Chemistry 201, Chapter 5, Gases Problem Set (PDF)

## Chapter Review Problems **Gas Laws** 30. A balloon is filled to a volume of 7.00 × 102 mL at a temperature of 20.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 × 102 K. What is the final volume of the balloon? 31. If 0.500 mol of nitrogen gas occupies a volume...

## Chapter Review Problems **Gas Laws** 30. A balloon is filled to a volume of 7.00 × 102 mL at a temperature of 20.0°C. The balloon is then cooled at constant pressure to a temperature of 1.00 × 102 K. What is the final volume of the balloon? 31. If 0.500 mol of nitrogen gas occupies a volume of 11.2 L at 0°C, what volume will 2.00 mol of nitrogen gas occupy at the same temperature and pressure? 32. Consider the following chemical equation. 2NO2(g) → N2O4(g) If 25.0 mL of NO2 gas is completely converted to N2O4 gas under the same conditions, what volume will the N2O4 occupy? 33. Complete the following table for an ideal gas. | P (atm) | V (L) | n (mol) | T | |---:|---:|---:|---:| | 5.00 | 2.00 | 2.00 | 155°C | | 0.300 | 2.00 | 2.00 | 155 K | | 4.47 | 25.0 | 2.01 | | | 2.25 | 10.5 | | 75°C | 34. Complete the following table for an ideal gas. | P (atm) | V (L) | n (mol) | T | |---:|---:|---:|---:| | 7.74 × 103 Pa | 12.2 mL | | 25°C | | | 43.0 mL | 0.421 mol | 223 K | | 455 torr | | 4.4 × 10-2 mol | 331°C | | 745 mm Hg | 11.2 L | 0.401 mol | | 35. The steel reaction vessel of a bomb calorimeter, which has a volume of 75.0 mL, is charged with oxygen gas to a pressure of 145 atm at 22°C. Calculate the moles of oxygen in the reaction vessel. 36. A 5.0-L flask contains 0.60 g O2 at a temperature of 22°C. What is the pressure (in atm) inside the flask? 37. A 2.50-L container is filled with 175 g argon. a. If the pressure is 10.0 atm, what is the temperature? b. If the temperature is 225 K, what is the pressure? 38. What volume is occupied by 2.0 g of He at 25°C and a pressure of 775 mm Hg? 40. A balloon has a volume of 175 cm3 at 19°C. At what temperature will the volume of the balloon have increased by 25.0% (at constant pressure)? 41. A compressed gas cylinder, at 13.7 MPa and 23°C, is in a room where a fire raises the temperature to 450.°C. What is the new pressure in the cylinder? 42. A container is filled with an ideal gas to a pressure of 40.0 atm at 0°C. a. What will be the pressure in the container if it is heated to 45°C? b. At what temperature would the pressure be 1.50 × 102 atm? c. At what temperature would the pressure be 25.0 atm? 43. An ideal gas is contained in a cylinder with a volume of 5.0 × 102 mL at a temperature of 30.°C and a pressure of 710. torr. The gas is then compressed to a volume of 25 mL, and the temperature is raised to 820.°C. What is the new pressure of the gas? 44. A compressed gas cylinder contains 1.00 × 103 g of argon gas. The pressure inside the cylinder is 2050. psi (pounds per square inch) at a temperature of 18°C. How much gas remains in the cylinder if the pressure is decreased to 650. psi at a temperature of 26°C? 45. A sealed balloon is filled with 1.00 L of helium at 23°C and 1.00 atm. The balloon rises to a point in the atmosphere where the pressure is 220. torr and the temperature is -31°C. What is the change in volume of the balloon as it ascends from 1.00 atm to a pressure of 220. torr? 46. A hot-air balloon is filled with air to a volume of 4.00 × 103 m3 at 745 torr and 21°C. The air in the balloon is then heated to 62°C, causing the balloon to expand to a volume of 4.20 × 103 m3. What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.) **Gas Density, Molar Mass, and Reaction Stoichiometry** 47. What mass of helium is required to fill a 1.5-L balloon at STP? 48. A student adds 4.00 g of dry ice (solid CO2) to an empty balloon. What will be the volume of the balloon at STP after all the dry ice sublimes (converts to gaseous CO₂)? 49. Calculate the volume of O2, at STP, required for the complete combustion of 125 g octane (C8H18) to CO2 and H2O. 50. The method used by Joseph Priestley to obtain oxygen made use of the thermal decomposition of mercuric oxide: Heat 2HgO(s) → 2Hg(l) + O2(g) What volume of oxygen gas, measured at 30.°C and 725 torr, can be produced from the complete decomposition of 4.10 g mercuric oxide? 51. In 1897 the Swedish explorer Andreé tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is Fe(s) + H2SO4(aq) → FeSO4(aq) + H2(g) The volume of the balloon was 4800 m3 and the loss of hydrogen gas during filling was estimated at 20.%. What mass of iron splints and 98% (by mass) H2SO4 were needed to ensure the complete filling of the balloon? Assume a temperature at 0°C, a pressure of 1.0 atm during filling, and 100% yield. 52. 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: 2NaN3(s) → 2Na(s) + 3N2(g) What mass of NaN3(s) must be reacted in order to inflate an air bag to 70.0 L at STP? **Gas Mixtures and Partial Pressures** 61. 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 carbon dioxide vaporizes? If 7.8 g solid carbon dioxide were placed in the same container but it already contained air at 740 torr, what would be the partial pressure of carbon dioxide and the total pressure in the container after the carbon dioxide vaporizes? 