Dr. Corell - Chemistry I Study Guideline Unit Ten: Gases ____________________________________________________ 1. Distinguish between a solid, a liquid and a gas. 2. Describe the structure of a gas on the molecular level using the Kinetic-Molecular Theory. 3. Calculate pressure in pascals, kilopascals, atomspheres, and mm Hg. 4. Calculate the partial pressure of a gas using Dalton’s Law. 5. Describe and calculate the effect of a change in temperature on the volume of a gas. 6. Describe and calculate the effect of a change in pressure on the volume of a gas. 7. Apply the ideal gas law to calculate the pressure, volume or temperature of a gas. 8. Determine the molar volume of a gas under a variety of conditions. The Gas Phase - Basic Vocabulary Word List atmosphere state manometer torr Pascal volume pressure barometer Gases represent one of the three phases of matter. Another word for “phase” is ______________. Gases have no definite shape, nor do they have a definite ______________. The force exerted by a gas on a unit area is called ______________. One Newton per square meter is a unit of pressure called ______________. The pressure of a column of mercury one millimeter high is another pressure, called the ______________. Atmosphere pressure is most often measured by use of a(n) ______________. A U-shaped tube called a(n) ______________ can also be used. Standard pressure is 760 torr; this quantity is another unit of pressure, called one ______________ . Pressure unit conversion problems 1. The air pressure for a certain tire is 129 kPa. What is this pressure in ATM? 2. The air pressure inside a submarine is 0.622 ATM. What is this in mm Hg? 3. The weather news gives the pressure as 1.17 ATM. What is this in mm Hg? 4. An experiment is performed at Sandia National Labs in New Mexico at an atmospheric pressure of 747.8 mm Hg. What is this pressure in ATM? 5. A bag of potato chips is sealed in a factory near sea-level. The atmospheric pressure at the factory is 761.3 mm Hg. The pressure inside the bag is the same. What is the pressure inside the bag of chips in Pa? Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 6. The same bag of chips is served as a snack on a flight across the US. On this plane the atmospheric pressure is maintained at 0.855 ATM. What is the difference in pressure inside the bag vs. out side the bag in Pa? 2 7. The pressure gauge on a compressed air tank reads 43.2 lb/in . What is this pressure in ATM? 2 8. The pressure in the tire of a car is 34.8 lb/in . What is the pressure in kPa? Open-end manometer An open-end manometer is an instrument used to determine the pressure of a given system. The manometer illustrated below consistes of a U-bend tube that contains mercury. One end of the manometer is open to the atmosphere. Examine the heights of the mercury columns and answer the questions that follow. 1. Which vessel contains a gas with a pressure greater then atmospheric pressure? Explain. 2. Which vessel contains a gas with a pressure less than atmospheric pressure? Explain. 3. If atmospheric pressure is 1 ATM, what is the pressure of gas B? 4. What would happen to the level of mercury in the tubes of B, if the entire apparatus were brought to the top of a high mountain? Explain. page 3 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 5. On a given day the barometric pressure is 755 torr. a. What is the equivalent reading in ATM? b. mm Hg? c. kPa? 6. As shown to the right, the manometer has a trapped gas in the container and is open to the atmosphere. There is a difference between the mercury levels of 42 mm and the atmospheric pressure is 752 mm Hg. a. What is the pressure of the gas in the manometer in mm Hg? b. If the atmospheric pressure were to increase to 762 mm Hg, what would happen to the level of the mercury on the right side of the tube? by how much? c. If the atmospheric pressure were then to decrease to 96.3 kPa, what would be the difference in height between the two columns of mercury? 