proportional to T)

  32. Kinetic molecular theory(at extreme conditions, ↑Pext) • Rethink our assumptions • Motion: particles travel in constant random straight-line motion except for collisions (i.e. no attraction/repulsion between particles) • At high external pressure, account for intermolecular forces • Pcontainer < Ptotal • Add pressure related to intermolecular attractions

  33. Kinetic molecular theory(at extreme conditions, ↑Pext) • Rethink our assumptions • Volume: particle size is tiny compared to the space between them • At high external pressure, account for volume of particles • Vcontainer > Vfree space • Subtract volume of particles

  34. van der Waals equation • Accounts for volume of particles • Vcontainer > Vfree space • Subtract volume of particles • “-nb” • Accounts for intermolecular forces • Pcontainer < Ptotal • Add pressure related to intermolecular attractions • “+an2/v2” Note: a & b are experimentally derived constants

  35. The world from N2(g)’s perspective(at 21˚C & 1 atm) • Average speed: • 0.29mi/s • Mean free path (distance traveled between collisions): • 6.6x10-8m • Collision frequency (divide most probable speed by mean free path): • 7.1x109collisions/s

  36. Any questions?

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