AP Chem – Unit 2 Part 2 AP Chemistry 2015-­‐2016 Unit 2: Chemical Reactions, Solution Stoichiometry, and Gases (Ch. 4-­‐5) Some Important Properties of Gases: • Unlike liquids, any gas always mixes thoroughly with any other gas in any proportion (i.e. they are miscible and form homogeneous solutions) • Gases are compressible: when pressure is applied, the volume of a gas decreases. Liquids and solids are relatively incompressible. A gas behaves most ideally at low pressures. • The volume of a gas expands on heating and contracts on cooling. This effect is much greater than for liquids and solids. • Gases have relatively low viscosity. • Most gases have relatively low densities under normal conditions (g/L) Gas Pressure (P = F/A) Manometer Barometer Units – Pascal (kg·∙m·∙s-­‐2 / m2 = N/m2) 1 atm = 101.325 kPa = 760 torr = 760 mm Hg = 14.7 lb/in2 (psi) 1 bar = 1 x 102 kPa Example Problem 1: A The pressure of a gas is measured as 49 torr. What is this pressure in mmHg, atm, and kPa? (A: 49 mm Hg / 0.064 atm / 6.5 kPa) AP Chem – Unit 2 Part 2 The Gas Laws The physical properties of any gas can be described completely (more or less) by four variables: • Pressure (P) – atm • Volume (V) – L • Temperature (T) – Kelvin • Amount (n) – moles Boyle’s Law: Pressure and Volume Charles’s Law: Temperature and Volume K = °C + 273.15 °C = K – 273.15 Gay-­‐Lussac’s Law: Pressure and Temperature The Combined Gas Law Avogadro’s Law: Volume and Amount Ideal Gas Law PV = nRT R = = = = = 0.08206 atm·∙L/mol·∙K 8.3145 KPa·∙L/mol·∙K 62.36 mmHg·∙L/mol·∙K 62.36 torr·∙L/mol·∙K 8.3145 J/mol·∙K = 1.9872 cal/mol·∙K Standard Temperature and Pressure Standard Molar Volume (V = nRT/P) = 22.42 liters These balloons each hold 1.0 L of gas at 25°C and 1 atm. How many moles of gas are in each balloon? How many molecules? AP Chem – Unit 2 Part 2 The Density and Molar Mass of a Gas MM =dRT / P Example Problem 2: The density of a gas was measured at 1.50 atm and 27°C and found to be 1.95 g/L. Calculate the molar mass of the gas. If this was a diatomic elemental gas, which element would it be? (Answer: 32.0 g/mol; O2) Practice Worksheet: Gas Law Problems 1. A gas at a pressure of 760. torr and having a volume of 1024 mL is changed to a pressure of 115 torr; what is the new volume if the temperature stays constant? (A: 6770 mL) 2. A sample of gas has a volume of 155 mL at 0°C. What will be the volume of the gas if it is warmed up to a temperature of 85°C? (A: 203 mL) 3. A sample of oxygen at 24.0°C and 745 torr was found to have a volume of 455 mL. How many grams of O2 were in the sample? (A: 0.586 g O2) 4. A sample of argon is trapped in a gas bulb at a pressure of 760. torr when the volume is 100. mL and the temperature is 35.0°C. What must its temperature be if its pressure becomes 720. torr and its volume 200. mL? (A: 584 K or 311°C) 5. Calculate the pressure exerted by 0.845 moles of nitrogen gas occupying a volume of 895 mL at a temperature of 42.0°C. (A: 24.4 atm) 6. A student collected a sample of a gas in a 0.220 L gas bulb until its pressure reached 0.757 atm at a temperature of 25.0°C. The sample weighed 0.299 g. What is the molar mass of the gas? Which of the following gases would the unknown be: Ar, CO2, CO, or Cl2? (A: 43.9 g/mol; CO2) AP Chem – Unit 2 Part 2 Stoichiometric Relationships with Gases Example Problem 3: A sample of nitrogen gas has a volume of 1.75 L at STP. How many moles of N2 are present? (A: 7.81 x 10-­‐2 mol) Example Problem 4: Air bags are deployed by the high-­‐temperature decomposition of sodium azide, NaN3. How many liters of N2 at 1.15 atm and 30.0°C are produced by the decomposition of 145 g of NaN3? (A: 72.5 L) 2 NaN3(s) à 2 Na(s) + 3 N2(g) Example Problem 5: Quicklime (CaO) is produced by the thermal decomposition of calcium carbonate. (a) Calculate the