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Chapter 5 Gases

Chapter 5 Gases. Kim Shih Ph.D. Gases Pushing. Gas molecules are constantly in motion As they move and strike a surface, they push on that surface push = force

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Chapter 5 Gases

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  1. Chapter 5Gases Kim Shih Ph.D.

  2. 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

  3. The Effect of Gas Pressure • Gas flows from an area of high pressure to an area of 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 • Differences in air pressure result in weather and wind patterns • The higher in the atmosphere you climb, the lower the atmospheric pressure is around you

  4. Pressure Imbalance in the Ear If there is a difference in pressure across the eardrum membrane, the membrane will be pushed out – what we commonly call a “popped eardrum”

  5. The Pressure of a Gas • Gas pressure is a 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

  6. Gases and Gas Pressure

  7. gravity Measuring Air Pressure • We measure air pressure with abarometer • Column of mercury supported by air pressure • Force of the air on the surface of the mercury counter balances the force of gravity on the column of mercury

  8. Practice – What happens to the height of the column of mercury in a mercury barometer as you climb to the top of a mountain? • The height of the column increases because atmospheric pressure decreases with increasing altitude • The height of the column decreases because atmospheric pressure decreases with increasing altitude • The height of the column decreases because atmospheric pressure increases with increasing altitude • The height of the column increases because atmospheric pressure increases with increasing altitude • The height of the column increases because atmospheric pressure decreases with increasing altitude • The height of the column decreases because atmospheric pressure decreases with increasing altitude • The height of the column decreases because atmospheric pressure increases with increasing altitude • The height of the column increases because atmospheric pressure increases with increasing altitude

  9. Common Units of Pressure

  10. Brain Exercises

  11. A high-performance bicycle tire has a pressure of 132 psi. What is the pressure in mmHg? Convert 45.5 psi into kPa

  12. Manometers • The pressure of a gas trapped in a container can be measured with an instrument called a manometer • 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 pressures 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

  13. Manometer for this sample, the gas has a larger pressure than the atmosphere, so

  14. The Gas Laws Ideal Gas: A gas whose behavior follows the gas laws exactly. The physical properties of a gas can be defined by four variables: P pressure T temperature V volume n number of moles

  15. The Gas Laws ---- Boyle’s Law Pressure of a gas is inversely proportional to its volume Boyle’s Law PV = k constant n and T

  16. Boyle’s Law PinitialVinitial = PfinalVfinal

  17. Boyle’s Law: A Molecular View • Pressure is caused by the molecules striking the sides of the container • When you decrease the volume of the container with the same number of molecules in the container, more molecules will hit the wall at the same instant • This results in increasing the pressure

  18. Boyle’s Law and Diving • Because water is more dense 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 • If your tank contained air at 1 atm of pressure, you would not be able to inhale it into your lungs • you can only generate enough force to overcome about 1.06 atm Scuba tanks have a regulator so that the air from the tank is delivered at the same pressure as the water surrounding you. This allows you to take in air even when the outside pressure is large.

  19. Boyle’s Law and Diving • If a diver holds her breath and rises to the surface quickly, the outside pressure drops to 1 atm • According to Boyle’s law, what should happen to the volume of air in the lungs? • Because the pressure is decreasing by a factor of 3, the volume will expand by a factor of 3, causing damage to internal organs. Always Exhale When Rising!!

  20. = k V T The Gas Laws ---- Charles’ Law Volume is directly proportional to temperature Charles’ Law V α T constant n and P

  21. = Vinitial Vfinal Tinitial Tfinal Charles’ Law

  22. If you plot volume vs. temperature for any gas at constant pressure, the points will all 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

  23. Charles’s 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 • 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

  24. = Vinitial Vfinal = k ninitial nfinal V n The Gas Laws ---- Avogadro’s Law Volume directly proportional to the number of gas molecules Avogadro’s Law V α n constant T and P

