# Chapter 5. Gases and the Kinetic-Molecular Theory

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1 Chapter 5. Gases and the Kinetic-Molecular Theory An Overview of the Physical States of Matter The reason we study gases in Chemistry: The observable properties of gases give us a window into what s happening at the. For example, ask yourself: Why Why Why 5.2 Gas Pressure and its Measurement 4 variables completely describe the state of any gas: Methods of measuring pressure: manometer barometer height of Hg an expression of pressure (Problem 5.6, Page 170.) On a cool, rainy day, the barometric pressure is 725 mm Hg. Calculate the barometric pressure in centimeters of water (cm H 2O). (d of Hg = 13.5 g/ml; d of H 2O = 1.00 g/ml) Convert this to ft of H 2O. Definition of pressure: SI unit of force: SI unit of area: therefore, 1 Pa = This is a very small unit!

2 1 atm = 1 atm = 1 atm = 1 mm Hg = The Gas Laws and Their Experimental Foundations Two important gas laws: Ideal gas law: Combined gas law: Start with the Combined Gas Law: Two special cases: 1. Constant T 2. Constant P Next, consider Avogadro s hypothesis and Avogadro s Law: Avogadro s hypothesis: Equal volumes of gases at the same temperature and pressure contain: Ex: Ar Ne H L 1.00 L 1.00 L 1.00 atm 1.00 atm 1.00 atm 0.ºC 0ºC 0ºC Avogadro s Law: at constant T & P, the volume of a gas is directly proportional to Two important consequences of Avogadro s hypothesis and Avogadro s Law: 1. We can focus on in stoichiometry problems: N 2 (g) + 3H 2 (g) 2NH 3 (g) Be careful: 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?

3 2. The molar volume of a gas at is. STP = This gives us these conversion factors: Be careful! 1) 2) Important Term: Molar molar molar mass molar volume of a gas molar enthalpy of combustion molar enthalpy of formation Example: Consider the following reaction: 3 MgCO 3(s) + 2HCl(aq) MgCl 2(aq) + H 2O(l) + CO 2(g) What volume of CO 2 gas, measured at 0 C and 1 atm pressure, will be formed by the complete reaction of 50.0 g of MgCO 3 with excess hydrochloric acid? (Given: the molar mass of MgCO 3 is 84.3 g/mol.) Example: Consider the following reaction: 2 Al(s) + 6HCl(aq) 2AlCl 3(aq) + 3H 2(g) 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? Example: What is the molar volume of an ideal gas at 760. torr and 546 K? Further Applications of the Ideal Gas Law and Gas Stoichiometry 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.

4 Dalton s Law of Partial Pressures 4 Definition of Partial Pressure: Easy way to express Dalton s Law: More useful form of Dalton s Law: where X A = Example: A 10.0 L container contains 5.00 g of oxygen and 7.50 g of nitrogen at 25.0 C. What is the partial pressure of each gas, and what is the total pressure? Collecting Gases Over Water example: (# 5.48, p. 172 ) Aluminum reacts with excess hydrochloric acid to form aqueous aluminum chloride and 35.8 ml of hydrogen gas over water at 27ºC and 751 mmhg. How many grams of aluminum reacted? First, determine vapor pressure of water at 27ºC from table, page ºC, P H2O = 25.2 torr 28ºC, P H2O = 28.3 torr extrapolate: P H2O = ( )/2 = torr at 27ºC 5.6 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 Main idea behind KMT: 4 Postulates of the KMT:

5 The Kinetic-Molecular Theory can be used to explain the properties of gases. The pressure of a gas is caused by 5 Boyle s Law Dalton s Law of Partial Pressure Two Boltzmann Distributions, based on temperature and mass: At two different temperatures Two different gases (e.g., O 2 and He) (fig. 5.12, p. 161) (fig. 5.17, p. 163) Effusion/Diffusion 1. Diffusion: 2. Effusion: 3. Graham s Law of effusion: the rate of effusion of a gas (through a small hole or orifice) is inversely proportional to the square root of the molar mass of the gas. r 1 r 2 = M 2 M 1 where r 1 = rate of effusion of gas 1, M 1 = molar mass of gas 1 4. 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? 5. Two important points: Lighter gases Diffusion works 5.7 Deviation from Ideal Behavior 1. What is an ideal gas? 2. What does it mean for a gas to deviate from ideal behavior?

6 3. Most gases deviate from ideal behavior at 6 and. 4. Plot of PV/nRT vs P This is easy to remember because: 5. Gases deviate from ideal behavior at high pressure because: 6. Gases deviate from ideal behavior at low temperature because: 7. The van der Waals equation is an attempt to correct the ideal gas equation for real gases. P + a n 2 V 2 ( V - n b ) = n R T 8. Pressure correction, because the pressure exerted by the gas is it would be if there were no attractive forces between gas molecules. 9. Volume correction, because the volume available to the molecule is the total volume of the container. 10. 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, a = b = (i.e., very little correction necessary) for CCl 4, a = b =

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