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Properties of Gases

CHAPTER 11 Chemistry: The Molecular Nature of Matter, 6th editionBy Jesperson, Brady, & Hyslop

1Describe properties of a gasRead a barometer & monometerUnit conversions for moles, temperature, pressure, and volumeExplain relationships between variables of state & predict effect of a change to a systemApply gas law to stoichiometry, molecular weight, and density problemsUnderstand the relationship between variables of state in terms of Kinetic Molecular TheoryCalculate mole fractions and partial pressuresCompare rates of effusionCompute variables of state using the real gas lawCHAPTER 11 Learning Objectives2 What is a gas?Define & measure variables of stateRelationships between variables of stateEquation of state for an ideal gasDaltons law of partial pressure & gas stoichiometryKinetic Molecular Theory & Grahams lawReal gas lawCHAPTER 11 Lecture Road Map3CHAPTER 11Properties of GasesIdeal Gas LawKinetic Molecular TheoryReal Gas LawVariables of StateDaltons LawGrahams LawAbsolute 0Relationships between variables of statePressureVolumeBoyles LawCharles LawGuy-LussacsLawAvagadrosLawMole Fraction& Mole %Pressure:Barometers & MonometersTemperature:K, C, F4GroupProblemIn groups of 3-5 brainstorm how to describe a gas.

What are some observable properties?

What variables would you use to describe a gas?5GroupProblemDescribe a gas:

Will expand to fill a volumeMostly empty space so can be compressedCan expand & contract with temperatureParticles constantly in motion & constantly collidingSome gases are heavier then others and sink to the floor rather then rise to the ceiling

6Variables of StatePhysical Properties of GasesPressure (P )

Volume (V )

Temperature (T )

Amount = moles (n) Despite wide differences in chemical properties, all gases more or less obey the same set of physical properties7Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EVariables of StateVolume (V)V = l w h for a cube

V = (4/3) r3 for a sphere

V = r2 h for a cylinderUnits of Volume: Liters (L)

1 L = 0.001 m3= 1000 cm3= 1000 mL

8Variables of State# of Moles (n) Avagadros number (NA) allows us to measure the number of particles of a gas as the number of moles:

NA = 6.02214129 1023 particles/mole

We can measure the number of moles of a gas by measuring its mass and knowing its Molar Mass

Molar Mass = mass / (# of moles)

M = m/n

9Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem10How many moles of the CFC pollutant CCl2F2 are in 50.0g? GroupProblem11

CH3CH2Calculate the mass of 3 moles of nerve agent VX:Variables of StateTemperature (T)Temperature is measured with a thermometer usually in C, F, or Kelvin.

0C = 273 K

1C = (1F -32) (5/9)12GroupProblemIf Room Temperature (RT) is 25C, what is RT in Kelvin? F?Write out a formula to convert F to K.13GroupProblemIf Room Temperature (RT) is 25C, what is RT in Kelvin? F?RT = 25C + 273 K = 298 K14Variables of StatePressure (P)Pressure is the force of the collisions of the gas distributed over the surface area of the container wallsEarth exerts gravitational force on everything with mass near itAtmospheric Pressure of earth: gravity pulling on gases creating a blanket around earth

Force = mass area15Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblemCalculate Atmospheric Pressure on Earth.

Identify information neededResearchSolve16GroupProblemCalculate Atmospheric Pressure on Earth.17Variables of StatePressure (P)A vacuum exerts zero pressure on a containers walls.

18Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EMeasure Atmospheric pressure with a barometer.

Toricelli Barometer: Tube that is 80 cm in lengthSealed at one endFilled with mercuryIn dish filled with mercury

Variables of StatePressure (P)19Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EChapter 11. Properties of Gases19Atmospheric pressure Pushes down on mercuryForces mercury up tubeWeight of mercury in tubePushes down on mercury in dishWhen two forces balanceMercury level stabilizesRead atmospheric pressure

Variables of StatePressure (P)20Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EChapter 11. Properties of Gases20If atmospheric pressure is highPushes down on mercury in dish & increase level in tube If atmospheric pressure is low Pressure on mercury in dish less than pressure from column & decrease level in tubeTherefore: Height of mercury in tube is the atmospheric pressure

Variables of StatePressure (P)21Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EChapter 11. Properties of Gases21

Variables of StatePressure (P)measured with a barometerP=gdhd=density of the liquidg= gravitational accelerationh=height of the column supported

22Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EChapter 11. Properties of Gases22Variables of StatePressure (P)Typical range of pressure for most places where people live 730 to 760 mm Hg

Top of Mt. Everest Atmospheric Pressure = 250 mm Hg

Standard Atmosphere (atm)Average pressure at sea level Pressure needed to support column of mercury 760 mm high measured at 0 C = 1 atm23Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EVariables of StatePressure (P) SI unit for pressure Pascal = Pa = 1 N/m21atm = 101,325 Pa = 101 kPa100 kPa = 0.9868 atm

Other units of pressure1.013 Bar = 1013 mBar = 1 atm760 mm Hg = 1 atm760 torr = 1 atmAt sea level 1 torr = 1 mm Hg 24Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem25Express Pressure in atm and kPa for a gas at 705 mmHg.

