chapter 5: gases

78
Copyright © 2011 Pearson Education, I \ CHAPTER 5 GASES

Upload: ducklingduck

Post on 18-Nov-2015

23 views

Category:

Documents


2 download

DESCRIPTION

Chemistry

TRANSCRIPT

  • 2009, Prentice-Hall, Inc.ManometerThe pressure of a gas trapped in a container can be measured with an instrument called a manometer

    The difference in the liquid levels is a measure of the difference in pressure between the gas and the atmosphere

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    Variables Affecting Gas Pressurevolume of containerif volume , pressure pressure and volume are inversely related volume gas molecules further apart and collide less frequently, so pressurevice versa

    *

    Copyright 2011 Pearson Education, Inc.

    Variables Affecting Gas Pressuretemperature of gasif temperature , pressuretemperature and pressure are directly related temperature, gas molecules move faster and collide with a greater frequency and energy, so pressure

    *

    Copyright 2011 Pearson Education, Inc.

    Boyles Lawpressure - volume changes

    volume (V) of a gas is inversely proportional to pressure (P), when temperature (T) remains constant

    as one variable increases, other decreases

    Pi Vi = Pf Vf (i: initial and f: final)

    *

    Copyright 2011 Pearson Education, Inc.

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Boyles Law: A Molecular ViewPressure is caused by the molecules striking the sides of the containerWhen you decrease the volume of the container with the same number of molecules in the container, more molecules will hit the wall at the same instantThis results in increasing the pressure

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    *Boyles Law and DivingScuba tanks have a regulator so that the air from the tank is delivered at the same pressure as the water surrounding you.This allows you to take in air even when the outside pressure is large.Tro: Chemistry: A Molecular Approach, 2/eBecause water is more dense than air, for each 10 m you dive below the surface, the pressure on your lungs increases 1 atmat 20 m the total pressure is 3 atmIf your tank contained air at 1 atm of pressure, you would not be able to inhale it into your lungsyou can only generate enough force to overcome about 1.06 atm

    Copyright 2011 Pearson Education, Inc.

    A 1.50 L sample of gas exerts a pressure of 5.00 atm. Calculate the final volume if the pressure changed to 3.00 atm.

    A balloon is put in a bell jar and the pressure is reduced from 782 torr to 0.500 atm. If the volume of the balloon is now 2.78 x 103 mL, what was it originally?*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Charless Lawvolume- temperature changesV of a gas is directly proportional to the Kelvin T, at constant P

    as one variable increases, other increases

    Vi = Vf

    Ti Tf

    *

    Copyright 2011 Pearson Education, Inc.

    If the lines are extrapolated back to a volume of 0, they all show the same temperature, 273.15 C, called absolute zeroIf you plot volume vs. temperature for any gas at constant pressure, the points will all fall on a straight line*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    The pressure of gas inside and outside the balloon are the sameAt high temperatures, the gas molecules are moving faster, so they hit the sides of the balloon harder causing the volume to become larger

    Charless Law A Molecular ViewThe pressure of gas inside and outside the balloon are the sameAt low temperatures, the gas molecules are not moving as fast, so they dont hit the sides of the balloon as hard therefore the volume is small

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    A 250 L balloon is heated from 25C to 40C. Calculate the final volume, assuming P is constant.

    The temperature inside a balloon is raised from 25.0 C to 250.0 C. If the volume of cold air was 10.0 L, what is the volume of hot air? *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Avogadros Law*Tro: Chemistry: A Molecular Approach, 2/eWhen pressure and temperature are constant, the volume is directly proportional to the number of gas moleculesV = constant x nmore moles of gas = larger volumeEqual volumes of gases contain equal numbers of moleculesthe gas doesnt matter

    *

    Copyright 2011 Pearson Education, Inc.

    *If 1.00 mole of a gas occupies 22.4 L at STP, what volume would 0.750 moles occupy?

    A 0.225 mol sample of He has a volume of 4.65 L. How many moles must be added to give 6.48 L?Tro: Chemistry: A Molecular Approach, 2/e

    Copyright 2011 Pearson Education, Inc.

    By combining the gas laws we can write a general equation

    PV = nRT

    P: pressure (atm)V: volume (L)n: # molesR: ideal gas constant (0.08206 atmL / molK)T: temperature (K)Ideal Gas Law*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    How many moles of gas are in a basketball with total pressure 24.3 psi, volume of 3.24 L at 25C?

