5.f^Chapter 5 Ending^39^50^,,^1419^2342%
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The following sections provide many aids to help you study this chapter. (Numbers in parentheses refer to pages, unless noted otherwise.)

Learning Objectives

Relevant section and/or sample problem (SP) numbers appear in parentheses.

Understand These Concepts
  1. How gases differ in their macroscopic properties from liquids and solids (5.1)

  2. The meaning of pressure and the operation of a barometer and a manometer (5.2)

  3. The relations among gas variables expressed by Boyle's, Charles's, and Avogadro's laws (5.3)

  4. How the individual gas laws are incorporated into the ideal gas law (5.3)

  5. How the ideal gas law can be used to study gas density and molar mass (5.4)

  6. The relation between the density and the temperature of a gas (5.4)

  7. The meaning of Dalton's law and the relation between partial pressure and mole fraction of a gas; how Dalton's law applies to collecting a gas over water (5.4)

  8. How the postulates of the kinetic-molecular theory are applied to explain the origin of pressure and the gas laws (5.5)

  9. The relations among molecular speed, average kinetic energy, and temperature (5.5)

  10. The meanings of effusion and diffusion and how their rates are related to molar mass (5.5)

  11. The relations among mean free path, molecular speed, and collision frequency (5.5)

  12. Why intermolecular attractions and molecular volume cause gases to deviate from ideal behavior at low temperatures and high pressures (5.6)

  13. How the van der Waals equation corrects the ideal gas law for extreme conditions (5.6)

Master These Skills
  1. Interconverting among the units of pressure (atm, mmHg, torr, pascal, psi) (SP 5.1)

  2. Reducing the ideal gas law to the individual gas laws (SPs 5.25.5)

  3. Applying gas laws to balancing a chemical equation (SP 5.6)

  4. Rearranging the ideal gas law to calculate gas density (SP 5.7) and molar mass of a volatile liquid (SP 5.8)

  5. Calculating the mole fraction and partial pressure of a gas (SP 5.9)

  6. Using the vapor pressure of water to find the amount of a gas collected over water (SP 5.10)

  7. Applying stoichiometry and gas laws to calculate amounts of reactants and products (SPs 5.11, 5.12)

  8. Using Graham's law to solve problems of gaseous effusion (SP 5.13)

Key Terms
Key Equations and Relationships
  • 5.1 Expressing the volume-pressure relationship (Boyle's law) (9):

  • 5.2 Expressing the volume-temperature relationship (Charles's law) (10):

  • 5.3 Expressing the pressure-temperature relationship (Amontons's law) (11):

  • 5.4 Expressing the volume-amount relationship (Avogadro's law) (12):

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  • 5.5 Defining standard temperature and pressure (12):

  • 5.6 Defining the volume of 1 mol of an ideal gas at STP (12):

  • 5.7 Relating volume to pressure, temperature, and amount (ideal gas law) (13):

  • 5.8 Calculating the value of R (13):

  • 5.9 Rearranging the ideal gas law to find gas density (18):


  • 5.10 Rearranging the ideal gas law to find molar mass (20):

    so or

  • 5.11 Relating the total pressure of a gas mixture to the partial pressures of the components (Dalton's law of partial pressures) (21):

  • 5.12 Relating partial pressure to mole fraction (22):

  • 5.13 Defining rms speed as a function of molar mass and temperature (31):

  • 5.14 Applying Graham's law of effusion (31):

  • 5.15 Applying the van der Waals equation to find gas P and V under extreme conditions (38):

Key Figures and Tables

Entries in bold contain frequently used data.

  • F5.1 The three states of matter (4)

  • T5.1 Common units of pressure (7)

  • F5.5 Boyle's law, the relationship between the volume and pressure of a gas (9)

  • F5.6 Charles's law, the relationship between the volume and temperature of a gas (10)

  • F5.9 Standard molar volume (13)

  • F5.11 The individual gas laws as special cases of the ideal gas law (14)

  • T5.2 Vapor pressure of water at different T (22)

  • F5.13 Stoichiometric relationships for gases (23)

  • F5.14 Distribution of molecular speeds at three T (27)

  • F5.16 Molecular description of Boyle's law (28)

  • F5.17 Molecular description of Dalton's law (28)

  • F5.18 Molecular description of Charles's law (29)

  • F5.19 Molecular description of Avogadro's law (29)

  • F5.20 The relationship between molar mass and molecular speed (30)

  • F5.23 Deviations from ideal behavior with increasing external pressure (35)

  • T5.4 Van der Waals constants for some common gases (38)

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Brief Solutions to Follow-up Problems
Page 42

Problems with colored numbers are in Appendix E and worked in detail in the Student Solutions Manual. Problem sections match those in the text and provide the numbers of relevant sample problems. Most offer Concept Review Questions, Skill-Building Exercises (grouped in pairs covering the same concept), and Problems in Context. The Comprehensive Problems are based on material from any section or previous chapter.

problem numbers in this section indicate their availability as online homework.

An Overview of the Physical States of Matter
Concept Review Questions
  • 5.1 How does a sample of gas differ in its behavior from a sample of liquid in each of the following situations?

    1. The sample is transferred from one container to a larger one.

    2. The sample is heated in an expandable container, but no change of state occurs.

    3. The sample is placed in a cylinder with a piston, and an external force is applied.

  • 5.2 Are the particles in a gas farther apart or closer together than the particles in a liquid? Use your answer to explain each of the following general observations:

    1. Gases are more compressible than liquids.

    2. Gases have lower viscosities than liquids.

    3. After thorough stirring, all gas mixtures are solutions.

    4. The density of a substance in the gas state is lower than in the liquid state.

Gas Pressure and Its Measurement

(Sample Problem 5.1)

Concept Review Questions
  • 5.3 How does a barometer work? Is the column of mercury in a barometer shorter when it is on a mountaintop or at sea level? Explain.

  • 5.4 How can a unit of length such as millimeter of mercury (mmHg) be used as a unit of pressure, which has the dimensions of force per unit area?

  • 5.5 In a closed-end manometer, the mercury level in the arm attached to the flask can never be higher than the mercury level in the other arm, whereas in an open-end manometer, it can be higher. Explain.