7. Draw an open-end manometer to show the heights of mercury if a trapped gas has a pressure of 720 mm Hg and the atmospheric pressure is 1 ATM. page 4 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 8. As shown in the diagram to the right, hydrogen gas is collected over water. The level of the hydrogen gas is read as 42.4 mL The temperature of the water is 24.0°C. At this temperuature, watervapor exherts a partial pressure of 22.4 mm Hg. If the total pressure is 748.0 mm Hg, what is the pressure exherted by the hydgrogen gas? 9. The manometer on the right is exposed to an atmospheric pressure of 748 mm Hg. The mercury colum connected to the trapped gas is 22 mm higher than the side exposed to the atmosphere. What is the pressure of the trapped gas? 10. Draw an open-end manometer to show the heights of mercury if a trapped gas has a pressure of 790.0 mm Hg and the atmospheric pressure is 98.0 kPa. page 5 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 11. A gas container is fitted with a manometer. The level of the mercury is 15.0 mm lower on the open side. If the lab barometer says the atmospheric pressure is 750.0 mm Hg, what is the pressure in ATM of the gas in the container? 12. A soccer ball is attached to an open ended manometer. The mercury level on the side attached to the ball is 34.0 mm lower. Atmospheric pressure is 770.0 mm Hg. What is the pressure in the ball in kPa? 13. The U-tube of a manometer is 26.4 mm high. With both ends open the manometer is filled with mercury until it is 13.2 mm high on both sides. What is the largest difference in mm Hg that this manometer can measure? 14. A manometer contains a sample of nitrogen gas at 88.3 kPa. The level of mercury on the open side is 12.8 mm lower. What is the atmospheric pressure in kPa? 15. An open end-manometer is connected to a canister of unknown gas. The atmospheric pressure is 1.03 ATM. The mercury level is 18.6 mm higher on the open side. What is the pressue of the gas in mm Hg? Partial Pressure Problems 1. What is the pressure of a mixture of helium, nitrogen and oxygen if their partial pressures are 600.0 mm Hg, 150.0 mm Hg and 102 mm Hg? 2. A flask contains a mixture of hydrogen and oxygen. The pressure being exerted by these gases is 1.14 ATM. If the partial pressure of the hydrogen in the mixture is 395 mm Hg, what is the PO2 in mm Hg? page 6 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 3. An environmental testing lab uses a pump and cylinder to collect air near a leaking natural gas line. The lab finds the total pressure in their sample is 776.134 mm Hg. Analyzing the sample, they find it contains oxygen, nitrogen and methane. What is the partial pressure of the methane in Pa if the partial pressure of the oxygen and nitrogen are 253.948 mm Hg and 515.390 mm Hg respectively. 4. A barometer shows the atmospheric pressure to be 762 mm Hg. What is the partial pressure of nitrogen if it makes up 78.0% of the air? 5. What partial pressure in mm Hg of oxygen is a scuba diver breathing if the total pressure is 6.35 ATM and the oxygen is 20.0% of the air? 6. What is the atmospheric pressure if the partial pressures of nitrogen, oxygen and argon are 77.75 kPa, 0.197 ATM and 14.9 mm Hg respectively? 7. The gases carbon dioxide, oxygen and argon are mixed in a container. If all three gases have the same partial pressure and the total pressure of the container is 32,680 Pa, what is the partial pressure of the argon in ATM? 8. The partial pressure of water vapor in a greenhouse is 139.0 mm Hg, which is 18.0 percent of the total pressure. What is the total pressure in the greenhouse? page 7 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I Boyle’s Law Among the earliest systematic collections of facts about the physical world were the careful measurements by Robert Boyle (1627-1691) of the pressures and corresponding volumes of confined samples of gases. The mathematical relationship between these properties of pressure and volume is known as Boyle’s law. 1. State Boyle’s law in the words found in your textbook. 