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Chapter 10: Properties of Gases:
The Air We Breathe
South Pole
Sept 24, 2006
15 February 2017
http://ozonewatch.gsfc.nasa.gov
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Chapter Outline
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10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
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The Properties of Gases
Neither definite shape nor definite volume
The Properties of Gases
Gases can be compressed.
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The Properties of Gases
All gases are miscible with all other gases.
http://catalog.flatworldknowledge.com/bookhub/4309?e=averill_1.0-ch13_s01
Chapter Outline
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
10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
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Kinetic Molecular Theory of Gases
1. Gas particles have tiny volumes compared
with their container’s volume
Kinetic Molecular Theory of Gases
2. They don’t interact with other gas
molecules, e.g. no intermolecular forces.
X
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Kinetic Molecular Theory of Gases
3.
They move randomly and constantly
Kinetic Molecular Theory of Gases
4. Elastic collisions with
walls of container and
other gas molecules
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Kinetic Molecular Theory of Gases
5. Have average kinetic energy that is proportional to
absolute Kelvin temperature:
KEavg = ½ mu2rms
rms velocity  1/M
= 32 g/mol
= 28
= 18
=4
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Graham’s Law of Effusion, p. 415
Effusion is the process
where a gas escapes
through a small pore in the
container wall into a region
of lower pressure.
Sample Exercise 10.1: Calculating
Relative Rates of Effusion
An odorous gas emitted by a hot spring was found to effuse
at 0.342 times the rate at which helium effuses. What is the
molar mass of the emitted gas?
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Chapter Outline
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

10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
Pressure = force/unit area
Molecules collide with the inside surface of the container.
The force of the collision is measured as pressure.
Pressure at Sea Level
Pounds/in2 (psi)
Atmospheres (atm)
Pascals (N/m2)
Torr (mmHg)
14.7 psi
1 atm
101.325 X 103 Pa
760 mmHg
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Torricelli’s Barometer
vacuum
Column of
mercury
760 mm Hg
Atmospheric
pressure
The pressure of the
atmosphere on the surface
of the mercury in the dish
is balanced by the
downward pressure
exerted by the mercury in
the column.
Elevation and Atmospheric
Pressure
0.35 atm
0.62 atm
0.83 atm
Sea level
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Chapter Outline
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
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

10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
State Variables for a Gas
P = pressure
V = volume
T = temperature
n = number of
moles
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Boyle’s Law: P and V
(n and T held constant)
 Gases are compressible
• Pressure ↑ as Volume ↓
 Boyle’s Law:
• P  1/V (T and n fixed)
• or, P × V = constant
• or, P1V1 = P2V2
• Decreasing volume increases
number of collisions/area; P↑
(KMT Postulates #3 & 4)
Boyle’s Law and Respiration
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Applying Boyle’s Law Example
A bubble of oxygen at the bottom of a lake floats up to the surface. The
pressure at the bottom of the lake is 4.75 atm and the volume is 5.65 mL.
At the surface, the new volume is 5.65 mL. Assuming that the
temperature and number of moles remained constant, what is the final
volume of the bubble?
Explaining Boyle’s Law Using Kinetic
Molecular Theory
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Charles’s Law: V and T
(n and P held constant)
 Charles’s Law:
• V  T (P, n constant)
V V
or, 1 = 2
T1 T2
Volume of a gas extrapolates
to zero at absolute zero (0 K
= −273°C).
Kinetic energy ↑ as T ↑; force of
collisions increases and gas
expands to maintain constant
P (KMT Post. #3, 4 & 5).
Jacques Alexandre Charles (1796-1823)
The French chemist Charles was most famous in his lifetime for his experiments in
ballooning. The first such flights were made by the Montgollier brothers in June 1783,
using a large spherical balloon made of linen and paper and filled with hot air. In
August 1783, however, a different group. supervised by Jacques Charles, tried a
different approach. Exploiting his recent discoveries in the study of gases, Charles
decided to inflate the balloon with hydrogen gas. Because hydrogen would escape
easily from a paper bag, Charles made a bag of silk coaled with a rubber solution.
Inflating the bag to its final diameter took several days and required nearly 500
pounds of acid and 1000 pounds of iron to generate the hydrogen gas. A huge crowd
watched the ascent on August 27, 1783. The balloon stayed aloft for almost 45
minutes and travelled about 15 miles. When it landed in a village, however, the
people were so terrified they tore if to shreds.
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Sample Exercise 10.4:
Applying Charles’ Law
Several students at a northern New England campus are hosting a party
celebrating the mid-January start of “spring” semester classes. They
decide to decorate the front door of their apartment building with party
balloons. The air in the inflated balloons is initially 70 oF. After an hour
outside, the temperature of the balloons is -12 oF. Assuming no air leaks
from the balloons and the pressure in them does not change significantly,
how much does their volume change? Express your answer as a
percentage of the initial volume.
Explaining Charles’ Law Using Kinetic
Molecular Theory
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Avogadro’s Law: V and n
(T and P held constant)
 Volume is directly proportional to the number
of moles of gas, V  n (T, P constant)
V
 constant
n
or ,
V1 V2