Skill-Building Exercises

(grouped in similar pairs)

  • On a cool, rainy day, the barometric pressure is 730 mmHg. Calculate the barometric pressure in centimeters of water (cmH2O) (d of Hg = 13.5 g/mL; d of H2O = 1.00 g/mL).

  • 5.7 A long glass tube, sealed at one end, has an inner diameter of 10.0 mm. The tube is filled with water and inverted into a pail of water. If the atmospheric pressure is 755 mmHg, how high (in mmH2O) is the column of water in the tube (d of Hg = 13.5 g/mL; d of H2O = 1.00 g/mL)?

  • 5.8 Convert the following:

    1. 0.745 atm to mmHg

    2. 992 torr to bar

    3. 365 kPa to atm

    4. 804 mmHg to kPa

  • 5.9 Convert the following:

    1. 76.8 cmHg to atm

    2. 27.5 atm to kPa

    3. 6.50 atm to bar

    4. 0.937 kPa to torr

  • In Figure P5.10, what is the pressure of the gas in the flask (in atm) if the barometer reads 738.5 torr?

  • Figure P5.10
  • In Figure P5.11, what is the pressure of the gas in the flask (in kPa) if the barometer reads 765.2 mmHg?

  • Figure P5.11
  • 5.12 If the sample flask in Figure P5.12 is open to the air, what is the atmospheric pressure (in atm)?

  • Figure P5.12
  • 5.13 What is the pressure (in Pa) of the gas in the flask in Figure P5.13?

Figure P5.13
Problems in Context
  • Convert each of the pressures described below to atm:

    1. At the peak of Mt. Everest, atmospheric pressure is only 2.75×102 mmHg.

    2. A cyclist fills her bike tires to 86 psi.

    3. The surface of Venus has an atmospheric pressure of 9.15×106 Pa.

    4. At 100 ft below sea level, a scuba diver experiences a pressure of 2.54×104 torr.

  • 5.15 The gravitational force exerted by an object is given by F = mg, where F is the force in newtons, m is the mass in kilograms, and g is the acceleration due to gravity (9.81 m/s2).

    1. Use the definition of the pascal to calculate the mass (in kg) of the atmosphere above 1 m2 of ocean.

    2. Osmium (Z = 76) is a transition metal in Group 8B(8) and has the highest density of any element (22.6 g/mL). If an osmium column is 1 m2 in area, how high must it be for its pressure to equal atmospheric pressure? [Use the answer from part (a) in your calculation.]

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The Gas Laws and Their Experimental Foundations

(Sample Problems 5.2 to 5.6)

Concept Review Questions
  • 5.16 A student states Boyle's law as follows: “The volume of a gas is inversely proportional to its pressure.” How is this statement incomplete? Give a correct statement of Boyle's law.

  • 5.17 In the following relationships, which quantities are variables and which are fixed: (a) Charles's law; (b) Avogadro's law; (c) Amontons's law?

  • 5.18 Boyle's law relates gas volume to pressure, and Avogadro's law relates gas volume to number of moles. State a relationship between gas pressure and number of moles.

  • 5.19 Each of the following processes caused the gas volume to double, as shown. For each process, state how the remaining gas variable changed or that it remained fixed:

    1. T doubles at fixed P.

    2. T and n are fixed.

    3. At fixed T, the reaction is CD2(g) C(g) + D2(g)

    4. At fixed P, the reaction is A2(g) + B2(g) 2AB(g).

Skill-Building Exercises

(grouped in similar pairs)

  • 5.20 What is the effect of the following on the volume of 1 mol of an ideal gas?

    1. The pressure is tripled (at constant T).

    2. The absolute temperature is increased by a factor of 3.0 (at constant P).

    3. Three more moles of the gas are added (at constant P and T).

  • 5.21 What is the effect of the following on the volume of 1 mol of an ideal gas?

    1. The pressure is reduced by a factor of 4 (at constant T).

    2. The pressure changes from 760 torr to 202 kPa, and the temperature changes from 37°C to 155 K.

    3. The temperature changes from 305 K to 32°C, and the pressure changes from 2 atm to 101 kPa.

  • 5.22 What is the effect of the following on the volume of 1 mol of an ideal gas?

    1. Temperature decreases from 800 K to 400 K (at constant P).

    2. Temperature increases from 250°C to 500°C (at constant P).

    3. Pressure increases from 2 atm to 6 atm (at constant T).

  • 5.23 What is the effect of the following on the volume of 1 mol of an ideal gas?

    1. Half the gas escapes (at constant P and T).

    2. The initial pressure is 722 torr, and the final pressure is 0.950 atm; the initial temperature is 32°F, and the final temperature is 273 K.

    3. Both the pressure and temperature decrease to one-fourth of their initial values.

  • A sample of sulfur hexafluoride gas occupies 9.10 L at 198°C. Assuming that the pressure remains constant, what temperature (in °C) is needed to reduce the volume to 2.50 L?

  • A 93-L sample of dry air cools from 145°C to −22°C while the pressure is maintained at 2.85 atm. What is the final volume?

  • 5.26 A sample of Freon-12 (CF2Cl2) occupies 25.5 L at 298 K and 153.3 kPa. Find its volume at STP.

  • A sample of carbon monoxide occupies 3.65 L at 298 K and 745 torr. Find its volume at −14°C and 367 torr.

  • A sample of chlorine gas is confined in a 5.0-L container at 328 torr and 37°C. How many moles of gas are in the sample?

  • If 1.47×10−3 mol of argon occupies a 75.0-mL container at 26°C, what is the pressure (in torr)?

  • You have 357 mL of chlorine trifluoride gas at 699 mmHg and 45°C. What is the mass (in g) of the sample?

  • A 75.0-g sample of dinitrogen monoxide is confined in a 3.1-L vessel. What is the pressure (in atm) at 115°C?

Problems in Context
  • 5.32 In preparation for a demonstration, your professor brings a 1.5-L bottle of sulfur dioxide into the lecture hall before class to allow the gas to reach room temperature. If the pressure gauge reads 85 psi and the temperature in the hall is 23°C, how many moles of sulfur dioxide are in the bottle? (Hint: The gauge reads zero when 14.7 psi of gas remains.)

