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Chapter 11

Chapter 11. Gases. 1. Group Work - Describing gases. Describe a gas sample. Describe the position and motion of atoms/molecules in a sample. Gases assume the volume and shape of their containers. Gases are the most compressible state of matter.

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Chapter 11

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  1. Chapter 11 Gases 1

  2. Group Work - Describing gases • Describe a gas sample. Describe the position and motion of atoms/molecules in a sample. • Gases assume the volume and shape of their containers. • Gases are the most compressible state of matter. • Gases will mix evenly and completely when confined to the same container. • Gases have much lower densities than liquids and solids. 2

  3. Substances That Exist as Gases 3 3

  4. Pressure of a Gas • Pressure = force/area • Pa = N/m2 • 1 atm = 760 torr = 760 mm Hg = 101.3 kPa 10 miles 0.2 atm 4 miles 0.5 atm Sea level 1 atm 4

  5. Atmospheric Pressure • Atmospheric Pressure: pressure exerted by Earth’s atmosphere; measured by a barometer • Standard atmospheric pressure: column of mercury is 760 mm high at 0oC at sea level. • What is 475 mmHg in atm? 5

  6. Pressure of Gas • Which image shows Patm > Pgas?

  7. Kinetic Molecular Theory • What causes the observed ideal gas behavior? • Model of gases is Kinetic Molecular Theory • 1. A gas consists of tiny particles, either atoms or molecules, moving about at random. • low density and compressible • 2. Volume of particles is negligible compared to the total volume of the gas; most of the volume is empty space • Xe at STP, only 0.025% of the volume is occupied by the atoms 7

  8. Kinetic Molecular Theory • 3. Gas molecules move independently of one another • no intermolecular forces to attract atoms/molecules • 4. Pressure arises from collisions of atoms/ molecules with walls of containers • no net energy loss from collisions • pressure is proportional to number of moles • 5. Average kinetic energy (KE) is proportional to the Kelvin temperature (T) Gas Simulation 8

  9. Ideal Gas Law • Ideal gas: pressure-volume-temperature behavior can be accounted for by the ideal gas equation • Many gases behave ideally at 0oC and 1 atm • STP = Standard temperature (0oC = 273.15K) and pressure (1 atm) • Convert variables to Kelvin and atm to correctly solve problems • K = oC + 273.15; 1 atm = 760 torr • Ideal gases behave according to the Ideal Gas Law: PV = nRT http://mc2.cchem.berkeley.edu/Java/molecules/index.html

  10. Ideal Gas Law • We can calculate volume of 1 mole of gas at 0oC and 1 atm. How many molecules (or atoms) will be in this sample? • 1 mol = 22.414 L

  11. STP: OoC and 1 atm

  12. Gases at STP • What is the volume of 0.5068 g of nitrogen gas at STP? • How many grams of neon gas will occupy a volume of 1.0 L at STP?

  13. Pressure-Volume Relationship • What happens if the pressure on the outside of a balloon is increased? What happens to the atoms inside the balloon? • What causes the can to be crushed? Can crush Crushing can be scaled up a little!

  14. The Gas Laws: Pressure-Volume Bicycle Pump Boyle’s Law 14 http://preparatorychemistry.com/Bishop_Boyles_frames.htm

  15. Boyle’s Law Practice • Why does a bag of potato chips expand as you drive from Phoenix to Flagstaff? • If a closed bag holds 0.568 L of gas at 0.989 atm, what is the volume of the bag if the pressure is decreased to 0.822 atm? • P1V1 = P2V2 • V2 = 0.683 L

  16. Temperature-Volume Relationship • What happens if the balloon is slowly heated? What will happen to the atoms inside?

  17. The Gas Laws: Temperature-Volume • Charles and Gay-Lussac Balloons in LN2 17

  18. Charles’ Law Practice • If a balloon holds 3.97 L of gas at 2.0oC, what will the volume be if the temperature of the gas increases to 90.0oC? • V1/T1 = V2/T2 • V2 = 5.24 L

  19. Mole-Volume Relationship • What happens as more atoms are added to the balloon? Where have you experienced this before?