Open Ended ManometerPgas = Patm Pgas > PatmGas pushes mercuryup tube Pgas < PatmAtmosphere pushes mercury down tube Variables of StatePressure (P)26Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem27

CO2 collected in a monometer in a lab with a barometric reading of 97 kPa. What is the Pressure of CO2?33 mmClosed-end ManometerArm farthest from vessel (gas) sealed Tube filled with mercuryThen open system to flask and some mercury drains out of sealed armVacuum exists above mercury in sealed arm

Variables of StatePressure (P)28Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E28Closed-end ManometerLevel of mercury in arm falls, as not enough pressure in the flask to hold up HgPatm = 0Pgas = PHg So directly read pressure

Variables of StatePressure (P)29Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E29GroupProblem30

Closed monometer437 mm205 mmWhat is the pressure of an unknown gas within this closed monometer?Ideal Gas LawBoyles Law

Volume will change to equalize pressure with atmosphere is not in a rigid vessel.

V 1/P31Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EIdeal Gas LawCharles LawIf Pressure is constant but freeze a balloon, it decreases in V

32Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EIdeal Gas LawCharles Law

If Pressure is constant but freeze a balloon, it decreases in V V T33Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EIdeal Gas LawGay Lussacs Law

Volume (V ) and number of moles (n) are constant P increases as T increases Showed that gas pressure is directly proportional to absolute temperatureT (K)PLow T, Low PHigh T, High P

34Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EWhat happens to gas pressure when you raise the temperature?

If the container can expand in response to the forceIn a rigid walled containerNo change in pressure is observed because the area increased.Pressure increases because the faster moving molecules hit the walls of the container with greater forceGroupProblem3535Boyles law: Charles Law:Guy-Lussacs Law:

is equivalent to

For any two conditions: Ideal Gas LawCombined Gas Law

36Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EChapter 11. Properties of Gases36

Boyles LawT1 = T2P1V1 = P2V2Charles LawP1 = P2Gay-Lussacs LawV1 = V2

Ideal Gas LawCombined Gas Law37Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem38N2 + H2 NH3

How much H2 at 0C and 0.86 atm do you need to react completely with 750 mL of N2 at 1.5 atm and 20C to form ammonia?

What is the number of moles of ammonium produced if the density of hydrogen is 0.08988 g/L?

Hint: is this equation balanced?GroupProblemA sample of helium gas occupies 500.0 mL at 1.21 atm Calculate the volume of the gas if the pressure is reduced to 491 torrIdeal Gas LawAvagadros LawV n

At standard temperature (273 K) And standard pressure (1 atm)1 mole of any gas will occupy the same volume40Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EWhat happens to gas pressure when you increase the number of molecules in the container?

If a container can expandIn a rigid walled containerNo pressure change is observed.

pressure increases because more molecules hit the walls of the container, thus exert a greater force on the containerGroupProblem4141Pressure is defined as the force of molecular collisions with the walls of the container per unit area.

Ideal Gas LawPutting It All Together

IfthenR is the universal gas constant42Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblemPlug in values of T, V, n and P for 1 mole of gas at STP (1 atm and 0.0 C) T = 0.0 C = 273.15 KP = 1 atmV = 22.4 Ln = 1 mol

R = 0.082057 L atm mol1 K1 43Ideal Gas LawPutting It All Together

IfthenR is the universal gas constantR = 0.0821 (Latm) / (molK) = 8.314 J / (molK) = 8.314 (kgm2) / (s2molK)PV = nRT44Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem45Calculate Molar Volume = the volume 1 mole of any gas occupies at 1 atm and 273 K

GroupProblem46Compare Molar volume at STP to Room Temperature(25C) assuming pressure remains constant47How many liters of N2(g) at 1.00 atm and 25.0 C are produced by the decomposition of 150. g of NaN3?

2NaN3(s) 2Na(s) + 3N2(g)GroupProblemGroupProblem48At what temperature will 1.50 moles of CH4 occupy a 1 L container at 10atm? 48GroupProblemPV = nRT

d = m / V

M = m / n

Write out the ideal gas law in terms of density & then in terms of molar mass49Ideal Gas LawConsidering Density & Molar MassPV = nRT

d = m / V

M = m / n

P (m / d) = nRT

PV = (m / M) RT

RT / P = M / d50Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem51At what temperature will 479.4 g of Br2 occupy a 1 L container at 25 atm? 51GroupProblem522H2O (l) + catalyst + hv 2H2 (g) + O2 (g)

Under the following conditions if 40.53 g of a 1 L Volume of water is split into hydrogen and oxygen gas, what is the volume the gas mixture if collected in a balloon (ignore water vapor)?

