One way to gain a physical understanding of b in the van

Problem 1QP Name five elements and five compounds that exist as gases at room temperature.

Problem 2QP List the physical characteristics of gases.

Problem 161AP The plot of Z versus P for a gas at 0°C is shown. Explain the causes of the negative deviation from ideal behavior at lower pressures and the positive deviation from ideal behavior at higher pressures.

Problem 2VC How would the calculated molar volume be affectcd if we neglected to subtract the partial pressure of water vapor from the total pressure? (a) It would be greater. ________________ (b) It would be smaller. ________________ (c) It would not change.

Problem 1VC The molar volume of hydrogen can be determined using the reaction of zinc metal and acid, as shown in Figure 11.24. When the reaction is complete, what does the space above the water in the graduated cylinder contain? (a) H2(g), Zn2+(aq), and H2O(g) ________________ (b) H2(g) and H2O(g) ________________ (c) H2(g), H2O(g), and air

Problem 3QP What are the basic assumptions of the kinetic molecular theory of gases?

Problem 3VC How would the calculated molar volume be affected if wc neglected to adjust the level of the graduated cylinder prior to reading the volume of gas collected? Assume that the level of water inside the graduated cylinder is higher than the level outside. (a) It would be greater. ________________ (b) It would be smaller. ________________ (c) It would not change.

Problem 4QP What does the Maxwell speed distribution curve tell us? Does Maxwell’s theory work for a sample of 200 molecules? Explain.

Problem 7QP What is the difference between gas diffusion and effusion?

Problem 8QP Compare the root-mean-square speeds of O2 and UF6 at 65°C.

Problem 9QP The temperature in the stratosphere is –23°C. Calculate the root-mean-square speeds of N2, O2, and O3 molecules in this region.

Problem 5QP Which of the following statements is correct? (a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated at constant volume, the molecules collide with one another more often.

How would the calculated molar volume be affected if some of the zinc metal failed to drop into the aqueous acid? (a) It would be greater. (b) It would be smaller. (c) It would not change.

Problem 6QP Three fluorine-containing gases are shown here. Which of the three gases will have the highest root-mcan-squarespeed? Which of the three gases will have the highest average kinetic energy at a given temperature?

The average distance traveled by a molecule between successive collisions is called the mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms?

Problem 11QP At a certain temperature the speeds of six gaseous molecules in a container are 2.0, 2.2, 2.6, 2.7, 3.3, and 3.5 m/s. Calculate the root-mean-square speed and the average speed of the molecules. These two average values are close to each other, but the root-mean-square value is always the larger of the two. Why?

Problem 12QP The 235U isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0.72 percent. To separate it from the more abundant 238U isotope, uranium is first converted to UF6, which is easily vaporized above room temperature. The mixture of the 235UF6 and 238UF6 gases is then subjected to many stages of effusion. Calculate how much faster 235UF6 effuses than 238UF6.

Problem 13QP An unknown gas evolved from the fermentation of glucose is found to effuse through a porous barrier in 15.0 min. Under the same conditions of temperature and pressure, it takes an equal volume of N2 12.0 min to effuse through the same barrier. Calculate the molar mass of the unknown gas and suggest what the gas might be.

Nickel forms a gaseous compound of the formula \(\mathrm{Ni}(\mathrm{CO})_{x}\). Given the fact that under the same conditions of temperature and pressure, methane \(\left(\mathrm{CH}_4\right)\) effuses 3.3 times faster than \(\mathrm{Ni}(\mathrm{CO})_x\), what is the value of x?

Problem 16QP Describe how a barometer and a manometer are used to measure gas pressure.

Problem 15QP Define pressure and give the common units for pressure.

Problem 17QP Why is mercury a more suitable substance to use in a barometer than water?

Problem 18QP Explain why the height of mercury in a barometer is independent of the cross-sectional area of the tube.

Problem 22QP The atmospheric pressure at the summit of Mt. McKinley is 581 mmHg on a certain day. What is the pressure in atmospheres, in kilopascals, and in bars?

Problem 21QP Why is it that if the barometer reading falls in one part of the world, it must rise somewhere else?

Problem 19QP Is the atmospheric pressure in a mine that is 500 m below sea level greater or less than 1 atm?

Convert 375 mmHg to atmospheres, bars, torr, and pascals.

Problem 20QP If the maximum distance that water may be brought up a well by a suction pump is 34 ft (10.3 m), how is it possible to obtain water and oil from hundreds of feet below the surface of Earth?

Problem 24QP Calculate the height of a column of ethylene glycol [CH2(OH)CH2(OH)] that would be supported by atmospheric pressure (1 atm). The density of ethylene glycol is 1.12 g/cm3.

Problem 25QP Calculate the height of a column of methanol (CH3OH) that would be supported by atmospheric pressure. The density of methanol is 0.787 g/cm3.

Problem 28QP State the following gas laws in words and also in the form of an equation: Boyle’s law, Charles’s law, Avogadro’s law, In each case, indicate the conditions under which the law is applicable, and give the units for each quantity in the equation.

