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5 - 1
GasesGases
PressurePressureBoyle’s LawBoyle’s LawCharles’ LawCharles’ Law
Gay-Lussac’s LawGay-Lussac’s LawAvogadro’s LawAvogadro’s Law
Ideal Gas EquationIdeal Gas EquationDalton’s LawDalton’s Law
Effusion and DiffusionEffusion and DiffusionKinetic-Molecular TheoryKinetic-Molecular Theory
Real GasesReal Gases
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
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SolidLiquidGas
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Observed propertiesObserved propertiesof matterof matter
StateProperty Solid Liquid Gas
Density High High Low (like solids)
Shape Fixed Takes shape Expands of lower part to fill
the of container
container
Compressibility Small Small Large
Thermal Very Small Moderateexpansion Small
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The gaseous stateThe gaseous state
In this state, the particles have sufficient energy to overcome all forces that attract them to each other.
Each particle is completelyseparated from the others.
This results in low densitiesand the fact that gases completely fill the container that holds them.
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Gas pressureGas pressure
Gases exhibit pressure on any container they are in.
Pressure is defined as a force per unit of area. Pressure = Force / Area
Several common unitsSeveral common units 1.00 atm = 760 torr
760 mm Hg 29.9 in Hg 14.7 lb/in2
1.01 x 105 Pa
force
area
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BarometerBarometer
Device used to measure atmospheric pressure.
Oneatm
760 mmHg
29.9 inHg
vacuum
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The gas lawsThe gas laws
Since gases are highly compressible and will expand when heated, these properties have been studied extensively.
The relationships between volume, pressure, temperature and moles are referred to as the gas lawsgas laws.
To understand the relationships, we must introduce a few concepts.
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Units we will be usingUnits we will be using
VolumeVolume liters, although other units could be used.
TemperatureTemperature Must use an absolute scale. K - Kelvin is most often used.
PressurePressure Atm, torr, mmHg, lb/in2.- use what is appropriate.
MolesMoles We specify the amounts in molar quantities.
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Gas lawsGas laws
Laws that show the relationship between volume and various properties of gases
Boyle’s LawBoyle’s LawCharles’ LawCharles’ Law
Gay-Lussac’s LawGay-Lussac’s LawAvogadro’s LawAvogadro’s Law
The Ideal Gas EquationIdeal Gas Equation combines several of these laws into a single relationship.
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Boyle’s lawBoyle’s law
The volume of a gas is inversely proportional to its pressure.
PV = kor
P1 V1 = P2 V2
Temperature and number of moles must be held constant!
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Boyle’s lawBoyle’s law
Increasing the pressureon a sample on gasdecreases it volume atconstant temperature.
Note the effect hereas weight is added.
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Charles’ lawCharles’ law
The volume of a gas is directly proportional to the absolute temperature (K).
VT
= k
or V1 V2
T1 T2
Pressure and number of molesmust be held constant!
=
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Charles’ lawCharles’ law
When you heat a sample of a gas, its volume increases.
The pressure and numberof moles must be held constant.
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Charles’ LawCharles’ Law
Placing an air filled balloon near liquid nitrogen (77 K)will cause the volume to be reduced. Pressure and the number of moles are constant.
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Gay-Lussac’s LawGay-Lussac’s Law
Law of of Combining Volumes.Law of of Combining Volumes.At constant temperature and pressure, the volumes of gases involved in a chemical reaction are in the ratios of small whole numbers.
Studies by Joseph Gay-Lussac led to a better understanding of molecules and their reactions.
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Gay-Lussac’s LawGay-Lussac’s Law
Example.Example.Reaction of hydrogen and oxygen gases.
Two ‘volumes’ of hydrogen will combine with one ‘volume’ of oxygen to produce two volumes of water.
We now know that the equation is:
2 H2 (g) + O2 (g) 2 H2O (g)
+H2 H2 O2 H2O H2O
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Avogadro’s lawAvogadro’s law
Equal volumes of gas at the same temperature and pressure contain equal numbers of molecules.
V = k n
V1 V2
n1 n2
=
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Avogadro’s lawAvogadro’s law
If you have more moles of a gas, it takes up morespace at the same temperature and pressure.
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Standard conditions (STP)Standard conditions (STP)
Remember the following standard conditions.
Standard temperature = 273.15 K
Standard pressure = 1 atm
At these conditions:
One mole of a gas has a volume of 22.422.4 liters.
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The ideal gas lawThe ideal gas law
A combination of Boyle’s, Charles’ and Avogadro’s Laws
PV = nRT
P = pressure, atm V = volume, L n = moles T = temperature, K R = 0.082 06 L atm/K mol
(gas law constant)
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ExampleExample
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)(0.08206 L atm K-1mol-1)(310.0 K) (3.50 atm)
= 14.5 L
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Ideal gas lawIdeal gas law
PVnT
( 1 atm ) ( 22.4 L )( 1 mol ) ( 273.15 K)
R =
= 0.08206 atm L mol-1 K-1
R =
R can be determined from standard conditions.
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Ideal gas lawIdeal gas law
When you only allow volume and one other factor to vary, you end up with one of the other gas laws.
