John C. Kotz
Paul M. Treichel
John Townsend
http://academic.cengage.com/kotz
Chapter 11
Gases and Their Properties
John C. Kotz • State University of New York, College at Oneonta
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BEHAVIOR OF GASES
Chapter 11
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Importance of Gases
PLAY MOVIE
• Airbags fill with N2 gas in an accident.
• Gas is generated by the decomposition of
sodium azide, NaN3.
• 2 NaN3 f 2 Na + 3 N2
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5
Hot Air Balloons —
How Do They Work?
PLAY MOVIE
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THREE
STATES
OF
MATTER
PLAY MOVIE
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General Properties
of Gases
• There is a lot of “free” space
in a gas.
• Gases can be expanded
infinitely.
• Gases occupy containers
uniformly and completely.
• Gases diffuse and mix
rapidly.
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Properties of Gases
Gas properties can be
modeled using math. Model
depends on—
•
•
•
•
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V = volume of the gas (L)
T = temperature (K)
n = amount (moles)
P = pressure
(atmospheres)
Pressure
Pressure of air is
measured with a
BAROMETER
(developed by
Torricelli in 1643)
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Pressure
Hg rises in tube until
force of Hg (down)
balances the force
of atmosphere
(pushing up).
P of Hg pushing down
related to
• Hg density
• column height
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Pressure
Column height
measures P of
atmosphere
• 1 standard atm
= 760 mm Hg
= 29.9 inches Hg
= about 34 feet of
water
SI unit is PASCAL,
Pa, where 1 atm =
101.325 kPa
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IDEAL GAS LAW
P V = n R T
Brings together gas
properties.
Can be derived from
experiment and theory.
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Boyle’s Law
If n and T are
constant, then
PV = (nRT) = k
This means, for
example, that P
goes up as V goes
down.
© 2009 Brooks/Cole - Cengage
Robert Boyle
(1627-1691).
Son of Earl of
Cork, Ireland.
Boyle’s Law
A bicycle pump is a good example of Boyle’s
law.
As the volume of the air trapped in the pump
is reduced, its pressure goes up, and air is
forced into the tire.
PLAY MOVIE
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Charles’s
Law
If n and P are
constant, then
V = (nR/P)T = kT
V and T are directly
related.
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Jacques Charles (17461823). Isolated boron
and studied gases.
Balloonist.
16
Charles’s original balloon
Modern long-distance balloon
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Charles’s Law
Balloons immersed in liquid N2 (at -196 ˚C) will
shrink as the air cools (and is liquefied).
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Charles’s Law
PLAY MOVIE
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Avogadro’s Hypothesis
Equal volumes of gases at the same
T and P have the same number of
molecules.
V = n (RT/P) = kn
V and n are directly related.
twice as many
molecules
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Avogadro’s Hypothesis
f
PLAY MOVIE
The gases in this experiment are all
measured at the same T and P.
2 H2(g) + O2(g)
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f
2 H2O(g)
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Combining the Gas Laws
•
•
•
•
•
V proportional to 1/P
V prop. to T
V prop. to n
Therefore, V prop. to nT/P
V = 22.4 L for 1.00 mol when
– Standard pressure and
temperature (STP)
– T = 273 K
– P = 1.00 atm
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Using PV = nRT
How much N2 is req’d to fill a small room
with a volume of 960 cubic feet (27,000 L)
to P = 745 mm Hg at 25 oC?
R = 0.082057 L•atm/K•mol
Solution
1. Get all data into proper units
V = 27,000 L
T = 25 oC + 273 = 298 K
P = 745 mm Hg (1 atm/760 mm Hg)
= 0.98 atm
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Using PV = nRT
How much N2 is req’d to fill a small room with a volume of 960
cubic feet (27,000 L) to P = 745 mm Hg at 25 oC?