2. In the mathematical statement of Boyle’s Law, PV = K, P represents _______________, V represents _______________ and K represents a _______________, which applies to specific sample of gas maintained at constant _______________ and _______________. 3. The following table gives pressure and volume reading for a confined sample of gas maintained at constant temperature. For each set of measurements, calculate K from the relationship, PV = K. P (ATM) V (mL) 0.20 K (ATM x mL) P (ATM) V (mL) 500 4.00 25.0 0.40 250 5.00 20.0 0.60 167 6.00 16.7 0.80 125 7.00 14.3 1.00 100 8.00 12.5 2.00 50.0 9.00 11.1 3.00 33.3 K (ATM x mL) 4. If the pressure of the previous sample were changed to 2.50 ATM, what volume would be expected? 5. If the pressure of the previous sample were changed to 0.50 ATM, what volume would be expected? page 8 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I On the following grid, plot the values from the table of Pressure vs. Volume. 500 450 400 350 300 250 Volume (mL) 200 150 100 50 0 1 2 3 4 5 6 Pressure (ATM) 7 8 9 6. Plot the points you predicted in questions 4 and 5 and the graph above. Circle these points in a different color. Do they fit the curve? Boyle’s Law - Practice Problems Show work or a labeled set up 1. P1 = 275 mm Hg P2 = 800.0 mm Hg V1 = 2.50 L V2 = __________ L 2. V1 = 400.0 mL V2 = 50.0 mL P1 = 1.00 ATM P2 = __________ ATM page 9 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 3. P1 = 0.925 ATM V1 = 3.55 L P2 = 1.00 ATM V2 = __________ L 4. V1 = 500.0 L V2 = 375 L P1 = 735 mm Hg P2 = __________ mm Hg 5. V1 = 8.30 mL P1 = 675 mm Hg V2 = 28.5 mL P2 = __________ mm Hg 6. P1 = 0.900 ATM P2 = 0.500 ATM V1 = 4.00 L V2 = __________ L 7. P1 = 1.00 ATM V1 = 0.850 L P2 = 1.15 ATM V2 = __________ L 8. V1 = 12.4 L V2 = 10.0 L P1 = 760 mm Hg P2 = __________ mm Hg 9. P1 = 742 mm Hg P2 = 1.00 ATM V1 = 127 mL What are the following in the appropriate labeled units: P1 = __________ ATM P2 = __________ mm Hg V2 = __________ mL 10. P1 = 1.07 ATM P2 = 760.0 mm Hg V1 = 47.8 mL What are the following in the appropriate labeled units: P1 = __________ mm Hg P2 = __________ ATM V2 = __________ mL 11. V1 = 765 mL V2 = 1.25 L P1 = 760.0 mm Hg What are the following in the appropriate labeled units: V1 = __________ L V2 = __________ mL P2 = __________ mm Hg page 10 Unit 10 Gases - Chapter Packet 12. V1 = 8260 mL V2 = 4.00 L Dr. Corell - Chemistry I P1 = 724 mm Hg What are the following in the appropriate labeled units: V1 = __________ L V2 = __________ mL P1 = __________ ATM P2 = __________ mm Hg P2 = __________ ATM 13. A sample of gas occupies 2.50 L at 1.15 ATM. What is its volume at standard pressure? 14. A 500.0-mL sample of gas at 760.0 mm Hg is compressed to 100.0 mL. What is its new pressure? 15. A sample of gas occupies 42.5 mL at 720.0 mm Hg. What is its volume at standard atmospheric pressure? 16. A sample of gas occupies 125 mL at standard pressure. What is the new pressure when the volume is compressed to 75.0 mL? 17. A cylinder fitted with a piston contains 14.0 L at a pressure of 7.50 ATM. The piston expands until the pressure is 1.00 ATM. What is the new volume? 18. The pressure on a 625-mL sample of gas is changed from 0.925 ATM to 1.45 ATM. What is the new volume? 19. In a small automobile engine, a typical cylinder has a maximum volume of 900.0 mL. When the piston moves to decrease the volume on the compression stroke, the volume become 125 mL at the time of ignition. If the original 900.0-mL volume had a pressure of 1.00 ATM, what is the new pressure in ATM? page 11 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 20. The cylinder of a typical bicycle pump has a volume of 1.25 L at standard pressure. A bicycle tire is to be inflated to a total pressure of 4.75 ATM. To reach this pressure the gas in the pump must be reduced to what volume? 21. A gas occupies a volume of 458 mL at a pressure of 1.01 kPa and a temperature of 295 K. When the pressure is changed, the volume becomes 477 mL. If the temperature has been held constant what is the new pressure? 22. A gas occupies a volume of 2.45 L at a pressure of 1.03 ATM and a temperature of 293 K. What volume will the gas occupy if the pressure changes to 0.980 ATM while the temperature remains unchanged? 