CH104 Chapter 7 Gases Gases & Kinetic Theory Pressure Gas Laws

CH104 CH104 Chapter 7 Chapter 7

GasesGases

Gases & Kinetic TheoryGases & Kinetic Theory

PressurePressure

Gas LawsGas Laws

Elemental states at 25Elemental states at 25ooCC

He

Rn

XeI

KrBrSe

ArClS

NeFO

P

NC

H

Li

Na

Cs

Rb

K

TlHgAuHfLsBa

Fr

PtIrOsReWTa PoBiPb

Be

Mg

Sr

Ca

CdAgZrY PdRhRuTcMoNb

AcRa

ZnCuTiSc NiCoFeMnCrV

In SbSn

Ga Ge

Al

Gd

Cm

Tb

Bk

Sm

Pu

Eu

Am

Nd

U

Pm

Np

Ce

Th

Pr

Pa

Yb

No

Lu

Lr

Er

Fm

Tm

Md

Dy

Cf

Ho

Es

At

Te

As

Si

B

6 - 2

SolidLiquid

Gas

Changes of StateChanges of State

Melting Pt = Melting Pt = Freezing PtFreezing Pt

Boiling PtBoiling Pt

SolidSolid

LiquidLiquid

VaporVapor

CondenseCondenseCondenseCondense

FreezeFreezeFreezeFreezeMeltMeltMeltMelt

VaporizeVaporizeVaporizeVaporize

Slow, close,Slow, close,Fixed Fixed

arrangementarrangement

Moderate, close,Moderate, close,Random Random

arrangementarrangement

Fast, far apart,Fast, far apart,RandomRandom

SolidSolid

LiquidLiquid

VaporVapor

Changes of StateChanges of State

FrostFrostDepositDepositDepositDeposit

SublimeSublimeSublimeSublimeFreeze DryFreeze Dry

We live at the bottom of an ocean of air

Atmospheric PressureAtmospheric Pressure

Atmosphere:A sea of colorless, odorless gases surrounding the earth

(in mole %)78.08 % N2

20.95 % O2

0.033 % CO2

0.934 % Ar

(in mole %)78.08 % N2

20.95 % O2

0.033 % CO2

0.934 % Ar

Atmosphere:Atmosphere:

Properties of matterProperties of matterSolids, liquids and gases can easily be recognized by their different properties.

DensityDensityThe mass of matter divided by it’s volume.

ShapeShapeIs it fixed or take the shape of the container?

CompressibilityCompressibilityIf we apply pressure, does the volume decrease?

Thermal expansionThermal expansionHow much does the volume change when heated?

SolidSolid

LiquidLiquid

VaporVapor

Slow moving, Slow moving, dense,dense,Fixed shapeFixed shape

Moderate Moderate movement,movement,Dense,Dense,Takes shape of containerTakes shape of container

Fast moving, Fast moving, Low density,Low density,Expands to fill containerExpands to fill container

DensityDensity ShapeShape CompressibilityCompressibility

Small Small compressibility,compressibility,

Very smallVery small heat expansion heat expansion

Large Large compressibility,compressibility,Expands w/ heatExpands w/ heat

SmallSmallcompressibility,compressibility,

Small heat expansionSmall heat expansion

1. All gases are made up of tiny particlestiny particles moving in moving in • straight linesstraight lines • in all directions • at various speeds.

Kinetic molecular theory of GasesKinetic molecular theory of Gases

Model to explain behavior of gases

VaporVapor

3.3. V of a gas V of a gas = V of containerV of container

V of a gas is mostly empty space.

2. Particles far apart have no effect onno effect on each othereach other. (Don’t attract or repel)

Kinetic molecular theory Kinetic molecular theory


4. The ave KE ave KE as the TT

•The The average KE average KE is theis the same same for all for all gases atgases at thethe same T. same T.

TTKEKE

(K.E. (K.E. T) T)

E is conservedE is conservedwhen colliding with each other or container walls.

For an Ideal GasIdeal Gas CollisionsCollisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)

E is conservedE is conservedwhen colliding with each other or container walls.