    What is the volume in Liters of 5.4 moles of O3 (ozone) at 290 K and 1.5 atm of pressure?

    *

    *

    Copyright 2011 Pearson Education, Inc.

    Standard ConditionsBecause the volume of a gas varies with pressure and temperature, chemists have agreed on a set of conditions to report our measurements so that comparison is easy we call these standard conditions

    STP = Standard Temperature and Pressure

    Standard pressure = 1 atmStandard temperature = 273 K0 C

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    A gas occupies 10.0 L at 44.1 psi and 27 C. What volume will it occupy at standard conditions?

    What mass of CO2 occupies a volume of 2.15 L at STP?

    How many molecules of Cl2 (chlorine gas) occupy 1.25 L at STP?*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Molar VolumeSolving the ideal gas equation for the volume of 1 mol of gas at STP gives 22.4 L6.022 x 1023 molecules of gasnotice: the gas is immaterial

    We call the volume of 1 mole of gas at STP the molar volumeit is important to recognize that one mole measures of different gases have different masses, even though they have the same volume

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Molar Volume*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Sample Problems4 Al (s) + 3 O2 (g) 2 Al2O3 (s)How many L of O2 are required to react with 50.0 g of Al at STP?

    2 NaN3 (s) 2 Na (s) + 3 N2 (g)How many g of NaN3 are required to produce 50.0 L of N2 at STP?

    *

    Copyright 2011 Pearson Education, Inc.

    Density at Standard ConditionsDensity is the ratio of mass to volumeDensity of a gas is generally given in g/LThe mass of 1 mole = molar massThe volume of 1 mole at STP = 22.4 L

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Calculate the density of N2(g) at STP*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.Densities of GasesIf we divide both sides of the ideal-gas equation by V and by RT, we get

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.We know thatmoles molar mass = mass

    Densities of GasesSo multiplying both sides by the molar mass ( ) gives

    n = m

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.Densities of GasesMass volume = density

    So,

    Note: One only needs to know the molecular mass, the pressure, and the temperature to calculate the density of a gas.

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.Molecular MassWe can manipulate the density equation to enable us to find the molecular mass of a gas:Becomes

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    PracticeCalculate the density of ozone, O3 at 50C and 1330 Torr of pressure.

    A 15.5 gram sample of an unknown gas occupied a volume of 5.75 L at 25C and a pressure of 1.08 atm. Calculate its molar mass.

    Calculate the density of N2 at 125C and 755 mmHg.

    *

    Copyright 2011 Pearson Education, Inc.

    Mixtures of GasesWhen gases are mixed together, their molecules behave independent of each otherall the gases in the mixture have the same volumeeach gass volume = the volume of the containersame temperaturesame average kinetic energyThe mixture can be thought of as one gaswe can measure the pressure, volume, and temperature of air as if it were a pure substancewe can calculate the total moles of molecules in an air sample, knowing P, V, and T, even though they are different molecules

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    *Composition of Dry AirTro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Partial PressureThe pressure of a single gas in a mixture of gases is called its partial pressureWe can calculate the partial pressure of a gas ifwe know what fraction of the mixture it composes and the total pressureor, we know the number of moles of the gas in a container of known volume and temperatureThe sum of the partial pressures of all the gases in the mixture equals the total pressureDaltons Law of Partial Pressuresbecause the gases behave independently

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    The partial pressure of each gas in a mixture can be calculated using the ideal gas law*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Find the partial pressure of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe. *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Mole Fraction*The fraction of the total pressure that a single gas contributes is equal to the fraction of the total number of moles that a single gas contributesThe ratio of the moles of a single component to the total number of moles in the mixture is called the mole fraction, cfor gases, = volume % / 100%The partial pressure of a gas is equal to the mole fraction of that gas times the total pressureTro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Find the mole fraction of neon in a mixture with total pressure 3.9 atm, volume 8.7 L, temperature 598 K, and 0.17 moles Xe

    Find the mole fractions and partial pressures in a 12.5 L tank with 24.2 g He and 4.32 g O2 at 298 K *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Collecting Gases*Tro: Chemistry: A Molecular Approach, 2/eGases are often collected by having them displace water from a containerThe problem is that because water evaporates, there is also water vapor in the collected gasThe partial pressure of the water vapor, called the vapor pressure, depends only on the temperature so you can use a table to find out the partial pressure of the water vapor in the gas you collectif you collect a gas sample with a total pressure of 758.2 mmHg* at 25 C, the partial pressure of the water vapor will be 23.78 mmHg so the partial pressure of the dry gas will be 734.4 mmHg Table 5.4*

    *

    Copyright 2011 Pearson Education, Inc.

