Chapter 13 Gases

Chapter 13GasesCopyright Cengage Learning. All rights reserved1

Section 13.1PressureWhy study gases? An understanding of real world phenomena. An understanding of how science “works.”Copyright Cengage Learning. All rights reserved2

Section 13.1PressureA Gas Uniformly fills any container.Mixes completely with any other gas.Exerts pressure on its surroundings.Copyright Cengage Learning. All rights reserved3

Section 13.1PressurePressureforcePr essure area SI units Newton/meter2 1 Pascal (Pa)1 standard atmosphere 101,325 Pa1 standard atmosphere 1 atm 760 mm Hg 760 torrCopyright Cengage Learning. All rights reserved4

Section 13.1PressureBarometer Device used to measureatmospheric pressure.Mercury flows out of thetube until the pressureof the column ofmercury standing on thesurface of the mercuryin the dish is equal tothe pressure of the airon the rest of thesurface of the mercuryin the dish.Copyright Cengage Learning. All rights reserved5

Section 13.1PressureManometer Device used formeasuring thepressure of a gasin a container.Copyright Cengage Learning. All rights reserved6

Section 13.1PressureCollapsing CanCopyright Cengage Learning. All rights reserved7

Section 13.1PressurePressure Conversions: An ExampleThe pressure of a gas is measured as 2.5atm. Represent this pressure in both torrand pascals.Where are we going? We want to convert from units of atm to unitsof torr and units of pascals.What do we know? 2.5 atmWhat information do we need? Equivalence statements for the units.Copyright Cengage Learning. All rights reserved8

Section 13.1PressurePressure Conversions: An ExampleThe pressure of a gas is measured as 2.5atm. Represent this pressure in both torrand pascals.How do we get there?æ 760 torr ö3 1.9 10torr(2.5 atm ) ç è 1 atm øæ 101,325 Pa ö52.5atm 2.5 10Pa() ç è 1 atm øCopyright Cengage Learning. All rights reserved9

Section 13.1PressureExerciseThe vapor pressure over a beaker of hot water ismeasured as 656 torr. What is this pressure inatmospheres?a)b)c)d)1.16 atm0.863 atm0.756 atm0.500 atm656 torr Copyright Cengage Learning. All rights reserved1 atm 0.863 atm760 atm10

Section 13.2Pressure and Volume: Boyle’s LawRobert Boyle’s ExperimentCopyright Cengage Learning. All rights reserved11

Section 13.2Pressure and Volume: Boyle’s LawA Sample of Boyle’s ObservationsCopyright Cengage Learning. All rights reserved12

Section 13.2Pressure and Volume: Boyle’s LawGraphing Boyle’s ResultsCopyright Cengage Learning. All rights reserved13

Section 13.2Pressure and Volume: Boyle’s LawBoyle’s Law Pressure and volume are inversely related(constant T, temperature, and n, # of moles ofgas).PV k (k is a constant for a given sample of air ata specific temperature)P1 V1 P2 V2Copyright Cengage Learning. All rights reserved14

Section 13.2Pressure and Volume: Boyle’s LawExerciseA sample of helium gas occupies 12.4 L at23 C and 0.956 atm. What volume will itoccupy at 1.20 atm assuming that thetemperature stays constant?9.88 LP1V1 P2V2(0.956 atm) (12.4 L) (1.20 atm) (V2)V2 9.88 LCopyright Cengage Learning. All rights reserved15

Section 13.3Volume and Temperature: Charles’s LawGraphing Data forSeveral GasesCopyright Cengage Learning. All rights reserved16

Section 13.3Volume and Temperature: Charles’s LawGraphing Data for Several Gases It is easier to write an equation for the relationshipif the lines intersect the origin of the graph. Use absolute zero for the temperature.Copyright Cengage Learning. All rights reserved17

Section 13.3Volume and Temperature: Charles’s LawCharles’s Law Volume and Temperature (in Kelvin) aredirectly related (constant P and n).V bT (b is a proportionality constant)K C 2730 K is called absolute zero.V1 V2 T1 T2Copyright Cengage Learning. All rights reserved18

