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Chapter 5: Gases

Chapter 5: Gases. AP Chemistry. An Overview of the Physical States of Matter. The Distinction of Gases from Liquids and Solids. 1. Gas volume changes greatly with pressure. 2. Gas volume changes greatly with temperature. 3. Gas have relatively low viscosity.

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Chapter 5: Gases

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  1. Chapter 5: Gases AP Chemistry

  2. An Overview of the Physical States of Matter The Distinction of Gases from Liquids and Solids 1. Gas volume changes greatly with pressure. 2. Gas volume changes greatly with temperature. 3. Gas have relatively low viscosity. 4. Most gases have relatively low densites under normal conditions. 5. Gases are miscible.

  3. Figure 5.1 The three states of matter.

  4. Demos: Syringe Crush the Can Mustard Container Characteristics of Gases • Easily compressible • Expand to fill their container • Exert pressure • Mix easily with other gases

  5. Jan Baptiste von Helmont (Flemish—a Belgian region; 1580-1644) Used Scientific Method in attempt to determine the source of “food” for plants Concluded it is not soil or water, but a mysterious vapor present in the air (carbon dioxide) Thought the vapors were like the Greek concept of unshapen material Chaos  Flemish translation is GAS

  6. Pressure Force exerted over an area caused by the collisions of particles with the walls of the container Pressure depends on: 1) # of molecules 2) intensity of collisions

  7. How is Gas Pressure Measured? Evangalista Torricelli (student of Galileo) showed air exerts a pressure by supporting an inverted column of Hg

  8. 760mm Mercury Barometer http://umpgal.gsfc.nasa.gov/www_root/homepage/uars-science/UARS_brochure/JPEGs/barometer.jpg At sea level 1 atm = 760 mmHg = 760 torr = 101.3 kPa= 14.7 psi

  9. A mercury barometer. Figure 5.3

  10. Visualizing Atmospheric Pressure Demonstrations well plate glass plate 1000 ml flask w/ notecard glass tube with vial cap drink holder

  11. Force lbs = psi Pressure = P = Area in2 F N = Pa P = P = A m2 Calculating Pressure Blaise Pascal(French, 1623-1662) In a fluid at rest, the pressure is transmitted equally in all directions Units of Pressure: (1000 Pa = 1 kPa) atm mmHg = torr

  12. C B A D E F Relationship between Pressure, Force, & Area Exs of force over a small area? C, D & F Exs of force over a large area? A, B & E

  13. Otto von Guerick’s Experiment for the King of Prussia (Magdeburg, 1656)

  14. Robert Boyle (Ireland, 1627-1691) Investigated the relationship between the pressure and volume of a gas 1662 - New Experiments Physico-Mechanical, Touching the Spring of Air and its Effects 2nd Ed.

  15. Figure 5.5 The relationship between volume and the pressure of a gas. Eqn of line? V = k (1/P) k = VP (T, n cnst)

  16. Jaques Charles (August 27, 1783 - Paris) “The superstitious peasants, believing the balloon to be a monster attacking from the sky, proceeded to rip it to shreds with scythes and pitchforks.”

  17. A skeptical observer asked: “What is the usefulness of these experiments?” Benjamin Franklin who witnessed the flight responded: “ And how useful is a newborn baby?” Reaction of sulfuric acid and iron filings generates H2 gas

  18. Jaques Charles & Nicolas Robert Dec 1, 1783 Tuileries Garden 2 hour, 27 mile flight Fuel was burned onboard to inflate the balloon instead of employing H2 gas Charles asserts that it is heated air that keeps the balloon aloft rather than smoke (the idea was widely rejected)

  19. Figure 5.6 The relationship between volume and the temperature of a gas. Eqn of line? V = kT k = V/T (P, n cnst)

  20. Absolute Zero: Value = 0 K = -273 oC stops!!! Molecular Motion:

  21. Amonton’s / Gay-Lussac’s Law Pressure – Temperature Relationship

  22. Amadeo Avogadro equal volumes of all gases at the same temperature and pressure contain the same number of molecules NA = 6.02 X 1023 = 602, 000, 000, 000, 000, 000, 000, 000