  • 5.33 A gas-filled weather balloon with a volume of 65.0 L is released at sea-level conditions of 745 torr and 25°C. The balloon can expand to a maximum volume of 835 L. When the balloon rises to an altitude at which the temperature is −5°C and the pressure is 0.066 atm, will it reach its maximum volume?

Rearrangements of the Ideal Gas Law

(Sample Problems 5.7 to 5.12)

Concept Review Questions
  • 5.34 Why is moist air less dense than dry air?

  • 5.35 To collect a beaker of H2 gas by displacing the air already in the beaker, would you hold the beaker upright or inverted? Why? How would you hold the beaker to collect CO2?

  • 5.36 Why can we use a gas mixture, such as air, to study the general behavior of an ideal gas under ordinary conditions?

  • 5.37 How does the partial pressure of gas A in a mixture compare to its mole fraction in the mixture? Explain.

  • The circle at right represents a portion of a mixture of four gases A (purple), B (brown), C (green), and D2 (orange).

    1. Which has the highest partial pressure?

    2. Which has the lowest partial pressure?

    3. If the total pressure is 0.75 atm, what is the partial pressure of D2?

Skill-Building Exercises

(grouped in similar pairs)

  • 5.39 What is the density of Xe gas at STP?

  • Find the density of Freon-11 (CFCl3) at 120°C and 1.5 atm.

  • How many moles of gaseous arsine (AsH3) occupy 0.0400 L at STP? What is the density of gaseous arsine?

  • 5.42 The density of a noble gas is 2.71 g/L at 3.00 atm and 0°C. Identify the gas.

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  • Calculate the molar mass of a gas at 388 torr and 45°C if 206 ng occupies 0.206 μL.

  • 5.44 When an evacuated 63.8-mL glass bulb is filled with a gas at 22°C and 747 mmHg, the bulb gains 0.103 g in mass. Is the gas N2, Ne, or Ar?

  • After 0.600 L of Ar at 1.20 atm and 227°C is mixed with 0.200 L of O2 at 501 torr and 127°C in a 400-mL flask at 27°C, what is the pressure in the flask?

  • 5.46 A 355-mL container holds 0.146 g of Ne and an unknown amount of Ar at 35°C and a total pressure of 626 mmHg. Calculate the moles of Ar present.

  • 5.47 How many grams of phosphorus react with 35.5 L of O2 at STP to form tetraphosphorus decaoxide?

  • How many grams of potassium chlorate decompose to potassium chloride and 638 mL of O2 at 128°C and 752 torr?

  • How many grams of phosphine (PH3) can form when 37.5 g of phosphorus and 83.0 L of hydrogen gas react at STP?

  • 5.50 When 35.6 L of ammonia and 40.5 L of oxygen gas at STP burn, nitrogen monoxide and water form. After the products return to STP, how many grams of nitrogen monoxide are present?

  • Aluminum reacts with excess hydrochloric acid to form aqueous aluminum chloride and 35.8 mL of hydrogen gas over water at 27°C and 751 mmHg. How many grams of aluminum reacted?

  • 5.52 How many liters of hydrogen gas are collected over water at 18°C and 725 mmHg when 0.84 g of lithium reacts with water? Aqueous lithium hydroxide also forms.

Problems in Context
  • 5.53 The air in a hot-air balloon at 744 torr is heated from 17°C to 60.0°C. Assuming that the moles of air and the pressure remain constant, what is the density of the air at each temperature? (The average molar mass of air is 28.8 g/mol.)

  • On a certain winter day in Utah, the average atmospheric pressure is 650. torr. What is the molar density (in mol/L) of the air if the temperature is −25°C?

  • 5.55 A sample of a liquid hydrocarbon known to consist of molecules with five carbon atoms is vaporized in a 0.204-L flask by immersion in a water bath at 101°C. The barometric pressure is 767 torr, and the remaining gas weighs 0.482 g. What is the molecular formula of the hydrocarbon?

  • A sample of air contains 78.08% nitrogen, 20.94% oxygen, 0.05% carbon dioxide, and 0.93% argon, by volume. How many molecules of each gas are present in 1.00 L of the sample at 25°C and 1.00 atm?

  • An environmental chemist sampling industrial exhaust gases from a coal-burning plant collects a CO2-SO2-H2O mixture in a 21-L steel tank until the pressure reaches 850. torr at 45°C.

    1. How many moles of gas are collected?

    2. If the SO2 concentration in the mixture is 7.95×103 parts per million by volume (ppmv), what is its partial pressure? [Hint: ppmv = (volume of component/volume of mixture) × 106.]

  • 5.58 “Strike anywhere” matches contain the compound tetraphosphorus trisulfide, which burns to form tetraphosphorus decaoxide and sulfur dioxide gas. How many milliliters of sulfur dioxide, measured at 725 torr and 32°C, can be produced from burning 0.800 g of tetraphosphorus trisulfide?

  • Freon-12 (CF2Cl2), widely used as a refrigerant and aerosol propellant, is a dangerous air pollutant. In the troposphere, it traps heat 25 times as effectively as CO2, and in the stratosphere, it participates in the breakdown of ozone. Freon-12 is prepared industrially by reaction of gaseous carbon tetrachloride with hydrogen fluoride. Hydrogen chloride gas also forms. How many grams of carbon tetrachloride are required for the production of 16.0 dm3 of Freon-12 at 27°C and 1.20 atm?

  • Xenon hexafluoride was one of the first noble gas compounds synthesized. The solid reacts rapidly with the silicon dioxide in glass or quartz containers to form liquid XeOF4 and gaseous silicon tetrafluoride. What is the pressure in a 1.00-L container at 25°C after 2.00 g of xenon hexafluoride reacts? (Assume that silicon tetrafluoride is the only gas present and that it occupies the entire volume.)

  • The four sketches below represent cylinder-piston assemblies holding gases. The piston at far left holds a reactant about to undergo a reaction at constant T and P:

    Which of the other three depictions best represents the products of the reaction?

