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Chapter 13 Gases 13.1 Pressure Objectives: 1) To learn about atmospheric pressure and the way in which barometers work 2) To learn the various units of pressure. 13.1: Pressure • Automobile tires, basketballs, balloons, and soda bottles. • What happens to a balloon when you place it in a freezer? – Why? 13.1 Pressure • Evangelista Torricelli invented the – BAROMETER: device to measure pressure – At sea level the height of the column of mercury is 760 mm. Pressure exerted by the atmospheric gases on the surface of the mercury in the dish keeps the mercury in the tube. 13.1: Pressure Weather: -low pressure STORMS -high pressure nice weather 13.1: Pressure Units of Pressure -mm Hg= torr Standard atmosphere (atm) 1 std. atm.=1,000 atm=760.0mm Hg=760.0 torr 1 std. atm=101, 325 Pascal 1.000 std. atm=14.69 psi Measuring pressure Atmospheric pressure-h Manometer Atmospheric pressure + h 13.1: Pressure The height of mercury in a mercury barometer is measured to be 732 mm. Represent this pressure in atm, torr, and pascals. 0.963 atm; 732 torr; 9.76 x 104 Pa The pressure of a gas is measured to be 2.79 x 105 Pa. Represent this pressure in atm, torr, and psi. 2.75 atm; 2.10 x 103 torr; 40.4 psi Homework, Self-Check exercise 13.1 13.2: Pressure and Volume: Boyle’s Law • Objectives: 1) To understand the law that relates the pressure and volume of a gas. 2) To do calculations involving this law. Robert Boyle: Irish scientist -studied the relationship between the pressure of the trapped gas and its volume P x V=const. PV=k Boyle’s Law Inversely proportional Figure 13.6: Illustration of Boyle’s law. P1V1=P2V2 13.2: Pressure and Volume: Boyle’s Law • A sample of neon gas has a pressure of 7.43 atm in a container with a volume of 45.1 L. This sample is transferred to a container with a volume of 18.4 L. What is the new pressure of the neon gas? Assume constant temperature. 18.2 atm 13.2: Pressure and Volume: Boyle’s Law • A steel tank of oxygen gas has a volume of 2.00L. If all of the oxygen is transferred to a new tank with a volume of 5.50 L, the pressure is measured to be 6.75 atm. What was the original pressure of the oxygen gas? Assume constant temperature. 18.6 atm Homework: 7-10 p. 435 13.3: Volume and Temperature: Charles’s Law • Objectives: 1) To learn about absolute zero. 2) To learn about the law relating the volume and temperature of a sample of gas at constant moles and pressure, and to do calculations involving that law. 13.3: Volume and Temperature: Charles’s Law • Objectives: 1) To learn about absolute zero. 2) To learn about the law relating the volume and temperature of a sample of gas at constant moles and pressure, and to do calculations involving that law. Jacques Charles (first solo H balloon flight) -showed that the volume of a gas (at constant pressure) increases with the temperature. Absolute zero: point where you get 0 volume -273oC 13.3: Volume and Temperature: Charles’s Law • Charles’s Law V/T= constant V1 = V2 T1 T2 13.3: Volume and Temperature: Charles’s Law • A 2.45 L sample of nitrogen gas is collected at 273 K and heated to 325K. Calculate the volume of the nitrogen gas at 325 K. Assume constant pressure. 2.92 L 13.3: Volume and Temperature: Charles’s Law • A sample of methane gas is collected at 285 K and cooled to 245K. At 245 K the volume of the gas is 75.0 L. Calculate the volume of the methane gas at 285K. Assume constant pressure. 87.2 L 13.3: Volume and Temperature: Charles’s Law • Consider a gas with a volume of 5.65 L at 27 C and 1 atm pressure. At what temperature will this gas have a volume of 6.69 L and 1 atm pressure. 82oC (355K) 13.3: Volume and Temperature: Charles’s Law • Consider a gas with a volume of 9.25L at 47oC and 1 atm pressure. At what temperature does this gas have a volume of 3.50 L and 1 atm pressure. -152oC (121K) 13.4: Volume and Moles: Avogadro’s Law • Objective: 1) To understand the law relating the volume and the number of moles of a sample of gas at constant temperature and pressure, and to do calculations involving this law. Avogadro’s Law V1 = V2 n1 n2 13.4: Volume and Moles: Avogadro’s Law If 2.55 mol of helium gas occupies a volume of 59.5 L at a particular temperature and pressure, what volume does 7.83 mol of helium occupy under the same conditions? 183 L 13.4: Volume and Moles: Avogadro’s Law If 4.35 g of neon gas occupies a volume of 15.0 L at a particular temperature and pressure, what volume does 2.00 g of neon gas occupy under the same conditions? 6.90 L 13.5 The Ideal Gas Law Ideal Gas Law PV=nRT R=Universal gas constant (proportionality constant) R= 0.08206 L atm/ oK Based on experimental measurements. Most gases obey this equation at 1 atm or lower and 0oC or higher 13.5 The Ideal Gas Law Ideal Gas Law When the number of moles and type of gas are a constant……. P1V1 = P2V2 T1 T2 13.5 The Ideal Gas Law A sample of neon gas has a volume of 3.45 L at 25oC and a pressure of 565 torr. Calculate the number of moles of neon present in the gas sample. 