62. A mixture of 1.00 g H2 and 1.00 g He is placed in a 1.00-L container at 27°C. Calculate the partial pressure of each gas and the total pressure. 63. Consider the flasks diagrammed below. What are the final partial pressures of H2 and N2 after the stopcock between the two flasks is opened? (Assume the final volume is 3.00 L.) What is the total pressure (in torr)? [Diagram of two flasks, one with 2.00 L of H2 at 475 torr and the other with 1.00 L of N2 at 0.200 atm] 64. If the initial pressures of the H2 and N2 in the flasks in Exercise 63 were 360. torr and 240. torr, respectively, what would be the final pressure after the stopcock is opened? 65. 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. 66. At 0°C a 1.0-L flask contains 5.0 × 10-2 mol N2, 1.5 × 102 mg O2, and 5.0 × 1021 molecules of NH3. What is the partial pressure of each gas, and what is the total pressure in the flask? 67. A sample of nitrogen gas was collected over water at 20.°C and a total pressure of 1.00 atm. A total volume of 2.50 × 102 mL was collected. What mass of nitrogen was collected? (At 20.°C the vapor pressure of water is 17.5 torr.) 68. 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.) 69. 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. (At 22°C the vapor pressure of water is 19.8 torr.) 70. The oxides of Group 2A metals (symbolized by M here) react with carbon dioxide according to the following reaction: MO(s) + CO2(g) → MCO3(S) A 2.85-g sample containing only MgO and CuO is placed in a 3.00-L container. The container is filled with CO2 to a pressure of 740. torr at 20.°C. After the reaction has gone to completion, the pressure inside the flask is 390. torr at 20.°C. What is the mass percent of MgO in the mixture? Assume that only the MgO reacts with CO2. **Kinetic Molecular Theory and Real Gases** 71. Calculate the average kinetic energy of the CH4 molecules in a sample of CH4 gas at 273 K and at 546 K. 72. Calculate the average kinetic energy of the N2 molecules in a sample of N2 gas at 273 K and at 546 K. 73. Calculate the root mean square velocity of the CH4 molecules in a sample of CH4 gas at 273 K and at 546 K. 74. Calculate the root mean square velocity of the N2 molecules in a sample of N2 gas at 273 K and at 546 K. 75. Do all the molecules in a 1-mol sample of CH4(g) have the same energy at 273 K? 76. Do all the molecules in a 1-mol sample of CH4(g) have the same velocity at 546 K? 77. Consider a 1-mol sample of CH4(g) at 273 K. If the temperature is increased, what happens to the average kinetic energy and the average velocity of the CH4 molecules? Explain. 78. Consider a 1.0-L container of neon gas at STP. Will the average kinetic energy, average velocity, and frequency of collisions of gas molecules with the walls of the container increase, decrease, or remain the same under each of the following conditions? a. The temperature is increased to 100°C. b. The temperature is decreased to -50°C. c. The volume is decreased to 0.5 L. d. The number of moles of neon is doubled. 79. Consider three identical flasks filled with different gases. Flask A: CO at 760 torr and 0°C Flask B: N2 at 250 torr and 0°C Flask C: H2 at 100 torr and 0°C a. In which flask will the molecules have the greatest average kinetic energy? b. In which flask will the molecules have the greatest average velocity? 80. Consider separate 1.0-L gaseous samples of H2, Xe, Cl2, and O2 all at STP. a. Rank the gases in order of increasing average kinetic energy. b. Rank the gases in order of increasing average velocity. c. How can separate 1.0-L samples of O2 and H2 each have the same average velocity? **Effusion and Diffusion** 81. The effusion rate of an unknown gas is measured and found to be 31.50 mL/min. Under identical experimental conditions, the effusion rate of O2 is found to be 30.50 mL/min. If the choices are CH4, CO, NO, CO2, and NO2, what is the identity of the unknown gas? 82. 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 (CH4) gas is 47.8 mL/min. What is the molar mass of the unknown gas? 83. One way of separating oxygen isotopes is by gaseous diffusion of carbon monoxide. The gaseous diffusion process behaves like an effusion process. Calculate the relative rates of effusion of 12C16O, 12C17O, and 12C18O. Name some advantages and disadvantages of separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide. 84. It took 4.5 minutes for 1.0 L helium to effuse through a porous barrier. How long will it take for 1.0 L Cl2 gas to effuse under identical conditions? **Deviation from Ideal Gas Law** 85. Calculate the pressure exerted by 0.5000 mol N2 in a 1.0000-L container at 25.0°C a. using the ideal gas law. b. using the van der Waals equation. c. Compare the results. 