kinetic theory and the behavior of ideal &...
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Kinetic Theory and the Kinetic Theory and the Behavior of Ideal & RealBehavior of Ideal & RealBehavior of Ideal & Real Behavior of Ideal & Real
GasesGases
Why study gases?
• An understanding of real world hphenomena.
• An understanding of how science “works.”
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A Gas
• ___________ fills any container.
• completely with any other gas• ______ completely with any other gas.
• Exerts _________ on its surroundings.
o
t760
C)0at (measured Hg mm 760
mb1013bar1.013
kPa 101.325 Pa 101,325
torr760
2in lb 14.7
mb1013bar 1.013
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• A manometer is used to measure the pressure inside closed containers
Open-end manometer. (a) The pressure of the trapped gas, Pgas equals the atmospheric pressure, Patm. Trapped gas pressure (b) higher and (c) lower than atmospheric pressure.
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Compressing a gas increases its pressure.
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Boyle’s J-Tube Experiment
PV
1
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_________________________Law
:LawsBoyle'For constant mols or concentration:
:LawsLussac'-Gay
)(when //V
:Law Charles'
)(when
y
212211
212211
PPTVT
TTVPVP
)(when //
:LawsLussac-Gay
212211 VVTPTP
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Example: What will be the the final pressure of a sample of oxygen with a volume of 850 m3 at 655 torr and 25.0oC if it is heated to 80 0oC and given a final volume of 1066to 80.0 C and given a final volume of 1066 m3?
ANALYSIS: Use the combined gas law with temperature in kelvins.
SOLUTION:
273 2)K(25 0
K)2.2730.80(
m1066
m 850 torr655
3
3
1
2
2
112
T
T
V
VPP
torr619
273.2)K(25.0m1066
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• The combined gas law can be generalized to include changes in the number of moles of sample
• The _________________law is
Latm
constant gas universal
R
nRTPV
K mol
Latm 0.0821
One mole of each gas occupies 22.4 at STP. Carbon dioxide is more dense that oxygen due to molar mass differences.
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Molar Mass of a Gas
Molar Mass = dRT/Pfd = density of gas
T = temperature in Kelvin
P = pressure of gas
Copyright © Houghton Mifflin Company. All rights reserved
Chapter 5 | Slide 175.4
The space above any liquid contains some of the liquid’s vapor
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Example: A sample of oxygen is collected over water at 20oC and a pressure of 738 torr. What is the partial pressure of oxygen?
ANALYSIS: The partial pressure of oxygen is less than the total pressure. Get the vapor pressure of water from tables of data or text
SOLUTION:
torr720. torr )54.17738(
torr 54.17
gas
vaporwater
P
P
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Dalton’s Law of Partial Pressures
• This is possible because the number of molesof each gas is _________________________________________________________________________________________
• Using the ideal gas equation for each gas
• For a given mixture of gases the volume andRT
VPn A
A
• For a given mixture of gases, the volume and temperature _________________for all gases
• Using C=V/RT gives
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AA
ZBA
AA
PP
CPCPCP
CPX
• The partial pressure of a gas can be calculated using the total pressure and mole fraction
total
A
ZBA
A
PPPP
totalAA PXP
• Gas volumes can be used in stoichiometry problems
O(g)H2)(O)(H2 222 gg
asjust
)(OH volumes2)(O volumes1
)(OH volumes2)(H volumes2
)(O volume1)(H volumes2
22
22
22
pressure) and re temperatu(same volumes2 volume1 volumes2
gg
gg
gg
)(OH moles 2)(O mole 1
)(OH moles 2)(H moles 2
)(O mole 1)(H moles 2
asjust
22
22
22
gg
gg
gg
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• The behavior of ideals gases can be explained
(a) Diffusion (b) Effusion
Kinetic Molecular Theory
• So far we have considered “what happens,” but not “why.”happens, but not why.
• In science, “what” always comes before “why.”
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Kinetic Molecular Theory
Postulates:
1 G ti l i ti1. Gas particles are in ______ motion, colliding with container walls.
Kinetic Molecular Theory
Postulates:
2 Gas particles have2. Gas particles have ______________size compared to the distances between them.
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Kinetic Molecular Theory
Postulates:
3 G ti l h tt ti3. Gas particles have ____ attraction for one another.
Kinetic Molecular Theory
Postulates:
4 Ab l t t t f th i4. Absolute temperature of the gas is a measure of the average ________ ________ of the gas particles.
5.6
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• Diffusion is the _____________intermingling of the molecules of one gas with another
• Effusion is the movement of gas molecules through a ______ ________into a ________.
• The rates of both diffusion and effusion depend on the ________ of the gas
l lmolecules
• The _________ the molecules, the ________diffusion and effusion occur
• Thomas Graham studied effusion
• He found that the effusion rate of a gas was ________ proportional to the square root of the density (d)square root of the density (d)
• This is known as Graham’s law
MdA
TP
)(rateeffusion
) and (constant d
1 rateeffusion
• Where Mi is the molar mass of species iA
B
A
B
M
M
d
d
B
A
)( rateeffusion
)( rateeffusion
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Diffusion
• The movement of one gas through another by thermal random motion.
