Gases Unit 10 How do gases behave? Gases are perhaps the most mysterious of all of the phases of matter. For the most part gases are invisible to us, and it was once believed that in the air there is no matter at all. Consider, however, how finely tuned our own bodies are to gases in general, and oxygen in particular. We would die in a few minutes if deprived of oxygen, and our respiration system is in constant motion to take advantage of this energy-providing gas. The goal of this unit is to discover how gases behave physically. Or to state it more specifically, how do gases behave as temperature, volume, or pressure change? The first lab is designed to give you enough equipment to discover these things on your own. We will then compare these observations to the known Gas Laws. Tentative Schedule: Day 1: Introduction to gases activity: Lab 10.1 Homework: Complete lab report. Day 2: Comparison of the Class Gas Laws to the known Gas Laws (Slides 1-8) Homework: Complete WS10.1 (Boyle s Law), 10.2 (Charles Law), and 10.3 (Gay-Lussac s Law). Day 3: Avogadro s Principle; Ideal Gas Law (Slides 9-11) Homework: Complete WS10.4 (Avogadro s Principle) and 10.5 (Ideal Gas Law). Day 4 Gases Review Homework: Complete How to ace the Gases Unit Day 5: Gases Test 1
Name Date: Period: Lab10.1 Introduction to Gases Activity Introduction: The goal of this activity is to see how three physical properties of gases- volume, pressure, and temperature - relate to one another. These processes are interacting constantly, but you may have never looked at them very deeply. At each station, design your own experiment, and take whatever measurements you think will be helpful. Not all of the equipment at each station is necessary to perform the experiment. At each station you are asked to determine the relationship between two specific gas properties. For example, at the first station you will measure how gas pressure affects gas volume. At the last station you can create any safe experiment you choose to see how gases behave physically. As for all experiments, safety is critical. You must wear goggles at all times to perform these experiments. If there is any question in your mind as to the safety of your experiment, do not perform it. Note that there will be up to four people at each station. Work together and share ideas. This report must be filled out and submitted for each group of two. This report will be graded on the validity of your experiment and the interpretation of your results. Although each experiment is brief, remember to include a control whenever possible, and to only include one independent variable. The best experiments will give data that can be graphed using numbers- these are quantitative experiments. Note: Pay particular attention to your graphs. Although time is limited, try to get enough data points to see if the relationship is linear, or if your lines are curved. Station 1: Syringe. This station contains a syringe and some books. Your goal is to discover how gas pressure and volume are related. Describe briefly the experiment you performed. (Remember, the best experiments give quantitative results) What did you discover about gas pressure and volume? Answer this question, and complete a brief graph, labeling both axes. 2
Please restack your books and clean your station before you leave. Station 2: Popcorn You have available a popcorn popper and some popcorn kernels, and a thermometer. Your goal is to discover how gas pressure and temperature are related. Describe what you did, and what you observed: What did you discover? For your experiment, hypothesize as to what gas may be involved in your experiment: Complete a brief graph that shows the relationship between temperature and pressure, labeling both axes: Please throw out any popped popcorn and clean your station before you leave. Station 3: Vacuum Pump. This station includes a mechanical vacuum pump, a balloon, a marshmallow, a glass of water, and a thermometer. Your goal is to discover how reduced pressure and volume are related. Safety warning: Use care when working with the large glass bell jar. Describe what you did, and what you observed: What did you discover? Consider the relationship between any pressure and reduced volume. Complete a brief graph summarizing this relationship: Please clean up this station and turn off the pump before you leave. 3