n1 n2
Increasing n increases the
number of collisions, gas
expands to keep pressure
constant (KMT Post. #3 & 4).
Explaining Avogadro’s Law Using
Kinetic Molecular Theory
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Amonton’s Law: P and T
(n and V held constant)
 P  T (n, V constant)
P
= constant
T
P P
or, 1 = 2
T1 T2
Increasing T will increase force
of collisions if volume is kept
constant; P will increase (KMT
Post. #3, 4 & 5).
Sample Exercise 10.5:
Applying Amonton’s Law
Labels on aerosol cans caution against their incineration because the
cans may explode when the pressure inside them exceeds 3.00 atm. At
what temperature in degrees Celcius might an aerosol can burst if its
internal pressure is 2.00 atm at 25 oC?
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Explaining Amonton’s Law Using
Kinetic Molecular Theory
Chapter Outline
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


10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
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The Combined Gas Law
Combining Boyle’s and Charles’ Law (where n is held constant)
Sample Exercise 10.6:
Applying the Combined Gas Law
The pressure inside a weather balloon as it is released is 798 mmHg. If
the volume and temperature of the balloon are 131 L and 20 oC, what is
the volume of the balloon when it reaches an altitude where its internal
pressure is 235 mmHg and T = -52 oC?
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Chapter Outline












10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
Ideal Gas Equation
Boyle’s law: V  1 (at constant n and T)
P
Charles’ law: V  T (at constant n and P)
Avogadro’s law: V  n (at constant P and T)
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Standard Temperature and Pressure (STP).
Experiments show that at STP,
1 mole of an ideal gas
occupies 22.414 L.
PV = nRT
Sample Exercise 10.7:
Applying the Ideal Gas Law
Bottles of compressed O2 carried by climbers ascending Mt. Everest are
designed to hold one kilogram of the gas. What volume of O2 can one
bottle deliver to a climber at an altitude where the temperature is -38 oC
and the atmospheric pressure is 0.35 atm? Assume that each bottle
contains 1.00 kg of O2.
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Chapter Outline
10.1 The Properties of Gases
10.2 Effusion and the Kinetic Molecular Theory of Gases
10.3 Atmospheric Pressure
10.4 The Gas Laws
10.5 The Combined Gas Law
10.6 Ideal Gases and the Ideal Gas Law
10.7 Densities of Gases
10.8 Gases in Chemical Reactions
10.9 Mixtures of Gases
10.10 Solubility of Gases and Henry’s Law
10.11 Gas Diffusion: Molecules Moving Rapidly
10.12 Real Gases
Densities and Molecular Weights of
Gases Using PV = nRT
PV = nRT
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Sample Exercise 10.8:
Calculating the Density of a Gas
According to the U.S National Weather Service, the air temperature in Phoenix, AZ
reached 78 oF on January 1, 2012, when the atmospheric pressure was 1024 millibars.
What is the density of the air? Assume the average molar mass of air is 28.8 g/mol,
which is the weighted average of the molar masses of the various gases in dry air.
Example: Calculating the Molecular
Weight from PV = nRT
1.018 g of Freon-113 gas is trapped in a 145 mL container at
760 mmHg and 50.0°C. What is the molar mass of Freon-113?
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Chapter Outline
10.1 The Properties of Gases
10.2 Effusion and the Kinetic Molecular Theory of Gases
10.3 Atmospheric Pressure
10.4 The Gas Laws
10.5 The Combined Gas Law
10.6 Ideal Gases and the Ideal Gas Law
10.7 Densities of Gases
10.8 Gases in Chemical Reactions
10.9 Mixtures of Gases
10.10 Solubility of Gases and Henry’s Law
10.11 Gas Diffusion: Molecules Moving Rapidly
10.12 Real Gases
Gas Laws & Stoichiometry
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Example: Combining Stoichiometry and
the Ideal Gas Law
Chlorine gas can be prepared in the laboratory by the reaction of
manganese dioxide with hydrochloric acid:
MnO2(s) + 4 HCl(aq)  MnCl2(aq) + 2 H2O(l) + Cl2(g)
How many grams of MnO2 should be added to excess HCl to obtain 275
mL of chlorine gas at 5.0°C and 650 mmHg?
Chapter Outline
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


