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Gases , Liquids , and Solids

Gases , Liquids , and Solids. Gases. Chapters 13.1 and 14. Kinetic Molecular Theory. “Particles of matter are always in motion and this motion has consequences.”. Kinetic Molecular Theory (for gases). Size Gases consist of large numbers of tiny particles, which have mass.

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Gases , Liquids , and Solids

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  1. Gases, Liquids, and Solids

  2. Gases Chapters 13.1 and 14

  3. Kinetic Molecular Theory “Particles of matter are always in motion and this motion has consequences.”

  4. Kinetic Molecular Theory(for gases) • Size Gases consist of large numbers of tiny particles, which have mass. The distance between particles is great.  Gas particles are neither attracted to nor repelled by each other.

  5. Kinetic Molecular Theory(for gases) Motion a) Gas particles are in constant, rapid, straight-line, random motion. They possess KE. b) Gas particles have elastic collisions (with each other and container walls) (no net loss of KE) e.g. elastic : pool balls (do not lose KE) inelastic: car crash (lose lots of KE)

  6. Kinetic Molecular Theory Energy 3. The average KE of the gas particles is directly proportional to the Kelvin temperature of the gas. (Reminder: KE = ½ mv2)

  7. Properties of Gases • very low density • (1/1000 that of solids or liquids) • indefinite volume, expand and contract • fluid • diffuse through each other • have mass • exert pressure • 1 mol at STP = 22.4 L (STP = 273 K, 1 atm)

  8. Effusion vs. Diffusion Effusion: escape rate of gas through a small opening Diffusion: one material moving through another – gases diffuse through each other

  9. Graham’s Law The kinetic energies of any two gases at the same temperature are equal: recall KE = ½ mv2

  10. Graham’s Law • Rate of gas effusion is related to MM of gas • KE= ½ mv2 • (m= molar mass, v=velocity (m/s) ) • ½ mava2= ½ mbvb2

  11. Practice Problems • The molar mass of gas "b" is 16.04 g/mol and gas "a" is 44.04 g/mol. If gas "b" is travelling at 5.25 x 109 m/s, how fast is gas "a" travelling? Both gases have the same KE. (3.17 x 109 m/s)

  12. Practice Problems 2.An unknown gas effuses through an opening at a rate 3.53 times slower than nitrogen gas. What is the molecular mass of the unknown gas? (349 g/mol)

  13. Gas Pressure • Pressure = Force/Area • Units • Force in N • Pressure in: • Pascals (N/m2) • Torr • mm Hg • atmospheres • Standard Pressure • 101.3 kPa • 760 torr • 760 mm Hg • 1 atm

  14. Units: Pascals: 1 Pa = 1 N/m2, 1 kPa = 1000 Pa mm Hg (or Torr) psi = lbs/in2 atm = atmospheres Standard Pressure @ sea level 1atm = 101.325 kPa = 760. mm Hg = 760. Torr = 14.7 psi

  15. Barometer • instrument used to measure atmospheric P, using a column of Hg • invented by Evangelista Torricelli in 1643

  16. Manometer • measures P of an enclosed gas relative to atmospheric P (open end) • Gas P = atmospheric P ± P of liquid in U-tube • Ask: Is the gas P higher or lower than atmospheric P? - If higher, add the pressure of the liquid to atm P. - If lower, subtract the pressure of the liquid from atm P.

  17. Manometer practice problems

  18. Manometer practice problems

  19. Dalton’s Law of Partial Pressures Ptotal= Pa + Pb + …

  20. Dalton’s Law Practice Problem A 1 L sample contains 78% N2, 21% O2 and 1.0% Ar. The sample is at a pressure of 1 atm (760. mm Hg). a) What is the partial pressure of each gas in mm Hg? b) What is the partial volume of each gas in mL?

  21. Application of Dalton’s Law Ptotal = total pressure (given) PH2O varies at different temperatures (see table…) Collecting gas by displacement of water

  22. Collecting Gas by Water Displacement The gas bubbles through the water in the jar and collects at the top due to its lower density. The gas has water vapor mixed with it. Ptotal = Pgas + PH2O Pdry gas = Ptotal – PH2O Ptotal is what is measured (= atmospheric P) PH2O can be found in standard tables of vapor pressure of water at different temperatures

  23. Vapor pressure of H2O at various temperatures Practice Problem: Hydrogen gas is collected over water at a total pressure of 95.0 kPa and temperature of 25oC. What is the partial pressure of the dry hydrogen gas? (A: 91.8 kPa)

  24. Mole Fraction • The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O2 present.  • The partial pressure of nitrogen was observed to be 590 mm Hg in air with a total atmospheric pressure of 760. mm Hg. Calculate the mole fraction of N2 present.

  25. Partial Pressure problems 1. Determine the partial pressure of oxygen (O2) collected over water if the temperature is 20.0oC and the total (atmospheric) gas pressure is 98.0 kPa. (95.7 kPa) 2. The barometer at an indoor pool reads 105.00 kPa. If the temperature in the room is 30.0oC, what is the partial pressure of the “dry” air? (100.76 kPa) 3. What is the mole fraction of hydrogen (H2) in a gas mixture that has a PH2 of 5.26 kPa? The other gases in the mixture are oxygen (O2), with a PO2 of 35.2 kPa and carbon dioxide with a PCO2 of 16.1 kPa. (0.0929)

  26. Describing Gases To describe a gas, you need: • Volume • Pressure • Temperature (K) • # particles (moles)  “Gas Laws”

  27. Constant Temperature What happens to P when V decreases? Constant Pressure What happens to V when T increases? Constant Volume What happens to P when T increases?