0.105 mol 13.5 The Ideal Gas Law A 0.250 mol sample of argon gas has a volume of 9.00 L at a pressure of 875 mm Hg. What is the temperature (in oC) of the gas? 232oC 13.5 The Ideal Gas Law Consider a sample of helium gas at 23oC with a volume of 5.60 L at a pressure of 2.45 atm. The pressure is changed to 8.75 atm and the gas is cooled to 15oC. Calculate the new volume of the gas using the ideal gas law equation. 1.53 L 13.5 The Ideal Gas Law Consider a sample of helium gas at 28oC with a volume of 3.80 L at a pressure of 3.15 atm. The gas expands to a volume of 9.50 L and the gas is heated to 43oC. Calculate the new pressure of the gas using the ideal gas law equation. 1.32 atm 13.6: Dalton’s Law of Partial Pressures Objectives: To understand the relationship between the partial and total pressures of a gas mixture, and to use this relationship in calculations. Scuba divers: use helium and oxygen instead of air. Air contains nitrogen that dissolves in the blood as a result of high pressure. Nitrogen bubbles out and the diver gets the bends. 13.6: Dalton’s Law of Partial Pressures John Dalton: For a mixture of gases in a container, the total pressure exerted is the sum of the partial pressures of the gases present. Partial pressure: pressure that the gas would exert if it were alone in the container. Dalton’s law of partial pressures: Ptotal=P1 + P2 + P3 Ptotal=ntotal (RT/V) The pressure doesn’t depend on the forces amongst the particles. The volume of the individual gas particles is not important. Figure 13.12: The production of oxygen by thermal decomposition. 13.6: Dalton’s Law of Partial Pressures A sample of solid potassium chlorate KClO3, was heated in a test tube and decomposed according to the reaction 2KClO3(s) 2KCl(s) + 3O2 The oxygen produced was collected by displacement of water at 22oC. The resulting mixture of O2 and H2O vapor had a total pressure of 754 torr and a volume of 0.650L. Calculate the partial pressure of O2 in the gas collected and the number of moles of O2 present. The vapor pressure of water at 22oC is 21 torr. 13.6: Dalton’s Law of Partial Pressures Ptotal=PO2 + PH2O 754=PO2 + 21 PO2= 733 torr nO2 =PO2V 733/760=0.964 atm RT nO2= (0.964 atm)(0.650L) (0.08206) (295) 13.6: Dalton’s Law of Partial Pressures A 5.00 g sample of helium gas is added to a 5.00 g sample of neon in a 2.50 L container at 27oC. Calculate the partial pressure of each gas and the total pressure. 12.3 atm He; 2.44 atm Ne; 14.7 atm total 13.6: Dalton’s Law of Partial Pressures A sample of oxygen gas is saturated with water vapor at 30.0oC. The total pressure is 753 torr and the vapor pressure of water at 30.0 C is 31.824 torr. What is the partial pressure of the oxygen gas in atm? 0.949 atm Homework: 23-30 and 33-36 13.6: Dalton’s Law of Partial Pressures A sample of oxygen gas is saturated with water vapor at 27oC. The total pressure is 785 torr and the partial pressure of oxygen is 758.3 torr. What is the vapor pressure of water at 27oC? 26.7 torr 13.8: The Kinetic Molecular Theory of Gases Objectives: To understand the basic postulates of the kinetic molecular theory Postulates of KMT. 13.9: The Implications of the Kinetic Molecular Theory Objectives: To understand the term temperature. To learn how the kinetic molecular theory explains the gas laws. 13.9: The Implications of the Kinetic Molecular Theory The temperature of a gas: how rapidly, its individual particles are moving. High temperatures: move very fast. Low temperatures: move slower. As the gas is heated to a higher temperature, the particles move faster, hitting the walls more often. Pressure increases with increasing temperature 13.10: Real Gases Objectives: To describe the properties of real gases. As real gases are compressed into smaller and smaller volumes, the particles of the gas begin to occupy a significant fraction of the available volume.. Start to attract to each other here PV=nRT not true 13.11:Gas Stoichiometry Objectives: 1) To understand the molar volume of an ideal gas. 2) To learn the definition of STP 3) To use these concepts and the ideal gas equation. 13.11:Gas Stoichiometry For 1 mol of an ideal gas at 0oC (273K) and 1 atm, the volume will be. V=nRT/P= (1.00mol)(0.08206)(273) = 22.4L 1 atm. 22.4 L is called the molar volume Standard temperature and pressure (abbreviated STP). Contains 1 mol of an ideal gas at STP. 13.11:Gas Stoichiometry A sample of argon gas has a volume of 3.45 L at STP. What is the mass of the argon? 6.15 g 13.11:Gas Stoichiometry A sample of hydrogen gas occupies a volume of 15.0L at STP. What volume will this sample occupy at 22oC and 2.50 atm? 6.48 L 13.11:Gas Stoichiometry When magnesium reacts with hydrochloric acid, hydrogen gas is produced: Mg(s) + 2HCl MgCl2(aq) + H2(g) Calculate the volume of hydrogen gas produced at STP by reacting 5.00 g Mg and an excess of HCl (aq) 4.61 L 13.11:Gas Stoichiometry When subjected to an electric current, water decomposes to hydrogen and oxygen gas: 2H2O(l) 2H2(g) + O2(g) If 25.0g of water is decomposed, what volume of oxygen gas is produced at STP? 15.5 L