For an Ideal GasIdeal Gas CollisionsCollisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)

5. Gas molecules exert pressurepressure as they collide with container walls

The The > > thethe # # ofof collisionscollisions (per unit time), (per unit time), thethe > > thethe pressure pressure


PressurePressure= = ForceForce per unit of per unit of Area.Area. Force

AreaAreaPP = = ForceForce

AreaArea

In the atmosphere, molecules of air (NN22, ,

OO22, Ar, H, Ar, H22OO, etc..) are constantly bouncing

off us.

We live at the bottom of an ocean of air

Atmospheric PressureAtmospheric Pressure

Atmosphere:A sea of colorless, odorless gases surrounding the earth

PressurePressureAt At higher elevationshigher elevations, there is , there is less less airair so the so the PP is less is less..

Boiling Point Boiling Point = Temp where molecules = Temp where molecules

overcome atmospheric Pressureovercome atmospheric Pressure

Sea LevelSea Level

760 torr760 torrDenver (5280’)Denver (5280’)630 torr630 torr

Mt. Evans,CO(14,000’)Mt. Evans,CO(14,000’)

Mt. Everest(20,000’)Mt. Everest(20,000’)

467 torr467 torr

270 torr270 torr HH22OOHH22OO

= 100 oC

= 95 oC

= 87 oC

= 73 oC

Measuring PressureMeasuring PressureAttempts to

pump water out of flooded

mines often failed because

HH22O can’t be O can’t be

lifted more than lifted more than 34 feet.34 feet.

Measuring PressureMeasuring PressureTorricelliTorricelli believed reason was that P of atmosphere could not hold anything heavier than a 34’ column of water.

Like drinking from a straw.

What causes the liquid to move up the straw to your mouth ?

Atmospheric Pressure Atmospheric Pressure

34’ columnof water

1 Atm1 Atm

The atmosphere

would support a column of

H2O> 34 feet high.

Measuring PressureMeasuring Pressure

Torricelli BarometerTorricelli BarometerPressure of the atmosphere supports aPressure of the atmosphere supports acolumn of column of Hg 760 mmHg 760 mm high. high.

1 atm

1 atm1 atm =760 mm Hg760 mm Hg760 torr760 torr29.92 in Hg14.7 lb/in2

101,325 Pa

vacuumvacuum

Mercury used because it’s so dense.

Blood pressureBlood pressure (systolic over diastolic):most often in mm Hgmm Hg. (ex. 120/80)120/80)

MeteorologistsMeteorologists refer to pressure systems in mm or inches of Hg. ex. 30.01 in30.01 in

STPSTPStandard Temperature & Standard Temperature & PressurePressure

1 atm

1 atm1 atm =760 mm Hg760 mm Hg760 torr760 torr29.92 in Hg14.7 lb/in2

101,325 Pa

00ooCC

273K273K

Gas lawsGas lawsLaws that show relationships between volume and properties of gases

Boyle’s LawBoyle’s LawCharles’ LawCharles’ LawGay-Lussac’s LawGay-Lussac’s Law

Boyle’s LawBoyle’s LawCharles’ LawCharles’ LawGay-Lussac’s LawGay-Lussac’s Law

Avogadro’s LawAvogadro’s LawIdeal Gas LawIdeal Gas LawDalton’s LawDalton’s Law

Avogadro’s LawAvogadro’s LawIdeal Gas LawIdeal Gas LawDalton’s LawDalton’s Law

CombinedCombinedGas LawGas Law

CombinedCombinedGas LawGas Law

V V is is inversely proportionalinversely proportional to to PP

when T is constant.when T is constant.

