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Chapter 5 Gases

Chemistry: A Molecular Approach , 1 st Ed. Nivaldo Tro. Chapter 5 Gases. Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA. 2008, Prentice Hall. Air Pressure & Shallow Wells. water for many homes is supplied by a well less than 30 ft. deep with a pump at the surface

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Chapter 5 Gases

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  1. Chemistry: A Molecular Approach, 1st Ed.Nivaldo Tro Chapter 5Gases Roy Kennedy Massachusetts Bay Community College Wellesley Hills, MA 2008, Prentice Hall

  2. Air Pressure & Shallow Wells • water for many homes is supplied by a well less than 30 ft. deep with a pump at the surface • the pump removes air from the pipe, decreasing the air pressure in the pipe • the outside air pressure then pushes the water up the pipe • the maximum height the water will rise is related to the amount of pressure the air exerts Tro, Chemistry: A Molecular Approach

  3. Atmospheric Pressure • pressure is the force exerted over an area • on average, the air exerts the same pressure that a column of water 10.3 m high would exert • 14.7 lbs./in2 • so if our pump could get a perfect vacuum, the maximum height the column could rise is 10.3 m Tro, Chemistry: A Molecular Approach

  4. Gases Pushing • gas molecules are constantly in motion • as they move and strike a surface, they push on that surface • push = force • if we could measure the total amount of force exerted by gas molecules hitting the entire surface at any one instant, we would know the pressure the gas is exerting • pressure = force per unit area Tro, Chemistry: A Molecular Approach

  5. The Effect of Gas Pressure • the pressure exerted by a gas can cause some amazing and startling effects • whenever there is a pressure difference, a gas will flow from area of high pressure to low pressure • the bigger the difference in pressure, the stronger the flow of the gas • if there is something in the gas’s path, the gas will try to push it along as the gas flows Tro, Chemistry: A Molecular Approach

  6. Atmospheric Pressure Effects • differences in air pressure result in weather and wind patterns • the higher up in the atmosphere you climb, the lower the atmospheric pressure is around you • at the surface the atmospheric pressure is 14.7 psi, but at 10,000 ft it is only 10.0 psi • rapid changes in atmospheric pressure may cause your ears to “pop” due to an imbalance in pressure on either side of your ear drum Tro, Chemistry: A Molecular Approach

  7. The Pressure of a Gas • result of the constant movement of the gas molecules and their collisions with the surfaces around them • the pressure of a gas depends on several factors • number of gas particles in a given volume • volume of the container • average speed of the gas particles Tro, Chemistry: A Molecular Approach

  8. gravity Measuring Air Pressure • use abarometer • column of mercury supported by air pressure • force of the air on the surface of the mercury balanced by the pull of gravity on the column of mercury Tro, Chemistry: A Molecular Approach

  9. Common Units of Pressure Tro, Chemistry: A Molecular Approach

  10. Examples • A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg? • Convert a pressure of 23.8 in Hg to kPa

  11. Manometers • the pressure of a gas trapped in a container can be measured with an instrument called amanometer • manometers are U-shaped tubes, partially filled with a liquid, connected to the gas sample on one side and open to the air on the other • a competition is established between the pressure of the atmosphere and the gas • the difference in the liquid levels is a measure of the difference in pressure between the gas and the atmosphere Tro, Chemistry: A Molecular Approach

  12. Manometer for this sample, the gas has a larger pressure than the atmosphere, so Tro, Chemistry: A Molecular Approach

  13. Boyle’s Law • pressure of a gas is inversely proportional to its volume • constant T and amount of gas • graph P vs V is curve • graph P vs 1/V is straight line • as P increases, V decreases by the same factor • P x V = constant • P1 x V1 = P2 x V2 Tro, Chemistry: A Molecular Approach

  14. Boyle’s Experiment • added Hg to a J-tube with air trapped inside • used length of air column as a measure of volume Tro, Chemistry: A Molecular Approach

  15. Tro, Chemistry: A Molecular Approach

  16. When you double the pressure on a gas, the volume is cut in half (as long as the temperature and amount of gas do not change) Tro, Chemistry: A Molecular Approach

  17. Boyle’s Law and Diving if your tank contained air at 1 atm pressure you would not be able to inhale it into your lungs • since water is denser than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atm • at 20 m the total pressure is 3 atm Tro, Chemistry: A Molecular Approach

  18. Examples • A cylinder with a movable piston has a volume of 7.25 L at 4.52 atm. What is the volume at 1.21 atm? • A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2780 mL, what was it originally?

