Gas Laws Supplemental Problems Key

Gas Laws - Supplemental Problems 1. In one city, a balloon with a volume of 6.0 L is filled with air at 101 kPa pressure. The balloon in then taken to a second city at a much higher altitude. At this second city, atmospheric pres-sure is only 91 kPa. If the temperature is the same in both places, what will be the new volume of the balloon? 𝑃1𝑉1 = 𝑃2𝑉2 𝑃1 = 101 𝑘𝑃𝑎 𝑉1 = 6. 0 𝐿 𝑃2 = 91 𝑘𝑃𝑎 𝑉2 =? 𝑉2 = 𝑃1𝑉1 𝑃2 = (100 𝑘𝑃𝑎)(6.0 𝐿) 91 𝑘𝑃𝑎 𝑉2 = 6. 7 𝐿 2. A certain mass of gas in a 2.25-L container has a pressure of 164 kPa. What will the new pressure be if the volume of the container is reduced to 1.50 L and the temperature stays constant? 𝑃1𝑉1 = 𝑃2𝑉2 𝑃1 = 164 𝑘𝑃𝑎 𝑉1 = 2. 25 𝐿 𝑃2 =? 𝑉2 = 1. 50 𝐿 𝑃2 = 𝑃1𝑉1 𝑉2 = (164 𝑘𝑃𝑎)(2.25 𝐿) 1.50 𝐿 𝑃2 = 246 𝑘𝑃𝑎 3. If 5.80 dm3 of gas is collected at a pressure of 92.0 kPa, what volume will the same gas occupy at 101.3 kPa if the temperature stays constant? 3 𝑃1𝑉1 = 𝑃2𝑉2 𝑉2 = 𝑃1𝑉1 𝑃2 𝑃1 = 92. 0 𝑘𝑃𝑎 𝑉1 = 5. 80 𝑑𝑚 𝑃2 = 101. 3 𝑘𝑃𝑎 𝑉2 =? 3 = (92.0 𝑘𝑃𝑎)(5.80 𝑑𝑚 ) 101.3 𝑘𝑃𝑎 3 𝑉2 = 5. 27𝑑𝑚 4. If the volume of an air pump used to inflate a football decreases from 480 mL to 375 mL, and the original pressure was 93.5 kPa, what is the new air pressure in the pump if the temperature stays constant? 𝑃1𝑉1 = 𝑃2𝑉2 𝑃1 = 93. 5 𝑘𝑃𝑎 𝑉1 = 480 𝑚𝐿 𝑃2 =? 𝑉2 = 375 𝑚𝐿 𝑃2 = 𝑃1𝑉1 𝑉2 = (93.5 𝑘𝑃𝑎)(480 𝑚𝐿) 375 𝑚𝐿 𝑃2 = 120 𝑘𝑃𝑎 5. Maintaining constant pressure, the volume of a gas is increased from 18.0 dm3 to 32.0 dm3 by heating it. If the original temperature was 18.0°C, what is the new temperature in degrees Celsius? 𝑉1 𝑇1 = 𝑉2 𝑇2 3 𝑉1 = 18. 0 𝑑𝑚 𝑇2 = 𝑉2𝑇1 𝑉1 3 𝑇1 = 18. 0 °𝐶 + 273 = 291 𝐾 𝑉2 = 32. 0 𝑑𝑚 𝑇2 =? 3 = (32.0 𝑑𝑚 )(291 𝐾) 3 18.0 𝑑𝑚 𝑇2 = 517𝐾 − 273 = 244°𝐶 6. A natural gas tank is constructed so that the pressure remains constant. On a hot day when the temperature was 33°C, the volume of gas in the tank was determined to be 3000.0 L. What would the volume be on a warm day when the temperature is 11°C? 𝑉1 𝑇1 = 𝑉2 𝑇2 𝑉1 = 3000. 0 𝐿 𝑇1 = 33. 0 °𝐶 + 273 = 306 𝐾 𝑉2 =? 𝑇2 = 11. 