gas formulas boyles law: relates gas pressure to volume at constant temperature

Transcription

1 gases 1

2 atmospheres atm ounds per square inch psi millimeters of mercury mm Hg Kilopascals ka sea level pressure 1 atm psi 760 mm Hg ka T V R pressure temperature Kelvins Degrees Celsius Degrees Fahrenheit K O C O F 1.8 o C + 3 stp volume Liters ounces Ccubic centimeters 1 liter 33.8 ounces 1000 cm ml Ideal gas constant L atm/mol K gas units K 5/9 ( O F - 3) + 73 standard temperature and pressure K (0 O C), 1 atm n number of moles r relative rate M O F 9/5(K - 73) + 3 g/mol molar mass x d mole fraction g/l density boyles law: relates gas pressure to volume at constant temperature 1 V 1 V V 1 V any units may be used for pressure () and volume (V) charles law: relates gas temperature to volume at constant pressure must use Kelvin for temperature (T) any units may be used for volume (V) gay-lussacs law: relates gas temperature to pressure at constant volume T pressure T temperature (K) 1 combined gas law for adding gas or multiple physical changes 1 V 1 V pressure T temperature (K) n 1 n T V volume n number of moles (mol); can remove any that are constant remove if constant ideal gas law: relates physical properties of a gas V nrt d M RT pressure (atm) V volume (liters) n # of moles (mol) gas density law (also good for molar mass) r 1 r M M 1 Avogadro s law law of partial pressures d density (g/l) pressure (atm) M molar mass (g/mol) R L atm mol K T temperature (K) R T temperature (K) grahams law of diffusion r 1, r diffusion rates (any units, since they cancel) M molar mass (g/mol) partial pressure of gas a gas formulas 1 mol.4 L At ST (O O C, 1 atm) moles of gas a x total pressure total moles of gas suggestions only T must be changed to Kelvin other units keep but make sure they cancel careful! mut use L atm mol K handy for density and molar mass suggestion: set up as heavy gas light gas light gas is x times faster faster means shorter time and higher speed look for problems that say ST or 1 atm, 73 K most problems are unit conversions using.4 L/mol or mol/.4 L for example a box at 1 atm pressure with 4 moles of helium and 1 atm of neon He 0.8 atm; Ne 0. atm

3 introduction to gases experiment 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. This lab has several stations. 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 each station safely design an experiment which accomplishes this task.. 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 student. 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. Station 1: syringe You have available some books and a closed 50 ml syringe. Design an experiment that teaches you something about gases Fill in all items below.. your procedure: conclusion your procedure should be repeatable by a stranger. your data should have units your conclusion should relate two physical properties: ressure, volume, or temperature. please restack the books when you are finished. your graph should have labeled units For the x and y axes. 3

4 Station : popcorn You have available some popcorn, a popcorn maker, and a thermometer. Design an experiment to relate pressure and temperature ofgases. your procedure: your procedure should be repeatable by a stranger. conclusion your data should have units your conclusion should relate two physical properties: pressure, volume, or temperature. Station 3: vacuum pump You have available a vacuum pump, a manometer (pressure measuring device), a bell jar, and various items to put in it. Design an experiment to discover something about the physical behavior of gases. your graph should have labeled units for the x and y axes. please throw out the popcorn when you are through your procedure: Your procedure should be repeatable by a stranger. conclusion your data should have units Bell jars are great devices for studying changes in pressure lease clean the bell jar when you are done. your conclusion should relate two physical properties: ressure, volume, or temperature. your graph should have labeled units for the x and y axes. 4

5 station 4: helium power You have available some helium balloons and paper clips, and a scale. Flink the balloon (make it hover) and determine what you can conclude from that. Your procedure: Calculation: Your procedure should be repeatable by a stranger. Conclusion Station 5: gas velocities Your instructor will make HCl and NH 3 gases collide in a tube. Use that to determine the relative velocity of gases. your procedure: Your procedure should be repeatable by a stranger. your data should have units conclusion Your conclusion should show a formula that relates the velocities of gases to their molecular weights lease clean the station when you are done. 5

6 conclusions Based on your experiments, create three gas laws that relate their pressure, volume, and temperature. State them in one complete sentence, and in a formula. Example: As the temperature of a gas increases in a closed container, the pressure decreases, and since it is a closed, rigid container, the volume is constant.: V 1 V. (The statement and formula may be wrong, but I hope you get the idea)

7 some common gases fun facts about gases composition of air gases and altitude 10 miles 0. atm Elements that exist as gases at 5 0 C and 1 atmosphere 4 miles 0.5 atm Sea level 1 atm and for liquids 10 m atm 7

8 gases just just bounce around the kinetic molecular theory of gases: 1. Gases molecules act like tiny points with almost no volume:. Gas molecules don t slow down when they collide (inelastic collisions) 3. Gas molecules exert neither attractive nor repulsive forces on one another. 4. The average energy of the gas is proportional to its Kelvin temperature. Average speed of gas molecules what can you conclude? more variability as when hotter or lighter hot gases move faster lighter gases move faster 8

