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Gases Chapter 11

Gases Chapter 11. Tro, 2 nd ed. WHY WE STUDY GASES. Our atmosphere: thin layer surrounds us and is critical to life on earth 78% N 2 & 21% O 2 at sea level, plus CO 2 & water vapor & noble gases (next slide) POLLUTANTS: (see page 378) SO x & NO x cause acid rain

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Gases Chapter 11

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  1. GasesChapter 11 Tro, 2nd ed.

  2. WHY WE STUDY GASES Our atmosphere: thin layer surrounds us and is critical to life on earth 78% N2 & 21% O2 at sea level, plus CO2 & water vapor & noble gases (next slide) POLLUTANTS: (see page 378) SOx & NOx cause acid rain CFC's destroy O3 uv protective layer CO2 may increase global warming (some is necessary or we would cool too much at night)

  3. Average Composition of Dry Air Gas Volume Percent Gas Volume Percent N2 78.08% He 0.0005% O2 20.95% CH4 0.0002% Ar 0.93% Kr 0.0001% CO2 0.033% Xe, H2, and N2O Trace Ne 0.0018%

  4. BEHAVIOR & PROPERTIESOF GASES: - can be compressed greatly - can expand to fill container uniformly - have low density compared to liquids & solids - may be mixed - always homogeneous mixtures because always in motion - a confined gas exerts constant pressure on walls of its container uniformly in all directions

  5. The Kinetic-Molecular Theory KMT is based on the motions of gas particles. A gas that behaves exactly as outlined by KMT is known as an ideal gas. While no ideal gases are found in nature, real gases can approximate ideal gas behavior under certain conditions of temperature and pressure.

  6. Principle Assumptions of the KMT (similar to pages 343-344) • Gases consist of tiny atomic particles. • The distance between particles is large compared with the size of the particles themselves. • Gas particles have no attraction for one another.

  7. Principle Assumptions of the KMT • Gas particles move in straight lines in all directions, colliding frequently with one another and with the walls of the container. • No energy is lost by the collision of a gas particle with another gas particle or with the walls of the container. All collisions are perfectly elastic.

  8. Principle Assumptions of the KMT • The average kinetic energy for particles is the same for all gases at the same temperature, and its value is directly proportional to the Kelvin temperature. Although each gas particle (atom or molecule) moves with its own velocity, the average velocity of all the particles gives an average kinetic energy to a container of gases.

  9. GAS PROPERTIES: four quantities define state of a gas 1. Quantity in moles or mass 2. Temperature in Kelvin 3. Volume in Liters 4. Pressure in Atmospheres (usually) We already know about mass/moles, temperature & volume. Learn about pressure!

  10. PRESSURE Pressure = Force/unit area Force = mass*acceleration Force causes something to move a distance D in work. Gravity is a weak force, g F = m*g, units = Newtons or lbs Common English unit of pressure is lbs/in2 (psi)

  11. The pressure resulting from the collisions of gas molecules with the walls of the balloon keeps the balloon inflated.

  12. GAS PRESSURE The pressure exerted by a gas depends on: - the number of gas molecules present - the temperature of the gas - the volume in which the gas is confined

  13. The pressure exerted by a gas is directly proportional to the number of molecules present. V = 22.414 LT = 0.000oC

  14. Dependence of Pressure on Temperature The pressure of a gas in a fixed volume increases with increasing temperature. When the pressure of a gas increases, its kinetic energy increases. The increased kinetic energy of the gas results in more frequent and energetic collisions of the molecules with the walls of the container.

  15. A tube of mercury is inverted and placed in a dish of mercury. Mercury Barometer The barometer is used to measure atmospheric pressure. The atmosphere above us exerts a pressure, called atmospheric pressure, which is measured by a barometer as shown above.

  16. Memorize: 1 torr = 1 mm Hg 1 atm = 760 torr exactly 1 atm = 14.7 lb/in2 (psi) 1 atm = 33.9 ft water

  17. PRESSURE CONVERSION PRACTICE A storm is heralded by falling atmospheric pressure. The weather report says the pressure is down to 28.5 inches of Hg. Convert this to torr and atmospheres. 28.5 inches * 25.4 torr = 723.9 torr 1 inch 723.9 torr * 1 atm = 0.953 atm 760 torr Now convert 684 torr to mm Hg, atm and psi.

