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Chapter 2 Answer Key Section 2.1, Page Section 2.2, Page 68 1. Compressibility and Expansion are the properties of gas that are used to operate the ballast tanks of the submarine. When water is pumped in, the air in the tank is compressed. When water is pumped out, the compressed air expands to fill the empty tanks. 2. Compressed gases must be kept away from heat sources and the containers must be handled with care. Increased temperature would cause the gas particles to move faster, and that would increase the pressure inside the container. Damaging a gas container could cause it to rupture or explode. Page 68, continued 3. The compressibility of gases allows the gas spring to absorb the shock of opening or closing the hatchback. 4. At the same temperature, two gases will have the same average kinetic energy. Their velocity will vary in proportion to their respective masses. 5. As the balloon rises, the pressure outside will decrease, but the number of particles inside stays the same. The particles will continue to hit the side of the balloon pushing outwards. As the balloon rises, the gas inside will expand, filling all the space of the balloon. Page 68, concluded 6. In diffusion, a gas mixes gradually with another gas in the container, until the particles are evenly distributed. In effusion, a gas escapes from a container though one or more small openings in the container, or through a porous barrier. 7. Fastest NH3, HF, CO, NO2, HI slowest 8. Answer: the molar mass of the unknown gas is 24.4 g/mol* 9. The molar mass of the unknown gas is 146 g/l 10.Curve 1 represents the gas with the greatest mass. (the gas with the lowest rate should be the one with the greatest mass.) *full answer for this question on the next slide Question 8, complete answer The effusion rate of an unknown gas is 43.0 mL/min. The effusion rate of CO2 is 32.0 mL/min. What is the molar mass of the unknown gas? Data: vx = 43.0 mL/min vCO = 32.0 mL/min 2 To find: MCO = 44.0 g/mol Mx = 24.4 g/mol 2 Answer: The molar mass of the unknown gas is about 24.4 g/mol Step 1: find molar mass of CO2 MCO = 12.0 g/mol + 2(16.0 g/mol) = 44.0 g/mol 2 Step 2: Use Graham’s Law vx vCO2 43 32 M CO2 Mx 44 Mx 43 6.6332 32 Mx 32 6.6332 Mx 43 M x (4.9363)2 24.367 Question 9, complete answer It takes 192 s for an unknown gas to effuse. Nitrogen gas (N2) diffuses across the same barrier in 84s. What is the molar mass of the unknown gas. Data: tx = 192 s tN = 84 s 2 To find: MN = 28.0 g/mol Mx = 146 g/mol 2 Answer: The molar mass of the unknown gas is about 146 g/mol Step 1: find molar mass of N2 MN = 2(14.0 g/mol) = 28.0 g/mol 2 Step 2: Use Graham’s Law variation Mx tx t N2 M N2 192 84 x 28 192 x 84 5.2915 192 5.2915 x 84 x 12.09485 x 146 .2855 Section 2.3, Page 74 • 1. Molecules striking the sides of a container cause pressure. • 2. the pressure is 0.905 atm or 91.7 kPa. • 3. a) 450 mmHg or 60.0 kPa b) 99.9 kPa or 749 mmHg c) 160 kPa or 1199 mmHg d) 159.9 kPa or 4. The pressure is 18mmHg or 2.4 kPa* *I think the book author intended a different answer, but I have answered what the question asked, not what I think it should have asked. Section 2.4.1, Page 97 1. 2. 3. 4. 5. 6. 7. 8. 9. V2= 240 mL V2= 97.9 mL P2= 140 kPa (or 1.4x102 kPa) P2= 66.5 kPa V2= 2.3 L P2= 1.2 x 102 kPa (or 120 kPa) V= 290 L (or 2.9 x 102 L P= 1.5 x 102 kPa (or 150 kPa) (a) P1= 108 kPa (b) The pressure was very high (good weather) but it is now falling (bad weather coming) 10. V= 8.32 L Section 2.4.2, Page 97, 98 11. a) 298 K b) 310 K c) 423 K 12. a) 100°C b) -175°C c) 152°C 13. The volume occupied by the gas will be 33L. 14. The volume of the balloon will be 2.1 L 15. The final temperature will be 606°C 16. The variation will be 660°C 17. The volume of CO2 in the dough is 0.12L 18. The volume of the chlorine is 33 mL 19. The gas must be heated to 55°C 20. The nitrogen will occupy 386 mL 21. The temperature is 369 