🎉 Announcing Numerade's $26M Series A, led by IDG Capital!Read how Numerade will revolutionize STEM Learning ## Chapter 10 ## Gases ## Educators KC ES PR HS + 1 more educators ### Problem 1 What are the basic postulates of kinetic molecular theory? How does the concept of pressure follow from kinetic molecular theory? KC Kevin C. Numerade Educator ### Problem 2 What is pressure? What causes pressure? ES Eugene S. University of Minnesota - Twin Cities ### Problem 3 How does pressure change as a function of altitude? KC Kevin C. Numerade Educator ### Problem 4 Explain the risks associated with uncontrolled decompression. ES Eugene S. University of Minnesota - Twin Cities ### Problem 5 What are the common units of pressure? List them in order of smallest to largest unit. KC Kevin C. Numerade Educator ### Problem 6 What is a manometer? How does it measure the pressure of a sample of gas? ES Eugene S. University of Minnesota - Twin Cities ### Problem 7 Summarize each of the simple gas laws (Boyle's law, Charles's law, and Avogadro's law). For each law, explain the relationship between the two variables it addresses and also state which variables must be kept constant. KC Kevin C. Numerade Educator ### Problem 8 Explain the source of ear pain experienced due to a rapid change in altitude. ES Eugene S. University of Minnesota - Twin Cities ### Problem 9 Why must scuba divers never hold their breath as they ascend to the surface? KC Kevin C. Numerade Educator ### Problem 10 Why is the second story of a house usually warmer than the ground story? ES Eugene S. University of Minnesota - Twin Cities ### Problem 11 Explain why hot-air balloons float above the ground. KC Kevin C. Numerade Educator ### Problem 12 What is the ideal gas law? Why is it useful? ES Eugene S. University of Minnesota - Twin Cities ### Problem 13 Explain how the ideal gas law contains within it the simple gas laws (show an example). KC Kevin C. Numerade Educator ### Problem 14 Define molar volume and give its value for a gas at STP. ES Eugene S. University of Minnesota - Twin Cities ### Problem 15 How does the density of a gas depend on temperature? Pressure? How does it depend on the molar mass of the gas? KC Kevin C. Numerade Educator ### Problem 16 What is partial pressure? What is the relationship between the partial pressures of each gas in a sample and the total pressure of gas in the sample? ES Eugene S. University of Minnesota - Twin Cities ### Problem 17 Explain how Boyle's law, Charles's law, Avogadro's law, and Dalton's law all follow from kinetic molecular theory. KC Kevin C. Numerade Educator ### Problem 18 Why do deep-sea divers breathe a mixture of helium and oxygen? ES Eugene S. University of Minnesota - Twin Cities ### Problem 19 When a gas is collected over water, is the gas pure? Why or why not? How can the partial pressure of the collected gas be determined? KC Kevin C. Numerade Educator ### Problem 20 How is the kinetic energy of a gas related to temperature? How is the root mean square velocity of a gas related to its molar mass? ES Eugene S. University of Minnesota - Twin Cities ### Problem 21 Describe how perfume molecules travel from the bottle to your nose. What is mean free path? KC Kevin C. Numerade Educator ### Problem 22 Explain the difference between diffusion and effusion. How is the effusion rate of a gas related to its molar mass? ES Eugene S. University of Minnesota - Twin Cities ### Problem 23 If a reaction occurs in the gas phase at STP, the mass of a product can be determined from the volumes of reactants. Explain. KC Kevin C. Numerade Educator ### Problem 24 Deviations from the ideal gas law are often observed at high pressure and low temperature. Explain this in light of kinetic molecular theory. ES Eugene S. University of Minnesota - Twin Cities ### Problem 25 The pressure in Denver, Colorado (elevation 5280 ft or 1600 m), averages about 24.9 in Hg. Convert this pressure to a. atm b. mmHg c. psi d. Pa KC Kevin C. Numerade Educator ### Problem 26 The pressure on top of Mount Everest (29,029 ft or 8848 m) averages about 235 mmHg. Convert this pressure to a. torr b. psi c. in Hg d. atm PR Pratik R. University of Florida ### Problem 27 The North American record for highest recorded barometric pressure is 31.85 in Hg, set in 1989 in Northway, Alaska. Convert this pressure to: a. mmHg b. atm c. torr d. kPa (kilopascals) PR Pratik R. University of Florida ### Problem 28 The world record for lowest pressure (at sea level) was 652.5 mmHg recorded inside Typhoon Tip on October 12, 1979, in the western Pacific Ocean. Convert this pressure to: a. torr b. atm c. in Hg d. psi ES Eugene S. University of Minnesota - Twin Cities ### Problem 29 If the barometric pressure is 762.4 mmHg, what is the pressure of the gas sample shown in each illustration? KC Kevin C. Numerade Educator ### Problem 30 If the barometric pressure is 751.5 mmHg, what is the pressure of the gas sample shown in each illustration? ES Eugene S. University of Minnesota - Twin Cities ### Problem 31 A sample of gas has an initial volume of 5.6 L at a pressure of 735 mmHg. If the volume of the gas is increased to 9.4 L, what is its pressure? KC Kevin C. Numerade Educator ### Problem 32 A sample of gas has an initial volume of 13.9 L at a pressure of 1.22 atm. If the sample is compressed to a volume of 10.3 L, what is its