Station 4: Balloon. This station contains balloons, string, a thermometer, and a hair drier. Caution: The hair drier must be kept from moisture, and will get hot. Your goal is to determine the relationship between volume and temperature. For this experiment you should obtain quantitative, graphable results. Describe what you did, and what you observed. Include a brief graph using real data. Describe what you observed: What did you discover? Consider the relationship between gas temperature and volume. Station 5: ( Varies) This station contains various equipment. Use it to create your own experiment that investigates a P,V,T relationship. Describe what you did, and what you observed: What did you discover? Consider the relationship between any of the following: temperature, pressure, and volume. Our Gas Laws Please be sure to complete this part: these are your own gas laws that you discovered :) 2. What did you learn about the interaction of pressure, temperature, and volume of gases? Summarize your results by using an up arrow ( ) for increasing, a down arrow ( ) for decreasing, and write constant if this property is unchanged. Support each case with examples. Temperature Volume Pressure Example 4
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Name: Date: Period: WS10.1 Boyles Law Practice Problems When you press on a closed syringe with only air in it, the volume goes down, and the pressure goes up. This shows the fundamental relationship between the pressure and volume of a gas at constant temperature. Boyle wrote it mathematically: P 1 V 1 =P 2 V 2 where P 1 is the original pressure P 2 is the final pressure V 1 is the original volume V 2 is the final volume For this formula any units can be used as long as they cancel. The preferred (SI) units are liters and atmospheres. Example: A 10 liter oxygen cylinder is under 800 atmospheres of pressure. When the oxygen is released to the air (1 atmosphere), what will the volume of the oxygen be? (800 atm)(10 L) Solution: P1 V1 P2 V 2; (800 atm)(10 L) (1 atm)(v 2); V2 8000 L (1 atm) 1. A balloon filled with helium gas has a volume of 500 ml at a pressure of 1 atm. After the balloon in released, it reaches an altitude of 6.5 km, where the pressure is 0.5 atm. What volume does the gas occupy at this height? 2. A sample of oxygen occupies a volume of 5 L at a pressure of 200 mm Hg. After undergoing an increase of pressure, the new volume is 2.5 L. What must the new pressure be? 3. If the pressure exerted on a 240 ml sample of hydrogen gas is increased from 325 mm Hg to 550 mm Hg, what will the final volume of the sample be? 13
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Name: Date: Period: WS10.2 Charles Law Practice Problems A balloon will expand as it is heated: as the temperature of a gas increases (at constant pressure), T1 T2 volume increases. Charles wrote this mathematically: V V For this formula any volume units may be used as long as they cancel, and Kelvin must be used for temperature. Remember K = O C + 273 Example: A sample of air has a volume of 140.0 ml at 67 C. To what temperature must the gas be lowered to reduce its volume to 50.0 ml? Solution: Be sure to use Kelvin, not Celsius. T 1 /V 1 =T 2 /V 2 T 2 = T 1 V 2 /V 1 = 340 K x 50 ml/140 ml = 121.4 K (that s -151.6 o C; very cold) Reality check : Both the temp and the volume decreased nearly by a factor of 3 1 2 1. A sample of hydrogen gas has a volume of 275 ml at 25 C. If the temperature is increased to 130 C, what is its new volume? 2. A 35 L oxygen sample originally has a temperature of 20 C. If the sample is cooled to 10 C, what is its new volume? 3. A nitrogen sample at 50 C occupies a volume of 800 cm 3. After heating, the sample occupies a volume of 1000 cm 3. What is the new temperature of the gas? 15
