Chapter 5 Gases Overview The reason we study gases in Chemistry The observable properties of gases give us a window into what s happening at the For example Why Why Why Pressure 4 variables completely describe the state of any gas Definition of pressure SI unit of force SI unit of area therefore 1 Pa This is a very small unit 1 atm 1 atm 1 atm 1 mm Hg Methods of measuring pressure manometer 5 2 barometer If H2O d 1 00 g cm3 were used as the liquid in a barometer instead of Hg d 13 6 g cm3 how would the height of the liquid compare What is the pressure in a container of gas connected to a mercury filled open end manometer if the level in the arm open to the atmosphere is 15 2 cm lower than in the arm connected to the container and if the atmospheric pressure is 765 mm Hg Boyle s Law 5 3 Charles s Law Example If the temperature of a certain gas increases from 200 K to 400 K what happens to the volume assuming that the pressure is held constant Example If the temperature of a certain gas increases from 200 C to 400 C what happens to the volume assuming that the pressure is held constant Avogadro s Hypothesis and Avogadro s Law Avogadro s hypothesis Equal volumes of gases at the same temperature and pressure contain Ex Ar Ne H2 1 00 L 1 00 L 1 00 L 1 00 atm 1 00 atm 1 00 atm 0 C 0 C 0 C 5 4 Avogadro s Law Two important consequences of Avogadro s hypothesis and Avogadro s Law 1 We can focus on in gas stoichiometry problems N2 g Be careful 3H2 g 2NH3 g 1 2 Example How many liters of nitrogen gas are required to react with 12 0 L of hydrogen gas to form ammonia if both gases are measured at the same temperature and pressure 2 The molar volume of a gas at is STP This gives us these conversion factors Be careful 1 2 5 5 Important Term Molar molar molar mass molar volume of a gas molar enthalpy of combustion molar enthalpy of formation molar heat capacity Example Consider the reaction below What volume of CO2 gas measured at 0 C and 1 atm pressure will be formed by the complete reaction of 50 0 g of MgCO3 with excess hydrochloric acid Given the molar mass of MgCO3 is 84 3 g mol MgCO3 s 2HCl aq MgCl2 aq H2O l CO2 g Example Consider the reaction below What volume of hydrogen gas measured at 0 C and 1 atm pressure will be formed by complete reaction of 108 g of solid aluminum 2 Al s 6HCl aq 2AlCl3 aq Example What is the molar volume of an ideal gas at 760 torr and 546 K a b c d 11 2 L 22 4 L 33 6 L 44 8 L 3H2 g 5 6 The Ideal Gas Law Example For the same reaction as above what mass of aluminum is required to produce 10 0 L of hydrogen gas measured at 35 C and 749 mm Hg 2 Al s The Combined Gas Law 6HCl aq 2AlCl3 aq 3H2 g 5 7 Molar Mass from density Derivation of an important relationship molar mass rearrange ideal gas law substitute rearrange Example Uranium hexafluoride is a solid at room temperature but it boils at 56 C Determine the density of uranium hexafluroide at 60 C and 745 torr Dalton s Law of Partial Pressures Definition of Partial Pressure Easy way to express Dalton s Law More useful form of Dalton s Law where X recall Junior High definition of fraction 5 8 Example A 10 0 L container contains a mixture of helium neon and argon gases At 125 C the mixture has a total pressure of 842 mm Hg The partial pressure of helium is 451 mm Hg and the partial pressure of neon is 114 mm Hg a What is the mole fraction of each gas in the mixture b What mass of argon is present in the mixture The Kinetic Molecular Theory of Gases Two main questions 1 What causes pressure 2 How can we explain the gas laws Boyle s Law Charles Law Avogadro s Law Dalton s Law 5 Postulates of the Kinetic Molecular Theory 1 Gases consist of individual in 2 The volume of gas particles is 3 Collisions between gas particles are 4 Attractions between gas particles are 5 The average kinetic energy of gas particles depends only on and is directly proportional to 5 9 The Kinetic Molecular Theory can be used to explain the properties of gases The pressure of a gas is caused by Boyle s Law Temperature and Molecular Velocities Two Boltzmann Distributions based on temperature and mass At two different temperatures Figure 5 19 p 211 Effusion Diffusion Diffusion Effusion Graham s Law of Effusion Two different gases e g O2 and He Figure 5 18 p 210 5 10 Three important points Lighter gases Diffusion works Rate is to time Example Suppose an unknown gas has been observed to effuse one half as fast as oxygen What is the molecular weight of the unknown gas Example A sample of N2O effuses from a container in 42 seconds How long would it take the same amount of gaseous I2 to effuse from the same container under identical conditions Deviation from Ideal Behavior What is an ideal gas What does it mean for a gas to deviate from ideal behavior Most gases deviate from ideal behavior at and This is easy to remember because 5 11 Plot of PV RT vs P for 1 mol of a gas To understand why real gases deviate from ideal behavior recall two of the postulates of the Kinetic Molecular Theory Gases deviate from ideal behavior at high pressure because Gases deviate from ideal behavior at low temperature because The van der Waals equation is an attempt to correct the ideal gas equation for real gases 2 P an V nb nRT V2 Pressure correction because the pressure exerted by the gas is it would be if there were no attractive forces between gas molecules Volume correction because the volume available to the molecule is the total volume of the container a and b are constants that are experimentally determined for each gas The constant a is a measure of The constant b is a measure of Example for He for CCl4 a 0 0342 a 20 39 b 0 02370 b 0 1383 i e very little correction necessary