pressure? ES Eugene S. University of Minnesota - Twin Cities ### Problem 33 A 48.3-mL sample of gas in a cylinder is warmed from 22 C to 87 C. What is its volume at the final temperature? KC Kevin C. Numerade Educator ### Problem 34 A syringe containing 1.55 mL of oxygen gas is cooled from 95.3 C to 0.0 C. What is the final volume of oxygen gas? ES Eugene S. University of Minnesota - Twin Cities ### Problem 35 A balloon contains 0.158 mol of gas and has a volume of 2.46 L. If we add 0.113 mol of gas to the balloon (at the same temperature and pressure), what is its final volume? KC Kevin C. Numerade Educator ### Problem 36 A cylinder with a moveable piston contains 0.553 mol of gas and has a volume of 253 mL. What is its volume if we add 0.365 mol of gas to the cylinder? (Assume constant temperature and pressure.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 37 What volume does 0.118 mol of helium gas at a pressure of 0.97 atm and a temperature of 305 K occupy? Would the volume be different if the gas was argon (under the same conditions)? KC Kevin C. Numerade Educator ### Problem 38 What volume does 12.5 g of argon gas at a pressure of 1.05 atm and a temperature of 322 K occupy? Would the volume be different if the sample were 12.5 g of helium (under identical conditions)? ES Eugene S. University of Minnesota - Twin Cities ### Problem 39 What is the pressure in a 10.0-L cylinder filled with 0.448 mol of nitrogen gas at a temperature of 315 K? KC Kevin C. Numerade Educator ### Problem 40 What is the pressure in a 15.0-L cylinder filled with 32.7 g of oxygen gas at a temperature of 302 K? ES Eugene S. University of Minnesota - Twin Cities ### Problem 41 A cylinder contains 28.5 L of oxygen gas at a pressure of 1.8 atm and a temperature of 298 K. How much gas (in moles) is in the cylinder? KC Kevin C. Numerade Educator ### Problem 42 What is the temperature of 0.52 mol of gas at a pressure of 1.3 atm and a volume of 11.8 L? ES Eugene S. University of Minnesota - Twin Cities ### Problem 43 An automobile tire has a maximum rating of 38.0 psi (gauge pressure). The tire is inflated (while cold) to a volume of 11.8 L and a gauge pressure of 36.0 psi at a temperature of 12.0 C. When the car is driven on a hot day, the tire warms to 65.0 C and its volume expands to 12.2 L. Does the pressure in the tire exceed its maximum rating? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.) KC Kevin C. Numerade Educator ### Problem 44 A weather balloon is inflated to a volume of 28.5 L at a pressure of 748 mmHg and a temperature of 28.0 C. The balloon rises in the atmosphere to an altitude of approximately 25,000 ft, where the pressure is 385 mmHg and the temperature is -15.0 C. Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude. ES Eugene S. University of Minnesota - Twin Cities ### Problem 45 A piece of dry ice (solid carbon dioxide) with a mass of 28.8 g sublimes (converts from solid to gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon, what is the volume of the balloon at a temperature of 22 C and a pressure of 742 mmHg? KC Kevin C. Numerade Educator ### Problem 46 A 1.0-L container of liquid nitrogen is kept in a closet measuring 1.0 m by 1.0 m by 2.0 m. Assuming that the container is completely full, that the temperature is 25.0 C, and that the atmospheric pressure is 1.0 atm, calculate the percent (by volume) of air that is displaced if all of the liquid nitrogen evaporates. (Liquid nitrogen has a density of 0.807 g>mL.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 47 A wine-dispensing system uses argon canisters to pressurize and preserve wine in the bottle. An argon canister for the system has a volume of 55.0 mL and contains 26.0 g of argon. Assuming ideal gas behavior, what is the pressure in the canister at 295 K? When the argon is released from the canister, it expands to fill the wine bottle. How many 750.0-mL wine bottles can be purged with the argon in the canister at a pressure of 1.20 atm and a temperature of 295 K? KC Kevin C. Numerade Educator ### Problem 48 Pressurized carbon dioxide inflators can be used to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain 16.0 g of carbon dioxide. At 298 K, to what gauge pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.45-L mountain bike tire? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 49 Which gas sample illustrated here has the greatest pressure?Assume that all the samples are at the same temperature. Explain. KC Kevin C. Numerade Educator ### Problem 50 This picture represents a sample of gas at a pressure of 1 atm, a volume of 1 L, and a temperature of 25 C. Draw a similar picture showing what would happen to the sample if the volume were reduced to 0.5 L and the temperature were increased to 250 C. What would happen to the pressure? ES Eugene S. University of Minnesota - Twin Cities ### Problem 51 Aerosol cans carry clear warnings against incineration because of the high pressures that can develop if they are heated. Suppose that a can contains a residual amount of gas at a pressure of 755 mm Hg and a temperature of 25 C. What would the pressure be if the can were heated to 1155 C? KC Kevin C. Numerade Educator ### Problem 52 A sample of nitrogen gas in a 1.75-L container exerts a pressure of 1.35 atm at 25 C. What is the pressure if the volume of the container is maintained constant and