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CH104 Chapter 8
Gases
Gases & Kinetic Theory
Pressure
Gas Laws
Elemental states at 25oC
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 State
Melting Pt = Freezing Pt
Boiling Pt
Solid
Liquid
Vapor
CondenseCondense
FreezeFreezeMeltMelt
VaporizeVaporize
Slow, close,Fixed
arrangement
Moderate, close,Random
arrangement
Fast, far apart,Random
Solid
Liquid
Vapor
Changes of State
FrostDepositDeposit
SublimeSublimeFreeze Dry
We live at the bottom of an ocean of air
Atmospheric 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 matterSolids, liquids and gases can easily be recognized by their different properties.
DensityThe mass of matter divided by it’s volume.
ShapeIs it fixed or take the shape of the container?
CompressibilityIf we apply pressure, does the volume decrease?
Thermal expansionHow much does the volume change when heated?
Solid
Liquid
Vapor
Slow moving, dense,Fixed shape
Moderate movement,Dense,Takes shape of container
Fast moving, Low density,Expands to fill container
Density Shape Compressibility
Small compressibility,
Very small heat expansion
Large compressibility,
Expands w/ heat
Smallcompressibility,
Small heat expansion
1. All gases are made up of tiny particles moving in • straight lines • in all directions • at various speeds.
Kinetic molecular theory of Gases
Model to explain behavior of gases
Vapor
3. V of a gas = V of container
V of a gas is mostly empty space.
2. Particles far apart have no effect on each other. (Don’t attract or repel)
Kinetic molecular theory
Kinetic molecular theory
4. The ave KE as the T
• The average KE is the same for all gases at the same T.
TKE
(K.E. a T)
E is conservedwhen colliding with each other or container walls.
For an Ideal Gas Collisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)
E is conservedwhen colliding with each other or container walls.
For an Ideal Gas Collisions are perfectly elastic & no E is gained or lost. (Like billiard balls exchanging E.)
5. Gas molecules exert pressure as they collide with container walls
The > the # of collisions (per unit time), the > the pressure
Kinetic molecular theory
Pressure= Force per unit of Area. Force
AreaP = Force
Area
In the atmosphere, molecules of air (N2, O2, Ar, H2O, etc..) are constantly bouncing
off us.
We live at the bottom of an ocean of air
Atmospheric Pressure
Atmosphere:A sea of colorless, odorless gases surrounding the earth
PressureAt higher elevations, there is less air so the P is less.
Boiling Point = Temp where molecules
overcome atmospheric Pressure
Sea Level
760 torrDenver (5280’)
630 torrMt. Evans,CO(14,000’)
Mt. Everest(20,000’)
467 torr
270 torr H2O
= 100 oC
= 95 oC
= 87 oC
= 73 oC
Measuring PressureAttempts to
pump water out of flooded
mines often failed because
H2O can’t be
lifted more than 34 feet.
Measuring PressureTorricelli 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
34’ columnof water
1 Atm
The atmosphere
would support a column of
H2O> 34 feet high.
Measuring Pressure
Torricelli BarometerPressure of the atmosphere supports acolumn of Hg 760 mm high.
1 atm
1 atm =760 mm Hg760 torr29.92 in Hg14.7 lb/in2
101,325 Pa
vacuum
Mercury used because it’s so dense.
Blood pressure (systolic over diastolic):most often in mm Hg. (ex. 120/80)
Meteorologists refer to pressure systems in mm or inches of Hg. ex. 30.01 in
STPStandard Temperature & Pressure
1 atm
1 atm =760 mm Hg760 torr29.92 in Hg14.7 lb/in2
101,325 Pa
0oC
273K
Gas lawsLaws that show relationships between volume and properties of gasesBoyle’s LawCharles’ LawGay-Lussac’s Law
Avogadro’s LawIdeal Gas LawDalton’s Law
CombinedGas Law
V is inversely proportional to P when T is constant.
Boyle’s law
V 1
Por V = k
1
Por PV = k
If P goes down V goes upP
V
P V
V
P
P1 = 1 Atm
1 LV1 =
P2 = 0.5 Atm
2 LP1V1 = P2V2 V2 =
P1V1 = V2
P2
1atm (1L) =
0.5 atm
2 L
Boyle’s law: V vs P
1 L
Boyle’s law: V vs P2 L
Drive to top of mountain - ears start popping.
Breathing at high altitudes is more difficult because the pressure of O2 is less.
It all “Boyle’s” down to Breathing in and out.
Boyle’s law
Charles’s law: V vs TThe volume of a gas is directly proportional to the absolute temperature (K).
T V
P
If T goes up V goes up
V1 = 125 mL
T1 = 273 K
Charles’s law: V vs T V1 = V2
T1 T2
V1 = V2
T1 T2
V2 =
T2 = 546 K
250 mL
(546K)125 mL = 273 K
T2V1 = V2
T1
A balloon indoors, where the temp is at 27oC, 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’ Law
V1 = V2
T1 T2
V1 = V2
T1 T2
= (250K)2.0 L = 300 K
T2V1 = V2
T1
Convert all temps to the Kelvin.
T1 = 27 + 273 = 300 K
T2 = -23 + 273 = 250 K
1.7 L
Gay-Lussac’s Law (PT)Pressure of a gas is directly proportional to
Absolute Temp (K) when Volume is constant
P1 = P2
T1 T2
P1 = P2
T1 T2
P T
V
If P goes up T goes up
Example: 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 Law
Assume the tire’s volume is fixed.