volume of CO2 at STP produced from the decomposition of 152 g calcium carbonate. (b) What if this reaction was carried out at 0.946 atm and 25°C? (A: (a) 34.1 L CO2 at STP; (b) 39.3 L CO2) Example Problem 6: A sample of methane gas having a volume of 2.80 L at 25°C and 1.65 atm was mixed with a sample of oxygen gas having a volume of 35.0 L at 31°C 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 125°C. (A: 2.47 L) AP Chem – Unit 2 Part 2 Practice Worksheet: Gas Density, Molar Mass, and Reaction Stoichiometry 1. What mass of helium is required to fill a 1.5-­‐L balloon at STP? 2. What volume of pure O2(g), collected at 27°C and 746 torr, would be generated by the decomposition of 125 g of a 50% by mass hydrogen peroxide solution? Ignore any water vapors that might be present. 3. Consider the combustion reaction between 50.0 mL of liquid methyl alcohol (density = 0.850 g/mL) and 22.8 L of O2 at 27°C and a pressure of 2.00 atm. Calculate the number of moles of H2O formed if the reaction goes to completion. 4. Hydrogen cyanide is prepared commercially by the reaction of methane, ammonia, and oxygen gas at high temperatures. The other product is gaseous water. What volume of hydrogen cyanide can be obtained from 20.0 L CH4, 20.0 L NH3, and 20.0 L O2? The volumes of all gasses are at the same temperature and pressure. 5. A gas consisting of only carbon and hydrogen has an empirical formula of CH2. The gas has a density of 1.65 g/L at 27°C and 734 torr. Determine the molar mass and the molecular formula of the gas. 6. Silicon tetrachloride and trichlorosilane are both starting materials for the production of electronics-­‐grade silicon. Calculate the densities of pure silicon tetrachloride vapor and pure trichlorosilane vapor at 85°C and 758 torr. Dalton’s Law of Partial Pressures PTotal = P1 + P2 + P3 + … AP Chem – Unit 2 Part 2 Example Problem 7: Mixtures of helium and oxygen can be used in scuba diving tanks to help prevent the “bends.” For a particular dive, 46 L of He at 25°C and 1.0 atm and 12 L O2 at 25°C and 1.0 atm were pumped into a tank with a volume of 5.0 L. Calculate the partial pressure of each gas and total pressure in the tank at 25°C. (A: PHe = 9.3 atm; PO2 = 2.4 atm; PTOTAL = 11.7 atm) Mole Fraction (χ): the ratio of the number of moles of a given compound in a mixture to the total number of moles in the mixture. Example Problem 8: The partial pressure of oxygen was observed to be 156 torr in air with a total atmospheric pressure of 743 torr. Calculate the mole fraction of O2 present. (A: 0.210) Example Problem 9: The mole fraction of nitrogen in the air is 0.7808. Calculate the partial pressure of N2 in air when the atmospheric pressure is 760. torr. (A: 593 torr) Gas Collection over Water Example Problem 10: A sample of solid potassium chlorate was heated in a test tube and decomposed. The oxygen produced was collected by displacement of water at 22°C and a total pressure of 754 torr. The volume of gas collected was 0.650 L, and the vapor pressure of water at 22°C is 21 torr. Calculate the partial pressure of O2 in the gas collected and the mass of KClO3 in the sample that was decomposed. (A: PO2 = 733 torr; 2.12 g KClO3) AP Chem – Unit 2 Part 2 Practice Worksheet: Partial Pressures 1. The partial pressure of CH4(g) is 0.175 atm and that of O2(g) is 0.250 atm in a mixture of the two gases. a. What is the mole fraction of each gas in the mixture? b. If the mixture occupies a volume of 10.5 L at 65°C, calculate the total number of moles of gas in the mixture? c. Calculate the number of grams of each gas in the mixture. 