Problem 26QP What pressure (in atm and in bars) is exerted by a column of isopropanol (C3H7OH) 264 m high? The density of isopropanol is 0.785 g/cm3.

Problem 27QP What pressure (in atm and in bars) is exerted by a column of toluene (C7H8) 87 m high? The density of toluene is 0.867 g/cm3.

Problem 29QP Explain why a helium weather balloon expands as it rises in the air. Assume that the temperature remains constant.

Problem 30QP Consider the following gaseous sample in a cylinder fitted with a movable piston. Initially there are n moles of the gas at temperature T, pressure P, and volume V. Choose the cylinder that correctly represents the gas after each of the following changes. (1) The pressure on the piston is tripled at constant n and T. (2) The absolute temperature is doubled at constant n and P. (3) n more moles of the gas are added at constant T and P. (4) Absolute temperature is halved at constant P.

Problem 31QP A gaseous sample of a substance is cooled at constant pressure. Which of the following diagrams best represents the situation if the final temperature is (a) above the boiling point of the substance and (b) below the boiling point but above the freezing point of the substance?

At 46°C, a sample of ammonia gas exerts a pressure of 5.3 atm. What is the pressure when the volume of the gas is reduced to one-fourth of the original value at the same temperature?

Problem 33QP A gas sample occupying a volume of 25.6 mL at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?

Problem 35QP The volume of a gas is 7.15 L. measured at 1.00 atm. What is the pressure of the gas in mmHg if the volume is changed to 9.25 L? (The temperature remains constant.)

Problem 34QP A sample of air occupies 3.8 L when the pressure is 1.2 atm. (a) What volume does it occupy at 6.6 atm? (b) What pressure is required to compress it to 0.075 L? (The temperature is kept constant.)

Problem 36QP Under constant-pressure conditions a sample of hydrogen gas initially at 88°C and 9.6 L is cooled until its final volume is 3 4 1. What is its final temperature?

A 28.4-L volume of methane gas is heated from \(35^{\circ} \mathrm{C}\) to \(72^{\circ} \mathrm{C}\)°C at constant pressure. What is the final volume of the gas?

Problem 38QP Molecular chlorine and molecular fluorine combine to form a gaseous product. Under the same conditions of temperature and pressure it is found that one volume of CI2 reacts with three volumes of F2 to yield two volumes of the product. What is the formula of the product?

What are standard temperature and pressure (STP)? What is the significance of STP in relation to the volume of 1 mole of an ideal gas?

Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases?

Problem 42QP A sample of nitrogen gas in a 4.5-L container at a temperature of 27°C exerts a pressure of 4.1 atm. Calculate the number of moles of gas in the sample.

What volume will 9.8 moles of sulfur hexafluoride \(\left(\mathrm{SF}_6\right)\) gas occupy if the temperature and pressure of the gas are \(105^{\circ} \mathrm{C}\) and \(9.4 \mathrm{~atm}\), respectively?

Given that 6.9 moles of carbon monoxide gas are present in a container of volume 30.4 L, what is the pressure of the gas (in atm) if the temperature is \(82^{\circ} \mathrm{C}\)?

Problem 45QP A certain amount of gas at 25°C and at a pressure of 0.800 atm is contained in a vessel. Suppose that the vessel can withstand a pressure no higher than 5.00 atm. How high can you raise the temperature of the gas without bursting the vessel?

Problem 46QP A gas-filled balloon having a volume of 2.50 L at 1.2 atm and 20°C is allowed to rise to the stratosphere (about 30 km above the surface of Earth), where the temperature and pressure are –23°C and 3.00 × 10-3 atm. respectively. Calculate the final volume of the balloon.

Problem 47QP The temperature of 2.5 L of a gas initially at STP is raised to 210°C at constant volume. Calculate the final pressure of the gas in atmospheres.

Problem 48QP The pressure of 6.0 L of an ideal gas in a flexible container is decreased to one-third of its original pressure, and its absolute temperature is decreased by one-half. What is the final volume of the gas?

Problem 49QP A gas evolved during the fermentation of glucose (wine making) has a volume of 0.67 L at 22.5°C and 1.00 atm What was the volume of this gas at the fermentation temperature of 36.5°C and 1.00 atm pressure?

Problem 51QP Calculate the volume (in liters) of 124.3 g of CO2 at STP.

Dry ice is solid carbon dioxide. A \(0.050-\mathrm{g}\) sample of dry ice is placed in an evacuated \(4.6-\mathrm{L}\) vessel at \(30^{\circ} \mathrm{C}\). Calculate the pressure inside the vessel after all the dry ice has been converted to \(\mathrm{CO}_2\) gas.

Problem 52QP A gas at 572 mmHg and 35.0°C occupies a volume of 6.15 L. Calculate its volume at STP.

At 741 torr and \(44^{\circ} \mathrm{C}\), 7.10 g of a gas occupies a volume of 5.40 L. What is the molar mass of the gas?

At STP, \(0.280 \mathrm{~L}\) of a gas weighs \(0.400 \mathrm{~g}\). Calculate the molar mass of the gas.