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Name: Date: Period: WS10.3 Gay-Lussac s Law Practice Problems Heating a sealed empty bottle is dangerous- it could explode. As the temperature of a gas increases in a closed non-expandable container, the pressure increases. Gay-Lussac wrote it mathematically: T1 T 2 P P 1 For this formula any units of pressure may be used as long as they cancel, and the temperature must be in Kelvin (remember K = O C + 273) Example: You have a closed aluminum can that can handle a pressure of 4 atmospheres before it bursts. If this closed 2 liter can at a pressure of 1.2 atmospheres is heated from 25 degrees Celsius to 100 degrees Celsius, will it burst? Solution: T P 1 1 T2 273 K 373 K ; ;227.5 P 1.2 atm x atm 2 2 373 K ; x atm x atm 373 K 227.5 K 1.64 atm. The can will handle up to 4 atmospheres, so it will not burst. 1. Before a trip from New York to Boston, the pressure in a car tire is 1.8 atm at 20 C. At the end of the trip, the pressure gauge reads 1.9 atm. What is the new Celsius temperature of the air inside the tire? 2. A sample of hydrogen at 47 C exerts a pressure of 250 mm Hg. If the gas is heated to 77 C at a constant volume, what will its new pressure be? 3. To what temperature must a sample of nitrogen at 300K and 0.625 atm be heated to so that its pressure becomes 1.125 atm? 17
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Name: Date: Period: WS10.4 Avogadro s Principle: Problems A mole of an ideal gas occupies 22.4 L at STP (standard temperature and pressure: 273K, 1 atm): 22.4 L of an ideal gas = 1 mole. All of these problems are solved using this relationship: 22.4L/mol, or 1 mol/22.4 L Example: How much did the hydrogen in the Hindenburg weigh, assuming STP and a volume of 200 million liters? mole H2 2 g H2 Solution: 200 millionlitersh 2 x x 17.9 million g Hydrogen 22.4 litersh mole H 2 2 1. Calculate the number of moles present for an ideal gas with a volume of 40 liters at STP. 2. What is the density of CO 2 gas in g/l at STP? Molar mass of CO 2 = 44 g/mol. 3. A gas is found to have a density of 2.595 g/l at STP. What is the molar mass of this gas in g/mol? 4. Calculate the volume that 2.0 kg of methane gas (CH 4 ) will occupy at STP 19
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Name: Date: Period: WS10.5 Ideal Gas Law Problems Combining the laws or principles of Boyle, Charles, Gay-Lussac, and Avogadro provides: PV = nrt Where P = pressure in atmospheres V = volume in Liters n = the number of moles R = 0.0821 atm L/mol K (note that R is always this number) T = temperature in Kelvin Note that all of these units must be used- this is the most common error (see below). Here are some helpful conversions: 1 atm = 760 mm Hg = 14.7 psi 1 L = 1000 ml T c + 273 = T k Example: What is the temperature of 2 moles of an ideal gas at 300 mm Hg and 12 liters of volume? Solution: convert to SI units and plug into the ideal gas equation. PV = nrt; T = PV/nR = (0.395 atm)(12 L)/ (2 mol)(0.0821 atm L/mol K) = 45.5 K ***Here are the most common errors:*** 1. Don t know where to start Solution: Find out what you are given- in all cases you get 3 of the four P V n T variables- it must be an ideal gas problem. Rearrange the equation to solve for the missing one, and plug in your correct units (see #2) 2. Didn t use Liters (L), atmospheres (atm), mole (mol), and Kelvin (K) units. Solution: use the helpful conversions above and convert to L atm mol K. 3. What do I do with grams in these problems? Solution: Convert to moles (n). If you have 16 grams of methane, then n = 1 since the molar mass of methane is 1 g/mol (12 +1+1+1+1). Similarly, if the question asks for grams, solve for n then convert moles to grams for example if you have 9 grams of water, that is half a mole (9/18). For all of these questions please circle your answer and be sure you have included your units. 1. What is the volume (in L) occupied by 0.25 mol of oxygen at 20 C and 740 mm Hg? 21
2. How many moles of chlorine are contained in a 10 ml tank at 27 C and 3.5 atm of pressure? 3. What is the pressure on a 6-L system containing 32 g Oxygen gas at 45 C? 4. How many grams of Neon gas are contained in a 200-mL tank at 421 C, with a pressure of 420 mm Hg? 5. How many molecule of H 2 O are present in a 230-mL container, held with a temperature 485K, with a pressure 12.8 psi? 22