P2 = ??P1 = 32 psiT1 = -20 + 273 = 253K T2 = 60 + 273 = 333K
P1 = P2
T1 T2
= (333K)32 psi = 253 K
T2P1 = P2
T1
42 psi
Boyle’s
Gay-Lussac’s
Charles’
PT
VV
T VP
TP
VGas LawsP1V1 = P2V2
V1 = V2
T1 T2
P1 = P2
T1 T2
Boyle’s
Gay-Lussac’s
Charles’
CombinedGas Law
PT
VV
T VP
TP
VGas 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 Law
Boiling Point = Temp where Vapor Pressure (Pvap) of molecules overcome
atmospheric Pressure
Sea Level = 100 oC
760 torrDenver (5280’) = 95 oC
630 torrMt. Evans,CO(14,000’) = 87 oC
Mt. Everest(20,000’) = 73 oC467 torr
270 torr H2O
Avogadro’s lawThe volume of a gas is directly
proportional to the number of molecules
V1 = V2
n1 n2
V1 = V2
n1 n2
More moles of a gas, takes up more space.
At Standard Temperature & Pressure (STP)
V of 1 mole of gas = 22.4 liters
Equal volumes of gas (at same T and P)
contain equal numbers of molecules.
Avogadro’s law
At T = 273 K (0ºC) P = 1 atm (760 mm)
1 mol He
4 g He
22.4 L
1 mol He
4 g He
22.4 L
1 mol N2
28 g N2
22.4 L
1 mol N2
28 g N2
22.4 L
1 mol CO2
44 g CO2
22.4 L
1 mol CO2
44 g CO2
22.4 L
Standard conditions (STP)When 36.0 g of liquid H2O is vaporized,
what will be the volume of the gas?
1 mole H2O
18.0 g H2O
22.4 liters
1 mole H2O= 44.8 36.0 g H2O
L
66 g CO2
Example: What volume (in Liters)
will 66 grams of CO2 occupy at STP?
1 mole CO2
44 g CO2
22.4 liters
1 mole CO2
= 33.6
STP
L
The Ideal gas lawA combination of • Boyle’s, • Charles’ , • Gay-Lussac’s and • Avogadro’s Laws
PV = 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 atmmol K
( 1 atm ) ( 22.4 L)( 1 mol ) ( 273 K)
PVnT
R =
= 0.0821 atm-L mol-1 K-1
R =
R (the gas constant) can easily be determined from standard conditions.
= 0.0821 atm-L
mol-K
The Ideal gas law
What is the volume of 2.00 moles of gas at3.50 atm and 310.0 K?
PV = nRT V = nRT P
= (2.00 mol)(0.0821 L• atm)(310. K) K . mol
(3.50 atm)
= 14.5 liters
The Ideal gas law
PV = nRT
The Ideal gas law
moles n = grams = g_
molecular weight MW
So: we can substitute for n.
PV = g R T MW
MW = g R T PV
What is the molecular weight of a gas if 25.0 g
of the gas occupies a volume of 15.0 liters at a pressure of .950 atm and a temperature of 50.0 ºC?
(25.0g)(0.0821 L atm )(323 K)mol K
(0 .950 atm)(15.0 L)
= 46.5 __g_
mol
The Ideal gas law
MW = g R T = PV
Remember
density =
The 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 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 = 1.75 g (.0821 L atm)( 300 K) L mol K = 44.3 g_
mol
The 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 Pressures
The total pressure of a gas mix = sum of the partial pressures of each gas.
Pair = PN2 + PO2 + PAr + PCO2 + PH2O
PT = P1 + P2 + P3 + .....
Each gas acts independently of the others.
Example: Air
Pair = PN2 + PO2 + PCO2 + PH2O
Typical values for Atmospheric air at 0 ºC (excluding argon):
PN2 = 594.7 mm PO2 = 160 mm
PH2O = 5.0 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.example: 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
has more water in it.
Low pressure
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 Gases
PCO2 ~ 40 mm Hg
Normal PO2 in the air =160 mm.
If drops
< 100 mm,
can’t diffuse into the blood.
Arterial Blood Gases (ABGs)
PBG = PO2 + PCO2
PO2 ~ 100 mm Hg
PCO2 ~ 46 mm Hg
Venous Blood Gases (VBGs)
PO2 ~ 40 mm Hg
We only use about 25% of the Oxygen we inhale.
The rest is exhaled along with the Nitrogen and some carbon dioxide.
THIS IS WHY CPR WORKS !!!
Bernoulli's Principle
Faster moving gases exert less pressure than slow moving gases.
Fast moving Gases Low P
Slow moving Gases
High P
Bernoulli's PrincipleSlow moving
Gases
Fast moving Gases
High P
Low P
Graham’s Law
lightweight gases move faster than heavy gases
KE=0.5 mv2
Diffusion (gasses intermingling when together)
Graham’s Law
AMW
BMW
B rateeffusion
A rateeffusion
Effusion (gas escaping through small hole;
ie balloon going flat)
UF6-235 needed for nuclear reactor
UF6-238
Gas Centrifuge: heavy spins to outside
Porous membrane: lighters go through faster