23. The cylinder of a motorcycle has a volume of 0.6250 L when the piston is at the top of the cylinder. When the piston is at the bottom of the cylinder the volume is 0.0600 L. If the cylinder is if filled with air at a pressure of 765.1 mm Hg when the piston is at the top, what is the pressure in kPa when the piston is at the bottom of the cylinder? 24. A discarded spray can contains only a small volume of the propellant gas at a pressure of 34,470 Pa. The volume of the can is 473.18 mL. If the can is run over by the garbage truck and flattened to a volume of 13.16 mL, what will the new pressure be if the can doesn’t explode? 25. A sample of 10.0 L of argon gas is stored in a cylinder at a temperature of 23.8°C and a pressure of 2 78.6 lb./in . The sample is transferred completely to another cylinder with a volume of 2.8 L. If the temperature is kept constant what is the pressure of the new cylinder in kPa? Charles’s Law If a gas is confined at constant pressure, such as in a cylinder with a movable piston, and subjected to an increase in temperature, the volume of the gas will increase. The table below gives measurements of temperature and volume taken from such an experiment. T (°C) V (L) T (°C) V (L) T (°C) V (L) 100.0 3.06 0.0 2.24 –100.0 1.42 50.0 2.65 –50.0 1.83 –150.0 1.01 page 12 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I On the following grid, plot the values from the table of Temperature vs. Volume. 4.0 3.5 3.0 2.5 Volume (L) 2.0 1.5 1.0 0.5 –300 –200 –100 0 100 Temperature (°C) 1. Extrapolate your curve until it reaches zero volume. What would this temperature be? __________°C This temperature is called absolute zero since no temperature can be lower. This is about –273°C. When given a temperature in Celsius simply add 273 to find the Kelvin temperature: K = °C +273. Kelvin temperature therefore start at zero. This is why Kelvin is called an absolute temperature scale. Circle the word that correctly completes the statement 2. If pressure is constant, the volume of a sample of gas (increases/decreases) as temperature increases. 3. At constant pressure, the volume of a sample of gas is (directly/inversely) proportional to the temperature as measured on the Kelvin scale. 4. Even at constant pressure, the volume of a sample of gas is NOT proportional to the temperature as measured on the Celsius scale because 0°C does not correspond to the (lowest/highest) possible temperature. 5. The straight-line graph relationship between volume and temperature illustrates (direct/indirect) proportionality. page 13 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I Fill in the blanks in the following statements. 6. When the temperature is increased from 20°C to 40°C, the temperature is not actually doubled. In order to have the temperature doubled, a sample at 20°C (__________K) must be heated to ________ degrees on the Kelvin scale which is _______ degrees on the Celsius scale. 7. In this mathematical statement of Charles’s law, V/T =K, V represents ________________, T represents __________________ on the _____________ scale and the K is a ______________, which applies to specific sample of gas maintained at constant _________________ and _______________. Charles’s Law - Practice Problems Show work or a labeled set up 1. V1 = 255 mL V2 = 300.0 mL T1 = 298 K T2 = __________ K 2. T1 = 273 K T2 = 325 K V1 = 4.75 L V2 = __________ L 3. V1 = 500.0 mL V2 = 700.0 mL T1 = 283 K T2 = __________ K 4. T1 = 25.0°C T2 = 15.0°C V1 = 7.50 L V2 = __________ L 5. T1 = 15.0°C T2 = 75.0°C V1 = 275 mL V2 = __________ mL 6. T1 = 0.00°C T2 = 100.0°C V1 = 8.00 L V2 = __________ L 7. V1 = 2.00 L V2 = 4.00 L T1 = 273 K T2 = __________ K T2 = __________ °C 8. Assuming constant pressure what will be the volume of a gas sample at 309 K if its volume at 215 K is 3.42 L? page 14 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 9. Calculate the final volume when a 75.0 mL sample of gas is heated from 5.00°C to 60.0°C at constant pressure. 