9 what are they like? typical density: about 1 g/l highly compressible distribution: fill up containers regardless of amount gases: appearance: often invisible... No reflection plane substances that lack intermolecular forces reaction rate compared to other phases interwoven: gases react much faster pressure units 1 atm 14.7 psi ka 760 mm Hg or Torr push in a closed syringe barrel As V goes down, goes up. T is constant 166 consider the physical behavior of gases. What will happen physically when you... heat a piston As T goes up, V goes up is constant heat a closed container As T goes up, goes up V is constant NH 4 Cl NH 3 HCl which gases move fastest? light gases move faster 40 g Ar 8 g N g H does the identify of the gas matter? Gas atoms occupy the same volumes This leads to the formulas V nrt d M RT : atm V: liters n: moles R: L atm/mol K T: K and d (g/l) (atm) M (g/mol) R L atm/mol K T (K) Boyle Charles Gay-Lussac Graham Avogadro Rate 1 1 V 1 V /V 1 /V M 1 mol.4 L T 1 / 1 / M Rate 1 inverse relationships: A 1 B 1 A B ; proportional relationships: A 1/ B 1 A /B At ST (O O C, 1 atm) a X a T and The partial pressure of a gas ( a ) proportional to its mole fraction (X a ). 9

10 gases: solved problems 1 Boyles, Charles, and Gay-Lussac s Formulas vice president sir robert boyle V x V 1 1 Boyles Law: A 0.4 liter engine cylinder at atmospheres of pressure increases to a pressure of 0 atmospheres when the spark plug fires. What is the volume in the cylinder at that pressure, assuming a constant temperature? in your head: pressure increased 10X; volume must decrease 10X answer is 0.04 L 1 V 1 V ( atm )( 0.4 L ) ( 0 atm )( x ) solution: x ( atm)(0.4 L) (0 atm) 0.04 L V 1 98 K T 596 K V x Charles Law: A liter balloon is heated until the gases inside warm from 5 to 33 degrees Celsius. What is the final volume of the balloon? in your head: temp is doubling...so will the volume answer will be 4 atm Jacques Charles solution: V 1 T V 98 K L 596 K x x ( L) (596K) (98 K) 4 L Boyle the V.. saw Charles watch TV in Gay-Lussac s Tee-ee Gay Lussacs Law: You have a closed fixed volume aluminum can with only air in it that can handle a pressure of 4 atmospheres before it bursts. If this closed liter can at a pressure of 1. atmospheres is heated from 5 degrees Celsius to 100 degrees Celsius, will it burst? ignore (fixed volume) 1 98 K T 373 K in your head: temp is going up by about 0%...so will the pressure answer will be about 1.5 atm won t burst solution: 1 T 98 K 1. atm 373 K x x (1. atm)(373 K) 1.50 atm answer: NO (98 K) 10

11 gases: solved sample problems ideal and combined gas laws T x n p 300/ atm v Ideal Gas Law: What is the temperature of moles of an ideal gas at 300 mm Hg and 1 liters of volume? solution: convert to SI units and plug into the ideal gas equation. latmolk : L, atm, mol, K V nrt; T V nr (0.395 atm)(1 L) ( mol) (0.081 L atm/mol K) 45.5 K most common error: non- SI units. remember LatmolK K V 1 T K Combined Gas Law: A gas has a temperature of 14 0 C, and a volume of 4.5 liters. If the temperature is raised to 9 0 C and the pressure is doubled to atm, what is the new volume of the gas? 1 1 atm, atm V x solution: convert to SI units and plug into the ideal gas equation. 1 V 1 V T V 1 V 1 T (1 atm) (4.5 L) (87 K) ( atm) (30K).37 L 11

12 why? gases: solved sample problems 3 avogadro s principle, graham s law Avogadro s rinciple:.4 L 1 mole of any ideal gas at 73 K, 1 atm handy for unit conversion S.T.. standard temperature and pressure atom s in the gas phase are tiny and equidistant at the same temp and pressure so the identity of the gas doesn t really matter. What is the density of CO gas in g/l at ST? solution- treat it as a unit conversion problem 44 g mol x 1mol.4 L.0 L g Graham s Law lightweight gases travel faster, but not that much faster Rate 1 M M Rate 1 Graham s Law M molar masses Compare the rates of diffusion of helium and CO. Rate He Rate CO 1

13 d m/v, and for each mole of gas V RT/, so. gases: solved problems 4 (density and molar mass) d M RT d density (g/l) pressure (atm) M molar mass (g/mol) R L atm/mol K T temperature (K) note M is not molarity A chemist has synthesized a greenish-yellow gaseous compound of chlorine and oxygen and finds that its density is 7.71 g/l at 36 C and.88 atm. Calculate the molar mass of the compound and determine its molecular formula. M drt 67.9 g/mol ClO too small (51.5 g/mol). molecular formula: ClO 13

14 p total 1 atm partial pressure: no surprise- the total pressure of a gas (such as air) is the sum of the individual pressures of each substance What is the partial pressure of each gas on the left? The pressure in the container must come equally from each gas particle: partial pressure of gas a red:.65 atm silver: atm moles of gas a total moles of gas The partial pressure of a gas in a mixture is proportional to its mole fraction. A mixture of gases contains 4.46 moles of neon (Ne), 0.74 mole of argon (Ar), and.15 moles of xenon (Xe). Calculate the partial pressures of the gases if the total pressure is.00 atm at a certain temperature. Solution: calculate the mole fraction of each and assign each fraction to the total pressure. Total moles moles artial pressures: x total pressure Ne: 4.46 moles Ne/7.35 moles total x.00 atm 1.1 atm Ar: 0.74 moles Ar/7.35 moles total x.00 atm 0.0 atm Xe:.15 moles Xe/7.35 moles total x.00 atm atm 14