the temperature is raised to 355 C? ES Eugene S. University of Minnesota - Twin Cities ### Problem 53 Use the molar volume of a gas at STP to determine the volume (in L) occupied by 33.6 g of neon at STP. KC Kevin C. Numerade Educator ### Problem 54 Use the molar volume of a gas at STP to calculate the density (in g>L) of nitrogen gas at STP. ES Eugene S. University of Minnesota - Twin Cities ### Problem 55 What is the density (in g>L) of hydrogen gas at 20.0 C and a pressure of 1655 psi? KC Kevin C. Numerade Educator ### Problem 56 A sample of N2O gas has a density of 2.85 g>L at 298 K. What is the pressure of the gas (in mmHg)? ES Eugene S. University of Minnesota - Twin Cities ### Problem 57 A 248-mL gas sample has a mass of 0.433 g at a pressure of 745 mmHg and a temperature of 28 C. What is the molar mass of the gas? KC Kevin C. Numerade Educator ### Problem 58 A 113-mL gas sample has a mass of 0.171 g at a pressure of 721 mmHg and a temperature of 32 C. What is the molar mass of the gas? ES Eugene S. University of Minnesota - Twin Cities ### Problem 59 A sample of gas has a mass of 38.8 mg. Its volume is 224 mL at a temperature of 55 C and a pressure of 886 torr. Find the molar mass of the gas. KC Kevin C. Numerade Educator ### Problem 60 A sample of gas has a mass of 0.555 g. Its volume is 117 mL at a temperature of 85 C and a pressure of 753 mmHg. Find the molar mass of the gas. ES Eugene S. University of Minnesota - Twin Cities ### Problem 61 A gas mixture contains each of these gases at the indicated partial pressures: N2, 215 torr; O2, 102 torr; and He, 117 torr. What is the total pressure of the mixture? What mass of each gas is present in a 1.35-L sample of this mixture at 25.0 C? KC Kevin C. Numerade Educator ### Problem 62 A gas mixture with a total pressure of 745 mmHg contains each of these gases at the indicated partial pressures: CO2, 125 mmHg; Ar, 214 mmHg; and O2, 187 mmHg. The mixture also contains helium gas. What is the partial pressure of the helium gas? What mass of helium gas is present in a 12.0-L sample of this mixture at 273 K? ES Eugene S. University of Minnesota - Twin Cities ### Problem 63 We add a 1.20-g sample of dry ice to a 755-mL flask containing nitrogen gas at a temperature of 25.0 C and a pressure of 725 mmHg. The dry ice sublimes (converts from solid to gas) and the mixture returns to 25.0 C. What is the total pressure in the flask? KC Kevin C. Numerade Educator ### Problem 64 A 275-mL flask contains pure helium at a pressure of 752 torr. A second flask with a volume of 475 mL contains pure argon at a pressure of 722 torr. If the two flasks are connected through a stopcock and the stopcock is opened, what is the partial pressure of each gas and the total pressure? ES Eugene S. University of Minnesota - Twin Cities ### Problem 65 A gas mixture contains 1.25 g N2 and 0.85 g O2 in a 1.55-L container at 18 C. Calculate the mole fraction and partial pressure of each component in the gas mixture. KC Kevin C. Numerade Educator ### Problem 66 What is the mole fraction of oxygen gas in air (see Table 10.2)? What volume of air contains 10.0 g of oxygen gas at 273 K and 1.00 atm? ES Eugene S. University of Minnesota - Twin Cities ### Problem 67 The hydrogen gas formed in a chemical reaction is collected over water at 30.0 C at a total pressure of 732 mmHg. What is the partial pressure of the hydrogen gas collected in this way? If the total volume of gas collected is 722 mL, what mass of hydrogen gas is collected? KC Kevin C. Numerade Educator ### Problem 68 The air in a bicycle tire is bubbled through water and collected at 25 C. If the total volume of gas collected is 5.45 L at a temperature of 25 C and a pressure of 745 torr, how many moles of gas were in the bicycle tire? ES Eugene S. University of Minnesota - Twin Cities ### Problem 69 The zinc within a copper-plated penny will dissolve in hydrochloric acid if the copper coating is filed down in several spots (so that the hydrochloric acid can get to the zinc). The reaction between the acid and the zinc is 2 H+(aq) + Zn(s)H2(g) + Zn2+(aq). When the zinc in a certain penny dissolves, the total volume of gas collected over water at 25 C is 0.951 L at a total pressure of 748 mmHg. What mass of hydrogen gas is collected? KC Kevin C. Numerade Educator ### Problem 70 A heliox deep-sea diving mixture contains 2.0 g of oxygen to every 98.0 g of helium. What is the partial pressure of oxygen when this mixture is delivered at a total pressure of 8.5 atm? ES Eugene S. University of Minnesota - Twin Cities ### Problem 71 Consider a 1.0-L sample of helium gas and a 1.0-L sample of argon gas, both at room temperature and atmospheric pressure. a. Do the atoms in the helium sample have the same average kinetic energy as the atoms in the argon sample? b. Do the atoms in the helium sample have the same average velocity as the atoms in the argon sample? c. Do the argon atoms, because they are more massive, exert a greater pressure on the walls of the container? Explain. d. Which gas sample has the faster rate of effusion? Aadit S. Numerade Educator ### Problem 72 A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. a. Which of the two gases exerts the greater partial pressure? b. The molecules or atoms of which gas will have the greater average velocity? c. The molecules of which gas will have the greater