R = 0.082057 L•atm/K•mol
Solution
2. Now calc. n = PV / RT
(0.974 atm)(2.7 x 104 L)
n=
(0.0821 Lįatm/Kįmol)(298 K)
n = 1.1 x 103 mol (or about 30 kg of gas)
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Gases and Stoichiometry
2 H2O2(liq) f 2 H2O(g) + O2(g)
Decompose 0.11 g of H2O2 in a flask with a
volume of 2.50 L. What is the pressure of O2
at 25 oC? Of H2O?
Bombardier beetle
uses decomposition
of hydrogen peroxide
to defend itself.
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Gases and Stoichiometry
2 H2O2(liq) f 2 H2O(g) + O2(g)
Decompose 0.11 g of H2O2 in a flask with a
volume of 2.50 L. What is the pressure of O2
at 25 oC? Of H2O?
Solution
Strategy:
Calculate moles of H2O2 and then
moles of O2 and H2O.
Finally, calc. P from n, R, T, and V.
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Gases and Stoichiometry
2 H2O2(liq) f 2 H2O(g) + O2(g)
Decompose 0.11 g of H2O2 in a flask with a volume of 2.50 L.
What is the pressure of O2 at 25 oC? Of H2O?
Solution
 1 mol 
0.11 g H2O2 
 0.0032 mol

 34.0 g 
 1 mol O 
2
0.0032 mol H2O2 
 = 0.0016 mol O2
 2 mol H2O 2 
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Gases and Stoichiometry
2 H2O2(liq) f 2 H2O(g) + O2(g)
Decompose 0.11 g of H2O2 in a flask with a volume of 2.50 L.
What is the pressure of O2 at 25 oC? Of H2O?
Solution
P of O2 = nRT/V
(0.0016 mol)(0.0821 Lįatm/Kįmol)(298 K)
=
2.50 L
P of O2 = 0.016 atm
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Gases and Stoichiometry
2 H2O2(liq) f 2 H2O(g) + O2(g)
What is P of H2O? Could calculate as above.
But recall Avogadro’s hypothesis.
V
P


n at same T and P
n at same T and V
There are 2 times as many moles of H2O as
moles of O2. P is proportional to n.
Therefore, P of H2O is twice that of O2.
P of H2O = 0.032 atm
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Dalton’s Law of Partial Pressures
2 H2O2(liq) f 2 H2O(g) + O2(g)
0.032 atm 0.016 atm
What is the total pressure in the flask?
Ptotal in gas mixture = PA + PB + ...
Therefore,
Ptotal = P(H2O) + P(O2) = 0.048 atm
Dalton’s Law: total P is sum of
PARTIAL pressures.
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Dalton’s Law
John Dalton
1766-1844
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GAS DENSITY
PLAY MOVIE
Higher
Density air
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Low
density
helium
GAS DENSITY
PV = nRT
n
P
=
V
RT
m
P
=
M• V
RT
where M = molar mass
and density (d) = m/V
m
PM
d=
=
V
RT
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d and M proportional
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The Disaster of Lake Nyos
• Lake Nyos in Cameroon
was a volcanic lake.
• CO2 built up in the lake
and was released
explosively on August
21, 1986.
• 1700 people and
hundreds of animals
died.
• See Chapter 14 for more
information
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USING GAS DENSITY
The density of air at 15 oC and 1.00 atm is 1.23
g/L. What is the molar mass of air?
1. Calc. moles of air.
V = 1.00 L
P = 1.00 atm
T = 288 K
n = PV/RT = 0.0423 mol
2. Calc. molar mass
mass/mol = 1.23 g/0.0423 mol = 29.1 g/mol
© 2009 Brooks/Cole - Cengage
KINETIC MOLECULAR THEORY
(KMT)
Theory used to explain gas laws. KMT
assumptions are
• Gases consist of molecules in
constant, random motion.
• P arises from collisions with container
walls.
• No attractive or repulsive forces
between molecules. Collisions elastic.
• Volume of molecules is negligible.