15 gas law problem including partial pressure Oxygen gas generated by the decomposition of potassium chlorate is collected as shown. T 4 O C K The volume of oxygen collected at 4 C and atmospheric pressure of 76 mmhg is 18 ml / atm V 0.18 L note how gas is collected by passing through water- some water vapor will sealed with water- some water vapor will be in bell jar Calculate the mass (in grams) of oxygen gas obtained. The pressure of the water vapor at 4 C is.4 mmhg. Strategy: 1. convert all units to L atm mol K; (Note that we must subtract the partial pressure of O ). Calculate n, then grams. (note we could find how much KClO 3 was used as well) V nrt n V RT (0.973 atm)(0.18 L) (0.081 L atm )(97 K) mol K moles O x 3.00 g O mol O g O 15

16 gas law problems Boyles Law 1) 1.00 L of a gas at standard temperature and pressure is compressed to 473 ml. Assuming the temperature does not change, what is the new pressure of the gas? 1 V 1 V 1V 1 V (.11 atm). In a thermonuclear device, the pressure of liters of gas within the bomb casing reaches 4.0 x 10 6 atm. When the bomb casing is destroyed by the explosion, the gas is released into the atmosphere where it reaches a pressure of 1.00 atm. What is the volume of the gas after the explosion? 1 V 1 V V 1V 1 (4.0 x 106 atm)(0.050 L) 1.00 atm.0 x 105 L (00,000 L) 3) Synthetic diamonds can be manufactured at pressures of 6.00 x 10 4 atm. If we took.00 liters of gas at 1.00 atm and compressed it to a pressure of 6.00 x 10 4 atm, what would the volume of that gas be? (3.33 x 10-5 L) 1 V 1 V V 1V 1 (1.00 atm)(.00 L) 3.33 x 10 5 L 6.0 x 104 atm 4) The highest pressure ever produced in a laboratory setting was about.0 x 10 6 atm. If we have a 1.0 x 10-5 liter sample of a gas at that pressure, then release the pressure until it is equal to 0.75 atm, what would the new volume of that gas be? 1 V 1 V V 1V 1 (.0 x 106 atm)(1.0 x 10 5 L) 0.75 atm 73 L (73 L) 5) Atmospheric pressure on the peak of Mt. Everest can be as low as 150 mm Hg, which is why climbers usually (but not always) bring oxygen tanks for the last part of the climb. If the climbers carry 10.0 liter tanks with an internal gas pressure of 3.04 x 10 4 mm Hg, what will be the volume of the gas when it is released from the tanks? 1 V 1 V V 1V 1 (1.00 atm)(1.00 L) L.11 atm (3.04 x 104 mm Hg)(10.0L) 150 mm Hg.0 x 103 L (.0 x 10 3 L) Charles Law 6) The temperature inside my refrigerator is about Celsius. If I place a balloon in my fridge that initially has a temperature of.0 0 C and a volume of liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? V T T 1.0 O C K 1 V V V 1T T 1 T 4.00 O C K (0.500 L)(77.1 K) (95.1 K) L (0.470 L) 7) A man heats a balloon in the oven. If the balloon initially has a volume of liters and a temperature of C, what will the volume of the balloon be after he heats it to a temperature of C? 0.0 O C K V 1 V V V 1T T 50. O C K (0.400 L)(53.1 K) (93.1 K) L (0.714 L) 8) On hot days, you may have noticed that potato chip bags seem to inflate, even though they have not been opened. If I have a 50. ml bag at a temperature of C, and I leave it in my car which has a temperature of C, what will the new volume of the bag be? V 1 V ; add to O C for K V V 1T (50. ml)(333.1 K) T 85 ml 1 (9.1 K) (85 ml) 9) A soda bottle is flexible enough that the volume of the bottle can change even without opening it. If you have an empty.00 L soda bottle at room temperature (5.0 0 C), what will the new volume be if you put it in your freezer ( C)? V 1 V ; add to O C for K V V 1T (.00 L)(69.1 K) T 1.80 L 1 (98.1 K) (1.80 L) 10) Some students believe that teachers are full of hot air. If I inhale.0 liters of gas at a temperature of C and it heats to a temperature of C in my lungs, what is the new volume of the gas? V 1 V ; add to O C for K V V 1T (.0 L)(311.1 K) (91.1 K).35 L (.35 L) 16