  23. An experiment to study the relationship between the volume and amount of a gas. Figure 5.7

  24. V1 V1 P1 P2 V2 V2 = = = n1 T1 T1 n2 T2 T2 P V V = k T V T (K) V1 P1 = = k k T1 n1 P V n T (K) Gas Laws PV = k inverse n and T P and V P1V1 = P2V2 direct n and P V and T direct P and T n and V P and T n and V direct

  25. Gas Behavior at Standard Conditions STP (Standard Temperature and Pressure): 0 oC and 1 atm Molar Volume: Value = 22.4 L/mol Volume of 1 mole of gas at STP

  26. Standard Molar Volume Figure 5.8

  27. V1 n1 n2 V2 = = T1 V1 T2 V2 PV nT = k T1 n1 n2 T2 Ideal Gas Law We know: P1V1 = P2V2 Combine to get… P1V1 = P2V2 P V = n K T PV = nRT

  28. Universal Gas Law Constant, R R = 0.0821 L · atm /mol · K Sample Problem 5.5: A steel tank has a volume of 438 L and is filled with 0.885 kg of O2. Calculate the pressure of O2 at 21oC.

  29. More Sample Problems????

  30. Sample Problem 5.6 The piston-cylinders depicted below contain a gaseous reaction carried out at a constant pressure. Before the reaction, the temperature is 150K; when it is complete, the temperature is 300K. Which of the following balanced equation describes the reaction? (1) A2 (g) + B2 (g)  2AB (g) (2) 2AB (g) + B­2 (g)  2AB2 (g) (3) A (g) + B2 (g)  AB2 (g) (4) 2AB2 (g)  A2 (g) + 2B2 (g) Before 150K After 300K

  31. Density of a Gas PV = nRT PV = m/M RT m/V = d = MP/RT

  32. mass PV = M RT m RT m d = VP V d RT M = P The Molar Mass of a Gas n = M =

  33. Figure 5.11 Determining the molar mass of an unknown volatile liquid based on the method of J.B.A. Dumas (1800-1884)

  34. Volume of flask = 213mL T = 100.00C P = 754 torr Mass of flask + gas = 78.416g Mass of flask = 77.834g atm*L 0.0821 m RT 0.582g 373K x mol*K = 84.4g/mol VP 0.213L x 0.992atm Sample Problem 5.7 Finding the Molar Mass of a Volatile Liquid PROBLEM: An organic chemist isolates from a petroleum sample a colorless liquid with the properties of cyclohexane (C6H12). She uses the Dumas method and obtains the following data to determine its molar mass: Is the calculated molar mass consistent with the liquid being cyclohexane? PLAN: Use unit conversions, mass of gas and density-M relationship. SOLUTION: m = (78.416 - 77.834)g = 0.582g x M = = M of C6H12 is 84.16g/mol and the calculated value is within experimental error.

  35. Sample Problem 5.8: Finding Molar Mass of a Volatile Liquid An organic chemist isolates a colorless liquid from a petroleum sample. She uses the Dumas method and obtains the following data: Volume (V) of flask = 213 ml T = 100.0 oC Mass of flask + gas = 78.416 g P = 754 torr Mass of flask = 77.834 g Calculate the molar mass of the gas.

  36. Sample Problem A gas is known to be one of the following nitrogen oxides: NO, NO2, N2O4, or N2O. It has a density of 1.96 g/L at 0 oC and 1.00 atm. Determine its identity by finding its molar mass.

  37. Quiz A sample of methane gas having a volume of 2.80 L at 25oC and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31oC and 1.25 atm. The mixture was then ignited to form carbon dioxide and water. Calculate the volume of CO2 formed at a pressure of 2.50 atm and a temperature of 125oC.

