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The Gas Laws

The Gas Laws. 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. Standard Atmospheric Pressure. One atmosphere is equal to 760 mm Hg, 760 torr, or 101.3 kPa (kilopascals).

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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

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