Problem 56QP Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are 250 K and 1.0 × 10-3 atm. respectively. How many ozone molecules are present in 1.0 L of air under these conditions?

Problem 57QP Assuming that air contains 78 percent N2, 21 percent O2, and 1.0 percent Ar. all by volume, how many molecules of each type of gas are present in 1.0 L of air at STP?

Problem 58QP A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and 27.0°C.(a) Calculate the density of the gas in g/L. (b) What is the molar mass of the gas?

Problem 60QP A certain anesthetic contains 64.9 percent C, 13.5 percent H, and 21.6 percent O by mass. At 20°C and 750 mmHg, 1.00 L of the gaseous compound weighs 2.30 g. What is the molecular formula of the compound?

Problem 61QP A compound has the empirical formula SF4, At 20°C, 0.100 g of the gaseous compound occupies a volume of 22.1 mL and exerts a pressure of 1.02 atm. What is the molecular formula of the gas?

Problem 59QP Calculate the density of hydrogen bromide (HBr) gas in g/L at 733 mmHg and 46°C.

Cite two pieces of evidence to show that gases do not behave ideally under all conditions. Under which set of conditions would a gas be expected to behave most ideally: (a) high temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, or (d) low temperature and low pressure?

Problem 64QP Write the van der Waa Is equation for a real gas. Explain the corrective terms for pressure and volume.

Problem 63QP Figure 11.21(a) shows that at 0°C. with the exception of H2, each of the gases has a pressure at which its compressibility factor is equal to 1—the point at which the curve crosses the ideal gas line. What is the significance of this point? Does each of these gases have a pressure at which the assumptions of ideal behavior (negligible molecular volume and no intermolecular attractions) are valid? Explain.

Problem 65QP (a) A real gas is introduced into a flask of volume V. Is the corrected volume of the gas greater or less than V? (b) Ammonia has a larger a value than neon does (see Table 11.5). What can you conclude about the relative strength of the attractive forces between molecules of ammonia and between atoms of neon?

Problem 66QP At 27°C, 10.0 moles of a gas in a 1.50-L container exert a pressure of 130 atm. Is this an ideal gas?

Problem 67QP Using the data shown in Table 11.5. calculate the pressure exerted by 2.50 moles of CO2 confined in a volume of 5.00 L at 450 K. Compare the pressure with that predicted by the ideal gas equation.

Problem 68QP State Dalton’s law of partial pressures and explain what mole fraction is. Does mole fraction have units?

Problem 69QP What are the approximate partial pressures of N2 and O2 in air at the top of a mountain where atmospheric pressure is 0.8 atm? (Sec Problem 11.49.)

Problem 70QP A mixture of gases contains 0.31 mol CH4, 0.25 mol C2H6, and 0.29 mol C3H8. The total pressure is 1.50 atm. Calculate the partial pressures of the gases.

Problem 71QP A 2.5-L. flask at 15°C contains a mixture of N2, He, and Ne at partial pressures of 0.32 atm for N2. 0.15 atm for He. and 0.42 atm for Ne. (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the N2 is removed selectively.

Problem 73QP A mixture of helium and neon gases is collected over water at 28.0°C and 745 mmHg. If the partial pressure of helium is 368 mmHg. what is the partial pressure of neon? (Vapor pressure of water at 28°C =28 3 mmHg.)

Helium is mixed with oxygen gas for deep-sea divers. Calculate the percent by volume of oxygen gas in the mixture if the diver has to submerge to a depth where the total pressure is 5.2 atm. The partial pressure of oxygen is maintained at 0.20 atm at this depth.

Problem 72QP Dry air near sea level, where atmospheric pressure is 1.00 atm, has the following composition by volume: N2, 78.08 percent; O2, 20.94 percent; Ar, 0.93 percent; CO2,0.05 percent. Calculate (a) the partial pressure of each gas in atmospheres and (b) the concentration of each gas in mol/L at 0°C. (Hint: Because volume is proportional to the number of moles present, mole fractions of gases can be expressed as ratios of volumes at the same temperature and pressure.)

Consider the three containers shown, all of which have the same volume and are at the same temperature. (a) Which container has the smallest mole fraction of gas A (red)? (b) Which container has the highest partial pressure of gas B (green)? (c) Which container has the highest total pressure?

Problem 75QP A sample of ammonia (NH3) gas is completely decomposed to nitrogen and hydrogen gases over heated iron wool. If the total pressure is 866 mmHg after the reaction, calculate the partial pressures of N2 and H2.

Problem 77QP The volume of the box on the right is twice that of the box on the left. The boxes contain helium atoms (red) and hydrogen molecules (green) at the same temperature. (a) Which box has a higher total pressure? (b) Which box has a higher partial pressure of helium?

Considering the hyperbaric chamber in problem 11.78, what chamber pressure would be required for a patient to receive the therapeutic partial pressure of \(\mathrm{O}_{2}\) (2.8 atm) without breathing a special mixture of gases through a mask? Assume that the air used to pressurize the chamber is 21 percent \(\mathrm{O}_{2}\) by volume.