86. Calculate the pressure exerted by 0.5000 mol N2 in a 10.000-L container at 25.0°C a. using the ideal gas law. b. using the van der Waals equation. c. Compare the results. d. Compare the results with those in Exercise 85. **Additional Problems** 93. Draw a qualitative graph to show how the first property varies with the second in each of the following (assume 1 mol of an ideal gas and T in Kelvin). a. PV versus V with constant T b. P versus T with constant V c. T versus V with constant P d. P versus V with constant T e. P versus 1/V with constant T f. PV/T versus P 94. At STP, 1.0 L Br2 reacts completely with 3.0 L F2, producing 2.0 L of a product. What is the formula of the product? (All substances are gases.) 95. A 2.747-g sample of manganese metal is reacted with excess HCl gas to produce 3.22 L of H2(g) at 373 K and 0.951 atm and a manganese chloride compound (MnCl₂). What is the formula of the manganese chloride compound produced in the reaction? 96. Equal moles of hydrogen gas and oxygen gas are mixed in a flexible reaction vessel and then sparked to initiate the formation of gaseous water. Assuming that the reaction goes to completion, what is the ratio of the final volume of the gas mixture to the initial volume of the gas mixture if both volumes are measured at the same temperature and pressure? 97. A 15.0-L tank is filled with H₂ to a pressure of 2.00 × 102 atm. How many balloons (each 2.00 L) can be inflated to a pressure of 1.00 atm from the tank? Assume that there is no temperature change and that the tank cannot be emptied below 1.00 atm pressure. 98. A bicycle tire is filled with air to a pressure of 100. psi at a temperature of 19°C. Riding the bike on asphalt on a hot day increases the temperature of the tire to 58°C. The volume of the tire increases by 4.0%. What is the new pressure in the bicycle tire? 99. Consider the three flasks in the diagram below. Assuming the connecting tubes have negligible volume, what is the partial pressure of each gas and the total pressure when all the stopcocks are opened? [Diagram of three interconnected flasks, one containing 1.00 L of He at 180. torr, another with 1.00 L of Ne at 0.450 atm, and the last with 2.00 L of Ar at 25.0 kPa] 100. A spherical glass container of unknown volume contains helium gas at 25°C and 1.960 atm. When a portion of the helium is withdrawn and adjusted to 1.00 atm at 25°C, it is found to have a volume of 1.75 cm3. The gas remaining in the first container shows a pressure of 1.710 atm. Calculate the volume of the spherical container. 101. A 2.00-L sample of O2(g) was collected over water at a total pressure of 785 torr and 25°C. When the O2(g) was dried (water vapor removed), the gas had a volume of 1.94 L at 25°C and 785 torr. Calculate the vapor pressure of water at 25°C. 102. Acetylene gas, C2H2(g), can be produced by reacting solid calcium carbide, CaC2, with water. The products are acetylene and calcium hydroxide. What volume of wet acetylene is collected at 25°C and 715 torr when 5.20 g calcium carbide is reacted with an excess of water? (At 25°C the vapor pressure of water is 23.8 torr.) 104. A 20.0-L stainless steel container was charged with 2.00 atm of hydrogen gas and 3.00 atm of oxygen gas. A spark ignited the mixture, producing water. What is the pressure in the tank at 25°C? at 125°C? 105. 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. 107. A compound contains only nitrogen and hydrogen and is 87.4% nitrogen by mass. A gaseous sample of the compound has a density of 0.977 g/L at 710. torr and 100.°C. What is the molecular formula of the compound? 108. A compound contains only C, H, and N. It is 58.51% C and 7.37% H by mass. Helium effuses through a porous frit 3.20 times as fast as the compound does. Determine the empirical and molecular formulas of this compound. 109. The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot CuO(s): Compound Hot CuO(s) N2(g) + CO2(g) + H2O(g) The product gas is then passed through a concentrated solution of KOH to remove the CO2. After passage through the KOH solution, the gas contains N2 and is saturated with water vapor. In a given experiment a 0.253-g sample of a compound produced 31.8 mL N2 saturated with water vapor at 25°C and 726 torr. What is the mass percent of nitrogen in the compound? (The vapor pressure of water at 25°C is 23.8 torr.) 110. A compound contains only C, H, and N. A chemist analyzes it by doing the following experiments. a. Complete combustion of 35.0 mg of the compound produced 33.5 mg CO2 and 41.1 mg H2O. b. A 65.2-mg sample of the compound was analyzed for nitrogen by the Dumas method (see Exercise 109), giving 35.6 mL of dry N2 at 740. torr and 25°C. c. The effusion rate of the compound as a gas was measured and found to be 24.6 mL/min. The effusion rate of argon gas, under identical conditions, is 26.4 mL/min. What is the formula of the compound? 112. Without looking at tables of values, which of the following gases would you expect to have the largest value of the van der Waals constant b: H2, N2, CH4, C2H6, or C3H8? 113. From the values in Table 5.3 for the van der Waals constant a for the gases H2, CO2, N2, and CH4, predict which of these gas molecules show the strongest intermolecular attractions.