A. What are the three states of matter chemists work with?

Chapter 10 and 12 The Behavior of Gases Chapter 10 The States of Matter A. What are the three states of matter chemists work with? Section 10.1 Pg 267 B. We will explain the behavior of gases using the Kinetic Molecular Theory: 1. What is KINETIC ENERGY? 2. Define the kinetic theory as it pertains to gases: 3. There are 3 basic assumptions of the kinetic theory of gases. Summarize them here: a. b. c. 4. If we opened a perfume bottle in Washington D.C., the gas molecules should reach Mexico City in about 90 minutes. Why don t they ever make it? 5. Define random walk Gas Pressure Pg 268 A. Define gas pressure B. Define a vacuum C. Define Atmospheric Pressure D. What is a barometer? E. What are the units used to measure pressure? (There are 3 commonly used) 1

F. Define standard conditions, both in temperature and pressure, when working with gases (STP)?(page 269, second paragraph) Practice converting between pressure units: Example 1 A gas is at a pressure of 1.5 atm. Convert this pressure to a. kilopascals b. millimeters of mercury What pressure, in kilopascals and in atmospheres, does a gas exert at 385 mm Hg? Example 3 The pressure at the top of Mount Everest is 33.7 kpa. Is that pressure greater or less than 0.25 atm? Kinetic Energy and Kelvin Temperature Page 269-271 A. Why do gas molecules contain kinetic energy? B. What happens to the amount of kinetic energy an object contains as it is heated? C. **The average kinetic energy of the particles of a substance is proportional to the temperature of the substance. D. **Particles of all substances at the same temperature have the same average kinetic energy. E. **Theoretically, there is no upper limit to which a substance s temperature can be raised. By contrast, however, there is a lower limit. F. What is the term used to describe the temperature at which the motion of particles ceases and therefore it has no kinetic energy? G. What are its values in Celsius and Kelvin? H. **The Kelvin scale is used to directly measure the kinetic energy of an object, NOT the Celsius scale. 2

Chapter 12 The Behavior of Gases as explained by The Kinetic Molecular Theory 12.1. Factors Affecting Gas Pressure, pg 330 bottom picture, pg 331 top picture How does adding molecules into a container, keeping volume and temperature constant, affect the pressure inside the container? How does removing molecules from a container, keeping volume and temperature constant, affect the pressure inside the container? The Effect of Changing the Size of the Container pg 331 bottom picture What happens to the pressure inside of a container when we reduce the volume, keeping temperature constant? What happens to the pressure inside of a container when we enlarge the volume, keeping the temperature constant? Temperature page 332 top picture How does raising the temperature of a gas affect the pressure if the volume is kept constant? How does lowering the temperature of a gas affect the pressure if the volume is kept constant? 12.3 The Gas Laws Page 333 State Boyle s Law in words Show Boyle s Law in an equation Show the graph illustrating Boyle s Law 3

Example 1 A high-altitude balloon contains 30.0 L of helium gas at 103 kpa. What is the volume when the balloon rises to an altitude where the pressure is only 25.0 kpa? (Assume that the temperature remains constant.) The pressure on 2.5 L of anesthetic gas changes from 105 kpa to 40.5 kpa. What will be the new volume if the temperature remains constant? Example 3 A gas with a volume of 4.0 L at a pressure of 205 kpa is allowed to expand to a volume of 12.0 L. What is the pressure in the container if the temperature remains constant? Charles Law for Temperature-Volume Changes Page 335 State Charles Law in words Show Charles Law in an equation Show the graph illustrating Charles Law Example 1 A balloon inflated in a room at 24 C has a volume of 4.0 L. The balloon is then heated to a temperature of 58 C. What is the new volume if the pressure remains constant? If a sample of gas occupies 6.8 L at 325 C, what will be its volume at 25 C, if the pressure does not change? Example 3 Exactly 5.0 L of air at - 50.0 C is warmed to 100 C. What is the new volume if the pressure remains constant? 4

Gay-Lussac s Law for Temperature-Pressure Changes Page 338 State Gay-Lussac s Law in words Show Gay-Lussac s Law in an equation Show the graph illustrating Gay-Lussac s Law Example 1 A gas left in a used aerosol can is at a pressure of 103 kpa at 25 C. If this can is thrown onto a fire, what is the pressure of the gas when its temperature reaches 928 C? A gas has a pressure of 6.58 kpa at 539 K. What will be the pressure at 211 K if the volume does not change? The Combined Gas Law Page 339 Show this law in an equation: Example 1 The volume of a gas-filled balloon is 30.0 L at 40 C and 153 kpa pressure. What volume will the balloon have at standard temperature and pressure? A gas at 155 kpa and 25 C occupies a container with an initial volume of 1 L. by changing the volume, the pressure of a gas increases to 605 kpa as the temperature is raised to 125 C. What is the new volume? 5