  18. Boyle’s Law At constant temperature (T), the volume (V) of a fixed mass of gas is inversely proportional to the Pressure (P). V = cb * 1/P, or V*P =cb P1V1 = cb = P2V2 P1V1 = P2V2 Memorize this!!!

  19. Graph of pressure versus volume. This shows the inverse PV relationship of an ideal gas.

  20. The effect of pressure on the volume of a gas.

  21. Boyle’s Law Problem An 8.00 L sample of N2 is at a pressure of 500.0 torr. What must be the pressure to change the volume to 3.00 L? (T is constant). First ask yourself if P will increase or decrease: V decreased, therefore P should increase. Second, rearrange Boyle’s Law: P2 = P1V1/V2 Third, plug in the data given: P2 = 500.0 torr * 8.00 L/ 3.00 L = 1333 torr (or 1.33 x 103 torr)

  22. Charles’ Law At constant pressure the volume of a fixed mass of gas is directly proportional to the absolute temperature. V = cc * T, or V/T = cc V1/T1 = cc = V2/T2 V1/T1 = V2/T2 Memorize this!

  23. Volume-temperature relationship of methane (CH4).

  24. Absolute Zero on the Kelvin Scale -273oC (more precisely –273.15oC) is the zero point on the Kelvin scale. It is the temperature at which an ideal gas would have zero volume.

  25. Effect of temperature on the volume of a gas. Pressure is constant at 1 atm. When temperature increases at constant pressure, the volume of the gas increases.

  26. Charles’ Law Problem A 255 mL sample of nitrogen at 75oC is confined at a pressure of 3.0 atmospheres. If the pressure remains constant, what will be the volume of the nitrogen if its temperature is raised to 250.oC? First, convert temperature to Kelvin ALWAYS! T1 = 75oC = 348 K T2 = 250.oC = 523 K Second, rearrange Charles’ Law V2 = V1T2/T1 Third, plug in data: V2 = 255 mL*523K/348K = 383 mL

  27. Gay-Lussac’s Law (added to chp) The pressure of a fixed mass of gas, at constant volume, is directly proportional to the Kelvin temperature. P = cg*T, or P/T = cc P1/T1 = cc = P2/T2 P1/T1 = P2/T2 Memorize this!

  28. Gay-Lussac’s Law Problem At a temperature of 40.oC an oxygen container is at a pressure of 2.15 atmospheres. If the temperature of the container is raised to 100.oC what will be the pressure of the oxygen? First convert to Kelvin: T1 = 40.oC = 313 K T2 = 100.oC = 373 K Second, write and solve the equation for the unknown: P2 = P1T2/T1 = 2.15 atm*373K/313K = 2.56 atm

  29. Standard Temperature and Pressure 273.15 K or 0.00oC Exactly 1 atm or 760 torr or 760 mm Hg or 14.7 psi or…

  30. Combined Gas Law A combination of Boyle’s, Gay-Lussac’s and Charles’ Law. P1V1 = P2V2 T1 T2 Used when pressure and temperature change at the same time while moles/mass is constant. Solve the equation for any one of the 6 variables

  31. Combined Gas Law Problem A sample of hydrogen occupies 465 ml at STP. If the pressure is increased to 950 torr and the temperature is decreased to –15oC, what would be the new volume? First convert to Kelvin: T1 = 273 K, T2 = 258 K Second, rearrange for V2 = P1V1T2/P2T1 Third, plug in data: V2 = 760 torr * 465 mL * 258 K = 352 mL 950 torr * 273 K

  32. Dalton’s Law ofPartial Pressures Each gas in a mixture exerts a pressure that is independent of the other gases present. The total pressure of a mixture of gases is the sum of the partial pressures exerted by each of the gases in the mixture. Ptotal = Pa + Pb + Pc + Pd + ….