  • Roasting galena [lead(II) sulfide] is an early step in the industrial isolation of lead. How many liters of sulfur dioxide, measured at STP, are produced by the reaction of 3.75 kg of galena with 228 L of oxygen gas at 220°C and 2.0 atm? Lead(II) oxide also forms.

  • 5.63 In one of his most critical studies into the nature of combustion, Lavoisier heated mercury(II) oxide and isolated elemental mercury and oxygen gas. If 40.0 g of mercury(II) oxide is heated in a 502-mL vessel and 20.0% (by mass) decomposes, what is the pressure (in atm) of the oxygen that forms at 25.0°C? (Assume that the gas occupies the entire volume.)

The Kinetic-Molecular Theory: A Model for Gas Behavior

(Sample Problem 5.13)

Concept Review Questions
  • 5.64 Use the kinetic-molecular theory to explain the change in gas pressure that results from warming a sample of gas.

  • 5.65 How does the kinetic-molecular theory explain why 1 mol of krypton and 1 mol of helium have the same volume at STP?

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  • 5.66 Is the rate of effusion of a gas higher than, lower than, or equal to its rate of diffusion? Explain. For two gases with molecules of approximately the same size, is the ratio of their effusion rates higher than, lower than, or equal to the ratio of their diffusion rates? Explain.

  • 5.67 Consider two 1-L samples of gas: one is H2 and the other is O2. Both are at 1 atm and 25°C. How do the samples compare in terms of (a) mass, (b) density, (c) mean free path, (d) average molecular kinetic energy, (e) average molecular speed, and (f) time for a given fraction of molecules to effuse?

  • 5.68 Three 5-L flasks, fixed with pressure gauges and small valves, each contain 4 g of gas at 273 K. Flask A contains H2, flask B contains He, and flask C contains CH4. Rank the flask contents in terms of (a) pressure, (b) average molecular kinetic energy, (c) diffusion rate after the valve is opened, (d) total kinetic energy of the molecules, (e) density, and (f) collision frequency.

Skill-Building Exercises

(grouped in similar pairs)

  • 5.69 What is the ratio of effusion rates for the lightest gas, H2, and the heaviest known gas, UF6?

  • 5.70 What is the ratio of effusion rates for O2 and Kr?

  • 5.71 The graph below shows the distribution of molecular speeds for argon and helium at the same temperature.

    1. Does curve 1 or 2 better represent the behavior of argon?

    2. Which curve represents the gas that effuses more slowly?

    3. Which curve more closely represents the behavior of fluorine gas? Explain.

  • The graph below shows the distribution of molecular speeds for a gas at two different temperatures.

    1. Does curve 1 or 2 better represent the behavior of the gas at the lower temperature?

    2. Which curve represents the gas when it has a higher ?

    3. Which curve is consistent with a higher diffusion rate?

  • 5.73 At a given pressure and temperature, it takes 4.85 min for a 1.5-L sample of He to effuse through a membrane. How long does it take for 1.5 L of F2 to effuse under the same conditions?

  • A sample of an unknown gas effuses in 11.1 min. An equal volume of H2 in the same apparatus under the same conditions effuses in 2.42 min. What is the molar mass of the unknown gas?

Problems in Context
  • 5.75 White phosphorus melts and then vaporizes at high temperature. The gas effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. How many atoms are in a molecule of gaseous white phosphorus?

  • Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the heaviest. [For this problem, use R = 8.314 J/(mol·K) and in kg/mol.] (a) Find the rms speed of He in winter (0.°C) and in summer (30.°C). (b) Compare the rms speed of He with that of Xe at 30.°C. (c) Find the average kinetic energy per mole of He and of Xe at 30.°C. (d) Find the average kinetic energy per molecule of He at 30.°C.

  • 5.77 A mixture of gaseous disulfur difluoride, dinitrogen tetrafluoride, and sulfur tetrafluoride is placed in an effusion apparatus. (a) Rank the gases in order of increasing effusion rate. (b) Find the ratio of effusion rates of disulfur difluoride and dinitrogen tetrafluoride. (c) If gas X is added, and it effuses at 0.935 times the rate of sulfur tetrafluoride, find the molar mass of X.

Real Gases: Deviations from Ideal Behavior
Skill-Building Exercises

(grouped in similar pairs)

  • 5.78 Do intermolecular attractions cause negative or positive de viations from the PV/RT ratio of an ideal gas? Use Table 5.4 to rank Kr, CO2, and N2 in order of increasing magnitude of these deviations.

  • 5.79 Does molecular size cause negative or positive deviations from the PV/RT ratio of an ideal gas? Use Table 5.4 to rank Cl2, H2, and O2 in order of increasing magnitude of these deviations.

  • 5.80 Does N2 behave more ideally at 1 atm or at 500 atm? Explain.

  • 5.81 Does SF6 (boiling point = 16°C at 1 atm) behave more ideally at 150°C or at 20°C? Explain.

Comprehensive Problems
  • An “empty” gasoline can with dimensions 15.0 cm by 40.0 cm by 12.5 cm is attached to a vacuum pump and evacuated. If the atmospheric pressure is 14.7 lb/in2, what is the total force (in pounds) on the outside of the can?

  • 5.83 Hemoglobin is the protein that transports O2 through the blood from the lungs to the rest of the body. In doing so, each molecule of hemoglobin combines with four molecules of O2. If 1.00 g of hemoglobin combines with 1.53 mL of O2 at 37°C and 743 torr, what is the molar mass of hemoglobin?

  • A baker uses sodium hydrogen carbonate (baking soda) as the leavening agent in a banana-nut quickbread. The baking soda decomposes according to two possible reactions:

    1. 2NaHCO3(s) Na2CO3(s) + H2O(l) + CO2(g)

    2. NaHCO3(s) + H+(aq) H2O(l) + CO2(g) + Na+(aq)

    Calculate the volume (in mL) of CO2 that forms at 200.°C and 0.975 atm per gram of NaHCO3 by each of the reaction processes.

