Worksheet – Gas Laws III Gas Laws: Combined Gas Law The following problems may be solved using the relationships described by either Charles’ or Boyles’ laws, together in the combined gas law. Show all the steps to the solution of the problem. V1P1/T1 = V2P2/T2 1. Carbon dioxide occupies a 2.54 dm3 container at STP. What will be the volume when the pressure is 150 KPa and 26oC? V2 = [2.54 dm3][101.3 KPa][26oC + 273K] = 1.88 dm3 [150 KPa ][273 K] 2. Oxygen occupies a fixed container of 5.5L at STP. What will happen to the pressure if the temperature rises to 300K? P2 = [5.5 L] [ 101.3 KPa][300 K] = 111.3 KPa [5.5 L] [273 K] 3. Methane is compressed in a closed 15.8 dm3 container at 101.3 KPa. If the volume drops to 8.7 dm3 and the temperature begins at 25oC and then drops to 18oC , what will the pressure of the gas be? P2 = [ 101.3 KPa][15.8 dm3][300 K] = 179.6 KPa [8.7 dm3 ][273 K] 4. A helium balloon is fully inflated at 1.2 L. When the clerk is filling the balloon, she stops to make sure it is not going to explode and checks the pressure. The pressure is 5.7 KPa and the temperature at the store is 24oC. The balloon is 0.75L full. She stops when the balloon is fully inflated and the pressure is 7.2 KPa. When the customer takes the balloon outside, it explodes. What was the temperature outdoors? T = [24oC + 273K][ 1.2 L][7.2 KPa] = 600 K [0.75 L][5.7 KPa] 5. Oxygen gas is added to a rebreather at the same rate as it would be in the open air. The volume is 4.8 dm3 and the temperature is 25 oC. The pressure is1 atm. Once the tank is lowered under the water the pressure increases to 2 atm and the temperature drops to 12oC. Is the tank in danger of exploding if it’s maximum volume is 5.0 dm3? V2 = [4.8 dm3][1 atm][12oC + 273K] = 2.1 dm3, not in danger of exploding [2 atm][25oC + 273K] 6. Ozone is formed due to electricity passing through the air and splitting some O2 atoms which then join briefly to form O3, ozone. Your olfactory sense can detect 1.00 mL ozone in 10 L of air at STP. You are surprised that the noreaster is accompanied by thunderstorms. You detect the scent of ozone in the air and the pressure is 94.5 Kpa and the temperature is 4 oC. What is the new volume of ozone? V2 = [1.00 mL][101.3 KPa][ 273K] = 1.09 mL [94.5 KPa][4 oC + 273K] 7. You are researching the gases that keep lily pads afloat. The cell vacuoles that contain the oxygen that keeps the plant afloat are approximately 17.7 L. They can expand and contract with changes in temperature and pressure, but that is the optimal volume at 25 oC and standard pressure. If the volume drops below 14.2 L the leaves are submerged. You observe the lily pads in the pond are below water level, so the volume is down. If the pressure is 98.2 KPa, what is the temperature? T = [25oC + 273K][17.7 L ][101.3 KPa] = 246.6 K [14.2 L ][98.2 KPa] 8. You like to skin dive. The best corals are at a depth of approximately 10m. You take a deep breath and dive. Your lung capacity is 2.4L total. The air temperature is 32 oC and the pressure is 101.3 Kpa. At 10 m the temperature is 21 oC and 141.2 Kpa. What is the volume of your lungs? V2 = [2.4 L][101.3 KPa][32 oC + 273K] = 1.66 L [141.2KPa][21 oC + 273K] 9. If you breathe 3.0 L of helium at 25 oC and 101.3 Kpa, you will talk funny. You think that would be fun. You breathe all the helium in a container at 15 oC and 110.6 Kpa and you aren’t talking funny. Why not? V2 = [3.0 L][101.3 KPa][15oC + 273K ] = 2.66 L, not enough volume to talk funny [110.6KPa][25 oC + 273K] 10. A researcher is studying the relationship between volume of burps and stress. Burps due to stress are just swallowed air. Your diaphragm detects pressure as discomfort at 210.0 Kpa. (body temperature is 37 oC). If you feel discomfort and you burp, into the researcher’s balloon, the balloon slightly inflates to 6.45 mL at 101.3 Kpa and 27 oC. What volume did the burp occupy in your body? V2 = [6.45 mL][101.3 KPa][37 oC + 273K] = 3.22 mL [210.0 KPa][27 oC + 273K] Ideal Gas Law The following problems may be solved using the relationships described by the Ideal Gas Law. Show all the steps to the solution of the problem. PV=nRT 11. Given the following sets of values, calculate the unknown quantity. a. P = 1.01 atm, V = ? n = 0.00831 mol, T = 25˚C [0.20L] b. P = ? V= 0.602 L, n = 0.00801 mol, T = 311 K [0.340 atm] 12. At what temperature would 2.10 moles of N2 gas have a pressure of 1.25 atm and in a 25.0 L tank? [181K] 13. When filling a weather balloon with gas you have to consider that the gas will expand greatly as it rises and the pressure decreases. Let’s say you put about 10.0 moles of He gas