10. What will be the new volume of a 1.75-L sample cooled from 25.0°C to Standard Temperature at constant pressure? 11. A 5.00-L sample of gas at 20.0°C is to be heated at constant pressure until the volume increases four fold. To what Kelvin temperature must this sample be heated? 12. A 10.0-L sample of gas at 300.0°C is to be cooled at constant pressure until it reaches half its original volume. At what Celsius temperature will this sample reach half its original volume? 3 13. A gas sample at 83.0°C occupies a volume of 1400 m . At what Celsius temperature will it occupy 3 1200 m ? 14. A tank of compressed CO2 has a temperature of 23.6°C and a volume of 31.4 L. The CO2 is completely transferred into a smaller tank with a volume of 25.0 L. Assuming constant pressure, what is the temperature of the gas in the smaller tank? 15. A gas has a temperature of 22.4°C and a volume of 10.6 mL. The sun rises and warms the gas to 27.8°C. If pressure is constant, what will be the new volume of the gas? 3 16. A gas at a temperature of –173°C has a volume of 0.105 dm . At what Celsius temperature will its volume be 0.140 L? Assume constant pressure. Gay-Lussac’s Law Just as volume/pressure and volume/temperature relationships fro gases can be determined, temperature/pressure relationships can be determined for constant volume samples of gases. 1. Measurements of _____________ and ______________ for constant volume samples of gases produce results much like the graph of _____________ and ______________ in the previous section. 2. The direct proportionality between _____________ and _____________ at constant _____________ can be expressed as P/T = K page 15 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I Gay-Lussac’s Law - Practice Problems 1. A tank of gas has a pressure of 2.75 ATM at 20.0°C. What will be the new pressure if the temperature is increased to 100.0°C? 2. A flask of gas is sealed at standard pressure and 25.0°C. What will be the pressure of the gas if the flask is cooled to standard temperature? 3. A tank of gas is filled to a pressure of 5.00 ATM at 75.0°C. At what temperature will the pressure equal 3.50 ATM? 4. If a confined gas has a pressure of 700.0 mm Hg at 15.0°C, what will be the temperature of the gas if the pressure is increased to 740 mm Hg? 5. The temperature of a tank of gas whose pressure is 650 mm Hg is changed from 27.0°C to 127.0°C. What will be the new pressure of the gas? Combined Gas Law 1. In some problems, we must consider relationships among the three variables __________, __________ and ______________ for a given sample of gas. Boyle’s, Charles’s and Gay-Lussac’s laws may be combined to give the formula: PV/T = K where P is _____________, V is ______________, T is ______________ and K is a ______________. Temperature must be expressed in ______________. 2. This relationship permits calculation of any one term when all others are known. It is not restricted by requirements of constant _____________, constant _____________ or constant _____________. However, the one other way of describing a gas, ______________, must remain constant. page 16 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I Combined Gas Law - Practice Problems 1. A sample of gas occupies 75.0 mL at a pressure of 725 mm Hg and 18.0°C. Calculate the volume at 800.0 mm Hg and 25.0°C? 2. A sample of gas occupies 3.75 L at a pressure of 1.15 ATM and 25.0°C. At what temperature will it occupy 4.00 L at standard pressure? 3. A sample of gas occupies 8.25 L at STP. What will its volume become at 735 mm Hg and 20.0°C? 4. A sample of gas occupies 0.575 L at 1.50 ATM and 125°C. At what pressure will its volume be 0.300 L at 20.0°C? 5. A sample of gas occupies 2.30 L at 825 mm Hg and 70.0°C. What is its volume STP? page 17 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 6. An air-filled balloon has a volume of 225 L at a pressure of 0.945 ATM and a temperature of 25.0°C. If the pressure changes to 0.999 ATM and the temperature changes to 0.00°C, what will be the new volume of the balloon. 