2. Helium is collected over water at 25°C and 1.00 atm total pressure. What total volume of gas must be collected to obtain 0.586 g of helium? (At 25°C, the vapor pressure of water is 23.8 torr.) 3. A piece of solid carbon dioxide, with a mass of 7.8 g, is placed in a 4.0-­‐L otherwise empty container at 27°C. What is the pressure in the container after all the CO2 vaporizes? If 7.8 g solid CO2 were placed in the same container but it already contained air at 740 torr, what would be the partial pressure of the CO2 and the total pressure in the container after the carbon dioxide vaporizes? The Kinetic Molecular Theory of Gases Postulates of the Kinetic-­‐Molecular Theory: 1. 2. 3. 4. 5. AP Chem – Unit 2 Part 2 • The Kinetic Theory and Boyle’s Law (P & V) • The Kinetic Theory and Gay-­‐Lussac’s Law (P & T) • The Kinetic Theory and Charles’s Law (T & V) • The Kinetic Theory and Avogadro’s Law (V & n) • The Kinetic Theory and Dalton’s Law (P & n) Distribution of Molecular Speeds (Boltzmann distribution) Kinetic Energy and Speed of Gas Particles Root Mean Square Velocity (µ) Maxwell’s Equation (R=8.314510 J/K·∙mol) Example Problem 10: Calculate the root mean square velocity of a helium atom in m/s. Convert to miles/hour. (A: 1.36 x 103 m/s) AP Chem – Unit 2 Part 2 Diffusion: Effusion: Graham’s Law of Effusion Example Problem 11: Calculate the ratio of the effusion rates of HCl(g) and NH3(g). Which should effuse faster and by how much? (A: NH3 can effuse 1.5 times faster.) Real Gases in the Real World Real gases do not behave ideally at what conditions? Example Problem 12: Consider a sample of 1.000 mol of CO2(g) confined to a volume of 3.000 L at 0.0°C. Calculate the pressure of the gas using the ideal gas equation. END OF CHAPTER AP MC REVIEW QUESTIONS -­‐ SOLUTIONS CH. 4 – 1.C, 2.C, 3. B, 4. C, 5. D, 6. A, 7. B, 8. B, 9.D, 10. A, 11. D, 12. A, 13. B, 14. C, 15. A CH. 5 – 1.C, 2.D, 3. A, 4. B, 5. D, 6. A, 7.B, 8. B, 9. C, 10. D, 11. B, 12. C, 13. A, 14. C, 15. A, 16. D AP Chem – Unit 2 Part 2 AP CHEMISTRY UNIT 2 REVIEW (Ch 5 –Gases) 1. Freon-­‐12 (CF2Cl2) is commonly used as the refrigerant in central home air conditioners. The system is initially charged to a pressure of 4.8 atm. Express this pressure in each of the following units: a. mm Hg b. torr c. kPa 2. An aerosol can contains 400. mL of compressed gas at 5.20 atm pressure. When all the gas is sprayed into a large plastic bag, the bag inflates to a volume of 2.14 L. What is the pressure of the gas inside the plastic bag? Assume temperature is constant. 3. Suppose two 200.0-­‐L tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of 135 atm in its respective tank at 24°C? 4. A person accidently swallows a drop of liquid oxygen, O2(l), which has a density of 1.149 g/mL. Assuming the drop has a volume of 0.050 mL, what volume of the gas will be produced in the person’s stomach at body temperature (37°C) and a pressure of 1.0 atm? 5. Consider the following unbalanced chemical equation: C6H12O6(s) + O2(g) à CO2(g) + H2O(g) What volume of oxygen gas, measured at 28°C and 0.976 atm, is needed to react with 5.00 g of C6H12O6? What volume of each product is produced under the same conditions? 6. Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide (NaN3) to decompose explosively according to the following reaction: 2 NaN3(s) à 2 Na(s) + 3 N2(g) What mass of NaN3(s) must be reacted to inflate an air bag at 70.0 L at STP? 7. A compound has the empirical formula CHCl. A 256-­‐mL flask, at 373 K and 750. torr, contains 0.800 g of the gaseous compound. Give the molecular formula. 8. Uranium hexafluoride is a solid at room temperature, but it boils at 56°C. Determine the density of uranium hexafluoride at 60°C and 745 torr. 9. Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc. Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose 240. mL of hydrogen gas is collected at 30.°C and has a total pressure of 1.032 atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? 