into a balloon that can inflate to hold 5000.0L. Currently, the balloon is not full because of the high pressure on the ground. What is the pressure when the balloon rises to a point where the temperature is -10.0˚C, and the balloon has completely filled with the gas. [0.0431 atm] 14. What volume is occupied by 5.03 g of O2 at 28˚C and a pressure of 0.998atm? [3.89 L] 15. Calculate the pressure in a 212 Liter tank containing 23.3 kg of argon gas at 25˚C? [67.2 atm] 16. If you were to take a volleyball scuba diving with you what would be its new volume if it started at the surface with a volume of 2.00L, under a pressure of 752.0 mmHg and a temperature of 20.0˚C? On your dive you take it to a place where the pressure is 2943 mmHg, and the temperature is 0.245°C. [0.477 L] 17. What is the volume of 1.00 mole of a gas at standard temperature and pressure? [22.4 L] 18. A 113L sample of helium at 27˚C is cooled at constant pressure to -78.0˚C. Calculate the new volume of the helium. [73.4 L] 19. What volume of He is occupied by 2.35 mol of He at 25˚C and a pressure of 0.980 atm? [58.7 L] 20. An aerosol can contains 400.0 ml of compressed gas at 5.2 atm pressure. When the gas is sprayed into a large plastic bag, the bag inflates to a volume of 2.14 L. What is the pressure of gas inside the plastic bag? [0.97 atm] 21. At what temperature does 16.3 g of nitrogen gas have a pressure of 1.25atm in a 25.0 L tank? [651 K] 22. You decide to go on a long hot air balloon ride, so you decide to bring some shampoo to wash your hair with. However there is some gas inside the shampoo bottle when you start to climb into the basket at the beginning of your journey. In fact, because you are a good scientist you decide to constantly take measurements of your surroundings. The shampoo bottle contains 435ml of gas, under a pressure of 1.10 atm, at a temperature of 30.0˚C. When you climb high into the air the bottle starts to expand eventually exploding and covering you and your companions with Pert Plus. Eager to explain this phenomenon you take some measurements: the pressure, you note, has dropped to 0.734 atm and the temperature has dropped to 5.00˚C. To what new volume did the gas inside the bottle expand? [598 mL] 23. What mass of CO2 is needed to fill an 80.0 L tank to a pressure of 150.0 atm at 27.0˚C? 24. Have you ever wondered what the pressure is under the glass bell jar when the vacuum pump is turned on? One way to measure it would be to see how a balloon changes when it is inside. At the beginning of the experiment you note that the volume of the balloon is 560.0 mL under standard pressure. When you turn on the vacuum pump the balloon grows to 780.0 ml. What is the pressure under the bell jar at this point? 25. At what temperature does 5.00g of H2 occupy a volume of 50.0 L at a pressure of 1.01atm? 26. How many moles of gas would you have if you had a volume of 38.0L under a pressure of 1432 mmHg at standard temperature? Ideal Gas Law – Gas Density and Molar Mass PV = nRT n = M/m0, where M is the mass of the gas, and m0 is the molar mass of the gas PV = (M/m0)RT Density of Gas (D) = M/V = Pm0/RT 27. A 40.0 g gas sample occupies 11.2 L at STP. Find the molecular weight of this gas. 28. A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds that its density is 7.71 g/L at 36oC and 2.88 atm. Calculate the molar mass of the compound. 29. The density of a gaseous organic compound is 3.38 g/L at 40oC and 1.97 atm. What is its molar mass? 30. Calculate the molecular weight of a gas if 35.44 g of the gas stored in a 7.50 L tank that exerts a pressure of 60.0 atm at a constant temperature of 35.5 °C. Dalton’s Law of Partial Pressures Ptotal = ΣPi = P1 + P2 + P3 + …… 31. If I place 3.0 moles of N2 and 4 moles of O2 in a 35.0 L container at a temperature of 25˚C, what will the pressure of the resulting mixture of gases be? 32. Two flasks are connected with a stopcock. The first flask has a volume of 5 liters and contains nitrogen gas at a pressure of 0.75 atm. The second flask has a volume of 8 L and contains oxygen gas at a pressure of 1.25 atm. When the stopcock between the flasks is opened and the gases are free to mix, what will the pressure be in the resulting mixture? 33. What is the relationship between the partial pressure of a gas species in the mixture and its mole fraction? [Hint: write all the equations out, substitute into Dalton’s Law of partial pressure, then go from there.] 34. What’s the partial pressure of carbon dioxide in a container that holds 5 moles of carbon dioxide, 3 moles of nitrogen, and 1 mole of hydrogen and has a total pressure of 1.05 atm?