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Gas Law Worksheet Challenge Problems: 6,8,16,17 These problems include one new law: The combined gas law: P 1 V 1 /T 1 = P 2 V 2 /T 2 (see #8, for example) 1. In a certain experiment a sample of helium in a vacuum system was compressed at 25 C from a volume of 200.0 ml to a volume of 0.240 ml where its pressure was found to be 30.0 mm Hg. What was the original pressure of the helium? 2. A hydrogen gas volume thermometer has a volume of 100.0 cm 3 when immersed in an ice-water bath at 0 C. When immersed in boiling liquid chlorine, the volume of the hydrogen at the same pressure is 87.2 cm 3. Find the temperature of the boiling point of chlorine in C. 3. 2.50 grams of XeF 4 is introduced into an evacuated 3.00 liter container at 80.0 C. Find the pressure in atmospheres in the container. 4. A lighter-than-air balloon is designed to rise to a height of 6 miles at which point it will be fully inflated. At that altitude the atmospheric pressure is 210 mm Hg and the temperature is -40 C. If the full volume of the balloon is 100,000.0 L, how many kilograms of helium will be needed to inflate the balloon? 5. How many liters of pure oxygen, measured at 740 mm Hg and 24 C, would be required to burn 1.00 g of benzene, C 6 H 6 (l), to carbon dioxide and water? (Hint: find the moles of oxygen needed from the balanced equation, then use gas laws.) 6. Air from the prairies of North Dakota in winter contains essentially only nitrogen, oxygen, and argon. A sample of air collected at Bismarck at -22 C and 98.90 kpa had 78.0 % N 2, 21.0% O 2, and 1.0% Ar. Find the partial pressures of each of these gases. 24
7. For a mole of ideal gas, sketch graphs of a. P vs. V at constant T. b. P vs. T at constant V. c. V vs. T at constant P. 8. What would be the partial pressure of N 2 in a container at 50 C in which there is 0.20 mole N 2 and 0.10 mole CO 2 at a total pressure of 101.3 kpa? 9. What volume of Ne at one atm and 25.0 C would have to be added to a sign having a volume of 250 ml to create a pressure of one mm Hg at that temperature? 10. Find the volume of a gas at 800.0 mm Hg and 40.0 C if its volume at 720.0 mm Hg and 15.0 C is 6.84 L. 11. 12.8 L of a certain gas are prepared at 100.0 kpa and -108 C. The gas is then forced into an 855 ml cylinder in which it warms to room temperature, 22.0 C. Find the pressure of this gas in kilopascals. 12. In a laboratory experiment, 85.3 ml of a gas are collected at 24 C and 733 mm Hg pressure. Find the volume at STP. 13. What is the mass of 18.9 L of NH 3 at 31.0 C and 97.97 kpa? 14. 0.279 moles of O 2 in a 1.85 L cylinder exert a pressure of 3.68 atm. What is the temperature in the cylinder (in C)? 15. A quantity of potassium chlorate is selected to yield, through heating, 75.0 ml of O 2 when measured at STP. If the actual temperature is 28 C and the actual pressure is 0.894 atm, what volume of oxygen will result? 25
16. A mixture of hydrocarbons contains three moles of methane, four moles of ethane, and five moles of propane. The container has a volume of 124 liters and the temperature is 22 C. Find the partial pressures of the three gases, in kpa. 17. How many liters of H 2 at 23 C and 733 mm Hg are released by the reaction between 1.98 grams of Na and unlimited water by the following equation? 2 Na + 2 H 2 O -- > H 2 + 2 NaOH Answers: 1) 0.0360 mm Hg 2) -35 C 3) 0.117 atm 4) 5.8 kg 5) 2.4 L 6) 77.1 kpa N 2, 20.8 kpa O 2, 9.89 kpa Ar 7) a - hyperbola, b&c - straight lines 8) 67 kpa N 2, 34 kpa CO 2 9) 0.329 ml 10) 6.69 L 11) 2680 kpa 12) 75.6 ml 13) 12.5 g 14) 24 C 15) 92.5 ml 16) 59.3 kpa methane, 79.0 kpa ethane, 98.8 kpa propane 17) 1.08 L 26