K or 96°C Section 2.4.3, Page 98 22.Answer: The temperature will be 97°C. 23.The thermometer will show -3.7°C. 24.The pressure will be 759 mmHg. 25.The manometer will show a pressure of 109 kPa. 26.The temperature in the freezer is -16°C. 27.The gas must be heated to 313°C. 28.The valve will open when the butane is 240°C. 29.The gas will exert a pressure of 271 kPa 30.The pressure exerted by the helium is 18.9 atm Section 2.4.4, Page 98 31.The volume of the container is 100 L (1x102 L) 32. The volume is 33. The balloon originally contained ≈4 mol of He. You add 0.5 mol of oxygen, making the new n≈4.5 mol. V 81L So V1≈72 L 1 4mol 4.5mol 34.Answer: 0.57 mol of air escaped from the tire. 35. Answer: 0.0098 mol of CO2 must be added to the balloon. 36. There are 6.34x10-3 g of oxygen in the swim bladder of the fish. 37. The total volume of argon is 77.3 L 38. a) 0.21 mol, b) 9.24x10-4 mol c) 3.7x10-3 mol 39. The volume occupied by the hydrogen is about 180 L 40. The amount of sulphur dioxide is 2.0x10-3 mol. 41. Neon will occupy 50.4 L 42. Hydrogen volume is 12 300 L 43. The volume of hydrogen sulphide is 1400 L 44. The volume of hydrogen is 24.5 L 45. There are 3.01x1023 molecules of helium 46. Seven or Eight envelopes (seven is the closest answer, but if you needed all the air, you would need eight envelopes) 47. SATP is a higher temperature than STP (25°C vs. 0°C). According to kinetic theory at a higher temperature the molecules would move faster, and try to expand to a greater volume. 48. The water is a liquid. It does not have a standard molar volume (only gases do), and liquid is a condensed form of matter. It will have less volume. 49.The air pressure in the tire is 190 kPa 50.It would take 24 mol of gas 51.Since the rubber ball is elastic, the volume can increase. If the volume increases the pressure may not. In the propane tank the volume is constant, so the pressure must increase. 52.Fifty two P1 n1 P2 n2 c) 71.4 kPa e) 175 mol a) 150 kPa b) 3.7 mol d) 158 kPa Page 104 1. P=104 kPa, V=2L, T=295K so n=PV / RT so n=0.085mol (for all three containers) a. The containers hold the same moles (0.085mol), and therefore molecules of gas b. The mass of the gases are: 0.34g, 2.7g, and 3.7g* 2. The pressure exerted by the methane is 971 kPa. 3. sample contains 4.10x10-2 mol of methane. 4. The temperature will be 497 K or 224°C *It could be argued that the answers should be rounded to just one significant digit, since the volume was given as 2L, rather than 2.0L, but that would render the answers (0.3g, 3g and 4g) somewhat meaningless. Page 104 continued 5. What quantity of methane gas is found in a sample with a volume of 500mL at 35C and 210 kPa P= 210 kPa PV=nRT V= 0.500 L n = PV / RT n= ? n= (210 x 0.5) / (8.31 x 308) T= 35+273= 308K n= 0.0410 mol The amount of methane is 0.041 moles (or 0.66g) 6. Determine the pressure exerted in a 50L cylinder if it contains 30 mol of air and is heated to 40C? P=? PV=nRT V= 50L P= nRT / V n= 30 mol P= (30 x 8.31 x 313) / 50 T= 40+273=313K P = 1560.6 kPa The pressure is 1.6 x 103 kPa Page 104 continued 9. The molar mass of the gas is 242 g/mol (2.4x102 g/mol) 10. The mass of sulphur dioxide is 99g 11. The molar mass of the gas is 1.3 x 102 g/mol 12. The molar mass of the gas is 44.2 g/mol. The gas could be Carbon dioxide or propane 13. The sample contains 0.500 moles 14. The volume of the balloon is 2.5x102 L 15. The pressure of the argon in the bulb is 78 kPa 16. The temperature of the chlorine gas is 23°C Page 104 continued 7. What volume does 50kg of oxygen gas occupy at a pressure of 150 kPa and a temperature of 125°C P=150 kPa V=? n= 1562 mol T=125+273=398K n= 50000g / 32g/mol= 1562 mol PV=nRT V= (nRT) / P V = (1562 x8.31x398) / 150 V= 34462L The volume is 3.4 x104 L 8. At what temperature does 10.5 g of ammoina (NH3) gas exert a pressure of 85 kPa in a 30 L container? P=85kPa n= 10.5g / 17 g/mol = 0.618 mol V=30L PV = nRT m=10.5g T = PV / nR