0 °𝐶 + 273 = 284 𝐾 𝑉2 = 𝑉1𝑇2 𝑇1 = (3000.0 𝐿)(284 𝐾) 306 𝐾 𝑉2 = 2780 𝐿 7. A 50.0-mL sample of gas is cooled from 119°C to 80.0°C. If the pressure remains constant, what is the final volume of the gas? 𝑉1 𝑇1 = 𝑉2 𝑇2 𝑉1 = 50. 0 𝑚𝐿 𝑇1 = 119 °𝐶 + 273 = 392 𝐾 𝑉2 =? 𝑇2 = 80 °𝐶 + 273 = 353 𝐾 𝑉2 = 𝑉1𝑇2 𝑇1 = (50.0 𝑚𝐿)(353 𝐾) 392 𝐾 𝑉2 = 45. 0 𝑚𝐿 8. A 10.0-L cylinder of gas is stored at room tem-perature (20.0°C) and a pressure of 1800 psi. If the gas is transferred to a 6.0-L cylinder, at what Celsius temperature would it have to be stored in order for the pressure to remain at 1800 psi? 𝑉1 𝑇1 = 𝑉2 𝑇2 𝑉1 = 10. 0 𝐿 𝑇1 = 20. 0 °𝐶 + 273 = 293 𝐾 𝑉2 = 6. 0 𝐿 𝑇2 =? 𝑇2 = 𝑉2𝑇1 𝑉1 = (6.0 𝐿)(293 𝐾) 10.0 𝐿 𝑇2 = 176𝐾 − 273 =− 97°𝐶 9. If the gas pressure in an aerosol can is 148.5 kPa at 23°C, what is the pressure inside the can if it is heated to 298°C? 𝑃1 𝑇1 = 𝑃2 𝑇2 𝑃1 = 148. 5 𝑘𝑃𝑎 𝑇1 = 23 °𝐶 + 273 = 296 𝐾 𝑃2 =? 𝑇2 = 298 °𝐶 + 273 = 571 𝐾 𝑃2 = 𝑃1𝑇2 𝑇1 = (148.5 𝑘𝑃𝑎)(571 𝐾) 296 𝐾 𝑃2 = 286 𝑘𝑃𝑎 10. A tank for compressed gas has a maximum safe pressure limit of 850 kPa. The pressure gauge reads 425 kPa when the temperature is 28°C. What is the highest temperature in degrees Celsius the tank can withstand safely? 𝑃1 𝑇1 = 𝑃2 𝑇2 𝑃1 = 425 𝑘𝑃𝑎 𝑇1 = 28 °𝐶 + 273 = 301 𝐾 𝑃2 = 850 𝑘𝑃𝑎 𝑇2 =? 𝑇2 = 𝑇1𝑃2 𝑃1 = (148.5 𝑘𝑃𝑎)(301 𝐾) 296 𝐾 𝑇2 = 602𝐾 − 273 = 330°𝐶 11. In a steel container, it was found that the pres-sure of the gas inside was 160 kPa when the container had been heated to 98°C. What had been the pressure of the gas when the temperature had been 50°C the previous day? 𝑃1 𝑇1 = 𝑃2 𝑇2 𝑃1 =? 𝑇1 = 50 °𝐶 + 273 = 323 𝐾 𝑃2 = 160 𝑘𝑃𝑎 𝑇2 = 98 °𝐶 + 273 = 371 𝐾 𝑃1 = 𝑃2𝑇1 𝑇2 = (160 𝑘𝑃𝑎)(323 𝐾) 371 𝐾 𝑃2 = 140 𝑘𝑃𝑎 12. A steel cylinder is filled with a gas at a temperature of 25.0°C and a pressure of 225.0 kPa. What will the pressure be if the temperature is raised to 47°C? 𝑃1 𝑃2 = 𝑇1 𝑇2 𝑃1 = 225. 0 𝑘𝑃𝑎 𝑇1 = 25. 0 °𝐶 + 273 = 298 𝐾 𝑃2 =? 