Section 13.3Volume and Temperature: Charles’s LawExerciseSuppose a balloon containing 1.30 L of air at24.7 C is placed into a beaker containing liquidnitrogen at –78.5 C. What will the volume of thesample of air become (at constant pressure)?0.849 LV1V2 T1T2(V2 )(1.30 L) (24.7 273 K)( - 78.5 273 K)V2 0.849 LCopyright Cengage Learning. All rights reserved19

Section 13.4Volume and Moles: Avogadro’s LawThe Relationship Between Volume and MolesCopyright Cengage Learning. All rights reserved20

Section 13.4Volume and Moles: Avogadro’s LawAvogadro’s Law Volume and number of moles are directlyrelated (constant T and P).V an (a is a proportionality constant)n1n2 V1V2Copyright Cengage Learning. All rights reserved21

Section 13.4Volume and Moles: Avogadro’s LawExerciseIf 2.45 mol of argon gas occupies a volume of 89.0 L,what volume will 2.10 mol of argon occupy under thesame conditions of temperature and pressure?76.3 LV1V 2n1n2V289.0 L 2.45 mol2.10 molV2 76.3 LCopyright Cengage Learning. All rights reserved22

Section 13.5The Ideal Gas Law We can bring all of these laws togetherinto one comprehensive law: V bT (constant P and n) V an (constant T and P) V k (constant T and n)PPV nRT(where R 0.08206 L·atm/mol·K, theuniversal gas constant)Copyright Cengage Learning. All rights reserved23

Section 13.5The Ideal Gas LawExerciseAn automobile tire at 23 C with an internal volumeof 25.0 L is filled with air to a total pressure of 3.18atm. Determine the number of moles of air in the tire.3.27 moln PV(3.18 atm)(25.0 L) 3.27 molL atmRT(0.08206)(23 273 K)mol KCopyright Cengage Learning. All rights reserved24

Section 13.5The Ideal Gas LawExerciseWhat is the pressure in a 304.0 L tank that contains5.670 kg of helium at 25 C?114 atmæ1000 g1 mol He ö æL atm ö5.670kgHe 0.08206 (25 273 K )ç ç1kg4.003gHemolKnRTèøøP è 114 atmV(304.0 L )Copyright Cengage Learning. All rights reserved25

Section 13.5The Ideal Gas LawExerciseAt what temperature (in C) does 121 mL of CO2at 27 C and 1.05 atm occupy a volume of 293 mLat a pressure of 1.40 atm?696 CP1V1T1 P2 V2T2 (1.05 atm)(121 mL)(27 273 K) (1.40 atm)(293 mL)T2T2 969 K - 273 696 CCopyright Cengage Learning. All rights reserved26

Section 13.6Dalton’s Law of Partial Pressures For a mixture of gases in a container,PTotal P1 P2 P3 . . . The total pressure exerted is the sum ofthe pressures that each gas would exert ifit were alone.Copyright Cengage Learning. All rights reserved27

Section 13.6Dalton’s Law of Partial Pressures The pressure of the gas is affected by thenumber of moles of particles present.The pressure is independent of the nature of theparticles.Copyright Cengage Learning. All rights reserved28

Section 13.6Dalton’s Law of Partial PressuresTwo Crucial Things We Learn From This Are: The volume of the individual particles is notvery important.The forces among the particles must notbe very important.Copyright Cengage Learning. All rights reserved29

Section 13.6Dalton’s Law of Partial PressuresCollecting a Gas Over Water Total pressure is the pressure of the gas thevapor pressure of the water.Copyright Cengage Learning. All rights reserved30

Section 13.6Dalton’s Law of Partial PressuresCollecting a Gas Over Water How can we find thepressure of the gascollected alone?Copyright Cengage Learning. All rights reserved31

Section 13.6Dalton’s Law of Partial PressuresExerciseConsider the following apparatus containing heliumin both sides at 45 C. Initially the valve is closed. After the valve is opened, what is the pressureof the helium gas?P 2.25 atmCopyright Cengage Learning. All rights reserved32