n=0.618 mol T= (85x30) / (0.618x8.31) T=? T=496.5 k The temperature would be about 497 K or 224° C Page 107 1. The gas must be brought to a temperature of 99.55 K or -173.45°C (1.0x102 K or -173°C) 2. The volume of the gas would be 67.34 L (67 L) 3. The volume of the gas would be 5.8L 4. The final temperature will be 231°C (or 504K) 5. The new volume of the balloon is 1.0 L 6. The missing quantities are: a. 88C b. 15.9 C c. 3.8x102 kPa d. 5 L* e. 1.03x103L * 4.605 L rounded to 1 SF. (a nasty trick to play on you!) 7. This is a nasty question, since both the volume and pressure can change, there are too many variables, so it cannot be solved using the general gas law a. No answer. b. No answer. 8. The volume of methane is 127 mL (or 0.127 L) 9. The new volume of the gas is 163 mL 10. The new temperature of the gas is 1.5x102K or 1.2x102°C 11. The temperature of the bulb is 310°C 12. The final volume of the gas is 1.5 times the original volume. 13. A pressure of 642 kPa must be applied. Page 113 1. The resulting pressure is 300.65 kPa 2. The partial pressure of Ar is 50.2 kPa 3. Find the percentages of the total pressure. 1. Partial pressure of Ne is 13.92 kPa(14kPa) 2. Partial pressure of He is 26.68 kPa(27kPa) 3. Partial pressure of Rd is 75.4 kPa (75 kPa) 4. The total pressure of mixture is 110 kPa (1.1x102 kPa) 5. The total number of moles is 2.92 mol. The partial pressures are: 1. 2. 3. 4. Methane (CH4) is 748.99 kPa ( 7.5x102 kPa) Oxygen (O2) is 484.64 kPa ( 4.8x102 kPa) Nitrogen (N2) is 1101.45 kPa (1.1x103 kPa) Propane (C3H8) is 237.9 kPa (2.4x102 kPa) 6. The partial pressure of CO2 is 0.7 atm. 7. The partial pressures of the gases are: 1. Carbon dioxide = 3.591 kPa (3.6 kPa) 2. Oxygen = 4.104 kPa ( 4.1 kPa) 3. Water vapour= 94.905 kPa (95 kPa) 8. The container has 64% chlorine inside. Chapter 2. Physical Properties of Gases (lines are drawn through questions which may have misprints in the textbook) 1. 2. 3. 4. Answer is Pressure of the gas is 69.6 kPa Pressure of CO2 is 103 kPa It moves towards the open end Since the end is closed, atmospheric pressure does not exert force on the mercury, so the difference in height is equal to the gas pressure. 5. (explanation pending) 6. The pressure in the cylinder is 57 atmospheres 7. The hydrogen will occupy 375 dm3 (or 375 L) 8. The final temperature of the gas is 49.3°C 9. About 1.7 L of water vapour will form in the cake 10.The volume of chlorine is 170 L 11.The final temperature will be 74°C 12.The final pressure will be 3.0x102 kPa 13. a)318 K b) 340 K c) 623 K 14. a) 200°C b) -165°C c) -48°C 15.The volume of CO2 in the dough is 0.56 L 16.The volume of argon is 2.6 L 17.The new volume of gas is 8.2 L 18.The heat increases the kinetic energy inside the balloon, this can increase the pressure until the balloon bursts. 19.The nitrogen will occupy 0.50 L 20.The volume of dry air is 21 L 21.The volume of the balloon is 2.1 L 22.The final temperature is 606°C 23.The final temperature of the oxygen is -233°C 24.The pressure in the tire is 252 kPa 25.A pressure of 6.4x102 kPa must be exerted. 26.The nitrogen will occupy 2.8 L 27.The volume of the balloon will be 2.2 L 28.The container can be safely heated to 374°C 29.The final temperature of argon is 273°C 30.The final temperature of neon is -67°C 31.The pressure of oxygen is 9.5x102 kPa 32.The pressure in the bulb will be 24 atm. 33.The volume of the bubble will be 21 mL 34.The molar mass of the gas is 48.2 g/mol 35. The molar mass of halothane is 197 g/mol 36. The molar mass of the gas is71.2 g/mol 37. The oxygen occupies a volume of L 38. The nitrogen occupies a volume of 0.33 L 39. a) 2.41g b) 1.75 g 40. The temperature is 12°C 41. The gas will occupy 5.0 L at 0°C 42. The increase in pressure is 127% 43. There are 0.18 mol of oxygen 44. The effusion rate of nitrogen is higher than the unknown gas, therefore, by Graham’s law, the molar mass of the unknown gas must be higher than nitrogen.