  33. Dalton’s Law Problem A container contains He at a pressure of 0.50 atm, Ne at a pressure of 0.60 atm, and Ar at a pressure of 1.30 atm. What is the total pressure in the container? Ptotal = PHe + PNe+ PAr Ptotal = 0.5 atm + 0.6 atm + 1.30 atm = 2.40 atm (Yes, it’s that easy.)

  34. Collecting a Gas Sample Over Water The pressure in the collection container is equal to the atmospheric pressure. The pressure of the gas collected plus the pressure of water vapor at the collection temperature is equal to the atmospheric pressure.

  35. Oxygen collected over water.

  36. Dalton’s Law Problem (again) A sample of O2 was collected in a bottle over water at a temperature of 25oC when the atmospheric pressure was 760.0 torr. The vapor pressure of water at 25oC is 23.8 torr. What is the pressure of the O2 gas? Pt = 760.0 torr = PO2 + PH2O PO2 = 760.0 torr – 23.8 torr = 736.2 torr

  37. Avogadro’s Law Equal volumes of different gases at the same temperature and pressure contain the same number of molecules. (Section 11.7) V is directly proportional to n, where n is moles (if at same T & P) V1/n1 = Ca = V2/n2 V1/n1 = V2/n2 Memorize this!

  38. Avogadro’s Law Problem If 0.500 moles of CO2 occupies 11.2 Liters, what volume will 0.670 moles of CO2 occupy at the same T & P? V2 = V1n2/n1 = 11.2 L * 0.670 mol/0.500 mol = 15.0 L

  39. IDEAL GAS LAW PV = nRT R = Ideal Gas Constant = 0.082057 L-atm/mol-K MEMORIZE THIS R VALUE AND UNITS!

  40. Ideal Gas Law Problem A balloon filled with 5.00 moles of helium gas is at a temperature of 25oC. The atmospheric pressure is 750. torr. What is the balloon’s volume? Convert T to K = 25oC + 273 = 298K Convert pressure to atmospheres: 750. torr (1 atm/760 torr) = 0.987 atm Rearrange: V = nRT/P = 5.00 mol(0.082057 L-atm/mol-K)298K 0.987 atm = 124 L

  41. Another Ideal Gas Law Problem A big balloon of H2 has a volume of 3.20 x 104 L, T is 20.0°C, P = 750.0 torr. How many moles of gas are in the balloon? n = PV RT = (750.0 torr/760 torr/atm) * 3.20 x 104 L 0.082057 L.atm/mol.K * 293.15 K = 1.31 x 103 moles of H2 gas

  42. PRACTICE WITH IDEAL GAS LAW: • What pressure will 1.00 mol H2 exert in a 250.0 mL container at 27oC? (98.5 atm) • What pressure will 1.00 mol H2 exert in a 250.0 mL container at 327oC? (197 atm) • What volume will 2.00 mol H2 exert if P is 98.5 atm and T is 27oC? (0.500 L)

  43. SUPER-COMBINEDGAS LAW Rearrange Ideal Gas Law to R = PV/nT At first set of conditions R = P1V1/n1T1 At second set R = P2V2/n2T2 Set them equal to each other: P1V1 = P2V2 n1T1 n2T2 This can be used to find any of the four simple gas laws.

  44. GROUP WORK: Derive Boyle’s Law, Charles’ Law, Gay-Lussac’s Law, and Avogadro’s Law from the super-combined gas law.

  45. Mole-Mass-Volume Relationships Volume of one mole of any gas at STP = 22.414 L. 22.414 L at STP is known as the molar volume of any gas.

  46. 22.414L

  47. Standard Molar Volume Problem The density of neon at STP is 0.900 g/L. What is the molar mass of neon? (0.900g/L)(22.414L/mol) = 20.2 g/mol

  48. Density of Gases grams liters

  49. Density of Gases depends on T and P

  50. Gas Density Problem The molar mass of SO2 is 64.07 g/mol. Determine the density of SO2 at STP. D = (64.07 g/mol)(1mol/22.414 L) = 2.858 g/L at STP

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