10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
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Dalton’s Law of Partial Pressures
 For a mixture of gases in a container:
• Ptotal = P1 + P2 + P3 + . . .
Total pressure depends only on total number moles
of gas, not on their identities
Mole Fraction & Partial Pressure
 Mole Fraction:
• Ratio of the # of moles of a given component
in a mixture to the total # of moles in a
mixture:
x1 
n1
n1

ntotal n1  n2  n3  ...
 Mole Fraction in Terms of Pressure:
• When V and T are constant, P  n
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Mole Fraction & Partial Pressure
Since P  n
x1 
n1
P
 1
ntotal Ptotal
And:
x1 
P1
Ptotal
Then…
P1  x1Ptotal
Sample Exercise 10.11: Calculating
Mole Fractions and Partial Pressures
Scuba divers who dive to depths below 50 meters
may breathe a gas mixture called Trimix during the
deepest parts of their dives. One formulation of the
mixture, called Trimix 10/70, is 10% oxygen, 70%
helium, and 20% nitrogen by volume. What is the
mole fraction of each gas in this mixture, and what is
the partial pressure of oxygen in the lungs of a diver
at a depth of 60 meters (where the ambient pressure
is 7.0 atm)?
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Collecting a Gas over Water
2 KClO3(s) → 2 KCl(s) + 3 O2(g)
Gases collected:
O2(g) and H2O(g)
Ptotal  PO2  PH2O
Sample Exercise 10.12: Calculating the Quantity
of a Gas Collected by Water Displacement
During the decomposition of KClO3, 92.0 mL of gas is
collected by the displacement of water at 25.0 oC. If
atmospheric pressure is 756 mmHg, what mass of O2 is
collected?
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Chapter Outline
10.1 The Properties of Gases
10.2 Effusion and the Kinetic Molecular Theory of Gases
10.3 Atmospheric Pressure
10.4 The Gas Laws
10.5 The Combined Gas Law
10.6 Ideal Gases and the Ideal Gas Law
10.7 Densities of Gases
10.8 Gases in Chemical Reactions
10.9 Mixtures of Gases
10.10 Solubility of Gases and Henry’s Law
10.11 Gas Diffusion: Molecules Moving Rapidly
10.12 Real Gases
Solubility of Gases
 Solubility of gases
depends on T and P
Solubility ↑ as Pressure ↑
Solubility ↓ as Temperature ↑
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Henry’s Law
 Henry’s Law:
• The higher the partial
pressure of the gas
above a liquid, the
more soluble
• Cgas  Pgas
• Cgas  kH Pgas
Solubility of Oxygen in Water
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Sample Exercise 10.13: Calculating
Gas Solubility Using Henry’s Law
Lake Titicaca is located high in the Andes Mountains between
Peru and Bolivia. Its surface is 3811 m above sea level, where the
average atmospheric pressure is 0.636 atm. During the summer,
the average temperature of the water’s surface rarely exceeds 15
oC. What is the solubility of oxygen in Lake Titicaca at that
temperature? Express your answer in molarity and in mg/L.
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Chapter Outline
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










10.1
10.2
10.3
10.4
10.5
10.6
10.7
10.8
10.9
10.10
10.11
10.12
The Properties of Gases
Effusion and the Kinetic Molecular Theory of Gases
Atmospheric Pressure
Relating P,T, and V: The Gas Laws
The Combined Gas Law
Ideal Gases and the Ideal Gas Law
Densities of Gases
Gases in Chemical Reactions
Mixtures of Gases
Solubilities of Gases and Henry’s Law
Gas Diffusion: Molecules Moving Rapidly
Real Gases
Gas Diffusion: Molecules Moving Rapidly
𝑢𝑟𝑚𝑠 =
3𝑅𝑇
𝑀
R = 8.314 J/mol K
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Practice Exercise 10:14
Calculating Root-Mean-Square Speeds
Calculate the root-mean-squared speed of nitrogen molecules at 25 oC.
Graham’s Law of Effusion:
Same for Diffusion!
𝑈𝑟𝑚𝑠,𝐴 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐴 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐴
=
=
=
𝑈𝑟𝑚𝑠,𝐵 𝑒𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐵 𝑑𝑖𝑓𝑓𝑢𝑠𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 𝐵
𝑀𝐵
𝑀𝐴
Problem 10.121
A flask of ammonia is connected to a flask of an unknown acid HX by a 1.00 m
glass tube. As the two gases diffuse down the tube, a white ring of NH 4X forms
68.5 cm from the ammonia flask. Identify element X.
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