3 7. A gas confined in a 515-cm container exerts a pressure of 107.4 kPa at 38.6°C. At what Celsius 3 temperature will it exert a pressure of 635.7 kPa if it is placed into a 644- cm container. Ideal Gas Law - Practice Problems 1. What volume would be occupied by 100.0 g of oxygen at a pressure of 1.50 ATM and a temperature of 25.0°C. 2. A balloon is inflated with 0.2494 g of helium to a pressure of 1.26 ATM. If the desired volume of the balloon is 1.250 L, what must the temperature be in degrees Celsius.. page 18 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 3. How many grams of argon would it take to fill a light bulb with a volume of 0.475 L of STP? 4. A welder’s acetylene (ethyne – C2H2) tank has a volume of 75.0 L. It is stored at a temperature 23.24°C and a pressure of 7667 kPa. How many grams of acetylene are in the tank? 5. What pressure is exerted by 27.55 g of fluorine in a 45.4 L container at –24.0°C? 6. 11.28 g of Dry ice (CO2(s)) are placed into 5.00 L evacuated chamber that is maintained at 35.1°C. What is the pressure in the chamber in kPa after all the dry ice has sublimed into gas? page 19 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 7. Bromine gas is placed into an evacuated demonstration bottle at STP. If the volume of the bottle is 0.255 L, how many atoms of bromine are in the bottle? 3 8. A sample of xenon gas occupies 0.308 m at a temperature of 52°C and a pressure of 149 kPa. Calculate the number grams of xenon present. 9. Find the molar mass of a gas if 1.000 x10–30 Gm3 of this gas has a mass of 2.87 g at 15.0°C and 745 mm Hg. 10. What will be the pressure of 0.0100 g of helium gas in a 4.5 x 1033 pm3 at 10,000.0°C? page 20 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I 11. Find the molar mass of a gas when 5.03 Mg occupies a volume of 4.44 x 1038 pm3 at 65.4°C and 1000.0 mm Hg. 12. What is the volume of hydrogen gas when 0.870 grams has a temperature of –250.0°C and a pressure of 100.0 ATM? 13. Find the molar mass of a gas when 3.89 g occupies a volume of 14.5 x 1023 nm3 at 13.5°C and 95.5 kPa of pressure. Gases Crossword ACROSS 1. Measure of average kinetic energy of molecules 19. Temperature scale used in conjunction with Charles’s law 4. ________________ molecular theory, proposed by Maxwell and Boltzman 20. Gas that is less dense than air 8. Abbreviation of 4 ACROSS 22. Describes chance or undirected motion. 9. Proposed that equal volumes of gases at the 24. Temperature scale in which zero degrees is same conditions contain equal numbers of the freezing point of water molecules 25. Major component of Earth’s atmosphere 11. Unit of pressure 27. Property or factor that remains the same 12. Scientist who related volume and pressure 28. The smallest hydrocarbon 13. Equivalent to 101.325 kPa 30. Part that moves in a traditional internal combustion engine due to combustion 15. At moderate temperatures and low pressures, gases act as if they were ________________ 33. Nearly 1% of atmospheric content 34. Liquid used in barometers 37. Force per unit area 36. Approximately 21% of atmosphere 38. Substance that flows page 21 Unit 10 Gases - Chapter Packet Dr. Corell - Chemistry I DOWN 2. Laboratory instrument used to measure pressure of a contained gas 3. Space that has a pressure of zero pascals 4. Unit on absolute temperature scale 5. One atmosphere pressure and 0°C 6. Instrument that measures atmospheric pressure 7. Occupies 22.4L at STP 10. Developed law of diffusion 14. Rate of diffusion is dependent upon molecular _________. 16. Describes collisions in which there is no energy loss 18. Scientist who developed law associated with partial pressures 21. Phase characterized by definite shape and volume 23. NH3 26. Speed in a particular direction 29. Unit of force 31. Phase containing most widely separated particles 32. Carbon monoxide formula 35. Rate of motion 17. Scientist who developed law relating temperature and volume 5 3 1 7 4 6 2 11 9 10 8 12 13 14 21 18 16 17 15 19 23 20 22 26 25 24 27 35 28 29 34 37 32 38 36 30 31 33 page 22
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