17 Gay-Lussc s Law 11) Determine the pressure change when a constant volume of gas at 1.00 atm is heated from 0.0 C to 30.0 C. 1 ; add to O C for K 1T (1.00 atm)(303.1 K) (93.1 K) 1.03 atm (1.03 atm) 1) A container of gas is initially at atm and 5.0 C. What will the pressure be at 15 C? 1T 1 ; add to O C for K T atm 1 (98.1 K) (0.668 atm) 13) A gas container is initially at 47.0 mm Hg and 77.0 K (liquid nitrogen temperature.) What will the pressure be when the container warms up to room temperature of 5.0 C? 1 ; add to O C for K 1T (0.500 atm)(398.1 K) (47 mm Hg)(98.1 K) (77.0 K) (18 mm Hg) 14) A gas thermometer measures temperature by measuring the pressure of a gas inside the fixed volume container. A thermometer reads a pressure of 48 ka at 0.00 C. What is the temperature when the thermometer reads a pressure of 345 ka? 1 ; add to O C for K T (73.1 K)(345 ka) 380. K 1 (48 ka) atm (380. K) 15) A gas is collected at.0 C and mm Hg. When the temperature is changed to 0.00 C, what is the resulting pressure? 1 ; add to O C for K 1T (745 mm Hg)(95.1 K) (73.1 K) 689 mm Hg (689 mm Hg) 16) A gas has a pressure of mm Hg at 40.0 C. What is the temperature at standard pressure ( 1 atm 760 mmhg)? ; add to 1 O C for K T (313.1 K)(760 mm Hg) 340 K 1 (699.0 mm Hg) (340. K) 17) If a gas is cooled from 33.0 K to K and volume is kept constant what final pressure would result if the original pressure was mm Hg? 1 1T (750 mm Hg)(73.15 K) (33 K) 634 mm Hg (634 mm Hg) Combined Gas Law roblems 18) If I initially have a gas at a pressure of 1.0 atm, a volume of 3.0 liters, and a temperature of 00. K, and then I raise the pressure to 14.0 atm and increase the temperature to 300. K, what is the new volume of the gas? 1 V 1 T V 1 T use Kelvin V 1V 1 T (1.0 atm)(3.0 L)(300. K) 9.6 L (00. K)(14.0 atm) (9.6 L) 19) A gas takes up a volume of 17.0 liters, has a pressure of.30 atm, and a temperature of 99 K. If I raise the temperature to 350. K and lower the pressure to 1.50 atm, what is the new volume of the gas? 1 V 1 T V 1 T use Kelvin V 1V 1 T (.30 atm)(17.0 L)(350. K) 30.5 L (99 K)(1.50 atm) (30.5 L) 0) A gas that has a volume of 8.0 liters, a temperature of C, and an unknown pressure has its volume increased to 34.0 liters and its temperature decreased to C. If I measure the pressure after the change to be.00 atm, what was the original pressure of the gas? 1 V 1 V T use Kelvin 1 V (.00 atm)(34.0 L)(318. K) T V.50 atm 1 (308 K)(8.0 L) (.50 atm) 1) A gas has a temperature of C, and a volume of 4.50 liters. If the temperature is raised to C and the pressure is not changed, what is the new volume of the gas? V 1 T V 1 T use Kelvin V V 1T (4.5.0 L)(30. K) T 4.74 L 1 (87 K) (4.74 L) ) If I have 17.0 liters of gas at a temperature of C and a pressure of atm, what will be the pressure of the gas if I raise the temperature to C and decrease the volume to 1.0 liters? 1 V 1 V T use Kelvin 1V 1 T V (88.89 atm)(17.0 L)(367. K) (340 K)(1.0 L) 136 atm (136 atm) 3) I have an unknown volume of gas at a pressure of atm and a temperature of 35 K. If I raise the pressure to 1.0 atm, decrease the temperature to 30. K, and measure the final volume to be 48.0 liters, what was the initial volume of the gas? 1 V 1 T V 1 T use Kelvin V 1 V (1.0 atm)(48.0 L)(35 K) T 117 L 1 (30 K)(0.500 atm) (117 L) 17

18 Ideal Gas Law roblems: V nrt; remember to use Liters, atmospheres, moles, and Kelvin 4) If I have 4.00 moles of a gas at a pressure of 5.60 atm and a volume of 1.0 liters, what is the temperature? V nrt; (05 K) 5) If I have an unknown quantity of gas at a pressure of 1.0 atm, a volume of 31.0 liters, and a temperature of C, how many moles of gas do I have? V nrt; T V nr (5.60 atm)(1.0 L) (4.00 mol)(0.081 L atm mol K ) 05 K n V RT (1.0 atm)(31.0 L) (0.081 L atm 1.6 mol )(360 K) mol K (1.6 mol) 6) If I contain 3.00 moles of gas in a container with a volume of 60.0 liters and at a temperature of 400. K, what is the pressure inside the container? V nrt; nrt V (3.00 mol)(0.081 L atm )(400. K) mol K 1.64 atm 60.0 L (1.64 atm) 7) If I have 7.70 moles of gas at a pressure of atm and at a temperature of C, what is the volume of the container that the gas is in? V nrt; V nrt (7.70 mol)(0.081 L atm )(39 K) mol K atm,310 L (,310 L) 8) If I have 17.0 moles of gas at a temperature of C, and a volume of liters, what is the pressure of the gas? V nrt; nrt V (17.0 mol)(0.081 L atm )(340. K) mol K L 5.34 atm 9) If I have an unknown quantity of gas at a pressure of atm, a volume of 5.0 liters, and a temperature of 300. K, how many moles of gas do I have? V nrt; n V RT (0.500 atm)(5.0 L) (0.081 L atm mol )(300. K) mol K (5.34 atm) (0.508 mol) 30) If I have 1.0 moles of gas held at a pressure of 78.0 atm and a temperature of 900. K, what is the volume of the gas? V nrt; V nrt (1.0 mol)(0.081 L atm )(900 K) mol K 19.9 L 78.0 atm (19.9 L) Graham s Law 31) In an effusion experiment, it required 4.05 s for a certain number of moles of an unknown gas to pass through a small opening into a vacuum. Under the same conditions it took 18.0 s for the same number of moles of O to effuse. Find the molecular mass of the unknown gas. unknown gas is 18 s/4.05 s 4.44 x faster 4.44 x smaller (15.1 g/mol).107 x smaller (3.0 g/mol)/ g/mol 3) Calculate the ratio of the effusion rates of hydrogen gas (H ) and uranium hexafluoride (UF 6 ), a gas used in the enrichment process to produce fuel for nuclear reactors r 1 UF r H ; H effuses 13.1 x faster than UF 6 (H effuses 13.1 x faster than UF 6 ) 33) Argon effuses through a hole under certain conditions of temperature and pressure at the rate of 5.0mL/min. At what velocity will xenon effuse through the same hole under the same conditions? r 1 r Xe Ar ; Ar effuses 1.81 x faster than Xe; 5.0 ml/min/ ml/min (.76 ml/min) 34) Compare the rates of diffusion of helium and CO. r 1 r M M ; He effuses 3.3 x faster than CO (He diffuses 3.3 x faster than CO ) 35) Two balloons of the same size and material are filled with H and O, respectively, at the same conditions. If the O escapes at the rate of 65 ml/hr, calculate the rate of escape of the H. r 1 r O 3.0 H ; H effuses 3.98 x faster than O ; 65 ml/hr x ml/hr (59 ml/hr) 36) If it takes 100 seconds for a sample of O to effuse down a capillary, how long would it take for the same number of moles of SO to effuse down the tube? r 1 (14 seconds) r SO O ; O effuses 1.4 x faster than SO ; 100 sec x sec 37) Which of the following as gases would diffuse the fastest? HCl b. H S c. H O d. HF e. CH 4 The lightest gas diffuses quickest: CH (CH 4 ) 4 38) If He gas diffuses at the rate of 1.00 mole per minute through a given container, calculate the diffusion rate of CH 4 under the same conditions. r 1 r CH 4 He ; He diffuses.00 x faster than SO ; 39) Calculate the relative rates of diffusion of the gases CO and CO. r 1 r CO CO ; CO diffuses 1.5 x faster than CO 1.00 mol/min (0.500 mol per minute) mol/min (CO is 1.5 x faster) 18

