Physics Courseware Physics I Ideal Gases


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1 Physics Courseware Physics I Ideal Gases Problem 1. How much mass of helium is contained in a 0.0 L cylinder at a pressure of.0 atm and a temperature of.0 C? [The atomic mass of helium is 4 amu] PV ( 1.01 )(0.0) Solution: The number of moles is: = (27 + ) The mass is m = nm = kg = kg Problem 2.A tank of compressed oxygen is at a temperature of 27 ºC and a pressure of 2,00 kpa. Calculate the mass of oxygen contained in the tank if its volume is 0.12m. [The molecular mass of O 2 is 2] Solution: First we calculate the number of moles: pv pv=n n = p=2,00 kpa = 2,00x Pa T=27+27=00K V=0.12m R=8.14J/K pv (200x Pa)(0.12m ) = 120 moles 8.14J/K(00K) Since each mole is 2 grams: Mass of oxygen = 120x2g =.8kg Problem. Calculate the molecular weight of a gas if.4 g of the gas stored in a 7.0 L tank exerts a pressure of 60.0 atm at a constant temperature of 4. C Solution: V = 7.L = 7. m T = = 18. 6K 1.01 P = 60 atm = 60.8 PV (60.8 )( ( 18.6).4 So the molecular mass is M = = ) = 17.2 moles
2 Problem 4. How many moles of gas are contained in ml at 21.0 C and 70.0 mm Hg pressure? Solution: The problem provides the following information: 1L 1m 6 V = 890mL = 890mL = 890 m 00mL 00L T = = 294K 1.01 P = 70 mmhg = 70mmHg = mmHg 6 PV (0.999 )(890 ) = 0.06 moles ( ) Problem g of H2 is contained in a 2.00 L container at 20.0 C. What is the pressure in this container in mm Hg? mass 1.09g Solution: The number of moles is: n = = = 0. 4 molecular mass in grams 2g V = 00L T = = 29K 2L = 2L = 2 m So the pressure is: In mmhg: P =.64 P n V ( 29) (0.4)(8.14) = = = 760mmHg pascal =,000 mmhg Problem 6. Calculate the volume.00 moles of a gas will occupy at 24.0 C and mm Hg. Solution: n = T = = 297K The pressure is: 1.01 P = 762.4mmHg = 762.4mmHg = mmHg And the volume is: n (8.14)(297) V = = = 0.07 m P 1.016
3 Problem 7. What volume will 20.0 g of Argon occupy at STP? mass 20 g = 0. molecular mass in grams 40 g STP stands for: P = 1 atm = 1.01, T = 0 C = 27K, so the volume is: n 0.(8.14)(27) V = = = m P 1.01 Problem 8. How many moles of gas would be present in a gas trapped within a 0.0 ml vessel at 2.0 C at a pressure of 2.0 atmospheres? Solution:The information given: 1L 1m 4 V = 0mL = 0mL = 1 m 00mL 00L T = = 298K 1.01 P = 2.0atm = 2.atm = 2. 4 PV (2. )(1 ) = 0.02 moles ( ) Problem 9. How many moles of a gas would be present in a gas trapped within a 7.0 liter vessel at C at a pressure of 2.0 atm? Solution: V = 7L = 7L = 7 m 00L T = = K 1.01 P = 2.0atm = 2.atm = 2. PV (2. )(7 ) =.2 moles 8.14 ( )
4 Problem. If the number of moles of a gas is doubled at the same temperature and pressure, will the volume increase or decrease? Solution: It will double! Problem 11. What volume will 1.27 moles of helium gas occupy at STP? Solution: n = STP stands for: P = 1 atm = 1.01, T = 0 C = 27K, so the volume is: n 1.27(8.14)(27) V = = = m P 1.01 Problem 12. At what pressure would 0. mole of nitrogen gas at 2.0 C occupy 8.90 L? Solution: n=1. V = 8.9L = 8.9L = 8.9 m 00L T = = 296K n 1.(8.14)(296) P = = = 414,000 V 8.9 Problem 1. What volume would 2.0 g of NO2 gas occupy at.12 atm and 18.0 C? mass 2 g Solution: The number of moles is: = molecular mass in grams 44g T = = 291K 1.01 The pressure is: P =.12atm =.16 n 0.727(8.14)(291) So the volume is: V = = = 0.00 m P.16
5 Problem 14. Find the volume of 2.40 mol of gas whose temperature is 0.0 C and whose pressure is 2.00 atm. Solution: The number of moles is: n = 2. 4 T = = 2K 1.01 The pressure is: P = 2 atm = n 2.4(8.14)() So the volume is: V = = = 0.047m P Problem 1. Calculate the molecular weight of a gas if.44 g of the gas stored in a 7.0 L tank exerts a pressure of 60.0 atm at a constant temperature of. C Solution: Let s find the number of moles: V = 7.L = 7.L = 7. m 00L T = = 08. K 1.01 P = 60 atm = 60atm = PV (60.78 )(7. ) = 17.8 moles 8.14( 08.) And the molecular weight is.44 g/17.8=1.99, so it could be hydrogen. Problem 16. How many moles of gas are contained in a 0.0 L cylinder at a pressure of 0.0 atm and a temperature of.0 C? Solution: V = 0L = 0L = 0 m 00L T = + 27 = 08K 1.01 P = 0 atm = 0atm = 1. PV (1. )(0 ) = 198 moles ( )