Problem 81QP Methane, the principal component of natural gas, is used for heating and cooking. The combustion process is If 15.0 moles of CH4 react with oxygen, what is the volume of CO2 (in liters) produced at 23.0°C and 0.985 atm?

Problem 78QP The Catalina hyperbaric chamber at the University of Southern California‘s Wrigley Marine Science Center treats mostly victims of diving accidents. In one treatment protocol, the chamber is pressurized to 4.6 atm with compressed air and the patient breathes a mixture of gases that contains oxygen. If the partial pressure of oxygen is 2.8 atm, what is the mole fraction of oxygen?

Problem 82QP When coal is burned, the sulfur present in coal is converted to sulfur dioxide (SO2), which is responsible for the acid rain phenomenon: If 3.15 kg of S reacts with oxygen, calculate the volume of SO2 gas (in mL) formed at 30.5°C and 1.04 atm.

Problem 80QP Consider the formation of nitrogen dioxide from nitric oxide and oxygen: If 9.0 L of NO is combined with excess O2 at STP, what is the volume in liters of the NO2 produced?

Problem 83QP In alcohol fermentation, yeast converts glucose to ethanol and carbon dioxide: If 5.97 g of glucose reacts and 1.44 L of CO2 gas is collected at 293 K and 0.984 atm. what is the percent yield of the reaction?

Problem 84QP A compound of P and F was analyzed as follow s: Heating 0.2324 g of the compound in a 378-cm3 container turned all of it to gas. which had a pressure of 97.3 mmHg at 77°C. Then the gas was mixed with calcium chloride solution, which converted all the F to 0.2631 g of CaF2. Determine the molecular formula of the compound.

Problem 85QP A quantity of 0.225 g of a metal M (molar mass 27.0 g/mol) liberated 0.303 L of molecular hydrogen (measured at 17°C and 741 mmHg) from an excess of hydrochloric acid. Deduce from these data the corresponding equation, and write formulas for the oxide and sulfate of M.

Problem 87QP Dissolving 3.00 g of an impure sample of calcium carbonate in hydrochloric acid produced 0.656 L of carbon dioxide (measured at 20.0°C and 792 mmHg). Calculate the percent by mass of calcium carbonate in the sample. State any assumptions.

What is the mass of the solid \(\mathrm{NH}_4 \mathrm{Cl}\) formed when \(73.0 \mathrm{~g}\) of \(\mathrm{NH}_3\) is mixed with an equal mass of \(\mathrm{HCl}\)? What is the volume of the gas remaining, measured at \(14.0^{\circ} \mathrm{C}\) and \(752 \mathrm{mmHg}\)? What gas is it?

Problem 89QP Ethanol (C2H5OH) burns in air: Balance the equation and determine the volume of air in liters at 45.0°C and 793 mmHg required to bum 185 g of ethanol. Assume that air is 21.0 percent O2 by volume.

Problem 90QP A piece of sodium metal reacts completely with water as follows: The hydrogen gas generated is collected over water at 25.0°C. The volume of the gas is 246 mL measured at 1.00 atm. Calculate the number of grams of sodium used in the reaction. (Vapor pressure of water at 25°C = 0.0313 atm.)

Problem 94AP The empirical formula of a compound is CH. At 200ºC, 0.145 g of this compound occupies 97.2 mL at a pressure of 0.74 atm. What is the molecular formula of the compound?

Nitroglycerin, an explosive compound, decomposes according to the equation \(4 \mathrm{C}_3 \mathrm{H}_5\left(\mathrm{NO}_3\right)_3(s) \longrightarrow 12 \mathrm{CO}_2(g)+10 \mathrm{H}_2 \mathrm{O}(g)+6 \mathrm{~N}_2(g)+\mathrm{O}_2(g)\) Calculate the total volume of gases when collected at 1.2 atm and \(25^{\circ} \mathrm{C}\) from \(2.6 \times 10^2 \mathrm{~g}\) of nitroglycerin. What are the partial pressures of the gases under these conditions?

Problem 95AP When ammonium nitrite (NH4NO2) is heated, it decomposes to give nitrogen gas. This property is used to inflate some tennis balls, (a) Write a balanced equation for the reaction, (b) Calculate the quantity (in grams) of NH4NO2 needed to inflate a tennis ball to a volume of 86.2 mL at 1.20 atm and 22°C.

Problem 88QP Calculate the mass in grams of hydrogen chloride produced when 5.6 L of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

Problem 92AP Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, N2+, or CH4? Explain.

A sample of zinc metal reacts completely with an excess of hydrochloric acid: \(\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_2(a q)+\mathrm{H}_2(g)\) The hydrogen gas produced is collected over water at \(25.0^{\circ} \mathrm{C}\) using an arrangement similar to that shown in Figure 11.23(a). The volume of the gas is \(7.80 \mathrm{~L}\), and the pressure is \(0.980 \mathrm{~atm}\). Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at \(25^{\circ} \mathrm{C}=23.8 \mathrm{mmHg}\).)

Problem 96AP The percent by mass of bicarbonate in a certain Alka-Seltzer product is 32.5 percent. Calculate the volume of CO2 generated (in mL) at 37°C and 1.00 atm when a person ingests a 3.29-g tablet. (Hint: The reaction is between and HCl acid in the stomach.)