10. At elevated temperatures, sodium chlorate decomposes to produce sodium chloride and oxygen gas. A 0.8765-­‐g sample of impure sodium chlorate was heated until the production of oxygen gas ceased. The oxygen gas collected over water occupied 57.2 mL at a temperature of 22°C and a pressure of 734 torr. Calculate the mass percent of NaClO3 in the original sample. 11. Calculate the root mean square velocity of the methane molecules in a sample of methane gas at 273 K and at 546 K. 12. The rate of effusion of a particular gas was measured and found to be 24.0 mL/min. Under the same conditions, the rate of effusion of pure methane gas is 47.8 mL/min. What is the molar mass of the unknown gas? 13. Calculate the pressure exerted by 0.5000 mol N2 in a 1.0000-­‐L container at 25°C a. using the ideal gas law b. using van der Waals equation c. compare the results Challenge Problems: 14. Metallic molybdenum can be produced from the mineral molybdenite, MoS2. The mineral is first oxidized in air to molybdenum trioxide and sulfur dioxide. Molybdenum trioxide is then reduced to metallic molybdenum using hydrogen gas. The balanced equations are: MoS2(s) + 7/2 O2(g) à MoO3(s) + 2 SO2(g) MoO3(s) + 3 H2(g) à Mo(s) + 3 H2O(l) AP Chem – Unit 2 Part 2 3
Calculate the volumes of air and hydrogen gas at 17°C and 1.00 atm that are necessary to produce 1.00 x 10 kg of pure molybdenum from MoS2. Assume air contains 21% oxygen by volume and assume 100% yield for each reaction. 15. A chemist weighs out 5.14 g of a mixture containing unknown amounts of BaO(s) and CaO(s) and places the sample in a 1.50-­‐L flask containing CO2(g) at 30.0 °C and 750. torr. After the reaction to form BaCO3(s) and CaCO3(s) was completed, the pressure of CO2(g) remaining was 230. torr. Calculate the mass percentages of CaO(s) and BaO(s) in the mixture. Answers: 3
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1. a. 3.6 x 10 mm Hg b. 3.6 x 10 torr c. 490 kPa 2. 0.972 atm 3
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3. for He: 4.44 x 10 g for H2: 2.24 x 10 g 4. 46 mL 5. 4.23 L O2 4.23 L CO2 4.23 L H2O 6. 135 g NaN3 7. C2H2Cl2 (molar mass = 96.9 g/mol) 8. 12.6 g/L 9. PH2 = 0.990 atm 0.625 g zinc 10. 18.0% 11. urms at 273K = 652 m/s urms at 546K = 922 m/s 12. 63.7 g/mol 13. a. 12.24 atm b. 12.13 atm c. the ideal gas law is higher by 0.91% 6
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14. 4.1 x 10 L air 7.42 x 10 L H2 15. 86.6% BaO and 13.4% CaO AP-­‐type Questions: (See additional AP RQ Practice Packets) 1. Propane, C3H8, is a hydrocarbon that is commonly used as fuel for cooking. (a) Write a balanced equation for the complete combustion of propane gas, which yields CO2(g) and H2O(l). (b) Calculate the volume of air at 30°C and 1.00 atmosphere that is needed to burn completely 10.0 grams of propane. Assume that air is 21.0 percent O2 by volume. (c) The heat of combustion of propane is -­‐2,220.1 kJ/mol. Calculate the heat of formation, ΔH°f, of propane given that ΔH°f of H2O(l) = -­‐285.3 kJ/mol and ΔH°f of CO2(g) = -­‐393.5 kJ/mol. (d) Assuming that all of the heat evolved in burning 30.0 grams of propane is transferred to 8.00 kilograms of water .
(specific heat = 4.18 J/g K), calculate the increase in temperature of water. 2. Answer the following questions about carbon monoxide, CO(g), and carbon dioxide, CO2(g). Assume that both gases exhibit ideal behavior. (a) Draw the complete Lewis structure (electron dot diagram) for the CO molecule and for the CO2 molecule. (b) Identify the shape of the CO2 molecule. (c) One of the two gases dissolves readily in water to form a solution with a pH below 7. Identify the gas and account for this observation by writing a chemical equation. (d) A 1.0 mol sample of CO(g) is heated at constant pressure. On the graph below, sketch the expected plot of volume verses temperature as the gas is heated.