  19. Charles’ Law • volume is directly proportional to temperature • constant P and amount of gas • graph of V vs T is straight line • as T increases, V also increases • Kelvin T = Celsius T + 273 • V = constant x T • if T measured in Kelvin Tro, Chemistry: A Molecular Approach

  20. Charles’ Law – A Molecular View • the pressure of gas inside and outside the balloon are the same • at low temperatures, the gas molecules are not moving as fast, so they don’t hit the sides of the balloon as hard – therefore the volume is small Tro, Chemistry: A Molecular Approach

  21. Charles’ Law – A Molecular View • the pressure of gas inside and outside the balloon are the same • at high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – causing the volume to become larger

  22. Charles’ Law – A Molecular View • the pressure of gas inside and outside the balloon are the same • at high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder – causing the volume to become larger

  23. The data fall on a straight line. If the lines are extrapolated back to a volume of “0,” they all show the same temperature, -273.15°C, called absolute zero

  24. Examples • A gas has a volume of 2.57 L at 0.00°C. What was the temperature at 2.80 L? • The temperature inside a balloon is raised from 25.0°C to 250.0°C. If the volume of cold air was 10.0 L, what is the volume of hot air?

  25. Avogadro’s Law • volume directly proportional to the number of gas molecules • V = constant x n • constant P and T • more gas molecules = larger volume • count number of gas molecules by moles • equal volumes of gases contain equal numbers of molecules • the gas doesn’t matter Tro, Chemistry: A Molecular Approach

  26. Examples • A 0.225 mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L? • A chemical reaction occurring in a cylinder equipped with a moveable piston produces 0.621 mol of a gaseous product. If the cylinder contianed 0.120 mol of gas before the reaction and had an initial volume of 2.18L, what was its volume after reaction?

  27. By combing the gas laws we can write a general equation • Ris called the gas constant • the value of R depends on the units of P and V • we will use 0.08206 and convert P to atm and V to L • the other gas laws are found in the ideal gas law if • two variables are kept constant • allows us to find one of the variables if we know the other 3 Ideal Gas Law Tro, Chemistry: A Molecular Approach

  28. Examples • How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25°C? • An 8.50L tire is filled with 0.520 mol of gas at a temperature of 305K. What is the pressure in atm and mmHg of gas in the tire?

  29. Standard Conditions • since the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy – we call these standard conditions • STP • standard pressure = 1 atm • standard temperature = 273 K • 0°C Tro, Chemistry: A Molecular Approach

  30. Examples • A gas occupies 10.0 L at 44.1 psi and 27°C. What volume will it occupy at standard conditions?

  31. Molar Volume • solving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L • 6.022 x 1023 molecules of gas • notice: the gas is immaterial • we call the volume of 1 mole of gas at STP the molar volume • it is important to recognize that one mole of different gases have different masses, even though they have the same volume Tro, Chemistry: A Molecular Approach

  32. Molar Volume Tro, Chemistry: A Molecular Approach

  33. Density at Standard Conditions • density is the ratio of mass-to-volume • density of a gas is generally given in g/L • the mass of 1 mole = molar mass • the volume of 1 mole at STP = 22.4 L Tro, Chemistry: A Molecular Approach

  34. Gas Density • density is directly proportional to molar mass Tro, Chemistry: A Molecular Approach

  35. Molar Mass of a Gas • one of the methods chemists use to determine the molar mass of an unknown substance is to heat a weighed sample until it becomes a gas, measure the temperature, pressure, and volume, and use the ideal gas law Tro, Chemistry: A Molecular Approach

  36. Examples • Calculate the density of a gas at 775 torr and 27°C if 0.250 moles weighs 9.988 g • A sample of gas has a mass of 827 mg. Its volume is 0.270L at a temperature of 88oC and a pressure of 975 mmHg. Find its molar mass

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