Problem 97AP Three flasks containing gases A (red) and B (blue) are shown here. (a) If the total pressure in (i) is 2.0 atm, what are the pressures in (ii) and (iii)? (b) Calculate the total pressure and the partial pressure of each gas after the valves are opened. The volumes of (i) and (iii) are 2.0 L each, and the volume of (ii) is 1.0 L. The temperature is the same throughout.

Problem 99AP In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at 43°C: This reaction separates nickel from other solid impurities, (a) Starting with 86.4 g of Ni. calculate the pressure of Ni(CO)4 in a container of volume 4.00 L. (Assume the preceding reaction goes to completion.) (b) At temperatures above 43°C, the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.

Problem 101AP A healthy adult exhales about 5.0 × 102 mL of a gaseous mixture with each breath. Calculate the number of molecules present in this volume at 37°C and 1.1 atm. List the major components of this gaseous mixture.

Problem 98AP Referring to the hyperbaric chamber in problem 11.78, in one treatment protocol, the chamber is pressurized to 6.0 atm with compressed air and the patient breathes a mixture of gases that is 47 percent oxygen by volume. In another protocol, the chamber is pressurized with compressed air to 2.8 atm and the patient breathes pure O2. Determine the partial pressure of O2 in each treatment protocol and compare the results.

The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the Northern Hemisphere to be higher in the summer or winter? Explain.

Sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) is called baking soda because when heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, some doughnuts, and cakes. (a) Calculate the volume (in liters) of \(\mathrm{CO}_{2}\) produced by heating 5.0 g of NaHCO3 at 180°C and 1.3 atm. (b) Ammonium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\) has also been used for the same purpose. Suggest one advantage and one disadvantage of using \(\mathrm{NH}_{4} \mathrm{HCO}_{3}\) instead of \(\left(\mathrm{NaHCO}_{3}\right)\) for baking.

On heating, potassium chlorate \(\left(\mathrm{KClO}_{3}\right)\) decomposes to yield potassium chloride and oxygen gas. In one experiment, a student heated 20.4 g of \(\mathrm{KClO}_{3}\) until the decomposition was complete. (a) Write a balanced equation for the reaction. (b) Calculate the volume of oxygen (in liters) if it was collected at 0.962 atm and \(18.3^{\circ} \mathrm{C}\).

Problem 106AP Propane (C3H8) burns in oxygen to produce carbon dioxide gas and water vapor. (a) Write a balanced equation for this reaction. (b) Calculate the number of liters of carbon dioxide measured at STP that could be produced from 7.45 g of propane.

Problem 105AP The volume of a sample of pure HCl gas was 189 mL at 25°C and 108 mmHg. It was completely dissolved in about 60 mL of water and titrated with an NaOH solution: 15.7 mL of the NaOH solution was required to neutralize the HCl. Calculate the molarity of the NaOH solution.

Some commercial drain cleaners contain a mixture of sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: \(\begin{array}{l} 2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\ 2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g) \end{array}\) The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of \(\mathrm{H}_{2}\) formed at \(23^{\circ} \mathrm{C}\) and 1.00 atm if 3.12 g of Al are treated with an excess of NaOH.

Problem 109AP Consider the apparatus shown here. When a small amount of water is introduced into the flask by squeezing the bulb of the medicine dropper, water is squirted upward out of the long glass tubing. Explain this observation. (Hint: Hydrogen chloride gas is soluble in water.)

Problem 107AP Consider the following apparatus. Calculate the partial pressures of helium and neon after the stopcock is opened. The temperature remains constant at 16°C.

Problem 108AP Nitric oxide (NO) reacts with molecular oxygen as follows: Initially NO and O2 are separated as shown here. When the valve is opened, the reaction quickly goes to completion. Determine what gases remain at the end and calculate their partial pressures. Assume that the temperature remains constant at 25°C.

A 180.0-mg sample of an alloy of iron and metal X is treated with dilute sulfuric acid, liberating hydrogen and yielding \(\mathrm{Fe}^{2+}\) and \(\mathrm{X}^{3+}\) ions in solution. It is known that the alloy contains 20.0 percent iron by mass. The alloy yields \(50.9 \mathrm{~mL}\) of hydrogen collected over water at \(22^{\circ} \mathrm{C}\) and a total pressure of 750.0 torr. What is element X?

Problem 111AP A certain hydrate has the formula MgSO4 • xH2O. A quantity of 54.2 g of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a 2.00-L container at 120°C. calculate x.

The apparatus shown below can be used to measure atomic and molecular speeds. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment, it is found that at \(850^{\circ} \mathrm{C}\) some bismuth \((\mathrm{Bi}\)) atoms struck the target at a point \(2.80 \mathrm{~cm}\) from the spot directly opposite the slit. The diameter of the cylinder is \(15.0 \mathrm{~cm}\), and it is rotating at 130 revolutions per second. (a) Calculate the speed (in \(\mathrm{m} / \mathrm{s}\) ) at which the target is moving. (Hint: The circumference of a circle is given by \(2 \pi r\), where r is the radius.) (b) Calculate the time (in seconds) it takes for the target to travel \(2.80 \mathrm{~cm}\). (c) Determine the speed of the \(\mathrm{Bi}\) atoms. Compare your result in part (c) with the \(u_{\mathrm{rms}}\) of \(\mathrm{Bi}\) at \(850^{\circ} \mathrm{C}\). Comment on the difference.