  • 5.85 A weather balloon containing 600. L of He is released near the equator at 1.01 atm and 305 K. It rises to a point where conditions are 0.489 atm and 218 K and eventually lands in the northern hemisphere under conditions of 1.01 atm and 250 K. If one-fourth of the helium leaked out during this journey, what is the volume (in L) of the balloon at landing?

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  • Chlorine is produced from sodium chloride by the electrochemical chlor-alkali process. During the process, the chlorine is collected in a container that is isolated from the other products to prevent unwanted (and explosive) reactions. If a 15.50-L container holds 0.5950 kg of Cl2 gas at 225°C, calculate:

    1. PIGL

  • 5.87 In a certain experiment, magnesium boride (Mg3B2) reacted with acid to form a mixture of four boron hydrides (BxHy), three as liquids (labeled I, II, and III) and one as a gas (IV).

    1. When a 0.1000-g sample of each liquid was transferred to an evacuated 750.0-mL container and volatilized at 70.00°C, sample I had a pressure of 0.05951 atm; sample II, 0.07045 atm; and sample III, 0.05767 atm. What is the molar mass of each liquid?

    2. Boron is 85.63% by mass in sample I, 81.10% in II, and 82.98% in III. What is the molecular formula of each sample?

    3. Sample IV was found to be 78.14% boron. Its rate of effusion was compared to that of sulfur dioxide and under identical conditions, 350.0 mL of sample IV effused in 12.00 min and 250.0 mL of sulfur dioxide effused in 13.04 min. What is the molecular formula of sample IV?

  • Three equal volumes of gas mixtures, all at the same T, are depicted below (with gas A red, gas B green, and gas C blue):

    1. Which sample, if any, has the highest partial pressure of A?

    2. Which sample, if any, has the lowest partial pressure of B?

    3. In which sample, if any, do the gas particles have the highest average kinetic energy?

  • Will the volume of a gas increase, decrease, or remain unchanged for each of the following sets of changes?

    1. The pressure is decreased from 2 atm to 1 atm, while the temperature is decreased from 200°C to 100°C.

    2. The pressure is increased from 1 atm to 3 atm, while the temperature is increased from 100°C to 300°C.

    3. The pressure is increased from 3 atm to 6 atm, while the temperature is increased from −73°C to 127°C.

    4. The pressure is increased from 0.2 atm to 0.4 atm, while the temperature is decreased from 300°C to 150°C.

  • 5.90 When air is inhaled, it enters the alveoli of the lungs, and varying amounts of the component gases exchange with dissolved gases in the blood. The resulting alveolar gas mixture is quite different from the atmospheric mixture. The following table presents selected data on the composition and partial pressure of four gases in the atmosphere and in the alveoli:

      Atmosphere (sea level) Alveoli
    Gas Mole % Partial Pressure (torr) Mole % Partial Pressure (torr)
    N2 78.6 569
    O2 20.9 104
    CO2 00.04 40
    H2O 00.46 47

    If the total pressure of each gas mixture is 1.00 atm, calculate:

    1. The partial pressure (in torr) of each gas in the atmosphere

    2. The mole % of each gas in the alveoli

    3. The number of O2 molecules in 0.50 L of alveolar air (volume of an average breath of a person at rest) at 37°C

  • Radon (Rn) is the heaviest, and only radioactive, member of Group 8A(18) (noble gases). It is a product of the disintegration of heavier radioactive nuclei found in minute concentrations in many common rocks used for building and construction. In recent years, health concerns about the cancers caused from inhaled residential radon have grown. If 1.0×1015 atoms of radium (Ra) produce an average of 1.373×104 atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 1.0 g of Ra?

  • At 1450. mmHg and 286 K, a skin diver exhales a 208-mL bubble of air that is 77% N2, 17% O2, and 6.0% CO2 by volume.

    1. How many milliliters would the volume of the bubble be if it were exhaled at the surface at 1 atm and 298 K?

    2. How many moles of N2 are in the bubble?

  • Nitrogen dioxide is used industrially to produce nitric acid, but it contributes to acid rain and photochemical smog. What volume of nitrogen dioxide is formed at 735 torr and 28.2°C by reacting 4.95 cm3 of copper (d = 8.95 g/cm3) with 230.0 mL of nitric acid (d = 1.42 g/cm3, 68.0% HNO3 by mass)?

  • In the average adult male, the residual volume (RV) of the lungs, the volume of air remaining after a forced exhalation, is 1200 mL. (a) How many moles of air are present in the RV at 1.0 atm and 37°C? (b) How many molecules of gas are present under these conditions?

  • In a bromine-producing plant, how many liters of gaseous elemental bromine at 300°C and 0.855 atm are formed by the reaction of 275 g of sodium bromide and 175.6 g of sodium bromate in aqueous acid solution? (Assume no Br2 dissolves.)

  • In a collision of sufficient force, automobile air bags respond by electrically triggering the explosive decomposition of sodium azide (NaN3) to its elements. A 50.0-g sample of sodium azide was decomposed, and the nitrogen gas generated was collected over water at 26°C. The total pressure was 745.5 mmHg. How many liters of dry N2 were generated?

  • 5.97 An anesthetic gas contains 64.81% carbon, 13.60% hydrogen, and 21.59% oxygen, by mass. If 2.00 L of the gas at 25°C and 0.420 atm weighs 2.57 g, what is the molecular formula of the anesthetic?

  • 5.98 Aluminum chloride is easily vaporized above 180°C. The gas escapes through a pinhole 0.122 times as fast as helium at the same conditions of temperature and pressure in the same apparatus. What is the molecular formula of aluminum chloride gas?

    1. What is the total volume of gaseous products, measured at 350°C and 735 torr, when an automobile engine burns 100. g of C8H18 (a typical component of gasoline)?

    2. For part (a), the source of O2 is air, which is about 78% N2, 21% O2, and 1.0% Ar by volume. Assuming all the O2 reacts, but no N2 or Ar does, what is the total volume of gaseous exhaust?

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  • An atmospheric chemist studying the pollutant SO2 places a mixture of SO2 and O2 in a 2.00-L container at 800. K and 1.90 atm. When the reaction occurs, gaseous SO3 forms, and the pressure falls to 1.65 atm. How many moles of SO3 form?