Section 13.6Dalton’s Law of Partial PressuresExercise27.4 L of oxygen gas at 25.0 C and 1.30atm, and 8.50 L of helium gas at 25.0 Cand 2.00 atm were pumped into a tank witha volume of 5.81 L at 25 C. Calculate the new partial pressure of oxygen.6.13 atm Calculate the new partial pressure of helium.2.93 atm Calculate the new total pressure of both gases.9.06 atmCopyright Cengage Learning. All rights reserved33

Section 13.7Laws and Models: A ReviewScientific Method A law is a generalization of observedbehavior.Laws are useful – We can predict behaviorof similar systems.Copyright Cengage Learning. All rights reserved34

Section 13.7Laws and Models: A Review A model can never be proved absolutelytrue.A model is an approximation and isdestined to be modified.Copyright Cengage Learning. All rights reserved35

Section 13.8The Kinetic Molecular Theory of Gases So far we have considered “whathappens,” but not “why.”In science, “what” always comes before“why.”Copyright Cengage Learning. All rights reserved36

Section 13.8The Kinetic Molecular Theory of GasesPostulates of the Kinetic Molecular Theory1. Gases consist of tiny particles (atoms ormolecules).Copyright Cengage Learning. All rights reserved37

Section 13.8The Kinetic Molecular Theory of GasesPostulates of the Kinetic Molecular Theory2. The particles are so small, comparedwith the distances between them that thevolume (size) of the individual particlescan be assumed to be negligible (zero).Copyright Cengage Learning. All rights reserved38

Section 13.8The Kinetic Molecular Theory of GasesPostulates of the Kinetic Molecular Theory3. The particles are in constant randommotion, colliding with the walls of thecontainer. These collisions with the wallscause the pressure exerted by the gas.Copyright Cengage Learning. All rights reserved39

Section 13.8The Kinetic Molecular Theory of GasesPostulates of the Kinetic Molecular Theory4. The particles are assumed not to attractor to repel each other.Copyright Cengage Learning. All rights reserved40

Section 13.8The Kinetic Molecular Theory of GasesPostulates of the Kinetic Molecular Theory5. The average kinetic energy of the gasparticles is directly proportional to theKelvin temperature of the gas.Copyright Cengage Learning. All rights reserved41

Section 13.9The Implications of the Kinetic Molecular Theory Meaning of temperature Kelvin temperature is directly proportional to theaverage kinetic energy of the gas particles.Relationship between Pressure and Temperature Gas pressure increases as the temperatureincreases because the particles speed up.Relationship between Volume and Temperature Volume of a gas increases with temperaturebecause the particles speed up.Copyright Cengage Learning. All rights reserved42

Section 13.9The Implications of the Kinetic Molecular TheoryConcept CheckYou are holding twoballoons of the samevolume. One containshelium, and one containshydrogen. Complete each ofthe following statementswith “different” or “thesame” and be prepared tojustify your answer.Copyright Cengage Learning. All rights reservedHeH243

Section 13.9The Implications of the Kinetic Molecular TheoryConcept Check Complete the followingstatement with “different”or “the same” and beprepared to justify youranswer. The pressures of the gasin the two balloons arethe same.Copyright Cengage Learning. All rights reservedHeH244

Section 13.9The Implications of the Kinetic Molecular TheoryConcept Check Complete the followingstatement with “different”or “the same” and beprepared to justify youranswer. The temperatures of thegas in the two balloons arethe same.Copyright Cengage Learning. All rights reservedHeH245

Section 13.9The Implications of the Kinetic Molecular TheoryConcept Check Complete the followingstatement with “different”or “the same” and beprepared to justify youranswer. The numbers of moles ofthe gas in the two balloonsthe sameare .Copyright Cengage Learning. All rights reservedHeH246

Section 13.9The Implications of the Kinetic Molecular TheoryConcept Check Complete the followingstatement with “different”or “the same” and beprepared to justify youranswer. The densities of the gas inthe two balloons aredifferent.Copyright Cengage Learning. All rights reservedHeH247

Section 13.9The Implications of the Kinetic Molecular TheoryConcept CheckSketch a graph of:I.Pressure versus volume at constanttemperature and moles.Copyright Cengage Learning. All rights reserved48