Just remember
Boyle Pressure
Charles Temperature
Avogadro Moles
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Ideal gas lawIdeal gas law
P1V1
n1T1
= R =P2V2
n2T2
This one equationsays it all.
Anything held constant will“cancels out” of the equation
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Ideal gas lawIdeal gas law
Example - if n and T are held constant
P1V1
n1T1
=P2V2
n2T2
This leaves us
P1V1 = P2V2 Boyle’s Law
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ExampleExample
If a gas has a volume of 3.0 liters at 250 K,what volume will it have at 450 K ?
P1V1
n1T1
=P2V2
n2T2
Cancel P and nThey don’t change
V1
T1
=V2
T2
We end up withCharles’ Law
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ExampleExample
If a gas has a volume of 3.0 liters at 250 K,what volume will it have at 450 K ?
V1
T1
=V2
T2
V2 = (3.0 l) (450 K)
(250 K)
= 5.4 L
P1V1
n1T1
=P2V2
n2T2
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Dalton’s law of Dalton’s law of partial pressurespartial pressures
The total pressure of a gaseous mixture is the sum of the partial pressure of all the gases.
PT = P1 + P2 + P3 + .....
Air is a mixture of gases - each adds it own pressure to the total.
Pair = PN2 + PO2 + PAr + PCO2 + PH2O
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Partial pressure examplePartial pressure example
Mixtures of helium and oxygen are used in scuba diving tanks to help prevent “the bends.”
For a particular dive, 46 liters of O2 and 12 liters of He were pumped in to a 5 liter tank. Both gases were added at 1.0 atm pressure at 25oC.
Determine the partial pressure for both gases in the scuba tank at 25oC.
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Partial pressure examplePartial pressure example
First calculate the number of moles of each gas using PV = nRT.
nO2 = = 1.9 mol
nHe = = 0.49 mol
(1.0 atm) (46 l)(0.08206 l atm K-1 mol-1)(298.15K)
(1.0 atm) (12 l)(0.08206 l atm K-1 mol-1)(298.15K)
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Partial pressure examplePartial pressure example
Now calculate the partial pressures of each.
PO2 = = 9.3 atm
PO2 = = 2.4 atm
Total pressure in the tank is 11.7 atm.
(1.9 mol) (298.15 K) (0.08206 l atm K-1 mol-1)(5.0 l)
(0.49 mol) (298.15 K) (0.08206 l atm K-1 mol-1)(5.0 l)
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Relates the rates of effusion of two gases to their molar masses.
This law notes that larger molecules move more slowly.
Graham’s lawGraham’s law
Rate A MM BRate B MM A
=
DiffusionDiffusion
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Diffusion and effusionDiffusion and effusion
DiffusionDiffusionThe random and spontaneous mixing of molecules.
EffusionEffusionThe escape ofmolecules throughsmall holes in abarrier.
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Kinetic-molecular theoryKinetic-molecular theory
This theory explains the behavior of gases.
• Gases consist of very small particles (molecules) which are separated by large distances.
• Gas molecules move at very high speeds - hydrogen molecules travel at almost 4000 mph at 25oC.
• Pressure is the result of molecules hitting the container. At 25 oC and 1 atm, a molecule hits another molecule and average of 1010 times/sec.
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Kinetic-molecular theoryKinetic-molecular theory
• No attractive forces exist between ideal gas molecules or the container they are in.
• Energy of motion is called kinetic energy.
Average kinetic energy = mv2
Because gas molecules hit each other frequently, their speed and direction is constantly changing.
The distribution of gas molecule speeds can be calculated for various temperatures.
12
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Kinetic-molecular theoryKinetic-molecular theoryFr
act
ion
havin
g e
ach
sp
eed
0 500 1000 1500 2000 2500 3000Molecular speed (m/s)
O2 at 25oCO2 at 700oCH2 at 25oC
Average speed
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We can plot the compressibility factor (PV/nRT)for gases. If the gas is ideal, it should alwaysgive a value of 1.
Obviously, none of these gases are ‘ideal.’
Real gasesReal gases
Com
pre
ssib
ility
fact
or
0 5 10Pressure, atm
H2
N2
CH4
C2H4
NH3
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Real gasesReal gases
As pressure approaches zero, all gases approach ideal behavior.
At high pressure, gases deviate significantly from ideal behavior.
Why?Why?
• Attractive forces actually do exist between molecules.
• Molecules are not points -- they have volume.
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Van der Waals equationVan der Waals equation
This equation is a modification of the ideal gas relationship. It accounts for attractive forces and molecular volume.
P +an2
V2 (V - nb) = nRT( )Correction for Molecular volume
Correction for attractiveforces between molecules
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Van der Waals constantsVan der Waals constants
a bGas Formula L2 atm mol-2 L mol-1
Ammonia NH3 4.170 0.037 07Argon Ar 1.345 0.032 19Chlorine Cl2 6.493 0.056 22Helium He 0.034 12 0.023 70Hydrogen H2 0.244 4 0.026 61
Nitrogen N2 1.390 0.039 13
Water H2O 5.464 0.030 49Xenon Xe 4.194 0.051 05