  • The thermal decomposition of ethylene occurs during ethylene transit in pipelines and formation of polyethylene. The decomposition reaction is

    If the decomposition begins at 10°C and 50.0 atm with a gas density of 0.215 g/mL and the temperature increases by 950 K,

    1. What is the final pressure of the confined gas (ignore the volume of graphite and use the van der Waals equation)?

    2. How does the PV/RT value of CH4 compare to that in Figure 5.23? Explain.

  • Ammonium nitrate, a common fertilizer, was used by terrorists in the tragic explosion in Oklahoma City in 1995. How many liters of gas at 307°C and 1.00 atm are formed by the explosive decomposition of 15.0 kg of ammonium nitrate to nitrogen, oxygen, and water vapor?

  • An environmental engineer analyzes a sample of air contaminated with sulfur dioxide. To a 500.-mL sample at 700. torr and 38°C, she adds 20.00 mL of 0.01017 M aqueous iodine, which reacts as follows:

    Excess I2 reacts with 11.37 mL of 0.0105 M sodium thiosulfate:

    What is the volume % of SO2 in the air sample?

  • Canadian chemists have developed a modern variation of the 1899 Mond process for preparing extremely pure metallic nickel. A sample of impure nickel reacts with carbon monoxide at 50°C to form gaseous nickel carbonyl, Ni(CO)4.

    1. How many grams of nickel can be converted to the carbonyl with 3.55 m3 of CO at 100.7 kPa?

    2. The carbonyl is then decomposed at 21 atm and 155°C to pure (>99.95%) nickel. How many grams of nickel are obtained per cubic meter of the carbonyl?

    3. The released carbon monoxide is cooled and collected for reuse by passing it through water at 35°C. If the barometric pressure is 769 torr, what volume (in m3) of CO is formed per cubic meter of carbonyl?

  • 5.105 Analysis of a newly discovered gaseous silicon-fluorine compound shows that it contains 33.01 mass % silicon. At 27°C, 2.60 g of the compound exerts a pressure of 1.50 atm in a 0.250-L vessel. What is the molecular formula of the compound?

  • 5.106 A gaseous organic compound containing only carbon, hydrogen, and nitrogen is burned in oxygen gas, and the volume of each reactant and product is measured under the same conditions of temperature and pressure. Reaction of four volumes of the compound produces four volumes of CO2, two volumes of N2, and ten volumes of water vapor. (a) What volume of O2 was required? (b) What is the empirical formula of the compound?

  • Containers A, B, and C are attached by closed stopcocks of negligible volume.

    If each particle shown in the picture represents 106 particles,

    1. How many blue particles and black particles are in B after the stopcocks are opened and the system reaches equilibrium?

    2. How many blue particles and black particles are in A after the stopcocks are opened and the system reaches equilibrium?

    3. If the pressure in C, PC, is 750 torr before the stopcocks are opened, what is PC afterward? (d) What is PB afterward?

  • Combustible vapor-air mixtures are flammable over a limited range of concentrations. The minimum volume % of vapor that gives a combustible mixture is called the lower flammable limit (LFL). Generally, the LFL is about half the stoichiometric mixture, the concentration required for complete combustion of the vapor in air. (a) If oxygen is 20.9 vol % of air, estimate the LFL for n-hexane, C6H14. (b) What volume (in mL) of n- hexane (d = 0.660 g/cm3) is required to produce a flammable mixture of hexane in 1.000 m3 of air at STP?

  • 5.109 By what factor would a scuba diver's lungs expand if she ascended rapidly to the surface from a depth of 125 ft without inhaling or exhaling? If an expansion factor greater than 1.5 causes lung rupture, how far could she safely ascend from 125 ft without breathing? Assume constant temperature (d of seawater = 1.04 g/mL; d of Hg = 13.5 g/mL).

  • When 15.0 g of fluorite (CaF2) reacts with excess sulfuric acid, hydrogen fluoride gas is collected at 744 torr and 25.5°C. Solid calcium sulfate is the other product. What gas temperature is required to store the gas in an 8.63-L container at 875 torr?

  • Dilute aqueous hydrogen peroxide is used as a bleaching agent and for disinfecting surfaces and small cuts. Its concentration is sometimes given as a certain number of “volumes hydrogen peroxide,” which refers to the number of volumes of O2 gas, measured at STP, that a given volume of hydrogen peroxide solution will release when it decomposes to O2 and liquid H2O. How many grams of hydrogen peroxide are in 0.100 L of “20 volumes hydrogen peroxide” solution?

  • 5.112 At a height of 300 km above Earth's surface, an astronaut finds that the atmospheric pressure is about 10−8 mmHg and the temperature is 500 K. How many molecules of gas are there per milliliter at this altitude?

  • 5.113 (a) What is the rms speed of O2 at STP? (b) If the mean free path of O2 molecules at STP is 6.33×10−8 m, what is their collision frequency? [Use R = 8.314 J/(mol·K) and in kg/mol.]

  • Acrylic acid (CH2==CHCOOH) is used to prepare polymers, adhesives, and paints. The first step to make acrylic acid involves the vapor-phase oxidation of propylene (CH2==CHCH3) to acrolein (CH2==CHCHO). This step is carried out at 330°C and 2.5 atm in a large bundle of tubes around which circulates a heat-transfer agent. The reactants spend an average of 1.8 s in the tubes, which have a void space of 100 ft3. How many pounds of propylene must be added per hour in a mixture whose mole fractions are 0.07 propylene, 0.35 steam, and 0.58 air?

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  • 5.115 Standard conditions are based on relevant environmental conditions. If normal average surface temperature and pressure on Venus are 730. K and 90 atm, respectively, what is the standard molar volume of an ideal gas on Venus?

  • 5.116 A barometer tube is 1.00×102 cm long and has a cross-sectional area of 1.20 cm2. The height of the mercury column is 74.0 cm, and the temperature is 24°C. A small amount of N2 is introduced into the evacuated space above the mercury, which causes the mercury level to drop to a height of 64.0 cm. How many grams of N2 were introduced?

