Unit 12 - Gases
Pressure
Pressure and Volume: Boyle’s Law
Volume and Temperature: Charles’s Law
Volume and Moles: Avogadro’s Law
Ideal Gas Law
Dalton’s Law of Partial Pressures
Kinetic Molecular Theory of Gases
Gas Stoichiometry
1
Unit 12 - Gases
Upon completion of this unit, you should be able to do the following:
1. Describe the effect of a change in temperature on a gas and
determine the new volume or gas pressure at the new temperature.
2. Use the combined gas law to determine the pressure, temperature
or volume of a gas when experimental conditions change.
3. Determine the molar mass, molar volume or density of a gas from
experimental data.
4. Apply the ideal gas law to determine the pressure, volume,
temperature or number of moles in a gas sample.
5. Calculate the partial pressure of a gas in a mixture given the mole
ratio of the mixture. Find the number of moles present given the
partial pressure ratio.
6. Use the postulates of the kinetic molecular theory to explain the
differences between the three phases of matter.
7. Use the gas laws to solve stoichiometry problems involving gaseous
reactants or products.
2
Pressure
• A gas expands to fill its container, is easily
compressed and mixes completely with other
gases. A gas exerts pressure on its
surroundings (see balloon). The air inside the
balloon pushes against the elastic sides.
• The gases most familiar to us form the earth’s
atmosphere. The mass of air in the
atmosphere is pulled toward the center of the
earth by gravity resulting in a pressure exerted
by the air. This is called atmospheric pressure.
3
Pressure
• One method of measuring atmospheric
pressure is to use a mercury barometer. The
weight of the atmosphere will support a
column of about 760 mm Hg.
4
Pressure
5
Pressure
• The unit “mm Hg” is also called torr. It is also
equal to 1 atmosphere, another unit of
measure for pressure.
• In engineering, the unit of pounds per square
inch, abbreviated as PSI, is used.
1 atm = 14.69 PSI
• The SI unit for pressure is called the Pascal,
abbreviated as Pa.
1 atm = 101,325 Pa
6
Pressure
• Atmospheric pressure is lower at higher
altitudes. At an altitude of 9600 feet, the
atmospheric pressure is 520 mm Hg. Convert
that pressure to atmospheres.
7
Pressure and Volume
The first careful studies of gases were made by
Robert Boyle in the late 1600’s.
8
Pressure and Volume
Sample of Boyle’s Data
140
Pressure (in Hg)
120
100
80
60
40
20
0
0
10
20
30
40
Volume (cubic inches)
50
60
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Pressure and Volume
• Note that the temperature and moles of gas
remained constant.
• As volume decreases, pressure increases. This
is an inverse relationship.
• He determined that the product of pressure
times volume equals a constant, or PV=k. This
is know as Boyle’s Law.
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Pressure and Volume
• Using Boyle’s Law, we can predict the new
volume of a gas if the pressure changes.
P1V1 = P2V2
(1 atm)(1L) = (2 atm)(x L)
x=½L
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Pressure and Volume
0.56 L
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Pressure and Volume
9.7 atm
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Volume and Temperature
Jacques Charles
showed that the
volume of a gas
increases as the
temperature of
the gas increases.
The solid lines are
actual data. The
dashed lines are
extrapolated to a
point defined as
absolute zero on
the Kelvin scale.
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Volume and Temperature
• Note that the pressure and moles of gas
remained constant.
• As volume increases, temperature increases.
This is a direct relationship.
• He determined the direct proportionality
between volume and temperature, or V=bT.
This is know as Charles’s Law.
• The units of temperature in this equation are in
degrees Kelvin.
15
Volume and Temperature
• We can also write Charles’s Law as
=
1.9L
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Volume and Temperature
-29 oC
17
Volume and Moles
• Experiments show that when the number of
moles of gas is doubled (at constant
temperature and pressure), the volume
doubles.
• The volume of a gas is directly proportional to
the number of moles of the gas, V = an. This is
known as Avogadro’s Law.
=
18
Volume and Moles
8.1 L
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Ideal Gas Law
• Combining these laws gives the equation
V=R
Where R is the combined proportionality constant
and is called the universal gas constant and is
equal to .08206 l-atm/oK-mol.
We can rewrite this as the Ideal Gas Law
PV = nRT
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Ideal Gas Law
.57 mol
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Ideal Gas Law
12.5 L
22
Ideal Gas Law
4.4 atm
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Ideal Gas Law
3.07 L
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Dalton’s Law of Partial Pressure
Many important gases contain a mixture of
components. One notable example is air. Scuba divers
who are going deeper than 150 feet use another
important mixture, helium and oxygen. Normal air is
not used because the nitrogen present dissolves in
blood in large quantities as a result of the high
pressures experienced by the diver under several
hundred feet of water. When the diver returns too
quickly to the surface, the nitrogen bubbles out of the
blood just as soda fizzes when it is opened, and the
diver gets decompression sickness – a very painful and
potentially fatal condition. Because helium gas is only
slightly soluble in blood, it does not cause this problem.
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Dalton’s Law of Partial Pressure
• Studies of gaseous mixtures show that each
component behaves independently of the
others. John Dalton was one of the first
scientists to study mixtures of gases. He
observed that the total pressure exerted is the
sum of the partial pressures of the gases. The
partial pressure of a gas is the pressure the gas
would exert if it were alone in the container.
Ptotal = P1 + P2 + P3
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Dalton’s Law of Partial Pressure
27
Dalton’s Law of Partial Pressure
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Dalton’s Law of Partial Pressure
2.59 x 10 -2 mol
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Kinetic Molecular Theory
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Kinetic Molecular Theory
The meaning of temperature
Per the KMT, the temperature of a gas reflects
how rapidly its individual particles are moving.
At high temperatures the particles move very
fast and hit the walls of the container
frequently. At low temperatures the particles
move slower and collide with the walls less
often. Temperature really is a measure of the
motions of the gas particles. Kelvin
temperature is directly proportional to the
average kinetic energy of the gas particles.
31
Kinetic Molecular Theory
The relationship between pressure and
temperature
As a gas is heated, the particles move faster,
hitting the walls of its rigid (constant volume)
container more frequently. The impacts
become more forceful as the particles move
faster. Pressure is due to collisions with the
wall, so as temperature increases, so does
pressure.
32
Kinetic Molecular Theory
The relationship between volume and
temperature
As a gas is heated, the particles move faster,
causing the pressure to increase. If we allow a
volume change so that pressure can be held
constant, the gas will expand to maintain
constant pressure. So, the KMT model predicts
that the volume will increase as the
temperature increases.
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Kinetic Molecular Theory
34
Gas Stoichiometry
3.13 L
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Gas Stoichiometry
7.81 x 10 -2 mol N2
36