CH104 Chapter 7 Gases Gases & Kinetic Theory Pressure Gas Laws.
-
Upload
egbert-allen -
Category
Documents
-
view
228 -
download
4
Transcript of 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
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
Kinetic molecular theory Kinetic molecular theory
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
The Ideal gas lawThe Ideal gas law
PV = nRTPV = nRT
The Ideal gas lawThe Ideal gas law
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
The Ideal gas lawThe Ideal gas law
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)
The Ideal gas lawThe Ideal gas law
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
Slow moving Slow moving GasesGases
High PHigh P
Bernoulli's PrincipleBernoulli's Principle
Slow moving Slow moving GasesGases
Slow moving Slow moving GasesGases
Fast moving Fast moving GasesGases
Fast moving Fast moving GasesGases
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
The “BendsThe “Bends””
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
The “BendsThe “Bends””
“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