  • What is the molar concentration of the cleaning solution formed when 10.0 L of ammonia gas at 33°C and 735 torr dissolves in enough water to give a final volume of 0.750 L?

  • 5.118 The Hawaiian volcano Kilauea emits an average of 1.5×103 m3 of gas each day, when corrected to 298 K and 1.00 atm. The mixture contains gases that contribute to global warming and acid rain, and some are toxic. An atmospheric chemist analyzes a sample and finds the following mole fractions: 0.4896 CO2, 0.0146 CO, 0.3710 H2O, 0.1185 SO2, 0.0003 S2, 0.0047 H2, 0.0008 HCl, and 0.0003 H2S. How many metric tons (t) of each gas are emitted per year (1 t = 1000 kg)?

  • To study a key fuel-cell reaction, a chemical engineer has 20.0-L tanks of H2 and of O2 and wants to use up both tanks to form 28.0 mol of water at 23.8°C. (a) Use the ideal gas law to find the pressure needed in each tank. (b) Use the van der Waals equation to find the pressure needed in each tank. (c) Compare the results from the two equations.

  • 5.120 For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain.

    1. Argon or xenon

    2. Water vapor or neon

    3. Mercury vapor or radon

    4. Water vapor or methane

  • How many liters of gaseous hydrogen bromide at 29°C and 0.965 atm will a chemist need if she wishes to prepare 3.50 L of 1.20 M hydrobromic acid?

  • 5.122 A mixture consisting of 7.0 g of CO and 10.0 g of SO2, two atmospheric pollutants, has a pressure of 0.33 atm when placed in a sealed container. What is the partial pressure of CO?

  • Sulfur dioxide is used to make sulfuric acid. One method of producing it is by roasting mineral sulfides, for example,

    A production error leads to the sulfide being placed in a 950-L vessel with insufficient oxygen. The partial pressure of O2 is 0.64 atm, and the total pressure is initially 1.05 atm, with the balance N2. The reaction is run until 85% of the O2 is consumed, and the vessel is then cooled to its initial temperature. What is the total pressure and partial pressure of each gas in the vessel?

  • 5.124 A mixture of CO2 and Kr weighs 35.0 g and exerts a pressure of 0.708 atm in its container. Since Kr is expensive, you wish to recover it from the mixture. After the CO2 is completely removed by absorption with NaOH(s), the pressure in the container is 0.250 atm. How many grams of CO2 were originally present? How many grams of Kr can you recover?

  • 5.125 When a car accelerates quickly, the passengers feel a force that presses them back into their seats, but a balloon filled with helium floats forward. Why?

  • Gases such as CO are gradually oxidized in the atmosphere, not by O2 but by the hydroxyl radical, ·OH, a hydroxide ion with one fewer electron. At night, the ·OH concentration is nearly zero but increases to 2.5×1012 molecules/m3 in polluted air during the day. At daytime conditions of 1.00 atm and 22°C, what is the partial pressure and mole percent of ·OH in air?

  • Aqueous sulfurous acid (H2SO3) was made by dissolving 0.200 L of sulfur dioxide gas at 19°C and 745 mmHg in water to yield 500.0 mL of solution. The acid solution required 10.0 mL of sodium hydroxide solution to reach the titration end point. What was the molarity of the sodium hydroxide solution?

  • 5.128 In the 19th century, J. B. A. Dumas devised a method for finding the molar mass of a volatile liquid from the volume, temperature, pressure, and amount of its vapor. He placed a sample of such a liquid in a flask that was closed with a stopper fitted with a narrow tube, immersed the flask in a hot water bath to vaporize the liquid, and then cooled the flask (Figure P5.128). Find the molar mass of a volatile liquid from the following:

    • Mass of empty flask = 65.347 g

    • Mass of flask filled with water at 25°C = 327.4 g

    • Density of water at 25°C = 0.997 g/mL

    • Mass of flask plus condensed liquid = 65.739 g

    • Barometric pressure = 1016.2 kPa

    • Temperature of water bath = 99.8°C

    Figure P5.128
  • During World War II, a portable source of hydrogen gas was needed for weather balloons, and solid metal hydrides were the most convenient form. Many metal hydrides react with water to generate the metal hydroxide and hydrogen. Two candidates were lithium hydride and magnesium hydride. What volume of gas is formed from 1.00 lb of each hydride at 750. torr and 27°C?

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  • 5.130 The lunar surface reaches 370 K at midday. The atmosphere consists of neon, argon, and helium at a total pressure of only 2×10−14 atm. Calculate the rms speed of each component in the lunar atmosphere. [Use R = 8.314 J/(mol·K) and in kg/mol.]

  • A person inhales air richer in O2 and exhales air richer in CO2 and water vapor. During each hour of sleep, a person exhales a total of about 300 L of this CO2-enriched and H2O-enriched air. (a) If the partial pressures of CO2 and H2O in exhaled air are each 30.0 torr at 37.0°C, calculate the masses of CO2 and of H2O exhaled in 1 h of sleep. (b) How many grams of body mass does the person lose in an 8-h sleep if all the CO2 and H2O exhaled come from the metabolism of glucose?

  • 5.132 Popcorn pops because the horny endosperm, a tough, elastic material, resists gas pressure within the heated kernel until it reaches explosive force. A 0.25-mL kernel has a water content of 1.6% by mass, and the water vapor reaches 170°C and 9.0 atm before the kernel ruptures. Assume the water vapor can occupy 75% of the kernel's volume. (a) What is the mass of the kernel? (b) How many milliliters would this amount of water vapor occupy at 25°C and 1.00 atm?

  • 5.133 Sulfur dioxide emissions from coal-based power plants are removed by flue-gas desulfurization. The flue gas passes through a scrubber, and a slurry of wet calcium carbonate reacts with it to form carbon dioxide and calcium sulfite. The calcium sulfite then reacts with oxygen to form calcium sulfate, which is sold as gypsum. (a) If the sulfur dioxide concentration is 1000 times higher than its mole fraction in clean dry air (2×10−10), how much calcium sulfate (kg) can be made from scrubbing 4 GL of flue gas (1 GL = 1×109 L)? A state-of-the-art scrubber removes at least 95% of the sulfur dioxide. (b) If the mole fraction of oxygen in air is 0.209, what volume (L) of air at 1.00 atm and 25°C is needed to react with all the calcium sulfite?