Problem 115AP Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 132 atm at 22°C, what is the mass of O2 present? How many liters of O2 gas at 1.00 atm and 22°C could the cylinder produce? (Assume ideal behavior.)

Problem 116AP The shells of hard-boiled eggs sometimes crack due to the rapid thermal expansion of the shells at high temperatures. Suggest another reason why the shells may crack.

Problem 112AP A mixture of Na2CO3 and MgCO3 of mass 7.63 g is combined with an excess of hydrochloric acid. The CO2 gas generated occupies a volume of 1.67 L at 1.24 atm and 26°C, From these data, calculate the percent composition by mass of Na2CO3 in the mixture.

Problem 114AP If 10.00 g of water is introduced into an evacuated flask of volume 2.500 L at 65°C, calculate the mass of water vaporized. (Hint: Assume that the volume of the remaining liquid water is negligible; the vapor pressure of water at 65°C is 187.5 mmHg.)

Problem 117AP Ethylene gas (C2H4) is emitted by fruits and is known to be responsible for their ripening. Based on this information, explain why a bunch of bananas ripens faster in a closed paper bag than in an open bowl.

Problem 118AP About 8.0 × 106 tons of urea [(NH2)2CO] is used annually as a fertilizer. The urea is prepared at 200°C and under high-pressure conditions from carbon dioxide and ammonia (the products are urea and steam). Calculate the volume of ammonia (in liters) measured at 150 atm needed to prepare 1.0 ton of urea.

Problem 119AP Some ballpoint pens have a small hole in the main body of the pen. What is the purpose of this hole?

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) can be obtained by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right)\). (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains 0.340 L of the gas at 718 mmHg and 24°C. If the gas weighs 0.580 g, calculate the value of the gas constant.

Problem 123AP Which of the following molecules has the largest a value: CH4. F2,C6H6, Ne?

Problem 120AP The gas laws are vitally important to scuba divers. The pressure exerted by 33 ft of seawater is equivalent to 1 atm pressure. (a) A diver ascends quickly to the surface of the water from a depth of 36 ft without exhaling gas from his lungs. By what factor will the volume of his lungs increase by the time he reaches the surface? Assume that the temperature is constant. (b) The partial pressure of oxygen in air is about 0.20 atm. (Air is 20 percent oxygen by volume.) In deep-sea diving, the composition of air the diver breathes must be changed to maintain this partial pressure. What must the oxygen content (in percent by volume) be when the total pressure exerted on the diver is 4.0 atm? (At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gases.)

Problem 124AP The following procedure is a simple though somewhat crude way to measure the molar mass of a gas. A liquid of mass 0.0184 g is introduced into a syringe like the one shown here by injection through the rubber tip using a hypodermic needle. The syringe is then transferred to a temperature bath heated to 45°C, and the liquid vaporizes. The final volume of the vapor (measured by the outward movement of the plunger) is 5.58 mL, and the atmospheric pressure is 760 mmHg. Given that the compound's empirical formula is CH2, determine the molar mass of the compound.

Two vessels are labeled A and B. Vessel A contains \(\mathrm{NH}_3\) gas at \(70^{\circ} \mathrm{C}\), and vessel B contains Ne gas at the same temperature. If the average kinetic energy of \(\mathrm{NH}_3\) is \(7.1 \times 10^{-21} \mathrm{~J} /\) molecule, calculate the root-mean-square speed of Ne atoms in \(\mathrm{m}^2 / \mathrm{s}^2\).

Problem 125AP In 1995 a man suffocated as lie walked by an abandoned mine in England. At that moment there was a sharp drop in atmospheric pressure due to a change in the weather. Suggest what might have caused the man’s death.

Problem 126AP Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide (CaO) and barium oxide (BaO) to form salts (metal carbonates). (a) Write equations representing these two reactions. (b) A student placed a mixture of BaO and CaO of combined mass 4.88 g in a 1 46-L flask containing carbon dioxide gas at 35°C and 746 mmHg. After the reactions were complete, she found that the CO2 pressure had dropped to 252 mmHg. Calculate the percent composition by mass of the mixture. Assume that the volumes of the solids are negligible.

Problem 127AP (a) What volume of air al 1.0 atm and 22°C is needed to fill a 0.98-L bicycle tire to a pressure of 5.0 atm at the same temperature? (Note that the 5.0 atm is the gauge pressure, which is the difference between the pressure in the tire and atmospheric pressure Before filling, the pressure in the tire was 1.0 aim.) (b) What is the total pressure in the tire when the gauge pressure reads 5.0 atm? (c) The tire is pumped by filling the cylinder of a hand pump with air at 1.0 aim and then, by compressing the gas in the cylinder, adding all the air in the pump to the air in the tire. If the volume of the pump is 33 percent of the tire’s volume, what is the gauge pressure in the tire after three full strokes of the pump? Assume constant temperature.