average kinetic energy? d. If a small hole were opened in the flask, which gas would effuse more quickly? ES Eugene S. University of Minnesota - Twin Cities ### Problem 73 Calculate the root mean square velocity and kinetic energy of F2, Cl2, and Br2 at 298 K. Rank the three halogens with respect to their rate of effusion. KC Kevin C. Numerade Educator ### Problem 74 Calculate the root mean square velocity and kinetic energy of CO, CO2, and SO3 at 298 K. Which gas has the greatest velocity? The greatest kinetic energy? The greatest effusion rate? ES Eugene S. University of Minnesota - Twin Cities ### Problem 75 We obtain uranium-235 from U-238 by fluorinating the uranium to form UF6 (which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio of effusion rates for 238UF6 and 235UF6. The atomic mass of U-235 is 235.054 amu, and that of U-238 is 238.051 amu. Aadit S. Numerade Educator ### Problem 76 Calculate the ratio of effusion rates for Ar and Kr. ES Eugene S. University of Minnesota - Twin Cities ### Problem 77 A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the gas. KC Kevin C. Numerade Educator ### Problem 78 A sample of N2O effuses from a container in 42 seconds. How long will it take the same amount of gaseous I2 to effuse from the same container under identical conditions? ES Eugene S. University of Minnesota - Twin Cities ### Problem 79 This graph shows the distribution of molecular velocities for two different molecules (A and B) at the same temperature. Which molecule has the higher molar mass? Which molecule has the higher rate of effusion? Aadit S. Numerade Educator ### Problem 80 This graph shows the distribution of molecular velocities for the same molecule at two different temperatures (T1 and T2). Which temperature is greater? Explain. ES Eugene S. University of Minnesota - Twin Cities ### Problem 81 Consider the chemical reaction: How many liters of hydrogen gas are formed from the complete reaction of 15.7 g C? Assume that the hydrogen gas is collected at a pressure of 1.0 atm and a temperature of 355 K. Aadit S. Numerade Educator ### Problem 82 Consider the chemical reaction: What mass of H2O is required to form 1.4 L of O2 at a temperature of 315 K and a pressure of 0.957 atm? ES Eugene S. University of Minnesota - Twin Cities ### Problem 83 CH3OH can be synthesized by the reaction: What volume of H2 gas (in L), at 748 mmHg and 86 C, is required to synthesize 25.8 g CH3OH? How many liters of CO gas, measured under the same conditions, are required? Aadit S. Numerade Educator ### Problem 84 Oxygen gas reacts with powdered aluminum according to the reaction: What volume of O2 gas (in L), measured at 782 mmHg and 25 C, completely reacts with 53.2 g Al? ES Eugene S. University of Minnesota - Twin Cities ### Problem 85 Automobile airbags inflate following serious impacts, which trigger the chemical reaction: If an automobile airbag has a volume of 11.8 L, what mass of NaN3 (in g) is required to fully inflate the airbag upon impact? Assume STP conditions. Aadit S. Numerade Educator ### Problem 86 Lithium reacts with nitrogen gas according to the reaction: What mass of lithium (in g) reacts completely with 58.5 mL of N2 gas at STP? ES Eugene S. University of Minnesota - Twin Cities ### Problem 87 Hydrogen gas (a potential future fuel) can be formed by the reaction of methane with water according to the equation: In a particular reaction, 25.5 L of methane gas (at a pressure of 732 torr and a temperature of 25 C) mixes with 22.8 L of water vapor (at a pressure of 702 torr and a temperature of 125 C). The reaction produces 26.2 L of hydrogen gas at STP. What is the percent yield of the reaction? Aadit S. Numerade Educator ### Problem 88 Ozone is depleted in the stratosphere by chlorine from CF3Cl according to this set of equations: What total volume of ozone at a pressure of 25.0 mmHg and a temperature of 225 K is destroyed when all of the chlorine from 15.0 g of CF3Cl goes through ten cycles of the above reactions? ES Eugene S. University of Minnesota - Twin Cities ### Problem 89 Chlorine gas reacts with fluorine gas to form chlorine trifluoride: A 2.00-L reaction vessel, initially at 298 K, contains chlorine gas at a partial pressure of 337 mmHg and fluorine gas at a partial pressure of 729 mmHg. Identify the limiting reactant and determine the theoretical yield of ClF3 in grams. Aadit S. Numerade Educator ### Problem 90 Carbon monoxide gas reacts with hydrogen gas to form methanol: A 1.50-L reaction vessel, initially at 305 K, contains carbon monoxide gas at a partial pressure of 232 mmHg and hydrogen gas at a partial pressure of 397 mmHg. Identify the limiting reactant and determine the theoretical yield of methanol in grams. ES Eugene S. University of Minnesota - Twin Cities ### Problem 91 Which postulate of the kinetic molecular theory breaks down under conditions of high pressure? Explain. KC Kevin C. Numerade Educator ### Problem 92 Which postulate of the kinetic molecular theory breaks down under conditions of low temperature? Explain. ES Eugene S. University of Minnesota - Twin Cities ### Problem 93 Use the van der Waals equation and the ideal gas equation to calculate the volume of 1.000 mol of neon at a pressure of 500.0 atm and a temperature of 355.0 K. Explain why the two values are different. (Hint: One way to solve the van der Waals equation for V is to use successive approximations. Use the ideal gas law to get a preliminary estimate for V.) Aadit S. Numerade Educator ### Problem 94 Use the van der Waals equation and the ideal gas equation to calculate the pressure exerted by 1.000 mol of Cl2 in a volume of 5.000 L at a temperature of 273.0 K. Explain why the two values are different. ES Eugene S. University of Minnesota - Twin Cities ### Problem 95 Pennies that are currently being minted are composed of zinc coated with copper. A student determines the mass of a penny to be 2.482 g and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved): The student collects the hydrogen produced over water at 25 C. The collected gas occupies a volume of 0.899 L at a total pressure of 791 mmHg. Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.) Aadit S. Numerade Educator ### Problem 96 A 2.85-g sample of an unknown chlorofluorocarbon decomposes and produces 564 mL of chlorine gas at a pressure of 752 mmHg and a temperature of 298 K. What is the percent chlorine (by mass) in the unknown chlorofluorocarbon? ES Eugene S. University of Minnesota - Twin Cities ### Problem 97 The mass of an evacuated 255-mL flask is 143.187 g. The mass of the flask filled with 267 torr of an unknown gas at 25 C is 143.289 g. Calculate the molar mass of the unknown gas. Aadit S. Numerade Educator ### Problem 98 A 118-mL flask is evacuated and found to have a mass of 97.129 g. When the flask is filled with 768 torr of helium gas at 35 C, it has a mass of 97.171 g. Is the helium gas pure? ES Eugene S. University of Minnesota - Twin Cities ### Problem 99 A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 82.66% carbon and 17.34% hydrogen by mass. The mass of 158 mL of the gas, measured at 556 mmHg and 25 C, is 0.275 g. What is the molecular formula of the compound? Aadit S. Numerade Educator ### Problem 100 A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 85.63% C and 14.37% H by mass. The mass of 258 mL of the gas, measured at STP, is 0.646 g. What is the molecular formula of the compound? ES Eugene S. University of Minnesota - Twin Cities ### Problem 101 Consider the reaction: If O2 is collected over water at 40.0 C and a total pressure of 745 mmHg, what volume of gas is collected for the complete reaction of 24.78 g of NiO? Aadit S. Numerade Educator ### Problem 102 Consider the reaction: If this reaction produces 15.8 g of Ag(s), what total volume of gas can be collected over water at a temperature of 25 C and a total pressure of 752 mmHg? ES Eugene S. University of Minnesota - Twin Cities ### Problem 103 :When hydrochloric acid is poured over potassium sulfide, 42.9 mL of hydrogen sulfide gas is produced at a pressure of 752 torr and 25.8 C. Write an equation for the gas-evolution reaction and determine how much potassium sulfide (in grams) reacted. Aadit S. Numerade Educator ### Problem 104 Consider the reaction: a. If 285.5 mL of SO2 reacts with 158.9 mL of O2 (both measured at 315 K and 50.0 mmHg), what is the limiting reactant and the theoretical yield of SO3? b. If 187.2 mL of SO3 is collected (measured at 315 K and 50.0 mmHg), what is the percent yield for the reaction? ES Eugene S. University of Minnesota - Twin Cities ### Problem 105 Ammonium carbonate decomposes upon heating according to the balanced equation: Calculate the total volume of gas produced at 22 C and 1.02 atm by the complete decomposition of 11.83 g of ammonium carbonate. Aadit S. Numerade Educator ### Problem 106 Ammonium nitrate decomposes explosively upon heating according to the balanced equation: Calculate the total volume of gas (at 125 C and 748 mmHg) produced by the complete decomposition of 1.55 kg of ammonium nitrate. ES Eugene S. University of Minnesota - Twin Cities ### Problem 107 Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. What is the mass difference between the two? Assume that the volume of the tire is 855 mL, that it is filled to a total pressure of 125 psi, and that the temperature is 25 C. Also, assume an average molar mass for air of 28.8 g/mol. Aadit S. Numerade Educator ### Problem 108 In a common classroom demonstration, a balloon is filled with air and submerged in liquid nitrogen. The balloon contracts as the gases within the balloon cool. Suppose a balloon initially contains 2.95 L of air at a temperature of 25.0 C and a pressure of 0.998 atm. Calculate the expected volume of the balloon upon cooling to -196 C (the boiling point of liquid nitrogen). When the demonstration is carried out, the actual volume of the balloon decreases to 0.61 L. How does the observed volume of the balloon compare to your calculated value? Explain the difference. ES Eugene S. University of Minnesota - Twin Cities ### Problem 109 Gaseous ammonia is injected into the exhaust stream of a coal-burning power plant to reduce the pollutant NO to N2 according to the reaction: Suppose that the exhaust stream of a power plant has a flow rate of 335 L/s at a temperature of 955 K, and that the exhaust contains a partial pressure of NO of 22.4 torr. What should be the flow rate of ammonia delivered at 755 torr and 298 K into the stream to react completely with the NO if the ammonia is 65.2% pure (by volume)? Aadit S. Numerade Educator ### Problem 110 The emission of NO2 by fossil fuel combustion can be prevented by injecting gaseous urea into the combustion