  28. Constant Volume and Temperature What happens to P when the # of particles is increased? Constant Temperature and Pressure What happens to V when the # of particles is increased?

  29. The Combined Gas Law What happens to a gas when various conditions are changed? The combined gas law includes Boyle’s,Charles’s, and Gay-Lussac’s Laws….

  30. Boyle’s Law (constant T) Demonstrates an inverse relationship between pressure and volume:

  31. Charles’s Law (constant P) Demonstrates a direct relationship between temperature and volume:

  32. Gay Lussac’s Law (constant V) Demonstrates a direct relationship between temperature and pressure

  33. Boyle's Law P1V1 = P2V2 The pressure on 2.50 L of anaesthetic gas is changed from 760. mm Hg to 304 mm Hg. What will be the new volume if the temperature remains constant? (6.25 L)

  34. Charles's Law V1 = V2 T1 T2 If a sample of gas occupies 6.8 L at 327oC, what will be its volume at 27oC if the pressure does not change? (3.4 L)

  35. Gay-Lussac's Law P1 = P2 T1 T2 A gas has a pressure of 50.0 mm Hg at 540. K. What will be the temperature, in oC, if the pressure is 70.0 mm Hg and the volume does not change? (483oC)

  36. Combined Gas Law P1V1 = P2V2 T1 T2 • If a gas has a pressure of 2.35 atm at 25oC, and fills a container of 543 mL, what is the new pressure if the container is increased to 750. mL at 50.1oC? (1.84 atm)

  37. Combined Gas Law • A sample of methane that initially occupies 250. mL at 500. Pa and 500. K is expanded to a volume of 700. mL. To what temperature will the gas need to be heated to lower the pressure of the gas to 200. Pa? (560. K)

  38. Ideal Gases • Based on kinetic molecular theory • Follows gas laws at all T and P • Assumes particles: - have no V  impossible - have no attraction to each other  if true, would be impossible to liquefy gases (e.g. CO2 is liquid at ³ 5.1 atm, < 56.6oC Real Gases • Because particles of real gases occupy space: • Follow gas laws at most T and P • At high P, individual volumes count • At low T, attractions count • The more polar the molecule, the more attraction counts  P decreases

  39. The Ideal Gas Law: PV = nRT • To describe a gas completely you need to identify: • V – Volume • P – Pressure • T – Temperature in K • n - # of moles The Ideal Gas Law: Can be used to derive the combined gas law Is usually used to determine a missing piece of information about a gas (requires the ideal gas constant R)

  40. Ideal Gas Law Most gases act like ideal gases most of the time. PV = nRT • P, V inversely related BOYLE • PT directly related GAY-LUSSAC • V, T directly related CHARLES • V, n directly related AVOGADRO R = universal gas constant

  41. R: The Ideal Gas Constant • Derived from ideal gas law using STP conditions: • standard temperature: 273K • standard pressure: 1 atm • volume of 1 mole of gas: 22.4 L The value of R depends on units of pressure used:

  42. Ideal Gas Law • Solve for R at STP: T = 0oC + 273 = 273 K; P = 1 atm R = PV = (1 atm)(22.4 L) = 0.0821 LŸatm nT (1 mol)(273 K) molŸK Note that the value of R depends on the units of pressure

  43. Ideal Gas Law Calculate the pressure, in atmospheres, of 1.65 g of helium gas at 16.0oC and occupying a volume of 3.25 L. P = ? PV = nRT V = 3.25 L n = 1.65 g (1 mol He) = 0.412 mol He 4.00 g He R = 0.0821 LŸatm/molŸK T = 16.0oC + 273 = 289 K P = nRT = (0.412 mol)(0.0821 LŸatm)(289 K) V 3.25 L molŸK = 3.01 atm

  44. Combined Gas Law Warmup • The volume of a gas-filled balloon is 30.0 L at 40oC and 153 kPa. What volume will the balloon have at STP? (A: 39.5 L) • A 3.50-L gas sample at 20oC and a pressure of 86.7 kPa expands to a volume of 8.00 L. The final pressure of the gas is 56.7 kPa. What is the final temperature of the gas, in oC? (A: 165oC, 438 K)

  45. Ideal Gas Law Practice • A sample of carbon dioxide with a mass of 0.250 g was placed in a 350. mL container at 127oC. What is the pressure, in kPa, exerted by the gas? (53.9 kPa)

  46. Ideal Gas Law Practice • A 500. g block of dry ice (solid CO2) vaporizes to a gas at room temperature. Calculate the volume of gas produced at 25oC and 975 kPa. (29.0 L CO2)

  47. Ideal Gas Law Practice • At what temperature will 7.0 mol of helium gas exert a pressure of 1.2 atm in a 25.0 kL tank? (5.2 x 104 K)

  48. Ideal Gas Law Practice • What mass of chlorine (Cl2) is contained in a 10.0 L tank at 27oC and 3.50 atm? Hint: begin by solving for n. (101 g)

  49. Density of Gases Measured in g/L (liquids and solids: g/mL) 1 mole of any gas = 22.4 L at STP (273 K and 1 atmosphere) You can use 22.4 L = 1 mol as a conversion factor at STP For non-standard conditions, use the ideal gas law.

  50. Finding Molar Mass of a Gas Using Its Density, at STP • What is the molar mass of a gas that has a density of 1.28 g/L at STP? (28.7 g/mol) • A 0.519 g gas sample is found to have a volume of 200. mL at STP. What is the molar mass of this gas? (58.1 g/mol) 3. A chemical reaction produced 98.0 mL of sulfur dioxide gas (SO2) at STP. What was the mass (in grams) of the gas produced? (0.280 g SO2)

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