    Collecting Gas by Water Displacement*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    *Vapor Pressure of WaterTro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    1.02 L of O2 collected over water at 293 K with a total pressure of 755.2 mmHg. Find mass O2.

    0.12 moles of H2 is collected over water in a 10.0 L container at 323 K. Find the total pressure.*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Reactions Involving Gases*P, V, T of Gas A

    mole A

    mole B

    P, V, T of Gas BTro: Chemistry: A Molecular Approach, 2/eThe principles of reaction stoichiometry from Chapter 4 can be combined with the gas laws for reactions involving gasesIn reactions of gases, the amount of a gas is often given as a volumeinstead of molesas weve seen, you must state pressure and temperatureThe ideal gas law allows us to convert from the volume of the gas to moles; then we can use the coefficients in the equation as a mole ratioWhen gases are at STP, use 1 mol = 22.4 L

    *

    Copyright 2011 Pearson Education, Inc.

    What volume of H2 is needed to make 35.7 g of CH3OH at 738 mmHg and 355 K?CO(g) + 2 H2(g) CH3OH(g)

    What volume of O2 at 0.750 atm and 313 K is generated by the thermolysis of 10.0 g of HgO?2 HgO(s) 2 Hg(l) + O2(g) How many grams of H2O form when 1.24 L H2 reacts completely with O2 at STP?O2(g) + 2 H2(g) 2 H2O(g)*Tro: Chemistry: A Molecular Approach, 2/e

    *

  • 2009, Prentice-Hall, Inc.Kinetic-Molecular TheoryThis is a model that aids in our understanding of what happens to gas particles as environmental conditions change.

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.Main Tenets of Kinetic-Molecular TheoryGases consist of large numbers of molecules that are in continuous, random motion.

    The combined volume of all the molecules of the gas is negligible relative to the total volume in which the gas is contained.

    Attractive and repulsive forces between gas molecules are negligible.

    2009, Prentice-Hall, Inc.*

  • 2009, Prentice-Hall, Inc.Main Tenets of Kinetic-Molecular TheoryEnergy can be transferred between molecules during collisions, but the average kinetic energy of the molecules does not change with time, as long as the temperature of the gas remains constant.

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.Main Tenets of Kinetic-Molecular TheoryThe average kinetic energy of the molecules is proportional to the absolute temperature.

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    Kinetic Energy and Molecular VelocitiesAverage kinetic energy of the gas molecules depends on the average mass and velocityKE = mv2Gases in the same container have the same temperature, therefore they have the same average kinetic energyIf they have different masses, the only way for them to have the same kinetic energy is to have different average velocitieslighter particles will have a faster average velocity than more massive particles

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Molecular Speed vs. Molar MassTo have the same average kinetic energy, heavier molecules must have a slower average speed

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Temperature and Molecular Velocities _KEavg = NAmu2NA is Avogadros numberKEavg = 1.5RTR is the gas constant in energy units, 8.314 J/molK1 J = 1 kgm2/s2Equating and solving we getNAmass = molar mass in kg/mol

    * As temperature increases, the average velocity increases

    Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Molecular VelocitiesAll the gas molecules in a sample can travel at different speedsHowever, the distribution of speeds follows a statistical pattern called a Boltzman distributionThere are different ways to find the average velocitymethod of choice is called the root-mean-square method, where the rms average velocity, urms, is the square root of the average of the sum of the squares of all the molecule velocities

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Boltzman Distribution*Tro: Chemistry: A Molecular Approach, 2/e

