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CH104 Chapter 7 Gases

CH104 Chapter 7 Gases. Gases & Kinetic Theory Pressure Gas Laws. Elemental states at 25 o C. H. He. Solid. Liquid. Li. Be. B. C. N. O. F. Ne. Gas. Na. Mg. Al. Si. P. S. Cl. Ar. K. Ca. Sc. Ti. V. Cr. Mn. Fe. Co. Ni. Cu. Zn. Ga. Ge. As. Se. Br. Kr. Rb.

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CH104 Chapter 7 Gases

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  1. CH104 Chapter 7 Gases Gases & Kinetic Theory Pressure Gas Laws

  2. Elemental states at 25oC H He Solid Liquid Li Be B C N O F Ne Gas Na Mg Al Si P S Cl Ar K Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Ga Ge As Se Br Kr Rb Sr Y Zr Nb Mo Tc Ru Rh Pd Ag Cd In Sn Sb Te I Xe Cs Ba Ls Hf Ta W Re Os Ir Pt Au Hg Tl Pb Bi Po At Rn Fr Ra Ac Ce Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu Th Pa U Np Pu Am Cm Bk Cf Es Fm Md No Lr 6 - 2

  3. Changes of State Fast, far apart, Random Vapor Condense Vaporize Boiling Pt Moderate, close, Random arrangement Liquid Melting Pt = Freezing Pt Melt Freeze Slow, close, Fixed arrangement Solid

  4. Changes of State Vapor Deposit Frost Liquid Sublime Freeze Dry Solid

  5. Atmospheric Pressure We live at the bottom of an ocean of air Atmosphere: A sea of colorless, odorless gases surrounding the earth

  6. (in mole %) 78.08 % N2 20.95 % O2 0.033 % CO2 0.934 % Ar Atmosphere:

  7. Properties of matter Solids, liquids and gases can easily be recognized by their different properties. Density The mass of matter divided by it’s volume. Shape Is it fixed or take the shape of the container? Compressibility If we apply pressure, does the volume decrease? Thermal expansion How much does the volume change when heated?

  8. Density Shape Compressibility Fast moving, Low density, Expands to fill container Vapor Large compressibility, Expands w/ heat Moderate movement, Dense, Takes shape of container Small compressibility, Small heat expansion Liquid Small compressibility, Very small heat expansion Slow moving, dense, Fixed shape Solid

  9. Kinetic molecular theory of Gases Model to explain behavior of gases Vapor • 1. All gases are made up of tiny particlesmoving in • straight lines • in all directions • at various speeds.

  10. Kinetic molecular theory 2. Particles far apart have no effect oneach other. (Don’t attract or repel) • 3. V of a gas = • V of container • V of a gas is mostly empty space.

  11. KE T Kinetic molecular theory 4. Theave KE as theT (K.E. a T) • The average KE is the same for all gases atthe same T.

  12. E is conserved • when colliding with each other or container walls. For an Ideal Gas Collisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)

  13. E is conserved • when colliding with each other or container walls. For an Ideal Gas Collisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)

  14. Kinetic molecular theory 5. Gas molecules exert pressure as they collide with container walls The > the # of collisions (per unit time), the > the pressure

  15. Force Area Pressure = Force per unit of Area. P = Force Area In the atmosphere, molecules of air (N2, O2, Ar, H2O, etc..) are constantly bouncing off us.

  16. Atmospheric Pressure We live at the bottom of an ocean of air Atmosphere: A sea of colorless, odorless gases surrounding the earth

  17. Pressure At higher elevations, there is less air so the P is less.

  18. Boiling Point = Temp where molecules overcome atmospheric Pressure H2O 270 torr Mt. Everest(20,000’) = 73 oC 467 torr Mt. Evans,CO(14,000’) = 87 oC 630 torr Denver (5280’) = 95 oC 760 torr Sea Level = 100 oC

  19. Measuring Pressure Attempts to pump water out of flooded mines often failed because H2O can’t be lifted more than 34 feet.

  20. Measuring Pressure Torricelli believed reason was that P of atmosphere could not hold anything heavier than a 34’ column of water.

  21. Like drinking from a straw. Atmospheric Pressure What causes the liquid to move up the straw to your mouth ?

  22. Measuring Pressure The atmosphere would support a column of H2O > 34 feet high. 1 Atm 34’ column of water

  23. Torricelli Barometer Pressure of the atmosphere supports a column of Hg 760 mm high. 1 atm = 760 mm Hg 760 torr 29.92 in Hg 14.7 lb/in2 101,325 Pa vacuum 1 atm Mercury used because it’s so dense.

  24. Blood pressure (systolic over diastolic): most often in mm Hg. (ex. 120/80) Meteorologists refer to pressure systems in mm or inches of Hg. ex. 30.01 in

  25. STP Standard Temperature & Pressure 1 atm = 760 mm Hg 760 torr 29.92 in Hg 14.7 lb/in2 101,325 Pa 0oC 273K 1 atm

  26. Gas laws Laws that show relationships between volume and properties of gases Boyle’s Law Charles’ Law Gay-Lussac’s Law Combined Gas Law Avogadro’s Law Ideal Gas Law Dalton’s Law

  27. 1 P 1 P V  or PV = k or V = k Boyle’s law V is inversely proportional to P when T is constant. If P goes down V goes up V P P V P V

  28. Boyle’s law: V vs P P1V1= P2V2 2 L V2 = P2 = 0.5 Atm P1V1 = V2 P2 P1 = 1 Atm 1atm (1L) = 0.5 atm 2 L 1 L V1 =

  29. Boyle’s law: V vs P 2 L • Drive to top of mountain - ears start popping. • Breathing at high altitudes is more difficult because the pressure of O2 is less. 1 L