  • 5.134 Many water treatment plants use chlorine gas to kill micro-organisms before the water is released for residential use. A plant engineer has to maintain the chlorine pressure in a tank below the 85.0-atm rating and, to be safe, decides to fill the tank to 80.0% of this maximum pressure. (a) How many moles of Cl2 gas can be kept in the 850.-L tank at 298 K if she uses the ideal gas law in the calculation? (b) What is the tank pressure if she uses the van der Waals equation for this amount of gas? (c) Did the engineer fill the tank to the desired pressure?

  • 5.135 At 10.0°C and 102.5 kPa, the density of dry air is 1.26 g/L. What is the average “molar mass” of dry air at these conditions?

  • 5.136 In A, the picture depicts a cylinder with 0.1 mol of a gas that behaves ideally. Choose the cylinder (B, C, or D) that correctly represents the volume of the gas after each of the following changes. If none of the cylinders is correct, specify “none.”

    1. P is doubled at fixed n and T.

    2. T is reduced from 400 K to 200 K at fixed n and P.

    3. T is increased from 100°C to 200°C at fixed n and P.

    4. 0.1 mol of gas is added at fixed P and T.

    5. 0.1 mol of gas is added and P is doubled at fixed T.

  • 5.137 Ammonia is esential to so many industries that, on a molar basis, it is the most heavily produced substance in the world. Calculate PIGL and PVDW (in atm) of 51.1 g of ammonia in a 3.000-L container at 0°C and 400.°C, the industrial temperature. (From Table 5.4, for NH3, a = 4.17 atm·L2/mol2 and b = 0.0371 L/mol.)

  • 5.138 A 6.0-L flask contains a mixture of methane (CH4), argon, and helium at 45°C and 1.75 atm. If the mole fractions of helium and argon are 0.25 and 0.35, respectively, how many molecules of methane are present?

  • 5.139 A large portion of metabolic energy arises from the biological combustion of glucose:

    (a) If this reaction is carried out in an expandable container at 37°C and 780. torr, what volume of CO2 is produced from 20.0 g of glucose and excess O2? (b) If the reaction is carried out at the same conditions with the stoichiometric amount of O2, what is the partial pressure of each gas when the reaction is 50% complete (10.0 g of glucose remains)?

  • 5.140 What is the average kinetic energy and rms speed of N2 molecules at STP? Compare these values with those of H2 molecules at STP. [Use R = 8.314 J/(mol·K) and in kg/mol.]

  • 5.141 According to government standards, the 8-h threshold limit value is 5000 ppmv for CO2 and 0.1 ppmv for Br2 (1 ppmv is 1 part by volume in 106 parts by volume). Exposure to either gas for 8 h above these limits is unsafe. At STP, which of the following would be unsafe for 8 h of exposure?

    1. Air with a partial pressure of 0.2 torr of Br2

    2. Air with a partial pressure of 0.2 torr of CO2

    3. 1000 L of air containing 0.0004 g of Br2 gas

    4. 1000 L of air containing 2.8×1022 molecules of CO2

  • 5.142 One way to prevent emission of the pollutant NO from industrial plants is by a catalyzed reaction with NH3:

    (a) If the NO has a partial pressure of 4.5×10−5 atm in the flue gas, how many liters of NH3 are needed per liter of flue gas at 1.00 atm? (b) If the reaction takes place at 1.00 atm and 365°C, how many grams of NH3 are needed per kL of flue gas?

  • 5.143 An equimolar mixture of Ne and Xe is accidentally placed in a container that has a tiny leak. After a short while, a very small proportion of the mixture has escaped. What is the mole fraction of Ne in the effusing gas?

  • 5.144 From the relative rates of effusion of 235UF6 and 238UF6, find the number of steps needed to produce a sample that is 3.0 mole % 235U, the enriched fuel used in many nuclear reactors from its natural abundance of 0.72%.

  • 5.145 A slight deviation from ideal behavior exists even at normal conditions. If it behaved ideally, 1 mol of CO would occupy 22.414 L and exert 1 atm pressure at 273.15 K. Calculate PVDW for 1.000 mol of CO at 273.15 K.

  • 5.146 In preparation for a combustion demonstration, a professor fills a balloon with equal molar amounts of H2 and O2, but the demonstration has to be postponed until the next day. During the night, both gases leak through pores in the balloon. If 35% of the H2 leaks, what is the O2/H2 ratio in the balloon the next day?

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  • 5.147 Phosphorus trichloride is important in the manufacture of insecticides, fuel additives, and flame retardants. Phosphorus has only one naturally occurring isotope, 31P, whereas chlorine has two, 35Cl (75%) and 37Cl (25%). (a) What different molecular masses (amu) can be found for PCl3? (b) Which is the most abundant? (c) What is the ratio of the effusion rates of the heavi est and the lightest PCl3 molecules?

  • 5.148 A truck tire has a volume of 218 L and is filled with air to 35.0 psi at 295 K. After a drive, the air heats up to 318 K. (a) If the tire volume is constant, what is the pressure? (b) If the tire volume increases 2.0%, what is the pressure? (c) If the tire leaks 1.5 g of air per minute and the temperature is constant, how many minutes will it take for the tire to reach the original pressure of 35.0 psi ( of air = 28.8 g/mol)?

  • 5.149 Allotropes are different molecular forms of an element, such as dioxygen (O2) and ozone (O3). (a) What is the density of each oxygen allotrope at 0°C and 760 torr? (b) Calculate the ratio of densities, , and explain the significance of this number.

  • 5.150 When gaseous F2 and solid I2 are heated to high temperatures, the I2 sublimes and gaseous iodine heptafluoride forms. If 350. torr of F2 and 2.50 g of solid I2 are put into a 2.50-L container at 250. K and the container is heated to 550. K, what is the final pressure? What is the partial pressure of I2 gas?