Boyle’s lawBoyle’s law

V 1

Por V = k

1

Por PV = kPV = k

If P goes downIf P goes downIf P goes downIf P goes down V goes upV goes upV goes upV goes upPP

VV

PP VV

VV

PP

PP11 = 1 Atm = 1 AtmPP11 = 1 Atm = 1 Atm

1 L1 LVV11 = =VV11 = =

PP22 = 0.5 Atm = 0.5 AtmPP22 = 0.5 Atm = 0.5 Atm

2 L2 LPP11VV11 = PP22VV22PP11VV11 = PP22VV22 VV22 = =VV22 = =

PP11VV11 = = VV22

PP22

PP11VV11 = = VV22

PP22

1atm (1L)1atm (1L) = =

0.5 atm0.5 atm

1atm (1L)1atm (1L) = =

0.5 atm0.5 atm

2 L2 L

Boyle’s law: V vs PBoyle’s law: V vs P

1 L1 L

Boyle’s law: V vs PBoyle’s law: V vs P2 L2 L

Drive to Drive to top of mountaintop of mountain - - ears start ears start poppingpopping. .

BreathingBreathing at high altitudes is at high altitudes is more more difficultdifficult because the pressure of O because the pressure of O22 is less.is less.

It all “Boyle’s” down to Breathing in and out.

Boyle’s lawBoyle’s law

Charles’s law: V vs TCharles’s law: V vs TThe The volume of a gasvolume of a gas is is directly proportionaldirectly proportional to the to the absolute temperatureabsolute temperature (K). (K).

T V

PP

If T goes upIf T goes upIf T goes upIf T goes up V goes upV goes upV goes upV goes up

VV11 = 125 mL

TT11 = 273 K = 273 K

Charles’s law: V vs TCharles’s law: V vs T VV11 = VV22

TT11 TT22

VV11 = VV22

TT11 TT22

VV22 ==

TT22 = 546 K = 546 K

250 mL250 mL250 mL250 mL

(546K546K))125 mL = 273 K273 K

(546K546K))125 mL = 273 K273 K

TT22VV11 = VV22

TT11

TT22VV11 = VV22

TT11

A balloon indoors, where the temp is at 2727ooCC,, has a volume of 2.0 liters. What will its volume be outside where the temperature is -23oC ? (Assume no change in pressure.)

Using Charles’ LawUsing Charles’ Law

VV11 = VV22

TT11 TT22

VV11 = VV22

TT11 TT22

= (250K250K))2.0 L = 300 K300 K

TT22VV11 = VV22

TT11

Convert all temps to the KelvinKelvin.

TT11 = 27 + 273 = = 27 + 273 = 300 K300 K

TT22 = -23 + 273 = = -23 + 273 = 250 K250 K

1.7 L1.7 L1.7 L1.7 L

Gay-Lussac’s Law (PGay-Lussac’s Law (PT)T)

Pressure of a gas Pressure of a gas is is directly proportionaldirectly proportional to to

Absolute Temp (K) when Absolute Temp (K) when Volume is constant Volume is constant

PP11 = PP22

TT11 TT22

PP11 = PP22

TT11 TT22

P T

VV

If P goes upIf P goes upIf P goes upIf P goes up T goes upT goes upT goes upT goes up

ExampleExample: an auto tire was inflated to a pressure of 32 psi when the temperature was -20ºC. After driving all day in a hot desert, the temperature of the tire has climbed to 60ºC. What is the pressure inside the tire?

Gay-Lussac’s LawGay-Lussac’s Law

Assume the tire’s volume is fixed.

P2 = ??P1 = 32 psiT1 = -20 + 273 = 253K T2 = 60 + 273 = 333K

PP11 = PP22

TT11 TT22

= (333K333K))32 psi = 253 K253 K

TT22PP11 = PP22

TT11

42 psi42 psi42 psi42 psi

Boyle’sBoyle’s

Gay-Lussac’sGay-Lussac’s

Charles’Charles’

PT

VVVV

T VPP

TPP

VVGas LawsGas LawsPP11VV1 1 = P= P22VV22

VV11 = = VV22

TT11 TT22

PP11 = = PP22

TT11 TT22

Boyle’sBoyle’s

Gay-Lussac’sGay-Lussac’s

Charles’Charles’

CombinedCombined

Gas LawGas Law

PT

VVVV

T VPP

TPP

VVGas LawsGas Laws

P1V1

T1

==P2V2

T2

A 10 m3 balloon contains helium on the ground where the temperature is 27ºC and the pressure is 740 torr. Find the volume at an altitude of 5300 m if pressure is 370 mm Hg and temperature is -33 ºC.