  30. Boyle’s law It all “Boyle’s” down to Breathing in and out.

  31. P T V Charles’s law: V vs T The volume of a gas is directly proportional to the absolute temperature (K). If T goes up V goes up

  32. Charles’s law: V vs T V1= V2 T1 T2 T2V1= V2 T1 V1 = 125 mL (546K)125 mL = 273 K 250 mL V2= T2 = 546 K T1 = 273 K

  33. Using Charles’ Law A balloon indoors, where the temp is at 27oC, has a volume of 2.0 liters. What will its volume be outside where the temperature is -23oC ? (Assume no change in pressure.) Convert all temps to the Kelvin. T1 = 27 + 273 = 300 K T2 = -23 + 273 = 250 K V1= V2 T1 T2 T2V1= V2 T1 =(250K)2.0 L = 300 K 1.7 L

  34. V P T Gay-Lussac’s Law (PT) Pressure of a gas is directly proportional to Absolute Temp (K) when Volume is constant P1= P2 T1 T2 If P goes up T goes up

  35. Gay-Lussac’s Law Example: an auto tire was inflated to a pressure of 32 psi when the temperature was -20ºC. After driving all day in a hot desert, the temperature of the tire has climbed to 60ºC. What is the pressure inside the tire? Assume the tire’s volume is fixed. P1= P2 T1 T2 P1 = 32 psi P2= ?? T2 = 60 + 273 = 333K T1 = -20 + 273 = 253K T2P1= P2 T1 =(333K)32 psi = 253 K 42 psi

  36. V T P P T V T P V Gas Laws P1V1 = P2V2 V1= V2 T1 T2 P1= P2 T1 T2 Boyle’s Charles’ Gay-Lussac’s

  37. V T P P T V P1V1 T1 P2V2 T2 = T P V Gas Laws Boyle’s Combined Gas Law Charles’ Gay-Lussac’s

  38. P1V1 T1 P2V2 T2 = T2P1V1 P2 T1 = V2 (240 K)(740 mm)(10 m3 ) (370 mm) (300 K) V2 = Combined Gas Law A 10 m3 balloon contains helium on the ground where the temperature is 27ºC and the pressure is 740 torr. Find the volume at an altitude of 5300 m if pressure is 370 mm Hg and temperature is -33 ºC. P1 = 740 mm P2 = 370 mm T1 = 27 + 273 = 300 K T2 = -33 + 273 = 240 K V1 = 10 m3 V2 = ? = 16 m3

  39. Boiling Point = Temp where Vapor Pressure (Pvap) of molecules overcome atmospheric Pressure H2O 270 torr Mt. Everest(20,000’) = 73 oC 467 torr Mt. Evans,CO(14,000’) = 87 oC 630 torr Denver (5280’) = 95 oC 760 torr Sea Level = 100 oC

  40. Avogadro’s law The volume of a gas is directly proportional to the number of molecules V1= V2 n1 n2 More moles of a gas, takes up more space.

  41. 1 mol He 4 g He 22.4 L 1 mol N2 28 g N2 22.4 L 1 mol CO2 44 g CO2 22.4 L 1 mol He 4 g He 22.4 L 1 mol N2 28 g N2 22.4 L 1 mol CO2 44 g CO2 22.4 L Avogadro’s law At Standard Temperature & Pressure (STP) V of 1 mole of gas = 22.4 liters At T = 273 K (0ºC) P = 1 atm (760 mm) Equal volumes of gas (at same T and P) contain equal numbers of molecules.

  42. Standard conditions (STP) When 36 g of liquid H2O is vaporized, what will be the volume of the gas? 1 mol 36g H2O 1 mole H2O 18 g H2O 22.4 liters 1 mole H2O = 44.8 L

  43. STP Example: What volume will 66 grams of CO2 occupy at STP? 66 g CO2 1 mole CO2 44 g CO2 22.4 liters 1 mole CO2 = 33.6 L

  44. The Ideal gas law V nT P V = RnT/P where R is a constant A combination of • Boyle’s, • Charles’ , • Gay-Lussac’s and • Avogadro’s Laws PV = nRT K Atm mol L L atm mol K

  45. The Ideal gas law R (the gas constant) can easily be determined from standard conditions. PV nT R = ( 1 atm ) ( 22.4 L) ( 1 mol ) ( 273 K) = 0.0821 atm-L mol-K R = =0.0821 atm-L mol-1 K-1

  46. The Ideal gas law • What is the volume of 2.00 moles of gas at • 3.50 atm and 310.0 K? • PV = nRT V = nRT • P • = (2.00 mol)(0.0821 L• atm)(310. K) • K . mol • (3.50 atm) = 14.5 liters

  47. The Ideal gas law PV = nRT moles n = grams = g_ molecular weight MW So: we can substitute for n. PV = g R T MW MW = g R T PV

  48. The Ideal gas law What is the molecular weight of a gas if 25 g of the gas occupies a volume of 15 liters at a pressure of .95 atm and a temperature of 50 ºC? (25g)(0.0821 L atm )(323 K) mol K (0 .95 atm)(15 L) MW = g R T = PV = 46.5 __g_ mol

  49. The Ideal gas law • can also be used with density of a gas Remember density = MW = g R T P V g V If the density of a gas is 1.75 _g_ L at 740 torr and 300 K, what is its MW? MW = d R T P

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