Problem 130AP Atop Mt. Everest, the atmospheric pressure is 210 mmHg and the air density is 0.426 kg/m3. (a) Calculate the air temperature, given that the molar mass of air is 29.0 g/mol.(b) Assuming no change in air composition, calculate the percent decrease in oxygen gas from sea level to the top of Mt. Everest.

Relative humidity is defined as the ratio (expressed as a percentage) of the partial pressure of water vapor in the air to the equilibrium vapor pressure (see Table 11.6) at a given temperature. On a certain summer day in North Carolina, the partial pressure of water vapor in the air is \(3.9 \times 10^3 \mathrm{~Pa}\) at \(30^{\circ} \mathrm{C}\). Calculate the relative humidity.

Problem 129AP Interstellar space contains mostly hydrogen atoms at a concentration of about/atom cm3. (a) Calculate the pressure of the H atoms. (b) Calculate the volume (in liters) that contains 1.0 g of H atoms. The temperature is 3 K.

Problem 128AP The running engine of an automobile produces carbon monoxide (CO), a toxic gas. at the rate of about 188 g CO per hour. A car is left idling in a poorly ventilated garage that is 6.0 m long, 4.0 m wide, and 2.2 m high at 20°C. (a) Calculate the rate of CO production in mol/min. (b) How long would it take to build up a lethal concentration of CO of 1000 ppmv (parts per million by volume)?

Problem 132AP Under the same conditions of temperature and pressure, why does 1 L of moist air w eigh less than 1 L of dry air? In weather forecasts, an oncoming low-pressure front usually means imminent rainfall. Explain.

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures 15.2 m long, 6.6 m wide, and 2.4 m high. (a) Calculate the mass of mercury vapor (in grams) in the room at 20°C. The vapor pressure of mercury at 20°C is \(1.7 \times 10^{-6} \mathrm{atm}\). (b) Does the concentration of mercury vapor exceed the air quality regulation of 0.050 mg \(\mathrm{Hg} / \mathrm{m}^{3}\) of air? (c) One way to deal with small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

Problem 133AP Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is 0.0050 cm, and the air inside contains 14 percent oxygen. Assuming that the pressure in the alveoli is 1.0 aim and the temperature is 37°C, calculate the number of oxygen molecules in one of the alveoli. (Hint: The volume of a sphere of radius r is .)

Problem 135AP Nitrogen dioxide (NO2,) cannot be obtained in a pure form in the gas phase because it exists as a mixture of NO2 and N2O4. At 25°C and 0.98 atm, the density of this gas mixture is 2.7 g/L. What is the partial pressure of each gas?

Problem 136AP Nitrogen dioxide (NO2)cannot be obtained in a pure form in the gas phase because it exists as a mixture of NO2 and N2O4. At 25°C and 0.98 atm, the density of this gas mixture is 2.7 g/L. What is the partial pressure of each gas?

Problem 138AP The atmosphere on Mars is composed mainly of carbon dioxide. The surface temperature is 220 K, and the atmospheric pressure is about 6.0 mmHg. Taking these values as Martian “STP,” calculate the molar volume in liters of an ideal gas on Mars.

Problem 137AP Lithium hydride reacts with water as follows: During World War II, U.S. pilots carried LiH tablets. In the event of a crash landing at sea, the LiH would react with the seawater and fill their life jackets and lifeboats with hydrogen gas. How many grams of LiH are needed to fill a 4.1-L life jacket at 0.97 atm and 12°C?

Problem 140AP A student tries to determine the volume of a bulb like the one shown in Figure 11.12. These are her results: mass of the bulb filled with dry air at 23°C and 744 mmHg = 91.6843 g; mass of evacuated bulb = 91.4715 g. Assume the composition of air is 78 percent N2, 21 percent O2, and 1 percent argon by volume. What is the volume (in mL) of the bulb? (Hint: First calculate the average molar mass of air, as shown in Problem 3.153.)

Problem 139AP Venus’s atmosphere is composed of 96.5 percent CO2, 3.5 percent N2, and 0.015 pcrccnt SO2 by volume. Its standard atmospheric pressure is 9.0 × 106 Pa. Calculate the partial pressures of the gases in pascals.

Problem 141AP Apply your knowledge of the kinetic theory of gases to the following situations. (a) Two flasks of volumes V1, and V2, (V2> V1) contain the same number of helium atoms at the same temperature. (i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures T1, and T2 (T2 > T1). (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is 74°C. Comment on the validity of the following statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each he atom is 1.47 x 103 m/s.

Problem 143AP Estimate the distance (in nm) between molecules of water vapor at 100°C and 1.0 atm. Assume ideal behavior. Repeat the calculation for liquid water at 100°C, given that the density of water is 0.96 g/cm3 at that temperature. Comment on your results. (Assume each water molecule to be a sphere with a diameter of 0.3 nm.) (Hint: First calculate the number density of water molecules. Next, convert the number density to linear density, that is, the number of molecules in one direction.)