19 density and molar mass problems partial pressure problems: a XaT 40) What is the density of CO at ST? mol.4 L x g 1.96 g/l mol 41) What is the density of CO at 100. degrees Celsius and 1.00 atm of pressure? d M R T x (1.00 atm)(44.01 g/mol) (0.081 L atm/mol K)(373 K) 1.44 g/l (1.44 g/l) 4) What is the density of CH 4 at ST? mol.4 L x g g/l mol 43) How much does the density of CH 4 change when it is cooled from 0.00 to to degrees Celsius at 1.00 atm? 44) What is the molar mass of a gas with a density of.4 g/l at ST? 45) What is the molar mass of acetylene gas if the density at ST is 1.16 g/l at ST? 46. What is the density of acetylene gas (6.04 g/mol) at 0.97 atm, 5 O C? 47) What element has a mass of 3.8g and occupies 5.60 L at ST? (0.716 g/l) d M R T (1.00 atm)(16.04 g/mol) g/l (0.081 L atm/mol K)(33 K) from above: g/l more dense (0.11 g L more dense) d M R T ; M drt d M R T ; M drt (.4 g/l)(0.081 L atm/mol K)(73 K) 1.00 atm (1.16 g/l)(0.081 L atm/mol K)(73 K) 1.00 atm d M R T (0.97 atm)(6.04 g/mol) 1.03 g/l (0.081 L atm/mol K)(98 K).4 L mol x 3.8 g 5.6 L 131 g/mol Xe (1.96 g/l) 50 g/mol (50 g/mol) 6.0 g/mol (6.0 g/mol) 1.03 g/l (Xe) 48) If a steel container holds 5.00 moles of gas and the total pressure is 5.00 atm., what is the partial pressure for each mole of gas? mol 5 atm 5 mol 1 atm ; each mole of gas has a partial pressure of 1 atm mol 49) If a steel container holds.00 moles of hydrogen gas and.00 moles of helium gas, and the total pressure is 4.00 atm., what is the partial pressure of each of the gases? 50) If a steel container holds 1.00 moles of oxygen gas and 3.00 moles of argon gas and the total pressure is 800 Torr, what is the partial pressure of each of the gases? 51) If a steel container holds 1.50 moles of nitrogen gas and.50 moles of helium gas at a total pressure of 760 mm Hg, what is the partial pressure of each of the gases? 5) A rigid container with a volume of 5.60 l holds 71.0g chlorine gas and 4.00g helium gas. If the total pressure is 760 mm Hg what is the partial pressure of both gases? short answer:we have equal moles of each gas 1 mole each so they each exert 380 mm Hg (1.96 g/l) a XaT mol gas X a 4 mole gases 0.5 for each gas; axa T atm.00 atm (.00 atm) a XaT X O 1.00 mol O 4.00 mole gases 0.5; XAr 0.75; O 0.5(800 Torr) 00 Torr; Ar 600 Torr ( O 00 Torr; Ar 600 Torr) X N 1.50 mol N 4.00 mole gases 0.375; XAr 0.65; N 0.375(760 mm Hg) 85 mm Hg; Ar 475 mm Hg ( N 85 mm Hg; Ar 475 mm Hg) moles Cl 71.0 g Cl x mol Cl g Cl 1.00 mol Cl moles He 4.00 g He x mol He 1.00 mol He 4.00 g He X Cl 1.00 mol Cl.00 mole gases 0.500; XHe 0.500; Cl 0.500(760 mm Hg) 380 mm Hg; He 380 mm Hg ( Cl 380 mm Hg; He 380 mm Hg) 53) A.4 liter glass bulb has a total pressure of 760 Torr at 0.0 C and contains three different gases, nitrogen, helium and argon. If the partial pressure of nitrogen is 50 Torr and the partial pressure of argon is 130 Torr, what is the number of moles of helium in the tank? He 760 Torr 380 Torr 380 Torr 0.5 atm half of the molecules. Since at ST.4 L 1 mol we have mol He V nrt; n V RT (0.500 atm)(.4 L) mol (0.081 L atm/mol K)(73 K) 19 (0.500 mol He)