T = 25CPatm = 1.025 atmdH2O = 1 g/mLmH2O = 40.53 gDaltons LawPartial PressureFor mixture of non-reacting gases in containerTotal pressure exerted is sum of the individual partial pressures that each gas would exert alonePtotal = Pa + Pb + Pc + Where Pa, Pb, and Pc are the partial pressures Partial pressure Pressure that particular gas would exert if it were alone in container53Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EDaltons LawPartial PressureAssuming each gas behaves ideally partial pressure of each gas can be calculated from ideal gas law

So total pressure is

54Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EDaltons LawPartial PressureRearranging

Or

Where ntotal = na + nb + nc + ntotal = sum of number moles of various gases in mixture

55Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem562H2O (l) + catalyst + hv 2H2 (g) + O2 (g)

With an excess of water (1L) we know that 40.53 g (or 2.25 moles) of water will split. what is the partial pressure of H2 gas and the partial pressure of O2 gas if it is collected in a 25L rigid container (ignore water vapor & change in water volume).

T = 25CPatm = 1.025 atmdH2O = 1 g/mLVH2Ototal = 1LVcontainer = 25LnH2O = 2.25 molesCollected gas pressure must be corrected for water vaporPtotal=Pgas + Vpwater

Daltons LawVapor Pressure5757FIG. 10.11 Collecting a gas over water. As the gas bubbles through the water, water vapor goes into the gas, so the total pressure inside the bottle includes the partial pressure of the water vapor at the temperature of the water.Chem FAQ How can the partial pressure of a gas collected over water be estimated? If the water levels are not the same inside the flask and outside, a correction has to be calculated and applied to the room pressure to obtain the true pressure in the flask. For example, if the water level is higher inside the flask than outside, the pressure in the flask is lower than atmospheric pressure. The difference in levels is in millimeters of water, so this has to be converted to the equivalent in millimeters of mercury before the room pressure is corrected.5832.5 mL of Hydrogen gas is collected over water at 25 C and 755 torr. What is the pressure of dry hydrogen gas? (VP25C = 23.76 mmHg)

GroupProblemCorrect Pt to find the Pdry gas: 755-23.76 torr=731.24 torr 731 torr = PhydrogenGroupProblem592H2O (l) + catalyst + hv 2H2 (g) + O2 (g)

Continuing the previous problem, what is the total pressure of the system if we include water vapor pressure (still ignoring change in volume of water)?

T = 25CPatm = 1.025 atmdH2O = 1 g/mLVH2Ototal = 1LVcontainer = 1.25LmH2O = 40.53 g (that reacts)Daltons LawMole FractionMole Fraction ()Ratio of number moles of given component in mixture to total number moles in mixture

60Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem612H2O (l) + catalyst + hv 2H2 (g) + O2 (g)

Continuing the previous problem, what is mole fraction of water vapor in the system?

T = 25CPatm = 1.025 atmdH2O = 1 g/mLVH2Ototal = 1LVcontainer = 1.25LmH2O = 40.53 g (that reacts)Daltons LawMole FractionIf V and T are constant then, = constant

For mixture of gases in one container

62Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EDaltons LawMole Fraction cancels, leaving

or

63Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EDaltons LawMole FractionPartial pressure of particular component of gaseous mixture Equals mole fraction of that component times total pressure

64Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem65The total pressure of a 1 L container of a room 298K gas mixture is 628 torr. What is the pressure of Cl2 if there are 20 mg of CO2 and 8 mg of Cl2?66Small Group Problems:22.4 L of He at 25 C are heated to 200.C. What is the resulting volume?A sample of fluorine gas occupies 275 mL at 945 torr and 72 C. What is the mass of the sample?What is the density of NO2 at 200 C and 600. torr?What is the molar mass of a gas with a density of 6.7 g/L at -73.C and a pressure of 2.49 atm?A sample of oxygen gas occupies 500.0 mL at 722 torr and 25 C. Calculate the temperature in C if the gas has a volume of 2.53 L at 491 mm Hg.What is the molar mass of a sample of gas if 2.22 g occupies a volume of 5.0 L a 35 C and 769 mm Hg?a.1.3 g/molb.0.015 g/molc.0.090 g/mold. None of theseWhat is the mole fraction of N2 in the atmosphere? 1.000atm Air = .7808 atm N2+ .2095 atm O2+ .0093 atm Ar + .00036 atm CO2Pump 520 mm Hg N2 and 250 mm Hg O2 into an empty gas cylinder. What is the overall pressure of the mixture?Kinetic Molecular Theory5 AssumptionsGas particles are tiny, their V is negligible.