Problem 142AP At what temperature will He atoms have the same urms value as N2 molecules at 25°C?

Problem 145AP A 5.72-g sample of graphite was heated with 68.4 g of O2 in a 8.00-1. flask. The reaction that took place was After the reaction was complete, the temperature in the flask was 182°C What was the total pressure inside the flask?

Problem 144AP Which of the noble gases would not behave ideally under any circumstance? Why?

Problem 147AP A stockroom supervisor measured the contents of a 25.0-gal drum partially filled with acetone on a day when the temperature was 18.0°C and atmospheric pressure was 750 mmHg, and found that 15.4 gal of the solvent remained. After tightly scaling the drum, an assistant dropped the drum while carrying it upstairs to the organic laboratory. The drum was dented, and its internal volume was decreased to 20.4 gal. What is the total pressure inside the drum after the accident? The vapor pressure of acetone at 18.0°C is 400 mmHg. (Hint: At the time the drum was sealed, the pressure inside the drum, which is equal to the sum of the pressures of air and acetone, was equal to the atmospheric pressure.)

Problem 148AP In 2.00 min, 29.7 mL of He effuses through a small hole. Under the same conditions of pressure and temperature, 10.0 mL of a mixture of CO and CO2 effuses through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

A 6.11-g sample of a \(\mathrm{Cu}-\mathrm{Zn}\) alloy reacts with \(\mathrm{HCl}\) acid to produce hydrogen gas. If the hydrogen gas has a volume of \(1.26 \mathrm{~L}\) at \(22^{\circ} \mathrm{C}\) and \(728 \mathrm{mmHg}\), what is the percent of \(\mathrm{Zn}\) in the alloy? (Hint: Cu does not react with \(\mathrm{HCl}\).)

A mixture of methane \(\left(\mathrm{CH}_{4}\right) \text { and ethane }\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)\) is stored in a container at 294 mmHg. The gasses are burned in air to form \(\mathrm{CO}_{2} \text { and } \mathrm{H}_{2} \mathrm{O} \text {. }\). If the pressure of \(\mathrm{CO}_{2}\) is 356 mmHg measured at the same temperature and volume as the original mixture, calculate the mole fractions of the gasses.

Problem 151AP One way to gain a physical understanding of b in the van der Waals equation is to calculate the “excluded volume.” Assume that the distance of closest approach between two similar atoms is the sum of their radii (2r). (a) Calculate the volume around each atom into which the center of another atom cannot penetrate. (b) From your result in part (a), calculate the excluded volume for 1 mole of the atoms, which is the constant b. How does this volume compare with the sum of the volumes of 1 mole of the atoms?

Problem 150AP Use the kinetic theory of gases to explain why hot air rises.

Problem 152AP A 5.00-mole sample of NH3 gas is kept in a 1.92-L container at 300 K. If the van der Waals equation is assumed to give the correct answer for the pressure of the gas, calculate the percent error made in using the ideal gas equation to calculate the pressure.

The root-mean-square speed of a certain gaseous oxide is 493 m/s at 20°C. What is the molecular formula of the compound?

Problem 154AP Referring to Figure 11.20. we see that the maximum of each speed distribution plot is called the most probable speed (ump) because it is the speed possessed by the largest number of molecules. It is given by . (a) Compare ump with urms for nitrogen at 25°C. (b) The following diagram shows the Maxwell speed distribution curves for an ideal gas at two different temperatures T1, and T2. Calculate the value of T2.

Problem 156AP Assuming ideal behavior, which of the following gases will have the greatest volume at STP? (a) 0.82 mole of He, (b) 24 g of N2, or (c) 5.0 × 1023 molecules of Cl2.

Problem 157AP Calculate the density of helium in a helium balloon at 25.0°C. (Assume that the pressure inside the balloon is 1.10 atm.)

Problem 155AP A gaseous reaction takes place at constant volume and constant pressure in a cylinder as shown here. Which of the following equations best describes the reaction? The initial temperature (T1) is twice that of the final temperature (T2).

Problem 158AP Helium atoms in a closed container at room temperature are constantly colliding with one another and with the walls of their container. Does this “perpetual motion” violate the law of conservation of energy? Explain.

Problem 159AP Sulfur hexafluoride (SF6) has a molar mass of 146 g/mol and neon (Ne) has a molar mass of 20 g/mol. However. the average kinetic energies of these two gases at the same temperature are the same. Explain.

Problem 160AP Consider the molar volumes shown in Figure I 1.23. (a) Explain why Cl2 and NH3 have molar volumes significantly smaller from that of an ideal gas. (b) Explain why H2, He, and Ne have molar volumes greater than that of an ideal gas. (Hint: Look up the boiling points of the gases shown in the figure.)

Problem 39QP Ammonia burns in oxygen gas to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the same temperature and pressure?

Problem 50QP An ideal gas originally at 0.85 atm and 66°C was allowed to expand until its final volume, pressure, and temperature were 94 mL, 0.60 atm, and 45°C, respectively. What was its initial volume?