  25. = Vinitial Vinitial Vfinal Vfinal Tinitial ninitial Tfinal nfinal The Gas Laws Summary Boyle’s Law: PinitialVinitial = PfinalVfinal Charles’ Law: Avogadro’s Law: =

  26. V V RT nR = = = k = k T n P P The General Gas Law Boyle’s Law: PV = nRT = k (n and T are constant) Charles’ Law: (n and Pare constant) Avogadro’s Law: (Pand T are constant) General Gas law: PinitialVinitial PfinalVfinal = ninitialTinitial nfinalTfinal

  27. L atm R = 0.082058 K mol The Ideal Gas Law Ideal Gas Law: PV = nRT R is the gas constant and is the same for all gases. T = 0 °C (273.15 K) Standard Temperature and Pressure (STP) for Gases P = 1 atm

  28. L atm 0.082058 K mol (273.15 K) (1 mol) nRT P (1 atm) The Ideal Gas Law What is the volume of 1 mol of gas at STP? V = = = 22.414 L

  29. Brain Exercises

  30. A gas occupies 10.0 L at 44.1 psi and 57 °F. What volume will it occupy at standard conditions? Calculate the volume occupied by 637 g of SO2 (MM 64.07) at 6.08 x 104 mmHg and –23 °C

  31. Density of Gas PV=nRT PV=(Mass/M.W.)RT P x M.W. = (Mass/V) RT PM=DRT Density is directly proportional to molar mass

  32. Density & Pressure • Pressure is the result of the constant movement of the gas molecules and their collisions with the surfaces around them • When more molecules are added, more molecules hit the container at any one instant, resulting in higher pressure • also higher density

  33. Calculate the density of a gas at 775 torr and 27 °C if 0.250 moles weighs 9.988 g Calculate the density of N2 at 125°C and 755 mmHg

  34. 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

  35. Calculate the molar mass of a gas with mass 0.311 g that has a volume of 0.225 L at 55°C and 886 mmHg What is the molar mass of a gas if 12.0 g occupies 197 L at 380 torr and 127 °C?

  36. Mixtures of Gases • When gases are mixed together, their molecules behave independent of each other • all the gases in the mixture have the same volume • all completely fill the container  each gas’s volume = the volume of the container • all gases in the mixture are at the same temperature • therefore they have the same average kinetic energy • Therefore, in certain applications, the mixture can be thought of as one gas • even though air is a mixture, we can measure the pressure, volume, and temperature of air as if it were a pure substance • we can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules

  37. Xi = Xi = Pi ni Moles of component Ptotal ntotal Total moles in mixture Partial Pressure and Dalton’s Law Dalton’s Law of Partial Pressures: The total pressure exerted by a mixture of gases in a container at constant V and T is equal to the sum of the pressures of each individual gas in the container. Ptotal = P1 + P2 + … + PN Mole Fraction (X) = or

  38. Lake Nyos

  39. Brain Exercises

  40. Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O2 at 298 K

  41. Collecting Gases • Gases are often collected by having them displace water from a container • The problem is that because water evaporates, there is also water vapor in the collected gas • The partial pressure of the water vapor, called the vapor pressure, depends only on the temperature • so you can use a table to find out the partial pressure of the water vapor in the gas you collect • if you collect a gas sample with a total pressure of 758.2 mmHg* at 25 °C, the partial pressure of the water vapor will be 23.78 mmHg – so the partial pressure of the dry gas will be 734.4 mmHg • Table 5.4*

  42. Collecting Gas by Water Displacement

  43. Vapor Pressure of Water

  44. 1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find mass O2. 0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.

  45. 2NaN3(s) 2Na(s) + 3N2(g) Stoichiometric Relationships with Gases The reaction used in the deployment of automobile airbags is the high-temperature decomposition of sodium azide, NaN3, to produce N2 gas. How many liters of N2 at 1.15 atm and 30.0 °C are produced by decomposition of 45.0 g NaN3? P, V, T of Gas A mole A mole B P, V, T of Gas B

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