𝑇2 = 47 °𝐶 + 273 = 320 𝐾 𝑃1𝑇2 𝑃2 = = 𝑇1 (225.0 𝑘𝑃𝑎)(320 𝐾) 298 𝐾 𝑃2 = 242 𝑘𝑃𝑎 13. A balloon is filled with gas at a pressure of 102.3 kPa and a temperature of 45.5°C. Its volume under these conditions is 12.5 L. The balloon is then taken into a decompression chamber where the volume is measured as 2.50 L. If the temperature is 36.0°C, what is the pressure in the chamber? 𝑃1𝑉1 𝑇1 = 𝑃2𝑉2 𝑇2 𝑃1 = 102. 3 𝑘𝑃𝑎 𝑉1 = 12. 5 𝐿 𝑇1 = 45. 5 °𝐶 + 273 = 318. 5 𝐾 𝑃2 =? 𝑉2 = 2. 50 𝐿 𝑇2 = 36. 0 °𝐶 + 273 = 309 𝐾 𝑃1𝑉1𝑇2 𝑃2 = 𝑇1𝑉2 = (102.3 𝑘𝑃𝑎)(12.5 𝐿)(309 𝐾) (318.5 𝐾)(2.50 𝐿) 𝑃2 = 496 𝑘𝑃𝑎 14. A weather balloon contains 14.0 L of helium at a pressure of 95.5 kPa and a temperature of 12.0°C. If this had been stored in a 1.50-L cylinder at 21.0°C, what must the pressure in the cylinder have been? 𝑃1𝑉1 𝑇1 = 𝑃2𝑉2 𝑇2 𝑃1 =? 𝑉1 = 1. 50 𝐿 𝑇1 = 21. 0 °𝐶 + 273 = 294 𝐾 𝑃2 = 95. 5 𝑘𝑃𝑎 𝑉2 = 14. 0 𝐿 𝑇2 = 12. 0 °𝐶 + 273 = 285 𝐾 𝑃1 = 𝑃2𝑉2𝑇1 𝑉1𝑇2 = (95.5 𝑘𝑃𝑎)(14.0 𝐿)(294 𝐾) (1.50 𝐿)(285 𝐾) 𝑃2 = 919 𝑘𝑃𝑎 15. How many moles of a gas will occupy 2.50 L at STP? 1 𝑚𝑜𝑙𝑒 𝑜𝑓 𝑔𝑎𝑠 𝑎𝑡 𝑆𝑇𝑃 = 22. 4 𝐿 𝑜𝑓 𝑔𝑎𝑠 2.50 𝐿 1 × 1 𝑚𝑜𝑙 22.4 𝐿 = 0. 112 𝑚𝑜𝑙 16. Calculate the volume that 3.60 g H2 gas will occupy at STP. 1 𝑚𝑜𝑙𝑒 𝑜𝑓 𝑔𝑎𝑠 𝑎𝑡 𝑆𝑇𝑃 = 22. 4 𝐿 𝑜𝑓 𝑔𝑎𝑠 3.60 𝑔 𝐻2 1 × 1 𝑚𝑜𝑙 𝐻2 2.02 𝑔 𝐻2 × 22.4 𝐿 𝐻2 1 𝑚𝑜𝑙 𝐻2 = 39. 9 𝐿 𝐻2 17. What volume is occupied by 0.580 mol of gas at 98.4 kPa and 11°C? 𝑃𝑉 = 𝑛𝑅𝑇 𝑃 = 98. 4 𝑘𝑃𝑎 𝑉= 𝑛𝑅𝑇 𝑃 𝑉 =? 𝑛 = 0. 580 𝑚𝑜𝑙 (0.580 𝑚𝑜𝑙)(8.31 = 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑅 = 8. 31 )(284 𝐾) 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑇 = 11°𝐶 + 273 = 284𝐾 𝑉 = 13. 9 𝐿 98.4 𝑘𝑃𝑎 18. When a sample of a gas was placed in a sealed container with a volume of 3.35 L and heated to 105°C, the gas vaporized and the resulting pressure inside the container was 170.0 kPa. How many moles of the gas was present? 𝑃𝑉 = 𝑛𝑅𝑇 𝑃 = 170. 0 𝑘𝑃𝑎 𝑛= 𝑃𝑉 𝑅𝑇 = 𝑉 = 3. 35 𝐿 𝑛 =? (170.0 𝑘𝑃𝑎)(3.35 𝐿) (8.31 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑅 = 8. 31 𝑇 = 105°𝐶 + 273 = 378𝐾 𝑛 = 0. 181 𝑚𝑜𝑙 )(378 𝐾) 19. An engineer wishes to design a container that will hold 14.0 mol of gas at a pressure no greater than 550 kPa and a temperature of 48°C. What is the minimum volume the container can have? 𝑃𝑉 = 𝑛𝑅𝑇 𝑃 = 550 𝑘𝑃𝑎 𝑉= 𝑛𝑅𝑇 𝑃 𝑉 =? 