P1 = 740 mm

T1 = 27 + 273 = 300 K

V1 = 10 m3

P2 = 370 mm

T2 = -33 + 273 = 240 K

V2 = ?

= 16 m3V2 = (240 K)(740 mm)(10 m3 )

(370 mm) (300 K)

P1V1

T1

==P2V2

T2

T2P1V1

P2 T1

== V2

Combined Gas LawCombined Gas Law

Boiling Point Boiling Point = Temp where Vapor = Temp where Vapor Pressure (PPressure (Pvapvap) of molecules overcome ) of molecules overcome

atmospheric Pressureatmospheric Pressure

Sea Level = 100 oCSea Level = 100 oC

760 torr760 torrDenver (5280’) = 95 oCDenver (5280’) = 95 oC

630 torr630 torrMt. Evans,CO(14,000’) = 87 oCMt. Evans,CO(14,000’) = 87 oC

Mt. Everest(20,000’) = 73 oCMt. Everest(20,000’) = 73 oC

467 torr467 torr

270 torr270 torr HH22OOHH22OO

Avogadro’s lawAvogadro’s lawThe The volume of a gas volume of a gas is directly is directly

proportional to the proportional to the number of moleculesnumber of molecules

VV11 = VV22

nn11 nn22

VV11 = VV22

nn11 nn22

More moles of a gas, takes up more space.

At Standard Temperature & Pressure At Standard Temperature & Pressure (STP)(STP)

V of 1 mole of gas = V of 1 mole of gas = 22.4 liters22.4 liters

Equal volumes of gas Equal volumes of gas (at same T and P)(at same T and P)

contain equal numbers of molecules.contain equal numbers of molecules.

Avogadro’s lawAvogadro’s law

At T = 273 KAt T = 273 K (0ºC) P = 1 atm1 atm (760 mm)

1 mol He1 mol He

4 g He4 g He

22.4 L22.4 L

1 mol He1 mol He

4 g He4 g He

22.4 L22.4 L

1 mol N1 mol N22

28 g N28 g N22

22.4 L22.4 L

1 mol N1 mol N22

28 g N28 g N22

22.4 L22.4 L

1 mol CO1 mol CO22

44 g CO44 g CO22

22.4 L22.4 L

1 mol CO1 mol CO22

44 g CO44 g CO22

22.4 L22.4 L

Standard conditionsStandard conditions ( (STPSTP))When 36 g of When 36 g of liquid Hliquid H22OO is vaporized, is vaporized,

what will be the volume of the what will be the volume of the gas?gas?

1 mole H1 mole H22OO

18 g H18 g H22O O

22.4 liters22.4 liters

1 mole 1 mole H2O= 44.81 mol 36g H1 mol 36g H22O O

L

66 g CO2

Example:Example: What volume will What volume will 66 66

gramsgrams of of COCO22 occupy at occupy at STPSTP??

1 mole CO2

44 g CO2

22.4 liters22.4 liters

1 mole CO1 mole CO22

= 33.6

STPSTP

L

The Ideal gas lawThe Ideal gas lawA combination of A combination of • Boyle’s, Boyle’s, • Charles’ , Charles’ , • Gay-Lussac’s and Gay-Lussac’s and • Avogadro’s LawsAvogadro’s Laws

PV = nRTPV = nRT

V nT

P

V = RnT/P where R is a constant

V nT

P

V = RnT/P where R is a constant

AtmL

K

mol L atm

mol K

( 1 atm ) ( 22.4 L)( 1 mol ) ( 273 K)

PVnT

R =

= 0.0821 atm-L mol0.0821 atm-L mol-1-1 K K-1-1

R =

R (the gas constant) can easily be determined from standard conditions.

= 0.0821 atm-L

mol-K

The Ideal gas lawThe Ideal gas law

What is the volume of 2.00 moles of gas at3.50 atm and 310.0 K?