    Chart1

    00

    0.00028940840.0005312498

    0.00115207740.0021097187

    0.00257147170.0046901143

    0.00452047230.0081987527

    0.0069620230.0125361805

    0.00985000810.0175806809

    0.01313033580.0231925112

    0.0167421960.029218688

    0.02061945530.0354981186

    0.02469215050.0418668646

    0.02888803880.0481633256

    0.0331341610.0542331445

    0.03735837830.0599336511

    0.04149084050.0651376937

    0.04546535180.0697367396

    0.04922060020.0736431641

    0.05270122510.0767916872

    0.05585870110.0791399567

    0.05865202420.0806683122

    0.06104819120.0813787977

    0.06302247150.0812935175

    0.06455847470.0804524502

    0.06564802360.0789108482

    0.06629084830.0767363588

    0.06649412060.074005999

    0.06627184890.0708031121

    0.06564416180.0672144209

    0.06463650360.0633272773

    0.063278770.0592271874

    0.06160441080.0549956731

    0.05964952340.0507085086

    0.0574519620.0464343513

    0.05505048270.0422337672

    0.0524839430.038158635

    0.04979057090.0342519009

    0.04700731440.0305476442

    0.04416928140.0270714078

    0.04130927310.0238407436

    0.03845741360.0208659214

    0.03564087570.018150752

    0.03288369780.0156934772

    0.03020668690.013487685

    0.02762740070.0115232146

    0.02516020050.0097870213

    0.02281636350.0082639788

    0.02060424690.0069376015

    0.01852949160.0057906786

    0.01659525750.0048058125

    0.01480247850.0039658624

    0.01315013080.0032542969

    0.01163550480.0026554598

    0.01025447430.0021547596

    0.00900175760.0017387901

    0.00787116440.0013953938

    0.00685582550.0011136764

    0.00594840290.0008839844

    0.00514127690.0006978526

    0.0044267120.0005479311

    0.00379699760.0004278983

    0.00324456770.0003323656

    0.0027620980.0002567798

    0.00234258250.0001973253

    0.00197939160.0001508305

    0.00166631360.0001146799

    0.001397580.0000867329

    0.00116787950.0000652507

    0.00097235980.0000488312

    0.00080662090.0000363519

    0.0006667010.0000269203

    0.00054905680.0000198317

    Low Molar Mass

    High Molar Mass

    molecular speed

    fraction of molecules

    Distribution Function

    Chart2

    0

    0.0002894084

    0.0011520774

    0.0025714717

    0.0045204723

    0.006962023

    0.0098500081

    0.0131303358

    0.016742196

    0.0206194553

    0.0246921505

    0.0288880388

    0.033134161

    0.0373583783

    0.0414908405

    0.0454653518

    0.0492206002

    0.0527012251

    0.0558587011

    0.0586520242

    0.0610481912

    0.0630224715

    0.0645584747

    0.0656480236

    0.0662908483

    0.0664941206

    0.0662718489

    0.0656441618

    0.0646365036

    0.06327877

    0.0616044108

    0.0596495234

    0.057451962

    0.0550504827

    0.052483943

    0.0497905709

    0.0470073144

    0.0441692814

    0.0413092731

    0.0384574136

    0.0356408757

    0.0328836978

    0.0302066869

    0.0276274007

    0.0251602005

    0.0228163635

    0.0206042469

    0.0185294916

    0.0165952575

    0.0148024785

    0.0131501308

    0.0116355048

    0.0102544743

    0.0090017576

    0.0078711644

    0.0068558255

    0.0059484029

    0.0051412769

    0.004426712

    0.0037969976

    0.0032445677

    0.002762098

    0.0023425825

    0.0019793916

    0.0016663136

    0.00139758

    0.0011678795

    0.0009723598

    0.0008066209

    0.000666701

    0.0005490568

    O2 @ 300 K

    Molecular Speed

    Fraction of Molecules

    Distribution Function

    Sheet1

    1.38E-231.00E+058.314323000.0020419158-0.00641488250.9983975646

    485000.0030628736-0.0096223238

    0.0012251495-0.0038489295

    SpeedLow Molar MassHigh Molar Mass0.0018377242-0.0057733943

    00000

    5.00E-012.89E-040.00053124980.00028940840.0001345909

    1.00E+001.15E-030.00210971870.00115207740.0005368116

    1.50E+002.57E-030.00469011430.00257147170.001202029