Example 3 A 5 L air sample at a temperature of 50 C has a pressure of 107 kpa. What will be the new pressure if the temperature is raised to 102 C and the volume expands to 7 L? Example 4 A given mass of air has a volume of 6 L at 101 kpa. What volume will it occupy at 25 kpa if the temperature does not change? The Ideal Gas Law Page 341 This equation considers a fourth variable that affects the behavior of gases the NUMBER OF PARTICLES! This equation incorporates Avogadro s hypotheses (1 mole of any gas = 22.4 L at STP) into the combined gas law from above: Write the Ideal Gas Law Equation here: Substitute the values of standard condition and solve for R A. Using Pressure in a kpa B. Using Pressure in an ATM C. Using Pressure in a mmhg **The advantage of the ideal gas law over the combined gas law is that it permits us to solve for the number of moles of a contained gas when P, V, and T are known. 6

Example 1 You fill a rigid steel cylinder that has a volume of 20 L with nitrogen gas to a final pressure of 20,000 kpa at 28 C. How many moles of nitrogen gas does the cylinder contain? How many grams is this? A deep underground cavern contains 2.24 x 10^6 L of methane gas, CH 4, at a pressure of 1.5 x 10^3 kpa and a temperature of 42 C. How many grams of methane does this natural-gas deposit contain? Example 3. When the temperature of a rigid hollow sphere containing 685 L of helium gas is held at 621 K, the pressure of the gas is 1.89 x 10^3 kpa. How many moles of helium does the sphere contain? Example 4 What pressure will be exerted by 0.45 mol of a gas at 25 C if it is contained in a 0.65 L vessel? Example 5 A child has a lung capacity of 2.2 L. How many grams of air do her lungs hold at a pressure of 102 kpa and a normal body temperature of 37 C? Air is a mixture, but you may assume it has a molar mass of 28 g/mole. Example 6 What volume will 12 grams of oxygen gas occupy at 25 C and a pressure of 52.7 kpa? 7

12.5 Avogadro s Hypothesis (Mole Map Review) Pg 347 Although gas molecules of different gases are different sizes, equal volumes of gases at the same temperature and pressure contain equal numbers of particles. In other words, even though Chlorine gas molecules are 35 times bigger than hydrogen gas molecules, equal numbers of the two gases would occupy the same volume at the same temperature and pressure. Example 1 Determine the volume occupied by.202 mole of a gas at STP What is the volume occupied by.742 mol of Argon at STP? Example 3 Determine the volume occupied by 14 grams of nitrogen gas at STP? Dalton s Law of Partial Pressures Page 350 Many gases, including air, are mixtures. Remember, the particles in a gas at the same temperature have the same average kinetic energy. Gas pressure depends only on the number of gas particles in a given volume and their average kinetic energy. The kind of particle is not important. Define partial pressure Define Dalton s law of partial pressures Example 1 Air contains oxygen, nitrogen, carbon dioxide, and trace amounts of other gases. What is the partial pressure of oxygen (P O2 ) at 101.3 kpa if the partial pressure of nitrogen, carbon dioxide, and other gases are 79.1 kpa, 0.04 kpa, and 0.94 kpa, respectively. 8

Determine the total pressure of a gas mixture that contains oxygen, nitrogen, and helium if the partial pressure of the gases is as follows: Oxygen = 20 kpa Nitrogen = 46.7 kpa Helium = 26.7 kpa Example 3: A mixture containing 0.538 mole of He (g), 0.315 mole Ne (g), and 0.103 mole Ar (g) is confined in a 7 Liter vessel at 25 C. a. Calculate the partial pressure of each of the gases in the mixture b. Calculate the total pressure of the mixture. Example 4: A mixture containing 2.5 grams each of CH 4 (g), C 2 H 4 (g), and C 4 H 10 (g) is contained in a 2 Liter flask at a temperature of 15 C. a. Calculate the partial pressure of each of the gases in the mixture. b. Calculate the total pressure of the mixture. 9

Collecting Gases over Water An experiment that is often encountered in general chemistry laboratories involve determining the number of moles of gas collected from a chemical reaction. Sometimes this gas is collected over water, or by water displacement. The volume of gas collected is measured by raising or lowering the bottle as necessary until the water levels inside and outside the bottle are the same. When this condition is met, the pressure inside the bottle is equal to the atmospheric pressure outside. The total pressure inside is the sum of the pressure of the gas collected and the pressure of water vapor in equilibrium with liquid water. Ptotal = Pwater + Pgas The pressure exerted by water vapor, Pwater, at various temperatures is found in Appendix B. 10

Example 1: When a gas was collected over water, the following data was obtained: Volume of gas = 25 ml; atmospheric pressure = 740 mm Hg; temperature = 25 C. What volume would the DRY gas occupy at STP? : When a gas was collected over water, the following data was obtained: Volume of gas = 40 ml; atmospheric pressure = 790 mm Hg; temperature = 30 C. What would the volume of the DRY gas occupy at STP? Diffusion and Graham s Law Page 352 Define diffusion Define effusion State Graham s Law of Diffusion Graham s law may be understood by an examination of the relationship of the mass and speed of a moving body to the force the body exerts when it strikes a stationary object: Show the mathematical proof that derives Graham s Law: Restate Graham s law of diffusion showing the relationship to the lighter gas and it s velocity as compared to the heavier gas. 11