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How to ace the Gases Test We have been observing the behavior of gases for several days. Our goal has been to determine how the physical properties of gases interrelate. To begin we created brief experiments at a series of stations where we explored the interactions of temperature, pressure, and volume within various gaseous systems. For each experiment we looked for changes in volume, pressure, ands temperature. We then compared these results to the Gas Laws of Boyle, Charles, Graham, and Gay-Lussac We also looked at a combination of these known as the ideal gas law, To ace the gases test you should be able to: 1. Describe the macroscopic (visible) properties of liquids, solids, and gases. A solid has/does not have a fixed volume and will/will not assume the shape of a container. A liquid has/does not have a fixed volume and will/will not assume the shape of a container A gas has/does not have a fixed volume and will/will not assume the shape and volume of a container 2. Accurately predict the behaviors of molecules as they undergo changes of pressure, temperature, volume, or the number of molecules. As the temperature increases in a non-expandable container like a sealed can, the increases and the remains constant. As the temperature increases in an expandable container like a balloon, the increases and the remains constant. As the pressure increases in a collapsible container like a syringe, the decreases and the remains constant. 3. Apply the Gas Laws to predict how one physical change will affect another if the third remains constant. If the pressure increases from 100 to 200 kilopascals in a 3 liter container and the temperature remains constant, what will the final volume be? (101.7 kilopascals = 1 atmosphere). If the temperature increases from 273 to 298 Kelvin in a 25 liter balloon and the pressure remains constant, what will the final volume be? 4. Be able to convert between degrees Celsius and Kelvin. If the temperature increases from 25 to 100 degrees Celsius in a non-expandable container at 1.2 atmospheres, what will the final pressure be? 5. Be able to solve gas law problems based on Avogadro s Principle 2. What is the density of CO 2 gas in g/l at STP? Molar mass of CO 2 = 44 g/mol. 6. Be able to solve gas law problems involving multiple changes (ideal gas law) Example: How many moles of chlorine are contained in a 10 ml tank at 27 C and 3.5 atm of pressure? As a final Review, complete the activity on the following page in class. If you are doing this at home, choose your own numbers for the volume of the syringe. 28
Name Period L2gasreview1 Gas Laws Review: Use the Gas Laws and Principles to solve each problem. 1. Take a 50 ml syringe, and set it to any big volume. My volume is ml Push down on it hard. The new volume is ml How much pressure did you apply (in atmospheres)? Show your work in the box. Circle your answer. This question is based on s Law 2. Set your syringe to any volume. I have just set my syringe to ml. Now warm it in your hands for 10 seconds. The new volume is. You warmed it from 25 O C to 37 O C. What is the new volume supposed to be? If your syringe didn t move this is probably because. This question is bases on s Law 3. This time I have set the syringe to ml. With one hand hold the syringe so it can t expand. Warm the syringe with the other hand. What is the new pressure in the syringe? This question is based on s Law 4. Now I am setting my syringe to ml. How many moles of gas are in your syringe? (Hint: one mole of gas = 22.4L. My syringe has moles of air in it. This question is based on s Principle. 5. Set your syringe to 40 ml. Push down on it until the volume is 20 ml. We can figure out the new pressure in our heads: it must be atm. Now warm it in your hands to 37 O C. Use this final data to figure out how many moles of gas are in the syringe. Final Volume: Final Pressure: Final Temperature: Number of moles: This question is based on the Law. 6. (L1 only; extra credit for L2). Assuming an average molecular mass of 30 g/mol, calculate the density of air in g/l using Avogadro s Principle. 29
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Gas Laws Worksheet Answer Key 1. 2. 3. 4. 5. 2 C 6 H 6 (g) + 15 O 2 (g) --> 12 CO 2 (g) + 6 H 2 O (g) 6. 7. 8. 9. 10. 11. 32
12. 13. 14. 15. 16. This can be done by a couple of methods. One possible way is: 17. 33