20 More gas problems 54) Helium takes up 5.71 liters at O.00 O C and 3.95 atmospheres. What is the volume of the same helium at 3.0 O F and 800 mm Hg? V 1V 1 (3.95 atm)(5.71 L) note that T did not change 1.5 L 1.05 atm 1 V 1 V (1.5 L) 55) 57 ml of oxygen in a gas tube goes from 17.0 O C to 4.0 O C from being out in the sun. The pressure in the tube is 39.0 pounds/in, but it does not change as the temperature increases. What is the volume of the tube after it has heated? must be some sort of expandable tube only T changes. V T T O C K (79 ml) 1 V V V 1T (57 ml)(315.1 K) T 79 ml T 4.0 O C K 1 (90.1 K) 56) An enormous (57,400 cubic meter) expandable helium balloon at.0 O C is heated up by a fire under it and the action of the sun on the dark plastic covering on top. There will be a small increase in pressure from 785 mm Hg to 790 mm Hg, but the major effect wanted is an increase in volume so the balloon can lift its cargo. To what temperature must the balloon get in order to fill out to 60,500 cubic meters? 1 V 1 T V 1 T use Kelvin T V 1 V (790 mm Hg)(60,500 M3 )(95 K) 1 (785 mm Hg)(57,400 M K ) (313 K) 57) What volume of air at standard pressure gets packed into an 11.0 ft 3 SCUBA tank at the same temperature at 15.8 atmospheres? note that T did not change, and V 1 V (15.8 atm)(11 ft3 ) 174 ft atm 3 1 V 1 V looking for original volume. (174 ft 3 ) 58) Air is roughly 0% oxygen and 80% nitrogen. What is the mass of air in an automobile tire of 19.7 L and internal pressure of 6. 7 SI at 4.0 O C? (You will have to use a weighted average for the molar mass of air.) 0.(3.0 g/mol) + 0.8(8.0 g/mol) 8.8 g/mol air molar mass of air (99.1 g) n V RT (4.6 atm)(19.7 L) 8.8 g V nrt: (0.081 L atm 3.44 mol; 3.44 mol x 99.1 g use L atm mol ; )(97 K) mol mol K 59) A constant pressure tank of gas at 1.01 atm has propane in it at 15.0 O C when it is at 55 cubic meters. What is its volume at 48.0 C? V 1 V V V 1T (55 m3 )(31 K) 84 m T (84 cubic meters) 1 (88 K) 3 use Kelvin 60) A SCUBA tank is filled with air at 16.7 atm at 4 C, but someone leaves it out in the sun to warm to 65 C. What is the tank pressure? 1 ; add to O C for K 1T (16.7 atm)(338.1 K) T 19.0 atm 1 (97.1 K) (19.0 atm) 61) What is the mass of neon in a 65 ml neon tube at 357 mm Hg & 5.0 O C? V nrt: use L atm mol ; n V RT (0.470 atm)(0.65 L) (0.081 L atm mol Ne; mol Ne x )(98 K) mol K (0.4 g) 6) The usual partial pressure of oxygen that people get at sea level is 0.0 atm., that is, a fifth of the usual sea level air pressure. eople accustomed to 1 atm. air pressure begin to become "lightheaded" at about 0.10 atm oxygen. As a rule of thumb, the air pressure decreases atm every 1000 feet. At what altitude should airplane cabins be pressurized? Up to about what altitude should you be able to use unpressurized pure oxygen? (Express your answer in feet above Mean Sea Level, or MSL.) (15,000 feet abovemsl) 63) Which diffuses faster, the bad smell from a cat-pan due to ammonia (NH 3 ) or an expensive French perfume with an average molecular weight of 170. g/mol? "How much faster does the faster one diffuse? 64) What is the mass of 15.0 liters of molecular chlorine gas at ST? 0.18 g mol 0.4 g Ne 0.1 atm O 0.5 atm air; 0.5 atm x 1000 feet/ atm 14,970 feet 15,000 feet r r ; NH 3 diffuses 3.16 x faster than the expensive French perfume, unfortunately mol.4 L x g mol Cl x 15 L 46.9 g (ammonia is 3.16 x faster) 0 (46.88 g)