6 Problem 17. Determine the number of moles of Krypton contained in a.2 liter gas tank at.80 atm and 2. C. If the gas is Oxygen instead of Krypton, will the answer be the same? Why or why not? PV ( )(.2 m ) = moles 8.14(298.6K) Oxygen at those conditions would give us the same value. Notice that the equation doesn t contain the mass. Problem 18. Determine the number of grams of carbon dioxide in a 40.6 ml tank at 1.80 atm and minus 0. C. Determine the number of grams of oxygen that the same container will contain under the same temperature and pressure. PV ( )(0.406 m ) = moles 8.14( ) The mass is: x44g=1.9 g If it were oxygen the mass would be x2=1.42 g Problem 19. Determine the volume of occupied by 2.4 grams of carbon dioxide gas at STP (27.1) n Solution: = = 44 V = m p 1.01 Problem 20. A sample of argon gas at STP occupies 6.2 liters. Determine the number of moles of argon and the mass in the sample Mass=2.09x40=0.g Problem 21. At what temperature will 0.64 moles of neon gas occupy 12.0 liters at 1.9 atmospheres? pv ( )( 12. ) Solution: T = = = K nr
7 Problem 22. A 0.6 g sample of gas occupies L at STP. What is the molecular weight of this gas? Solution: It is 0.6 Problem 2. A 40.0 g gas sample occupies 11.2 L at STP. Find the molecular weight of this gas. Solution: It is 80.0 Problem 24. A 12.0 g sample of gas occupies 19.2 L at STP. What is the molecular weight of this gas? , so M=12.0/0.87=14 Problem g. of a gas occupies 48.0 L at mm Hg and 20.0 C. What is its molecular weight? PV (700 / )(48 m ) = 1.8 moles 8.14(29.1K) M=96.0/1.8=48.98 Problem g. of a gas occupies L at kpa at 0.0 C. What is its molecular weight? PV (79.97 )(4.167 m ) = moles 8.14(1.1K ) M=20.8/0.128=162.7 Problem 27. At STP.00 liters of an unknown gas has a mass of 9.0 grams. Calculate its molar mass. 0.19, so M= 9.0/0.19=70.9 Problem 28. At STP 0.20 liter of an unknown gas has a mass of 1.00 gram. Calculate its molar mass , so M= 1/0.0111=89.6
8 Problem 29. At STP.0 ml of an unknown gas has a mass of 0.20 gram. Calculate its molar mass , so M= 0.2/ =7. Problem g of a gas occupies 4.0 L at 20. C and atm. What is its molar mass? PV ( )(4. m ) = moles 8.14(29.6K) so M= 1.089/0.166=6. Problem g of a gas occupies 20.0 ml at STP. What is its molar mass? What gas is it? Hint  calculate molar mass of the gas , so M= 0.19/0.0111=17 could be ammonia Problem 2. If grams of a gas are enclosed in a 0.00 liter vessel at 27.1 K and atmospheres of pressure, what is the molar mass of the gas? What gas is this? PV ( )(0 m ) = 4.46 moles 8.14(27.1K) M=9.006/4.46=2 It is hydrogen. Problem. A 0.00 liter tank at minus 1.00 C contains grams of helium gas and.00 grams of nitrogen gas. a. Determine the moles of helium gas in the tank. b. Determine the moles of nitrogen gas in the tank. c. Determine the mole fraction of helium gas in the tank. d. Determine the partial pressure of helium gas in the tank. e. Determine the partial pressure of nitrogen gas in the tank. f. Determine the total pressure of the mixture in the tank. g. Determine the volume that the mixture will occupy at STP.
9 Problem 4. Determine the number of moles of Krypton contained in a.2 liter gas tank at.80 atm and 2. C. If the gas is Oxygen instead of Krypton, will the answer be the same? Why or why not? [1 atm=1,00 ] PV Solution: The number of moles is = 0.77 moles The same answer if it were oxygen instead of krypton, because the law is universal for all ideal gasses.
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