Example 1: Place the following gases in order of increasing average molecular speed at 25 C: Ne, HBr, SO 2, NF 3, CO. Compare the rate of diffusion of nitrogen gas to helium gas: Example 3 Compare the rate of diffusion of argon to neon gas: Example 4: A gas of unknown molecular mass was allowed to effuse through a small opening under constant pressure conditions. It required 105 seconds for 1.0 L of the gas to effuse. Under identical experimental conditions it required 31 seconds for 1.0 L of oxygen gas to effuse. Calculate the molar mass of the unknown gas. (Remember that the faster the rate of effusion, the shorter the time required for effusion of 1.0 L; that is, rate and time are inversely proportional.) Example 5: An unknown gas composed of homonuclear diatomic molecules effuses at a rate that is only.355 times that of oxygen at the same temperature. Calculate the molar mass of the unknown, and identify it. 12

Further Applications of the Gas Laws: (Honors Only) The ideal-gas equation can be used to determine many relationships involving the physical properties of gases. A. Gas Densities and Molar Mass Using the ideal-gas equation, derive the formula for solving for density, in grams per liter units. Example Problem 1: What is the density of carbon tetrachloride vapor at 714 mm Hg and 125 C? Example Problem 2: The mean molar mass of the atmosphere at the surface of Titan, Saturn s largest moon, is 28.6 g/mole. The surface temperature is 95K, and the pressure is 1.6 atm. Assuming ideal behavior, calculate the density of Titan s atmosphere. B. Calculating the Molar Mass of a Gas Starting with the ideal gas equation, derive the formula for solving for the molar mass of a gas, in grams/mole units. Example Problem 1: Calculate the molar mass of a gas is 2.5 grams occupies 0.875 L at 685 mm Hg and 35 C. 13

Example Problem 2: Calculate the molar mass of a vapor that has a density of 7.135 g/l at 12 C and 743 mm Hg Example Problem 3: In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below 100 C in a boiling water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor = 1.012 g; volume of bulb = 354 cm 3 ; pressure = 742 torr; temperature = 90 C. Example Problem 4: The molar mass of a volatile substance was determined by the Dumas-bulb method described above. The unknown vapor had a mass of 0.846 grams; the volume of the bulb was 354 cm 3 ; pressure 752 torr; and temperature of 100 C. Calculate the molar mass of the unknown vapor. 14

Volumes of Gases in Chemical Reactions Understanding the properties of gases is important because gases are often reactants or products in chemical reactions. For this reason we are often faced with calculating the volumes of gases consumed or produced in reactions. We have seen that the coefficients in balanced chemical equations tell us the relative amounts (in moles) of reactants or products in a reaction. The number of moles, in turn, is related to P, V, and T. Example Problem 1: The safety air bags in automobiles are inflated by nitrogen gas generated by the rapid decomposition of sodium azide, NaN 3. NaN 3 (s) 2Na (s) + 3N 2 (g) If an airbag has a volume of 36 L and is to be filled with nitrogen gas at a pressure of 1.15 atm at a temperature of 26 C, how many grams of sodium azide must be decomposed? Example Problem 2: In the first step in the industrial process for making nitric acid, ammonia reacts with oxygen in the presence of a suitable catalyst to form nitric oxide and water vapor. 4NH 3 (g) + 5 O 2 (g) 4NO(g) + 6H 2 O(g) How many liters of ammonia at 850 C and 5 atm are required to react with 50 grams of oxygen gas in this reaction? Example Problem 3: Solid calcium hydride reacts with water to form hydrogen gas and aqueous calcium hydroxide. This reaction is sometimes used to inflate life rafts, weather balloons, and the like, where a simple, compact means of generating hydrogen gas is desired. How many grams of calcium hydride are needed to generate 53.5 L of hydrogen gas if the pressure of hydrogen is 814 torr at 21 C? 15

Example Problem 4: The metabolic oxidation of glucose in our bodies produces carbon dioxide, which is expelled from our lungs as a gas. Calculate the volume of dry carbon dioxide produced at body temperature (37 C) and 0.97 atm when 24.5 g of glucose is consumed in this reaction. Example Problem 5: Acetylene gas, C 2 H 2, can be prepared by the reaction of calcium carbide with water; CaC 2 (s) + 2 H 2 O (l) Ca(OH) 2 (s) + C 2 H 2 (g) Calculate the volume of acetylene that is collected over water at 26 C by reaction of 0.887 grams of calcium carbide if the total pressure of the gas is 726 torr. The vapor pressure of the water can be found in our appendix B. 16