𝑛 = 14. 0 𝑚𝑜𝑙 (14.0 𝑚𝑜𝑙)(8.31 = 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑅 = 8. 31 )(321 𝐾) 𝑇 = 48°𝐶 + 273 = 321𝐾 𝑉 = 67. 9 𝐿 550 𝑘𝑃𝑎 20. What is the molar mass of a sample of gas that has a density of 2.85g/L at 101 kPa pressure and 29°C? 𝑚 𝑚 𝐷𝑉 𝑃𝑉 = 𝑛𝑅𝑇 𝑛 = 𝑀 →𝑚 = 𝑛𝑀 𝐷 = 𝑉 →𝑚 = 𝐷𝑉 𝑛𝑀 = 𝐷𝑉→𝑛 = 𝑀 𝑃𝑉 = 𝑛𝑅𝑇→𝑃𝑉 = ( 𝑃 = 101 𝑘𝑃𝑎 𝑀= 𝐷𝑅𝑇 𝑃 = 𝐷𝑉 𝑀 )𝑅𝑇→𝑃 = 𝐷 = 2. 85 𝑔/𝐿 (2.85 𝑔/𝐿)(8.31 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝐷𝑅𝑇 𝑀 𝑅 = 8. 31 )(302 𝐾) 101 𝑘𝑃𝑎 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑇 = 29°𝐶 + 273 = 302𝐾 𝑀 =? 𝑀 = 70. 8 𝑔/𝑚𝑜𝑙 21. How many grams of gas are present in a sample that has a molar mass of 44 g/mol and occupies a 1.8-L container at 108 kPa and 26.7°C? 𝑚 𝑚 𝑃𝑉 = 𝑛𝑅𝑇 𝑛 = 𝑀 𝑃𝑉 = 𝑛𝑅𝑇→𝑃𝑉 = ( 𝑀 )𝑅𝑇 𝑃 = 108 𝑘𝑃𝑎 𝑉 = 1. 8 𝐿 𝑚 =? 𝑀 = 44 𝑔/𝑚𝑜𝑙 𝑅 = 8. 31 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑇 = 26. 7°𝐶 + 273 = 299. 7𝐾 𝑚= 𝑀𝑃𝑉 𝑅𝑇 = (44 𝑔/𝑚𝑜𝑙)(108 𝑘𝑃𝑎)(1.8 𝐿) (8.31 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 )(299.7 𝐾) 𝑚 = 3. 4 𝑔 22. What is the molar mass of a gas if 142 g of the gas occupies a volume of 45.1 L at 28.4°C and 94.6 kPa? 𝑚 𝑚 𝑃𝑉 = 𝑛𝑅𝑇 𝑛 = 𝑀 𝑃𝑉 = 𝑛𝑅𝑇→𝑃𝑉 = ( 𝑀 )𝑅𝑇 𝑃 = 94. 6 𝑘𝑃𝑎 𝑉 = 45. 1 𝐿 𝑚 = 142 𝑔 𝑀 =? 𝑅 = 8. 31 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 𝑇 = 28. 4°𝐶 + 273 = 301. 4𝐾 𝑀= 𝑚𝑅𝑇 𝑃𝑉 = (142 𝑔)(8.31 𝐿∙𝑘𝑃𝑎 𝑚𝑜𝑙∙𝐾 )(301.4 𝐾) (94.6 𝑘𝑃𝑎)(45.1 𝐿) 𝑚 = 83. 4 𝑔/𝑚𝑜𝑙 23. Determine the volume of hydrogen gas needed to make 8 L of water vapor. 2𝐻2(𝑔) + 𝑂2(𝑔)→2𝐻2𝑂(𝑔) 8 𝐿 𝐻2𝑂 1 × 1 𝑚𝑜𝑙 𝐻2𝑂 22.4 𝐿 𝐻2𝑂 × 2 𝑚𝑜𝑙 𝐻2 2 𝑚𝑜𝑙 𝐻2𝑂 × 22.4 𝐿 𝐻2 1 𝑚𝑜𝑙 𝐻2 = 8𝐿𝐻 2 24. Calculate the volume of chlorine gas at STP that is required to completely react with 3.50 g of silver, using the following equation: 2Ag(s) + Cl2 (g) → 2AgCl(s). 3.50 𝑔 𝐴𝑔 1 × 1 𝑚𝑜𝑙 𝐴𝑔 107 𝑔 𝐴𝑔 × 1 𝑚𝑜𝑙 𝐶𝑙2 2 𝑚𝑜𝑙 𝐴𝑔 × 22.4 𝐿 𝐶𝑙2 1 𝑚𝑜𝑙 𝐶𝑙2 = 0. 366 𝐿 𝐶𝑙2 25. Use the reaction shown to calculate the mass of iron that must be used to obtain 0.500 L of hydrogen at STP. 3Fe(s) + 4H2O(l) → Fe3O4 (s)+ 4H2 (g) 0.500 𝐿 𝐻2 1 × 1 𝑚𝑜𝑙 𝐻2 22.4 𝐿 𝐻2 × 3 𝑚𝑜𝑙 𝐹𝑒 4 𝑚𝑜𝑙 𝐻2 × 55.8 𝑔 𝐹𝑒 1 𝑚𝑜𝑙 𝐹𝑒 = 0. 934 𝑔 𝐹𝑒