21 65) A 50. Kg tank of liquid butane (C 4 H 10 ) is ignited. How many liters of carbon dioxide at 10. O C are produced at 1.00 atm? find moles of CO and plug into ideal gas law C 4 H O 8 CO + 10 H O molc 50,000 g C 4 H 10 x 4 H 10 x 4 mol CO 17,06 mol CO 58.1 g C 4 H 10 molc 4 H n 10 (555,157 L) V nrt (17,06 mol)(0.081 L atm )(393 K) mol K V nrt; 555,157 L 1.00 atm 66) How many liters of gas at 950. mmhg and O.00 0 C are produced by burning 3.00 liters of acetylene (C H ) at 5.00 atm and 0.0 OC? find mol acetylene, then mol gases produced, and plug into ideal gas law V nrt; n CH V RT (5.00 atm)(3.00 L) (0.081 L atm mol K )(93 K) mol C H C H + 5 O 4 CO + H O each mol acetylene produces 3 mol gases 3 mol gases mol C H x 17 mol gases mol C H V nrt (17 mol)(0.081 L atm )(73 K) mol K V nrt; 39,75 L 1.5 atm (39,75 L of gases produced) 67) 5.00 grams of octane (C 8 H 18 ) and enough oxygen to burn it are in an automobile cylinder compressed to 0 atm at 8 O C. The mixture explodes and heats the cylinder to 150 C. What is the pressure in the (same sized) cylinder after the explosion? find mol octane, then mol gases produced, and plug into combined gas law mol octane 5.00 g octane x g octane mol CO C 8 H O 16 CO + 18 H O each mol octane produces 17 mol gases 17 mol gases mol octane x mol gases n mol octane (494 atm) 1 V 1 V 1 n 1 n T ; V 1 V so (0 n 1 n T 1natm)(0.744 T mol)(43 K) 494 atm n( mol)(91 K) 68) If 0.515g of magnesium is added to excess HCl, it makes hydrogen gas and magnesium chloride. The hydrogen is collected at 3.0 O C and 735 mm Hg. What is the volume of hydrogen? find mol hydrogen, then mol gases produced, and plug into into ideal gas law Mg + HCl MgCl + H V nrt; g Mg x V nrt mol Mg 4.3 g Mg x mol H mol Mg 0.01 mol H n (0.01 mol)(0.081 L atm )(96 K) mol K L atm (0.533 L) 69) How many liters of ammonia (NH 3 ) at ST are produced when 10.0 g of hydrogen is combined with excess nitrogen? find moles of NH 3 and plug into ideal gas law N + 3H NH g H x mol H.01 g H x mol NH 3 3 mol H mol NH 3 x.4 L NH 3 mol NH L NH 3 (74.3 L) 70) How many milliliters of hydrogen at 000 O C and mm Hg are produced if 15.0 g of magnesium reacts with excess sulfuric acid? find moles of H and plug into ideal gas law Mg + H SO 4 MgSO 4 + H mol Mg 15.0 g Mg x 4.3 g Mg x mol H mol Mg mol H V nrt (0.617 mol)(0.081 L atm V nrt; )(73 K) mol K L 750 ml 1.84 atm 71) What is the mass of 5.0 liters of fluorine gas at.85 atm, 450. O C? (750 ml) n V RT (.85 atm)(5.0 L) 38.0 g F (0.081 L atm 1.0 mol x 45.6 g F V nrt )(73 K) mol F use L atm mol K mol K (45.6 g) 7) A 9.00 liter tank has 150. atmospheres of bromine in it at 7.0 O C. What is the added mass of the tank due to the gas? V nrt use L atm mol K n V RT (150 atm)(9.00 L) g Br (0.081 L atm 54.8 mol x 8760 g Br )(300 K) mol Br mol K (8760 g) 73) A 50.0 L tank of 1000 g of liquid butane (C 4 H 10 ) is rated to 10.0 atmospheres. Is it safe out in the sun where the temperature may reach 40 O C? find moles of moles butane and solve for T using ideal gas law to find maximum safe temperature (yes) molc 1000 g C 4 H 10 x 4 H mol C 58.1 g C 4 H 4 H 10 n 10 V nrt; T V nr (10.0 atm)(50.0 L) (17. mol)(0.081 L atm mol K ) 354 K 81 O C; yes 1

22 74) If 100. g of ice is heated in a 3.33 liter sealed container containing air at 1.00 atm until it reaches 10 O C, what is the resulting pressure? 100. g H O x mol H O g H O 5.55 mol H O V nrt; HO nrt V (5.55 mol)(0.081 L atm )(375 K) mol K atm 3.33 L total air + stea m 1.00 atm atm 5.31 atm (5.31 atm) 75) Each year there are fatalities resulting from teachers placing dry ice in a,00l soda bottle and letting it pressurize. Given that L soda bottles are rated to 150 SI, how many grams of CO can be placed in a L soda bottle containing 1 atmosphere of air at 5 O C before it bursts? V nrt; 150 SI x atm 14.7 SI 10.0 atm gases 9.0 atm CO + 1 atm air n V RT (9.0 atm)(.00 L) (0.081 L atm mol K )(98 K) 0.75 mol CO g CO x g CO mol CO (33.1 g) 76) If all the air (average molar mass 8.8 g/mol) in a typical classroom with a volume of 10,000. liters at 5.0 O C and 1.00 atm were condensed to a liquid and placed on a scale, what would it s mass be? n V RT (1.00 atm)(10,000. L)) (0.081 L atm mol air x )(98 K) mol K 8.8 g air mol air 11,77 g (11,77 g) 77) What is the density of of propane gas (C 3 H 8 ) at 37.0 O C and 45 in Hg? (.54 cm I inch) 45 inches Hg x 54 mm inch atm 760 mm Hg d M R T x (81.88 atm)(44.1 g/mol) (0.081 L atm/mol K)(310 K) atm 14 g/l (147 g/l) 78) Isopropyl alcohol, C 3 H 7 OH, makes a good fuel for cars. What volume of oxygen at 735 mm Hg and 3.0 O Cis needed to burn 1.00 kilogram of isopropyl alcohol? C 3 H 8 O + 9 O 6 CO + 8 H O 1000 g C 3 H 8 O x mol C 3H 8 O 60.1 gc 3 H 8 O x 4.5 mol O mol C 3 H 8 O mol O n V nrt; V nrt (188 L) 79) The dirigible Hindenburg had 3.7 x 10 6 m 3 of hydrogen in its gas bags at 1.10 atm and 7.00 O C. What was the mass of the hydrogen in pounds? (453.6 g 1 pound, 1 cubic meter 1000 liters) 3.7 x 10 6 m 3 H x 1000 L m 3 (74.88 mol)(0.081 L atm )(96 K) mol K 188 L atm 3.7 x 10 9 L V nrt; n V (1.10 atm)(3.7 x 109 L) RT (0.081 L atm mol K )(80 K) 1.77 x.01 g H 108 mol H x x pound H 7.84 x 10 mol H g H 5 lb H (7.84 x 10 5 lb H )