mixture. The urea reduces NO (which oxidizes in air to form NO2) according to the reaction: Suppose that the exhaust stream of an automobile has a flow rate of 2.55 L>s at 655 K and contains a partial pressure of NO of 12.4 torr. What total mass of urea is necessary to react completely with the NO formed during 8.0 hours of driving? ES Eugene S. University of Minnesota - Twin Cities ### Problem 111 An ordinary gasoline can measuring$30.0 \mathrm{~cm}$by$20.0 \mathrm{~cm}$by$15.0 \mathrm{~cm}$is evacuated with a vacuum pump. Assuming that virtually all of the air can be removed from inside the can and that atmospheric pressure is$14.7 \mathrm{psi},$what is the total force (in pounds) on the surface of the can? Do you think that the can will withstand the force? Aadit S. Numerade Educator ### Problem 112 Twenty-five milliliters of liquid nitrogen (density = 0.807 g>mL) is poured into a cylindrical container with a radius of 10.0 cm and a length of 20.0 cm. The container initially contains only air at a pressure of 760.0 mmHg (atmospheric pressure) and a temperature of 298 K. If the liquid nitrogen completely vaporizes, what is the total force (in lb) on the interior of the container at 298 K? ES Eugene S. University of Minnesota - Twin Cities ### Problem 113 A 160.0-L helium tank contains pure helium at a pressure of 1855 psi and a temperature of 298 K. How many 3.5-L helium balloons will the helium in the tank fill? (Assume an atmospheric pressure of 1.0 atm and a temperature of 298 K.) Aadit S. Numerade Educator ### Problem 114 An 11.5-mL sample of liquid butane (density = 0.573 g>mL) is evaporated in an otherwise empty container at a temperature of 28.5 C. The pressure in the container following evaporation is 892 torr. What is the volume of the container? ES Eugene S. University of Minnesota - Twin Cities ### Problem 115 A scuba diver creates a spherical bubble with a radius of 2.5 cm at a depth of 30.0 m where the total pressure (including atmospheric pressure) is 4.00 atm. What is the radius of the bubble when it reaches the surface of the water? (Assume that the atmospheric pressure is 1.00 atm and the temperature is 298 K.) Aadit S. Numerade Educator ### Problem 116 A particular balloon can be stretched to a maximum surface area of 1257 cm2. The balloon is filled with 3.0 L of helium gas at a pressure of 755 torr and a temperature of 298 K. The balloon is then allowed to rise in the atmosphere. If the atmospheric temperature is 273 K, at what pressure will the balloon burst? (Assume the balloon is a sphere.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 117 A catalytic converter in an automobile uses a palladium or platinum catalyst (a substance that increases the rate of a reaction without being consumed by the reaction) to convert carbon monoxide gas to carbon dioxide according to the reaction: A chemist researching the effectiveness of a new catalyst combines a 2.0 : 1.0 mole ratio mixture of carbon monoxide and oxygen gas (respectively) over the catalyst in a 2.45-L flask at a total pressure of 745 torr and a temperature of 552 C. When the reaction is complete, the pressure in the flask has dropped to 552 torr. What percentage of the carbon monoxide was converted to carbon dioxide? Aadit S. Numerade Educator ### Problem 118 A quantity of N2 occupies a volume of 1.0 L at 300 K and 1.0 atm. The gas expands to a volume of 3.0 L as the result of a change in both temperature and pressure. Find the density of the gas at these new conditions. ES Eugene S. University of Minnesota - Twin Cities ### Problem 119 A mixture of CO(g) and O2(g) in a 1.0-L container at 1.0 * 103 K has a total pressure of 2.2 atm. After some time the total pressure falls to 1.9 atm as the result of the formation of CO2. Determine the mass (in grams) of CO2 that forms. Aadit S. Numerade Educator ### Problem 120 The radius of a xenon atom is 1.3 * 10-8 cm. A 100-mL flask is filled with Xe at a pressure of 1.0 atm and a temperature of 273 K. Calculate the fraction of the volume that is occupied by Xe atoms. (Hint: The atoms are spheres.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 121 A natural-gas storage tank is a cylinder with a moveable top whose volume can change only as its height changes. Its radius remains fixed. The height of the cylinder is 22.6 m on a day when the temperature is 22 C. The next day the height of the cylinder increases to 23.8 m when the gas expands because of a heat wave. Find the temperature on the second day, assuming that the pressure and amount of gas in the storage tank have not changed. Aadit S. Numerade Educator ### Problem 122 A mixture of 8.0 g CH4 and 8.0 g Xe is placed in a container, and the total pressure is found to be 0.44 atm. Determine the partial pressure of CH4. ES Eugene S. University of Minnesota - Twin Cities ### Problem 123 A steel container of volume 0.35 L can withstand pressures up to 88 atm before exploding. What mass of helium can be stored in this container at 299 K? Aadit S. Numerade Educator ### Problem 124 Binary compounds of alkali metals and hydrogen react with water to liberate H2(g). The H2 from the reaction of a sample of NaH with an excess of water fills a volume of 0.490 L above the water. The temperature of the gas is 35 C, and the total pressure is 758 mmHg. Determine the mass of H2 that was liberated and the mass of