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The Gas Laws

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  1. The Gas Laws

  2. The Gas Laws • The gas laws describe HOW gases behave. • They can be predicted by theory. • The amount of change can be calculated with mathematical equations.

  3. Standard Atmospheric Pressure • Oneatmosphereis equal to 760 mm Hg, 760 torr, or 101.3 kPa (kilopascals).

  4. Standard Atmospheric Pressure • Perform the following pressure conversions. a) 144 kPa = _____ atm (1.42) b) 795 mm Hg = _____ atm (1.05)

  5. Standard Atmospheric Pressure • Perform the following pressure conversions. c) 669 torr = ______ kPa (89.2) d) 1.05 atm = ______ mm Hg (798)

  6. Standard Atmospheric Pressure • Air pressure at higher altitudes, such as on a mountaintop, is slightly lower than air pressure at sea level.

  7. Standard Atmospheric Pressure • Air pressure is measured using abarometer.

  8. Pressure and the Number of Molecules • More molecules mean more collisions between the gas molecules themselves and more collisions between the gas molecules and the walls of the container. • Number of molecules is DIRECTLY proportional to pressure.

  9. Pressure and the Number of Molecules • Doublingthe number of gas particles in a basketball doubles the pressure.

  10. Pressure and the Number of Molecules • Gases naturally move from areas of high pressure to low pressure because there is empty space to move in.

  11. If you double the number of molecules, 1 atm

  12. If you double the number of molecules, you double the pressure. 2 atm

  13. 4 atm • As you remove molecules from a container,

  14. 2 atm • As you remove molecules from a container, the pressure decreases.

  15. 1 atm • As you remove molecules from a container, the pressure decreases until the pressure inside equals the pressure outside.

  16. Changing the Size (Volume) of the Container • In a smaller container, molecules have less room to move. • The molecules hit the sides of the container more often, striking a smaller area with the same force.

  17. Changing the Size (Volume) of the Container • As volume decreases, pressure increases. • Volume and pressure are INVERSELY proportional.

  18. 1 atm • As the pressure on a gas increases, 4 Liters

  19. As the pressure on a gas increases, the volume decreases. 2 atm 2 Liters

  20. Temperature and Pressure • Raising the temperature of a gas increases the pressure if the volume is held constant. • At higher temperatures, the particles in a gas have greater kinetic energy.

  21. Temperature and Pressure • They move faster and collide with the walls of the container more often and with greater force, so the pressure rises.

  22. 300 K • If you start with 1 liter of gas at 1 atm pressure and 300 K and heat it to 600 K, one of 2 things happens.

  23. 600 K 300 K • Either the volume will increase to 2 liters at 1 atm,

  24. 600 K 300 K • or the pressure will increase to 2 atm while the volume remains constant.

  25. Ideal Gases • In this unit we will assume the gases behave ideally. • Ideal gases do not really exist, but this makes the math easier and is a close approximation.

  26. Kinetic Molecular Theory of Gases • Gas particles are much smaller than the spaces between them. The particleshave negligible volume. • There are no attractive or repulsive forces between gas molecules.

  27. Kinetic Molecular Theory of Gases • Gas particles are in constant, random motion. Until they bump into something (another particle or the side of a container), particles move in a straight line.

  28. Kinetic Molecular Theory of Gases • No kinetic energy is lost when gas particles collide with each other or with the walls of their container. • All gases have the same kinetic energy at a given temperature.

  29. Temperature • Temperature is a measure of the average kinetic energy of the particles in a sample of matter.

  30. Ideal Gases • There are no gases for which this is true. • Real gases behave more ideally at high temperature and low pressure.

  31. Ideal Gases • At low temperature, the gas molecules move more slowly, so attractive forces are no longer negligible. • As the pressure on a gas increases, the molecules are forced closer together and attractive forces are no longer negligible. • Therefore, real gases behave more ideally at high temperature and low pressure.

  32. Avogadro’s Law • Avogadro’s law states that equal volumes of different gases (at the same temperature and pressure) contain equal numbers of atoms or molecules.

  33. Avogadro’s Law • has the same number of particles as .. 2 Liters of Helium 2 Liters of Oxygen

  34. Avogadro’s Law • The molar volume for a gas is the volume that one mole occupies at 0.00ºC and 1.00 atm. • 1 mole = 22.4 L at STP (standard temperature and pressure). • As a result, the volume of gaseous reactants and products can be expressed as small whole numbers in reactions.

  35. Problem • How many moles are in 45.0 L of a gas at STP? 2.01 moles

  36. Problem • How many liters are in 0.636 moles of a gas at STP? 14.2 L

  37. Avogadro’s Law • V = K xn (K is some constant) • V / n = K • Easier to use: V1 V2 = n1 n2

  38. Example • Consider two samples of nitrogen gas. Sample 1 contains 1.5 mol and has a volume of 36.7 L. Sample 2 has a volume of 16.5 L at the same temperature and pressure. Calculate the number of moles of nitrogen in sample 2.

  39. Example V1 • Sample 1 contains 1.5 mol and has a volume of 36.7 L. Sample 2 has a volume of 16.5 L. Calculate the number of moles of nitrogen in sample 2. V2 36.7 L 16.5 L = n1 n2 1.5 mol n2 = 0.67 mol

  40. Problem • If 0.214 mol of argon gas occupies a volume of 652 mL at a particular temperature and pressure, what volume would 0.375 mol of argon occupy under the same conditions? V2 = 1140 mL

  41. Problem • If 46.2 g of oxygen gas occupies a volume of 100. L at a particular temperature and pressure, what volume would 5.00 g of oxygen gas occupy under the same conditions? V2 = 10.8 L

  42. Boyle’s Law • At Boyle’s lawstates that the pressure and volume of a gas at constant temperature are inversely proportional. • Inversely proportional means as one goes up the other goes down.

  43. Boyle’s Law

  44. Boyle’s Law • P x V = K (K is some constant) • P1 V1 = P2 V2

  45. Boyle’s Law • The P-V graph for Boyle’s law results in a hyperbola because pressure and volume are inversely proportional.

  46. P V

  47. Example • A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume?

  48. Example • First, make sure the pressure and volume units in the question match. • A balloon is filled with 25 L of air at 1.0 atm pressure. If the pressure is changed to 1.5 atm, what is the new volume? THEY DO!

  49. Example P1 • A balloon is filled with 25L of air at 1.0atm pressure. If the pressure is changed to 1.5atm, what is the new volume? V1 = P2 V2 V2 1.0 atm (25 L) 1.5 atm V2 = 17 L