PV = nRTPV = nRT V = nRT P

= (2.00 mol)(0.0821 L• atm)(310. K) K . mol

(3.50 atm)

= 14.5 liters


PV = nRTPV = nRT


moles n = grams = g_

molecular weight MW

So: we can substitute for n.

PV = PV = gg R T R T MWMW

MW = g R T PV

What is the molecular weight of a gas if 25 g

of the gas occupies a volume of 15 liters at a pressure of .95 atm and a temperature of 50 ºC?

(25g)(0.0821 L atm )(323 K)mol K

(0 .95 atm)(15 L)

= 46.5 __= 46.5 __g_g_

molmol


MW = g R T = PV

Remember

density =

The Ideal gas lawThe Ideal gas law• can also be used with density of a gas

g

V

MW = d R T P

If the density of a gas

is 1.75 _g_

L

at 740 torr and 300 K,

what is its MW?

MW = g R T P V

740 torr ( 1 atm ) (760 torr)


MW = d R T P

If density of a gas = 1.75 g_

L

at 740 torr and 300 K,

What is its MW?

MW = 1.751.75 gg (.0821 L atm)( 300 K) LL mol K = 44.3 g_

mol

The Ideal gas lawThe Ideal gas law• can solve for density of a gas if needed

MW = d R T P

d = P MW RT

Dalton’s law of Partial PressuresDalton’s law of Partial Pressures

The total pressure of a gas mix = sum of the partial pressures of each gas.

Pair = PN2 + PO2 + PAr + PCO2 + PH2O

PPTT == PP11 + P + P22 + P + P33 + ..... + .....

Each gas acts independently of the others.Each gas acts independently of the others.

Example: AirExample: Air

Pair = PN2 + PO2 + PCO2 + PH2O

Typical values for Atmospheric airAtmospheric air at 0 ºC (excluding argon):

PN2 = 594.7 mmPN2 = 594.7 mm PO2 = 160 mmPO2 = 160 mm

PH2O = 5.0 mmPH2O = 5.0 mmPCO2 = 0.3 mmPCO2 = 0.3 mm

Pair = 594.7 mm + 160 mm + 0.3 mm + 5.0 mm

As T of air increases, more H2O is found in the mix.exampleexample: at 20 ºC, the PH2O = 18 mm

Since total pressure (760 mm) can’t change,

the other gases are diluted

to make room for the water.

Pair = 594.7 mm + 160 mm + 0.3 mm + 5.0 mm

Pair = PN2 + PO2 + PCO2 + PH2O

Air moving over warm water Air moving over warm water

has more water in it.has more water in it.

Low pressure Low pressure

is often associated with this air.is often associated with this air.

Typhoons and hurricanes

are associated with very warm, moist air.

Pair = PN2 + PO2 + PCO2 + PH2O = 760 mm

Values are for 97% oxygen saturation at pH = 7.4.

Blood GasesBlood Gases

PPCOCO22 ~ 40 mm Hg ~ 40 mm Hg

Normal PO2 in the air =160 mm.

If drops

< 100 mm,

can’t diffuse into the blood.

Arterial Blood Gases (ABGs)Arterial Blood Gases (ABGs)

PPBGBG = = PPOO22 + + PPCOCO22

PPOO22 ~ 100 mm Hg ~ 100 mm Hg

PCO2 ~ 46 mm Hg

Venous Blood Gases (VBGs)Venous Blood Gases (VBGs)

PO2 ~ 40 mm Hg

We only use about 25% of the OxygenOxygen we inhale.

The rest is exhaled along with the NitrogenNitrogen and some carbon dioxide.

THIS IS WHY CPRCPR WORKS !!!

Bernoulli's PrincipleBernoulli's Principle

Faster moving gases gases exert less pressurepressure than slow moving gases.