NaH that reacted. ES Eugene S. University of Minnesota - Twin Cities ### Problem 125 In a given diffusion apparatus, 15.0 mL of HBr gas diffused in 1.0 min. In the same apparatus and under the same conditions, 20.3 mL of an unknown gas diffused in 1.0 min. The unknown gas is a hydrocarbon. Find its molecular formula. Aadit S. Numerade Educator ### Problem 126 A sample of N2O3(g) has a pressure of 0.017 atm. The temperature (in K) is doubled, and the N2O3 undergoes complete decomposition to NO2(g) and NO(g). Find the total pressure of the mixture of gases assuming constant volume and no additional temperature change. ES Eugene S. University of Minnesota - Twin Cities ### Problem 127 When 0.583 g of neon is added to an 800-cm3 bulb containing a sample of argon, the total pressure of the gases is 1.17 atm at a temperature of 295 K. Find the mass of the argon in the bulb. Aadit S. Numerade Educator ### Problem 128 A gas mixture composed of helium and argon has a density of 0.670 g>L at 755 mmHg and 298 K. What is the composition of the mixture by volume? ES Eugene S. University of Minnesota - Twin Cities ### Problem 129 A gas mixture contains 75.2% nitrogen and 24.8% krypton by mass. What is the partial pressure of krypton in the mixture if the total pressure is 745 mmHg? Aadit S. Numerade Educator ### Problem 130 A 10-L container is filled with 0.10 mol of H2(g) and heated to 3000 K, causing some of the H2(g) to decompose into H(g). The total pressure is 3.0 atm. Find the partial pressure of the H(g) that forms from H2 at this temperature. (Assume two significant figures for the temperature.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 131 A mixture of NH3(g) and N2H4(g) is placed in a sealed container at 300 K. The total pressure is 0.50 atm. The container is heated to 1200 K, at which time both substances decompose completely according to the equations: 2 NH3(g) N2(g) + 3 H2(g); N2H4(g) N2(g) + 2 H2(g). After decomposition is complete, the total pressure at 1200 K is 4.5 atm. Find the percent of N2H4(g) in the original mixture. (Assume two significant figures for the temperature.) HS Harsh S. Numerade Educator ### Problem 132 A quantity of CO gas occupies a volume of 0.48 L at 1.0 atm and 275 K. The pressure of the gas is lowered and its temperature is raised until its volume is 1.3 L. Determine the density of the CO under the new conditions. ES Eugene S. University of Minnesota - Twin Cities ### Problem 133 When CO2(g) is put in a sealed container at 701 K and a pressure of 10.0 atm and is heated to 1401 K, the pressure rises to 22.5 atm. Some of the CO2 decomposes to CO and O2. Calculate the mole percent of CO2 that decomposes. Aadit S. Numerade Educator ### Problem 134 The world burns approximately 3.5 * 1012 kg of fossil fuel per year. Use the combustion of octane as the representative reaction and determine the mass of carbon dioxide (the most significant greenhouse gas) formed per year. The current concentration of carbon dioxide in the atmosphere is approximately 394 ppm (by volume). By what percentage does the concentration increase each year due to fossil fuel combustion? Approximate the average properties of the entire atmosphere by assuming that the atmosphere extends from sea level to 15 km and that it has an average pressure of 381 torr and average temperature of 275 K. Assume Earth is a perfect sphere with a radius of 6371 km. ES Eugene S. University of Minnesota - Twin Cities ### Problem 135 The atmosphere slowly oxidizes hydrocarbons in a number of steps that eventually convert the hydrocarbon into carbon dioxide and water. The overall reaction of a number of such steps for methane gas is: Suppose that an atmospheric chemist combines 155 mL of methane at STP, 885 mL of oxygen at STP, and 55.5 mL of NO at STP in a 2.0-L flask. The flask stands for several weeks at 275 K. If the reaction reaches 90.0% of completion (90.0% of the limiting reactant is consumed), what is the partial pressure of each of the reactants and products in the flask at 275 K? What is the total pressure in the flask? Aadit S. Numerade Educator ### Problem 136 Two identical balloons are filled to the same volume, one with air and one with helium. The next day, the volume of the air-filled balloon has decreased by 5.0%. By what percent has the volume of the helium-filled balloon decreased? (Assume that the air is four-fifths nitrogen and one-fifth oxygen, and that the temperature did not change.) ES Eugene S. University of Minnesota - Twin Cities ### Problem 137 A mixture of CH4(g) and C2H6(g) has a total pressure of 0.53 atm. Just enough O2(g) is added to the mixture to bring about its complete combustion to CO2(g) and H2O(g). The total pressure of the two product gases is found to be 2.2 atm. Assuming constant volume and temperature, find the mole fraction of CH4 in the mixture. Aadit S. Numerade Educator ### Problem 138 A sample of$\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})$has a pressure of$7.8 \mathrm{kPa}$. After some time, a portion of it reacts to form$\mathrm{C}_{6} \mathrm{H}_{6}(g) .$The total pressure of the mixture of gases is then$3.9 \mathrm{kPa}$. Assume the volume and the temperature do not change. What fraction of$\mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})\$ has undergone reaction?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 139