    2.00E+004.52E-030.00819875270.00452047230.0021225952

    2.50E+006.96E-030.01253618050.0069620230.0032879574

    3.00E+009.85E-030.01758068090.00985000810.0046848087

    3.50E+001.31E-020.02319251120.01313033580.0062972776

    4.00E+001.67E-020.0292186880.0167421960.0081071526

    4.50E+002.06E-020.03549811860.02061945530.0100941378

    5.00E+002.47E-020.04186686460.02469215050.0122361349

    5.50E+002.89E-020.04816332560.02888803880.0145095482

    6.00E+003.31E-020.05423314450.0331341610.0168896049

    6.50E+003.74E-020.05993365110.03735837830.0193506874

    7.00E+004.15E-020.06513769370.04149084050.0218666712

    7.50E+004.55E-020.06973673960.04546535180.0244112629

    8.00E+004.92E-020.07364316410.04922060020.0269583332

    8.50E+005.27E-020.07679168720.05270122510.0294822396

    9.00E+005.59E-020.07913995670.05585870110.0319581338

    9.50E+005.87E-020.08066831220.05865202420.0343622498

    1.00E+016.10E-020.08137879770.06104819120.0366721679

    1.05E+016.30E-020.08129351750.06302247150.038867052

    1.10E+016.46E-020.08045245020.06455847470.0409278573

    1.15E+016.56E-020.07891084820.06564802360.0428375051

    1.20E+016.63E-020.07673635880.06629084830.0445810247

    1.25E+016.65E-020.0740059990.06649412060.04614566

    1.30E+016.63E-020.07080311210.06627184890.0475209416

    1.35E+016.56E-020.06721442090.06564416180.0486987241

    1.40E+016.46E-020.06332727730.06463650360.0496731894

    1.45E+016.33E-020.05922718740.063278770.0504408182

    1.50E+016.16E-020.05499567310.06160441080.0510003311

    1.55E+015.96E-020.05070850860.05964952340.0513526014

    1.60E+015.75E-020.04643435130.0574519620.051500543

    1.65E+015.51E-020.04223376720.05505048270.0514489763

    1.70E+015.25E-020.0381586350.0524839430.0512044746

    1.75E+014.98E-020.03425190090.04979057090.0507751957

    1.80E+014.70E-020.03054764420.04700731440.0501707013

    1.85E+014.42E-020.02707140780.04416928140.0494017674

    1.90E+014.13E-020.02384074360.04130927310.0484801903

    1.95E+013.85E-020.02086592140.03845741360.04741859

    2.00E+013.56E-020.0181507520.03564087570.0462302157

    2.05E+013.29E-020.01569347720.03288369780.0449287547

    2.10E+013.02E-020.0134876850.03020668690.0435281486

    2.15E+012.76E-020.01152321460.02762740070.0420424182

    2.20E+012.52E-020.00978702130.02516020050.0404855

    2.25E+012.28E-020.00826397880.02281636350.038871095

    2.30E+012.06E-020.00693760150.02060424690.0372125318

    2.35E+011.85E-020.00579067860.01852949160.035522645

    2.40E+011.66E-020.00480581250.01659525750.0338136688

    2.45E+011.48E-020.00396586240.01480247850.0320971473

    2.50E+011.32E-020.00325429690.01315013080.0303838606

    2.55E+011.16E-020.00265545980.01163550480.0286837669

    2.60E+011.03E-020.00215475960.01025447430.0270059601

    2.65E+019.00E-030.00173879010.00900175760.0253586419

    2.70E+017.87E-030.00139539380.00787116440.0237491082

    2.75E+016.86E-030.00111367640.00685582550.0221837475

    2.80E+015.95E-030.00088398440.00594840290.0206680524

    2.85E+015.14E-030.00069785260.00514127690.0192066397

    2.90E+014.43E-030.00054793110.0044267120.0178032816

    2.95E+013.80E-030.00042789830.00379699760.0164609429

    3.00E+013.24E-030.00033236560.00324456770.0151818261

    3.05E+012.76E-030.00025677980.0027620980.013967421

    3.10E+012.34E-030.00019732530.00234258250.0128185586

    3.15E+011.98E-030.00015083050.00197939160.0117354672

    3.20E+011.67E-030.00011467990.00166631360.0107178314

    3.25E+011.40E-030.00008673290.001397580.0097648504

    3.30E+011.17E-030.00006525070.00116787950.0088752965

    3.35E+019.72E-040.00004883120.00097235980.0080475733

    3.40E+018.07E-040.00003635190.00080662090.0072797709

    3.45E+016.67E-040.00002692030.0006667010.0065697196

    3.50E+015.49E-040.00001983170.00054905680.0059150404

    Sheet2

    Sheet3

    *

    Copyright 2011 Pearson Education, Inc.