Fast moving Fast moving GasesGases

Fast moving Fast moving GasesGases Low PLow P

Slow moving Slow moving GasesGases


High PHigh P

Bernoulli's PrincipleBernoulli's Principle





High PHigh P

Low PLow P

Graham’s LawGraham’s Law

lightweight gases move faster than heavy gases

KE=0.5 mv2

Diffusion (gasses intermingling when together)

Graham’s LawGraham’s Law

AMW

BMW

B rateeffusion

A rateeffusion

Effusion (gas escaping through small hole;

ie balloon going flat)

UF6-235 needed for nuclear reactor

UF6-238Gas Centrifuge: heavy spins to outside

Porous membrane: lighters go through faster

HENRY’S LAWHENRY’S LAWThe solubility of a gassolubility of a gas in a liquid is directly directly related to the pressurepressure on the liquid.

P SolTT

If P goes upIf P goes upIf P goes upIf P goes up Gas solubility goes upGas solubility goes up(more gas will dissolve)(more gas will dissolve)

Gas solubility goes upGas solubility goes up(more gas will dissolve)(more gas will dissolve)

If P goes downIf P goes downIf P goes downIf P goes down Gas solubility goes downGas solubility goes down(gases escape)(gases escape)

Gas solubility goes downGas solubility goes down(gases escape)(gases escape)

HENRY’S LAWHENRY’S LAW

P SolTT

Soda under high pressure

Soda under low pressure

Example: opening a sodaExample: opening a soda.

When a diver deep in the water breathes airmore nitrogen gas dissolvesnitrogen gas dissolves in his blood becausethe pressure is greater.

If he ascends to quickly, it comes out of his blood like tiny bubbles in a carbonated beverage.

These bubbles collect at the jointscausing extreme pain.

The “BendsThe “Bends””

Lots of Lots of dissolved Ndissolved N22

High PHigh P

Less dissolved Less dissolved gasesgases

Lower PLower P

Quick ascent Quick ascent Get bubbles in blood & Get bubbles in blood & joints joints extreme painextreme pain


Lots of Lots of dissolved gasesdissolved gases

High PHigh P

Less Less dissolved dissolved

gasesgases

Lower PLower PNN22 accumulatesaccumulates in in

brainbrain, , spinal cordspinal cord, , and peripheral and peripheral

nerves. Bubbles here nerves. Bubbles here can can cause paralysis cause paralysis and convulsions.and convulsions.

Effects often Effects often irreversible.irreversible.

NN22 accumulatesaccumulates in in

brainbrain, , spinal cordspinal cord, , and peripheral and peripheral

nerves. Bubbles here nerves. Bubbles here can can cause paralysis cause paralysis and convulsions.and convulsions.

Effects often Effects often irreversible.irreversible.

Bends was first

discovered in

workers who

were excavating

inside Caissons.

Rapid ascent fromRapid ascent from

the high pressurethe high pressure

environment to theenvironment to the

surface caused thesurface caused the

““bendsbends” in these” in these

workers.workers.

CAISSON


“Nitrogen Narcosis”,

= nitrogen euphoria or raptures of the deep.

(Effect somewhat like that observed

when alcohol levels rise in the blood.)

So, So, HeliumHelium

often often substitutedsubstituted for for

NN22 in divers air. in divers air.

Nitrogen NarcosisNitrogen Narcosis

The solubility of a gassolubility of a gas in a liquid is inversely inversely related to the temperaturetemperature .

If T goes upIf T goes upIf T goes upIf T goes up Gas solubility goes downGas solubility goes down(gases escape)(gases escape)

Gas solubility goes downGas solubility goes down(gases escape)(gases escape)

Temperature vs SolubilityTemperature vs Solubility

Gas SolubilityGas Solubility

TT

SS

TT SS

TT

SS

Temperature vs SolubilityTemperature vs SolubilityCold HCold H22O holds more gas than warm HO holds more gas than warm H22OO

If hot rivers lose too much dissolved OIf hot rivers lose too much dissolved O22

the fish can’t survive.the fish can’t survive.

Carbonated beverages bottled cold.

Temperature vs SolubilityTemperature vs Solubility

Divers with bends often packed in ice for transport

to hyperbaric chamber.

Gas LawsGas Laws

Henry’sHenry’s

PP SolubilitySolubility

SolubilitySolubility

TTPP

TT

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CH104 Chapter 7 Gases Gases & Kinetic Theory Pressure Gas Laws