  20. The Gas Laws: Moles-Volume • Avogadro’s Law 20 Figure 9.9

  21. Avogadro’s Law Practice • If we have a closed container that holds 1.08 moles of gas with a volume of 16.7 L. What will be the new volume of the container if 0.65 more moles of gas are injected? • V1/n1 = V2/n2 • V2 = 26.8 L

  22. Gas Laws Summary • Boyle’s Law (T, n constant) • PV = constant P1V1 = P2V2 • Charles’ Law (P, n constant) • V / T = constant V1/T1 = V2/T2 • Avogadro’s Law (P, T constant) • V / n = constant V1/n1 = V2/n2 • Combined Gas Law (n constant) • P1V1 / T1 = P2V2 / T2 Pressure in basketball Gas Simulation http://mc2.cchem.berkeley.edu/Java/molecules/index.html 22

  23. Gas Laws Practice • Draw the level of the piston in (a) and (b) under the specified conditions.

  24. What would happen if we: Dec Vol Cons Atoms • increase the pressure of a container at constant temperature? • increase temperature at constant pressure? • increase the temperature at a constant volume? • Increase number of gas particles? Inc Temp Cons Vol Cons Vol Double Atoms http://www.mhhe.com/physsci/chemistry/essentialchemistry/flash/gasesv6.swf

  25. Practice Calcs - Which equation? • A small bubble rises from the bottom of a lake, (T = 8.0oC, P = 6.41 atm, V = 2.1 mL) to the water’s surface (T = 25.0oC, P = 1.02 atm). What is the final volume of the bubble? • If a closed cylinder holds 50.0 L of O2 gas at 18.5 atm and 21.0oC, what volume will the gas occupy if the temperature is maintained while the pressure is reduced to 1.00 atm? • The volume of a nitrogen cylinder is 11.28 L. What mass of nitrogen gas is in the cylinder if the pressure is 775 torr and the temperature is 5.3oC?14 mL; 925 L; 14 g N2

  26. Gas Stoichiometry • There are 2 methods for solving these problems. • If 2 variables in Ideal Gas Law are unknown, use stoichiometry first to find moles of gas (n) to plug into equation. • If only 1 variable in Ideal Gas Law is unknown, solve it first, then use moles of gas (n) in stoichiometry. • What is the volume of CO2 produced at 370 C and 1.00 atm when 5.60 g of glucose are used up in the reaction: C6H12O6 (s) + O2 (g) --> CO2 (g) + H2O (l) 26

  27. Gas Stoichiometry Practice • N2(g) + H2(g) NH3(g) • How many grams of ammonia can be made with 689 L of hydrogen and excess nitrogen at 350oC and 7.80 atm? • Answer: • How many L of O2 are needed to react 28.0 g NH3 at24°C and 0.950 atm? NH3(g) + O2(g)  NO(g) + H2O(g) • Answer: airbags 27

  28. Group Quiz #24 • What mass of solid sodium azide (NaN3) is needed to generate 75.2 L of nitrogen gas (and solid sodium) at 100.0oC and 1.00 atm? • (Hint: Start with a balanced chemical equation!)

  29. Further Applications • Gas densities (d), units of g/L • Use MM, P, R, and T to solve • Molar mass (MM), units of g/mol • Use d, P, R, and T to solve • Use units to arrange variables to solve for density and molar mass 29

  30. Practice Problem • Calculate the density of bromine gas at 50.0oC and 785.0 torr. Pouring Br2 30

  31. Practice Problem • An unknown diatomic gas has a density of 3.164 g/L at STP. What is the identity of the gas? • Answer: Cl2 31

  32. Dalton’s Law of Partial Pressures • Dalton’s Law of Partial Pressures: In a mixture of gases, each exerts a partial pressure the same as it would exert alone. 32

  33. Dalton’s Law of Partial Pressures • We can only measure the total pressure of a system • Knowing what fraction of moles belong to each gas, we can calculate their partial pressures. • Mole fraction: • XA = nA / (nA + nB) (moles of A ÷ total moles) • Calculating partial pressure: • PA = XA * PT (mole fraction * total pressure)

  34. Dalton’s Law of Partial Pressures

  35. Dalton’s Law of Partial Pressures • A mixture of gases contains 0.102 mol of CO, 0.598 mol of CO2, and 0.679 mol of O2. Calculate the mol fraction and partial pressures of the gases if the total pressure is 1.50 atm at room temperature. • Answers: • XCO = 0.0739; PCO = 0.111 atm • XCO2 = 0.434; PCO2 = 0.651 atm • XO2 = 0.492; PO2 = 0.738 atm

  36. Summary

  37. Diffusion/Effusion • Diffusion: gradual mixing of one gas with another (applet link) • Lighter gas diffuses more quickly than heavier gas • Effusion: escape of a gas through a pinhole (used to separate different mass species) effusion 37

  38. Speed vs. Temperature Avg KE of gas • Molecular Speeds depend on Temperature: 38

  39. Effusion and Diffusion • Which molecule will escape from a leaky balloon fastest? 39

  40. Group Work • Which gas in each pair below will effuse faster? • CH4 and N2 • O2 and CO2 • CO and NH3 • Cl2 and H2 • Kr and SO2

  41. The End

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