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Kinetic Molecular Theory
Because we assume molecules are in
motion, they have a kinetic energy.
KE = (1/2)(mass)(speed)2
At the same T, all gases have
the same average KE.
As T goes up for a gas, KE also
increases — and so does speed.
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Kinetic Molecular Theory
At the same T, all gases have the same
average KE.
As T goes up, KE also increases — and so
does speed.
PLAY MOVIE
© 2009 Brooks/Cole - Cengage
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Kinetic Molecular Theory
Maxwell’s equation
2
u =
3 RT
M
Root mean square speed
where u is the speed and M is the
molar mass.
• speed INCREASES with T
• speed DECREASES with M
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Distribution of
Gas Molecule
Speeds
PLAY MOVIE
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• Boltzmann plots
• Named for Ludwig
Boltzmann doubted
the existence of
atoms.
• This played a role in
his suicide in 1906.
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Velocity of Gas Molecules
Molecules of a given gas have a range of
speeds.
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Velocity of Gas Molecules
Average velocity decreases with increasing
mass.
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GAS DIFFUSION AND
EFFUSION
DIFFUSION is the gradual mixing of
molecules of different gases.
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GAS EFFUSION
EFFUSION is the movement of molecules
through a small hole into an empty
container.
See Figure 11.19
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GAS DIFFUSION AND
EFFUSION
Molecules effuse thru holes in a
rubber balloon, for example, at
a rate (= moles/time) that is
• proportional to T
• inversely proportional to M.
Therefore, He effuses more
rapidly than O2 at same T.
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He
GAS DIFFUSION AND
EFFUSION
Graham’s law governs
effusion and diffusion
of gas molecules.
Rate for A
=
Rate for B
M of B
M of A
Rate of effusion is
inversely proportional
to its molar mass.
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Thomas Graham, 1805-1869.
Professor in Glasgow and London.
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Gas Diffusion
relation of mass to rate of diffusion
PLAY MOVIE
See Active Figure 11.18
© 2009 Brooks/Cole - Cengage
• HCl and NH3 diffuse
from opposite ends
of tube.
• Gases meet to form
NH4Cl
• HCl heavier than NH3
• Therefore, NH4Cl
forms closer to HCl
end of tube.
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Using KMT to Understand
Gas Laws
Recall that KMT assumptions are
• Gases consist of molecules in
constant, random motion.
• P arises from collisions with container
walls.
• No attractive or repulsive forces
between molecules. Collisions elastic.
• Volume of molecules is negligible.
© 2009 Brooks/Cole - Cengage
Avogadro’s Hypothesis and
Kinetic Molecular Theory
PLAY MOVIE
P proportional to n —
when V and T are constant
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Gas Pressure, Temperature,
and Kinetic Molecular Theory
PLAY MOVIE
P proportional to T —
when n and V are constant
© 2009 Brooks/Cole - Cengage
Boyle’s Law and Kinetic
Molecular Theory
PLAY MOVIE
P proportional to 1/V —
when n and T are constant
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Deviations from
Ideal Gas Law
• Real molecules have
volume.
• There are
intermolecular
forces.
– Otherwise a gas could
not become a liquid.
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Deviations from Ideal Gas Law
Account for volume of molecules and
intermolecular forces with VAN DER
WAALS’s EQUATION.
Measured V = V(ideal)
Measured P
(
P
2
n a
+ ----2
V
)
V
-
nb
nRT
vol. correction
intermol. forces
© 2009 Brooks/Cole - Cengage
J. van der Waals,
1837-1923,
Professor of
Physics,
Amsterdam.
Nobel Prize 1910.
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Deviations from Ideal Gas Law
Cl2 gas has a = 6.49, b = 0.0562
For 4.00 mol Cl2 in a 4.00 L tank at 100.0 oC.
P (ideal) = nRT/V = 30.6 atm
P (van der Waals) = 26.0 atm
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