23 Vocab and concepts 1. What is a gas? a substance that lacks intermolecular forces. Compare gases to liquids gases are typically more dense, reactive, compressible; less visible, and lack intermolecular forces. 3. Discuss the physical behavior of gases. Gases pressurize when compressed, expand when heated if expandable, pressurize when heated if nonexpendable, lighter gases travel faster than heavy gases, and any gas occupies.4 L at ST 4. Assume money is proportional to happiness derive a formula $ 1 1 $ 5. Assume that work is inversely proportional to income.derive a formula W 1 $ 1 W $ 6. Rearrange the combined gas law to solve for 1 V 1 V T ; 1V 1 T V 7. Ideal gas law If 4.0 grams of a neon at a pressure of 5.4 mm Hg has a volume of 10 microliters, what is the temperature in Celsius? V nrt; T V nr (5.4/760 atm)(1. x 10 6 L) (4.0/0 mol)(0.081 L atm mol K ) 5. x 10-7 K O C 8. graham s law: Which diffuses faster, the bad smell from a cat-pan due to ammonia (NH 3 ) or an expensive French perfume with an average molecular weight of 170 g/mol? "How much faster does the faster one diffuse? If the rate of diffusion of ammonia is 1 meters per second, what is the rate of diffusion of the perfume? r 1 r ; NH 3 diffuses 3.16 x faster than the expensive French perfume, 1 m/s Avogadro s law How many liters of water can be made from 34 grams of oxygen gas and 6.0 grams of hydrogen gas at ST? What is limiting reactant for this reaction? get n then v H + O H O 4g 3g 36 g g 3.8m/s 6g 54 g theoretical yield 38.5 g H O.15 mol x.4l/mol 48 mol water if you pointed out tht it is a solid and not a gas, good point! gases review: one problem of each major type 10. Boyles law 1.70 L of a gas at standard temperature and pressure is compressed to 473 ml. What is the new pressure of the gas? Note that the temperature does not change. 1V 1 V 1 V 1 V (1.00 atm)(1.70 L) L.35 atm 11. Charles law The temperature inside refrigerator is about 4 0 Celsius. If I place a balloon in my fridge that initially has a temperature of 0 C and a volume of 0.5 liters, what will be the volume of the balloon when it is fully cooled by my refrigerator? V 1 V V V 1T (0.500 L)(77.1 K) T 1 (95.1 K) L 1. gay-lussac s law A SCUBA tank is filled with air at 16.7 atm at 4 C, but someone leaves it out in the sun to warm to 65 C. What is the tank pressure? 1 ; add to O C for K 1T (16.7 atm)(338.1 K) T 19.0 atm 1 (97.1 K) 13. Combined gas law If I initially have a gas at a pressure of 1 atm, a volume of 3 liters, and a temperature of 00 K, and then I raise the pressure to 14 atm and increase the temperature to 300 K, what is the new volume of the gas? 1 V 1 V T V 1V 1 T (1.0 atm)(3.0 L)(300. K) (00. K)(14.0 atm) 9.6 L 15. Gas density What is the density of acetylene gas (6.04 g/mol) at 0.97 atm, 5 O C? 16. Molar mass: What is the molar mass of a gas with a density of.4 g/l at 300K, 1 atm? 14. Gas problems involving a chemical reaction If g of magnesium is added to HCl, it makes hydrogen gas and magnesium chloride. The hydrogen is collected at 3 C and 735 mm Hg. What is the volume of hydrogen? V nrt; g Mg x V nrt Mg + HCl MgCl + H d M R T (0.97 atm)(6.04 g/mol) (0.081 L atm/mol K)(98 K) 1.03 g/l d M R T ; M drt (.4 g/l)(0.081 L atm/mol K)(300 K) 1.00 atm 59.1 g/mol 17. artial pressure: ) If a steel container holds 1.50 moles of nitrogen gas and.50 moles of helium gas at a total pressure of 760 mm Hg, what is the partial pressure of each of the gases? X N 1.50 mol N 4.00 mole gases 0.375; XAr 0.65; N 0.375(760 mm Hg) 85 mm Hg; Ar 475 mm Hg mol Mg 4.3 g Mg x mol H mol Mg 0.01 mol H n (0.01 mol)(0.081 L atm )(96 K) mol K L atm 3