When the driver of an automobile applies the brakes, the passengers are pushed toward the front of the car, but a helium balloon is pushed toward the back of the car. Upon forward acceleration, the passengers are pushed toward the back of the car, but the helium balloon is pushed toward the front of the car. Why? ### Problem 140

Suppose that a liquid is 10 times denser than water. If you were to sip this liquid at sea level using a straw, what is the maximum length your straw can be?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 141

The generic reaction occurs in a closed container:

A reaction mixture initially contains 1.5 L of A and 2.0 L of B. Assuming that the volume and temperature of the reaction mixture remain constant, what is the percent change in pressure if the reaction goes to completion? ### Problem 142

One mole of nitrogen and one mole of neon are combined in a closed container at STP. How big is the container?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 143

Exactly equal amounts (in moles) of gas A and gas B are combined in a 1-L container at room temperature. Gas B has a molar mass that is twice that of gas A. Which statement is true for the mixture of gases and why?
a. The molecules of gas B have greater kinetic energy than those of gas A.
b. Gas B has a greater partial pressure than gas A.
c. The molecules of gas B have a greater average velocity than those of gas A.
d. Gas B makes a greater contribution to the average density of the mixture than gas A. ### Problem 144

Which gas would you expect to deviate most from ideal behavior under conditions of low temperature: F2, Cl2, or Br2? Explain.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 145

The volume of a sample of a fixed amount of gas is decreased from 2.0 L to 1.0 L. The temperature of the gas in kelvins is then doubled. What is the final pressure of the gas in terms of the initial pressure? ### Problem 146

Which gas sample has the greatest volume at STP?
a. 10.0 g Kr
b. 10.0 g Xe
c. 10.0 g He

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 147

Draw a depiction of a gas sample, as described by kinetic molecular theory, containing equal molar amounts of helium, neon, and krypton. Use different color dots to represent each element. Give each atom a "tail" to represent its velocity relative to the others in the mixture. ### Problem 148

Assign one of the three simple gas laws to each member of your group. For the assigned gas law, have each member write two equations, draw a graph, and describe it in a complete sentence. Have each group member present his or her law to the group.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 149

Review the ideal gas law. Without referring back to the text, use algebra to write the ideal gas law and solve for each of the individual variables it contains. Have each group member solve for a different variable and present answers to the group. Jennifer H.

### Problem 150

Hydrogen peroxide (H2O2) decomposes in the presence of a catalyst to form water and oxygen. The catalyst is added to 5.00 mL of a hydrogen peroxide solution at 25.0 C, and 49.5 mL of gas is collected over water at a total pressure of 763.8 mmHg.
a. Write and balance the chemical reaction. (Note: catalysts do not appear in balanced chemical equations.)
b. Look up the vapor pressure of water under these conditions.
c. What is the partial pressure of oxygen collected over the water?
d. How many moles of oxygen are collected?
e. How many grams of hydrogen peroxide were in the original sample?
f. What is the concentration (in mol>L) of the hydrogen peroxide solution?
g. Which part of this process is conceptually most difficult for your group?

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 151

A box contains equal amounts of helium, argon, and krypton (all gases) at 25 C. Using complete sentences, describe the temperatures, masses, average velocities, and average kinetic energy of the three kinds of gas in the mixture. What do they have in common? What are the differences? How are these properties related? ### Problem 152

Calculate the pressure exerted by 1 mol of an ideal gas in a box that is 0.500 L and at 298 K. Have each group member calculate the pressure of 1 mol of the following real gases in the same box at the same temperature: He, Ne, H2, CH4, and CO2 using the van der Waals equation. Compare group members' answers and compare all answers with the pressure of an ideal gas. Assuming that the van der Waals equation predictions are accurate, account for why the pressure of each gas is higher or lower than that predicted for an ideal gas.

ES
Eugene S.
University of Minnesota - Twin Cities

### Problem 153

When fuels are burned in air, such as in an automobile engine, some of the nitrogen in the air oxidizes to form nitrogen oxide gases such as NO and NO2 (known collectively as NOx). The U.S. Environmental Protection Agencey (EPA) sets standards for air quality of several pollutants including NO2. According to the EPA, NO2 levels in U.S. cities are not to exceed a yearly average of 53 ppb or a 1-hour average of 100 ppb. Another pollutant associated with automobile exhaust is ozone (O3). The EPA standard for ozone is an 8-hour average of 70 ppb. Breathing air with elevated levels of NO2 or O3 can cause asthma and other respiratory problems. The graph on the next page shows the average concentration of nitrogen
dioxide (NO2) and ozone (O3) gases in units of parts per billion by volume (ppbv) over seven days in a large city.

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