    Temperature vs. Molecular SpeedAs the absolute temperature increases, the average velocity increasesthe distribution function spreads out, resulting in more molecules with faster speeds

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Calculate the rms velocity of O2 at 25 C*Tro: Chemistry: A Molecular Approach, 2/eCalculate the rms velocity of CH4 (MM 16.04) at 25 C

    *

    Copyright 2011 Pearson Education, Inc.

    Mean Free PathMolecules in a gas travel in straight lines until they collide with another molecule or the containerThe average distance a molecule travels between collisions is called the mean free pathMean free path decreases as the pressure increases

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Diffusion and EffusionThe process of a collection of molecules spreading out from high concentration to low concentration is called diffusion

    The process by which a collection of molecules escapes through a small hole into a vacuum is called effusion

    The rates of diffusion and effusion of a gas are both related to its rms average velocity

    For gases at the same temperature, the rate of gas movement is inversely proportional to the square root of its molar mass

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Effusion*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    2009, Prentice-Hall, Inc.EffusionThe difference in the rates of effusion for helium and nitrogen, for example, explains a helium balloon would deflate faster.

    2009, Prentice-Hall, Inc.*

    Copyright 2011 Pearson Education, Inc.

    Grahams Law of EffusionFor two different gases at the same temperature, the ratio of their rates of effusion is given by the following equation:

    *Thomas Graham (18051869) Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    *Calculate the molar mass of a gas that effuses at a rate 0.462 times N2Calculate the ratio of rate of effusion for oxygen to hydrogen

    *

    Copyright 2011 Pearson Education, Inc.

    Ideal vs. Real Gases*Tro: Chemistry: A Molecular Approach, 2/eReal gases often do not behave like ideal gases at high pressure or low temperatureIdeal gas laws assume

    1.no attractions between gas molecules2.gas molecules do not take up spacebased on the kinetic-molecular theoryAt low temperatures and high pressures these assumptions are not valid

    *

    Copyright 2011 Pearson Education, Inc.

    Real Gas BehaviorBecause real molecules take up space, the molar volume of a real gas is larger than predicted by the ideal gas law at high pressures

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    The Effect of Molecular VolumeAt high pressure, the amount of space occupied by the molecules is a significant amount of the total volumeThe molecular volume makes the real volume larger than the ideal gas law would predictvan der Waals modified the ideal gas equation to account for the molecular volumeb is called a van der Waals constant and is different for every gas because their molecules are different sizes

    *Johannes van der Waals (18371923) Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Real Gas BehaviorBecause real molecules attract each other, the molar volume of a real gas is smaller than predicted by the ideal gas law at low temperatures

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    The Effect of Intermolecular AttractionsAt low temperature, the attractions between the molecules is significantThe intermolecular attractions makes the real pressure less than the ideal gas law would predictvan der Waals modified the ideal gas equation to account for the intermolecular attractionsa is another van der Waals constant and is different for every gas because their molecules have different strengths of attraction

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    van der Waals EquationCombining the equations to account for molecular volume and intermolecular attractions we get the following equationused for real gases

    a = correction factor for the interaction between atoms/gas molecules.Attractive + repulsive forces.b = correction factor for the volume occupied by atoms/gas molecules.

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    Real GasesA plot of PV/RT vs. P for 1 mole of a gas shows the difference between real and ideal gases

    It reveals a curve that shows the PV/RT ratio for a real gas is generally lower than ideal for low pressures meaning the most important factor is the intermolecular attractions

    It reveals a curve that shows the PV/RT ratio for a real gas is generally higher than ideal for high pressures meaning the most important factor is the molecular volume

    *Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    PV/RT Plots*Tro: Chemistry: A Molecular Approach, 2/e

    *

    Copyright 2011 Pearson Education, Inc.

    van der Waals Equation 1If sulfur dioxide were an ideal gas, the pressure at 0C exerted by 1.000 mol occupying 22.41 L would be 1.000 atm. Use the van der Waals equation to estimate the real pressure.What would be the real pressure using the van der Waals equation?Given: a = 6.865 L2atm/mol2, b = 0.05679 L/mol

    *

    *

    **

    *

    *picture from Tro Intro Chem 2nd ed.*

    *

    *

    **

    *

    *

    *

    **

    *

    *

    **

    *

    *

    *

    *

    *

    *

    *

    *

    *

    **

    *

    *

    *

    *

    *

    **

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *

    *