  38. Dalton’s Law of Partial Pressure 1803—For a mixture of gases in a container, the total pressure exerted is the sum of the pressures each gas would exert if it were alone (Assume ideal gases—size of gas does not matter; no intermolecular forces between gas particles) Ptotal = dP1 + dP2+ dP3 +…

  39. 2/14 4/14 8/14 Mole Fraction, Χ X1 = n1/ntotX2 = n2/ntot Xgn = Xppl = Xor = Xgn = Xppl= Xor= P1 = X1Ptotal P2 = X2Ptotal Pgrn = Pppl = Por = 0.14 0.57 0.29 0.14 X 100 atm = 14 atm 0.29 X 100 atm = 29 atm 0.57 X 100 atm = 57 atm 2 4 8 Ptotal = 100 atm

  40. n1 n1 = ntotal n1 + n2 + n3 +... c1 = P1= c1 x Ptotal where c1 is the mole fraction

  41. Sample Problem 5.9: Applying Dalton’s Law of Partial Pressures • In a study of O2 uptake by muscle at high altitude, a physiologist prepares an atmosphere consisting of 79 mol% N2, 17 mol% 16O2, and 4.0 mol% 18O2. (The isotope 18O will be measured to determine the O2 uptake.) The pressure of the mixture is 0.75atm to simulate high altitude. Calculate the mole fraction and partial pressure of 18O2 in the mixture.

  42. Figure 5.12 Collecting a water-insoluble gaseous reaction product and determining its pressure.

  43. Sample Problem 5.10 • Acetylene (C2H2), an important fuel in welding, is produced in the laboratory when calcium carbide (CaC2) reaction with water: • CaC2(s) + 2H2O(l) C2H2(g) + Ca(OH)2(aq) • For a sample of acetylene that is collected over water, the total gas pressure (adjusted to barometric pressure) is 738torr and the volume is 523mL. At the temperature of the gas (230C), the vapor pressure of water is 21torr. How many grams of acetylene are collected?

  44. PROBLEM: The alkali metals [Group 1A(1)] react with the halogens [Group 7A(17)] to form ionic metal halides. What mass of potassium chloride forms when 5.25L of chlorine gas at 0.950atm and 293K reacts with 17.0g of potassium? PLAN: After writing the balanced equation, we use the ideal gas law to find the number of moles of reactants, the limiting reactant and moles of product. P = 0.950atm V = 5.25L 2K(s) + Cl2(g) 2KCl(s) 0.950atm T = 293K n = unknown = = 0.207mol PV x 293K RT 2mol KCl 2mol KCl atm*L 0.207mol Cl2 17.0g = 0.435mol K 0.0821 2mol K 1mol Cl2 mol*K mol K 39.10g K 74.55g KCl mol KCl Sample Problem 5.11 Using the Ideal Gas Law in a Limiting-Reactant Problem SOLUTION: x 5.25L n = Cl2 = 0.414mol KCl formed Cl2 is the limiting reactant. 0.435mol K = 0.435mol KCl formed 0.414mol KCl = 30.9 g KCl

  45. Another Gas Stoichiometry Problem? 1) The reaction that occurs to inflate a frontal impact air bag is: 2 NaN3 (s)  2 Na (s) + 3 N2 (g) How many grams of sodium azide are needed to produce 40.0 L of nitrogen to fill an air bag at a pressure of 1.30 atm and a temperature of 28.0 oC?

  46. Postulate 1: Particle Volume Postulate 2: Particle Motion Postulate 3: Particle Collisions Postulates of the Kinetic-Molecular Theory Because the volume of an individual gas particle is so small compared to the volume of its container, the gas particles are considered to have mass, but no volume. Gas particles are in constant, random, straight-line motion except when they collide with each other or with the container walls. Collisions are elastic therefore the total kinetic energy(Kk) of the particles is constant.

  47. Distribution of molecular speeds at three temperatures. Figure 5.14

  48. A molecular description of Boyle’s Law What happens to gases when Pext increases? Why aren’t solids/liquids compressible? Figure 5.15

  49. Figure 5.16 A molecular description of Dalton’s law of partial pressures. Why does each gas contribute to the total pressure in proportion to its mole fraction?

  50. Figure 5.17 A molecular description of Charles’s Law What does temperature measure on the molecular scale?

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