Particles travel in a straight line, in random directions.

0 intermolecular attraction.

Elastic collisions, no Energy is lost.

If KE T, then assume average KE T.67Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblemCompare to observations from beginning of class.Describe the relationships of state variables in terms of Kinetic Molecular Theory:P 1 / VP TV TV n6869Boyles Law

Decrease in V, means gas particles hit wall more oftenIncrease P

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EKinetic Molecular TheoryBoyles Law6970Guy-Lussacs Law

As T increasesKEave increase Speeds of molecules increases Gas particles hit wall more often as V same So P increase

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Kinetic Molecular TheoryGuy-Lussacs Law7071Charles Law:

As T increasesKEave increases Speeds of molecules increasesGas particles hit wall more often as pressure remains the sameSo volume increases

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Kinetic Molecular TheoryCharles Law7172For ideal gas at constant T and P V is directly proportional to n

Kinetic Theory of Gases account for thisAs the number of moles of gas particles increase at same T Holding T and P constantMust V must increase

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EKinetic Molecular TheoryAvagadros Law7273Expected from kinetic theory of gasesAll gas particles are independent of each other Volume of individual particles is unimportantIdentities of gases do not matterConversely, can think of Dalton's Law of Partial Pressures as evidence for kinetic theory of gasesGas particles move in straight lines, neither attracting nor repelling each otherParticles act independentlyOnly way for Dalton's Law to be valid

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EKinetic Molecular TheoryDaltons Theory7374If KEave = 0, then T must = 0.Only way for KEave = 0, is if v = 0 since m 0.When gas molecules stop moving, then gas as cold as it can get Absolute zero

Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EKinetic Molecular TheoryAbsolute 074Kinetic Molecular TheoryDerivation of PV = nRT & Important equations:

PV = nRT

KE = (3/2) RT

75Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EWalk through derivations on the board, give a handout?75Kinetic Molecular TheoryGrahams Law of Effusion

EffusionDiffusionGas mixing through VacuumGases mixing76Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EKinetic Molecular TheoryDerivation of Grahams Law of EffusionWe can describe how fast a gas will effuse

Some Important Equations:

rms =(3RT) / M

(rms)A /(rms)B = (MB /MA)77Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EDefine effusion rate as room mean squared7778

(constant P and T)Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EKinetic Molecular TheoryGrahams Law of Effusion

And dA MM (constant V and n)Therefore, heavier gases effuse slower then lighter gases78GroupProblem79CO2H2O1 mWhich gas will travel the farthest? How far will the CO2 travel down the tube before meeting the gaseous water?Real Gas LawReview AssumptionsKinetic Molecular Theory & Ideal Gas LawReal Gas LawGas particles are tiny, their V is negligible.Particles travel in a straight line, in random directions.0 intermolecular attraction.Elastic collisions, no Energy is lost.If KE T, then assume average KE T.Real gases do not obey the ideal gas law!80Real Gas LawExperimental Data

Gas molecules have finite volumesThey take up spaceLess space of kinetic motionsVmotions < Vcontainer Particles hit walls of container more oftenPressure is higher compared to ideal81Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EDParticles do attract each otherEven weak attractions means they hit walls of container less oftenTherefore, pressure is less than ideal gas

Real Gas LawExperimental Data82Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6E

Real Gas LawExperimental Data83Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EReal Gas LawReview AssumptionsKinetic Molecular Theory & Ideal Gas LawReal Gas LawGas particles are tiny, their V is negligible.Particles travel in a straight line, in random directions.0 intermolecular attraction.Elastic collisions, no Energy is lost.If KE T, then assume average KE T.Gas particles do take up Volume:Vmeas nb

Attractive forces between molecules exist and effect a particles path.Pmeas + [(n2a) / V2]84Real Gas LawVan Der Waals Equation for Real Gases

corrected P corrected Va and b are van der Waal's constantsObtained by measuring P, V, and T for real gases over wide range of conditionsTable X.X. in your textbook.85Jesperson, Brady, Hyslop. Chemistry: The Molecular Nature of Matter, 6EGroupProblem86Use the Real Gas Law to calculate the Vapor Pressure of 1 mole water in a 1 Liter container at the following Temperatures:TPvapor0C75C100C127C427CTc of water is 647K?

86CHAPTER 11Properties of GasesIdeal Gas LawKinetic Molecular TheoryReal Gas LawVariables of StateDaltons LawGrahams LawAbsolute 0Relationships between variables of statePressureVolumeBoyles LawCharles LawGuy-LussacsLawAvagadrosLawMole Fraction& Mole %Pressure:Barometers & MonometersTemperature:K, C, F87