• Diffusion is a very slow process in air because the mean free path is very short (for N2 at STP it is 6.6x10-8 m). Given the nitrogen molecule’s high velocity, the collision frequency is very high also (7.7x109
collisions/s)collisions/s).
• Diffusion also follows Graham's law:
M
1diffusionofRate
Diffusion of agas particlethrough aspace filledwith otherparticles
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NH3(g) + HCl(g) = NH4Cl(s)
The inverserelation betweendiffusion rate and
Due to it’s lightmass ammonia
molar mass.mass, ammonia travels 1.46 timesas fast as hydrogen chloride
NH3(g) + HCl(g) NH4Cl(s)
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Relative Diffusion Rates of NH3 and HCl
A Practical Example of Using Gas Density Diffusion Separation andDensity, Diffusion, Separation and Purification for Enriched Uranium
Gaseous Diffusion Separation ofGaseous Diffusion Separation of Uranium 235 / 238
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Gaseous Diffusion Separation of Uranium 235 / 238
Purified solid mixed U3O8 ,UO3 ,and, UO2 containing all uranium isotopes are converted to all isotopic forms of UF6(g)
Gaseous Diffusion Separation of Uranium 235 / 238
Purified solid mixed U3O8 ,UO3 ,and, UO2
t i i ll i i tcontaining all uranium isotopes are converted to all isotopic forms of UF6(g)
At Start: 235UF6 vs 238UF6
0.72 % 99.28 %
after approximately 2000 runs235UF6 is > 99% Purity
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The Gas Laws Can Be Explained by KMT
When the gas volume is madeWhen the gas volume is made smaller going from (a) to (b), the frequency of collisions per unit area of the containers’ wall increases. Thus the pressure increases.
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The kinetic theory and the pressure-temperature law (Gay-Lussac’s law). The pressure increases from (a) to (b) as measured by the amount of mercury that must be added to maintain a constant volume.
The kinetic theory and the temperature-volume law (Charles’ law). The pressure is the same in both (a) and (b). At higher temperatures the volume increases because the gas molecules have higher velocities.
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Kinetic Molecular Theory
• Particles are _________ masses in
constant, random, straight line , , g
motion.
• Particles are separated by ______
distances.
• Collisions are _____ and ______.
Prentice-Hall © 2007General Chemistry: Chapter 6Slide 45 of 46
• No ________ between particles.
• Total energy remains __________.
Pressure – Assessing Collision Forces
• Translational kinetic energy,2
k mu2
1e
N• Frequency of collisions,
• Impulse or momentum transfer,
V
Nuv
muI
N
Prentice-Hall © 2007General Chemistry: Chapter 6Slide 46 of 46
• Pressure proportional to impulse times frequency
2muV
NP
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Pressure and Molecular Speed
• Three dimensional systems lead to:
2umV
N
3
1P
2u
um is the modal speeduav is the simple averageurms
Prentice-Hall © 2007General Chemistry: Chapter 6Slide 47 of 46
Pressure
um3
1PV 2
A NAssume one mole:
3RT
uM3RT
umRT3
3
2
2A
NPV=RT so:
NAm = M:
Prentice-Hall © 2007 General Chemistry: Chapter 6 Slide 48 of 46
M
3RTurms Rearrange:
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Distribution of Molecular Speeds
M
3RTurms
Prentice-Hall © 2007 General Chemistry: Chapter 6 Slide 49 of 46
Determining Molecular Speed
Prentice-Hall © 2007 General Chemistry: Chapter 6 Slide 50 of 46
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Temperature)um
2
1(
3
2um
3
1PV 22
A NN AModify:
(T)R
2
3e
e3
2RT
Ak
k
N
N A
PV=RT so:
Solve for ek:
Prentice-Hall © 2007 General Chemistry: Chapter 6 Slide 51 of 46
Conclusion: Average _______ __________is directly proportional to _____________
6-8 Gas Properties Relating to the
Kinetic-Molecular Theory
• Diffusion– Net rate is proportional to
molecular speed.
• Effusion– A related phenomenon.
Prentice-Hall © 2007General Chemistry: Chapter 6Slide 52 of 46
p
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Plots of PV/nRT Versus P for Several Gases (200 K)
Copyright © Houghton Mifflin Company. All rights reserved
5–53
• J. D. van der Waals corrected the ideal gas equation in a simple, but useful, way
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2
2
nRTnbVan
P measuredmeasured
valuegas ideal to measured reduces :
valuegas ideal toup measured brings : 2
2
2
Vnb
PV
an
V
measured
measuredmeasured
measured
constantsder WaalsVan theasknown are b and a
0.023700.03421HeHelium,mol L
mol atmL
Substance122
ba
0.03049 5.464 OH Water,
0.03707 4.170 NH Ammonia,
0.02661 0.02444 H Hydrogen,
0.01709 0.2107 Ne Neon,
0.02370 0.03421 He Helium,
2
3
2