Transcript Slide 1

Chapter 14
The Behavior of
Gases
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# of particles related gas pressure
The pressure of a gas :
• the force per unit area that the particles exert on
the walls of their container.
Pressure =
force
area
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# of particles related to gas pressure
Pump more air inside a ball
 more particles
 mass of air inside increases
more collision (inner wall of ball)
higher pressure (at a given temp) inside the
ball
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# of particles related to gas pressure
pressure (of a gas) 
mass
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Defining Gas
According to the kinetic theory,
• all matter is composed of particles in constant
motion, and
• pressure is caused by the force of (g) particles
striking the walls of their container.
The more often (g) particles collide with the walls
of their container, the > the pressure.
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# of particles related to gas pressure
pressure

# particles (mol)
Doubling the # of
gas particles in a
basketball doubles
the pressure
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Quick write
The pressure inside a balloon always = to the
atm pressure.
How does the balloon adjust the pressure inside
when it is transferred to places of different
temperatures?
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Temperature Related to Pressure
At higher temp
• the (g) particles possess more KE
• move faster
• collide with the walls of the container more
often and with greater force,
• so the pressure rises.
i.e. When temp increases, pressure also increases.
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Temperature Related to Pressure
• At constant volume (of the container),
pressure

K temp.
e.g. gas in a glass bottle. When temp increases,
pressure increases.
• At constant pressure,
volume of a gas

K temp.
e.g. gas in a balloon. When temp increases, → bigger.
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Barometer
• The height of the Hg column measures the
pressure exerted by the atm.
• We live at the bottom of an ocean of air.
• The highest pressures occur at the lowest altitudes.
• When going up a mountain, atm pressure decreases
because the depth of air above you is less.
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Barometer
standard
atmosphere (atm)
• the pressure that
supports a 760-mm
column of Hg.
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Pressure Units
• Because the pascal is a small pressure unit, it is
more convenient to use kilopascal (kPa)
• 1 std atm pressure is equivalent to 101 kPa.
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Pressure Units (3)
• Pounds per square inch (psi) continues to be
widely used in engineering and almost all
nonscientific applications in the U.S.
• Pressure inside car tires. e.g. 36 psi
Equivalent Pressures
1 atm = 760 mmHg = 760 Torrs = 14.7 psi = 101.3 kPa
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The Gas Laws
ideal gases
(kinetic theory) 5 statements.
(1) particles do not attract or repel each other.
(2) particles are much smaller than the spaces
between them. (total volume of particles ≈ 0)
Assumptions are not true when pressure is very
high ; total volume of particles becomes
significant.
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The Gas Laws
(3) (g) particles are in constant, random
motion.
(4) No KE is lost when (g) particles collide
with each other or with the walls of their
container.(perfectly elastic)
(5) All (g) have the same KE at a given temp.
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Boyle’s Law: Pressure and Volume
Robert Boyle
(1627-1691),
(English).
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Boyle’s Law: Pressure and Volume
After performing many expts with (g) at constant
temp, Boyle got 4 findings.
(1) If the pressure of a (g) increases, its volume decreases
proportionately.
(2) If the pressure of a gas decreases, its volume increases
proportionately.
(3) If volume of a (g) increases, its pressure decreases
proportionately.
(4) If volume of a (g) decreases, its pressure increases
proportionately.
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Boyle’s Law: Pressure and Volume
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Boyle’s Law: Pressure and Volume
Boyle’s law
 the pressure and volume of a (g) at constant
temperature are inversely proportional.
1
P
V
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Boyle’s Law: Pressure and Volume
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Boyle’s Law
• At a constant temp, the pressure exerted by
a (g) depends on the frequency of collisions
between (g) particles and the container.
the same # of particles is squeezed into a
smaller space → the frequency of collisions
increases →increasing the pressure.
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Boyle’s Law
1
P 
V
• In math terms, this law is expressed as follows.
P1V1 = P2V2
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Applying Boyle’s Law (1)
Example 1
A sample of compressed methane has a volume of
648 mL at a pressure of 503 kPa. To what pressure
would the methane have to be compressed in order
to have a volume of 216 mL?
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Example 2 (Boyle’s Law)
A high-altitude balloon contains 30.0 L of He (g) at
103 kPa. What is the volume when the balloon
rises to an altitude where the pressure is only 25.0
kPa? (Assume that the temp remains constant.)
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Charles’s Law
When the temp of a sample of (g) is increased
and the volume is free to change, the pressure
does not change. (e.g. balloon)
Instead, the volume of the (g) increases in
proportion to the increase in K temp.
Charles’s law : at constant pressure, the volume of a given
mass of (g) is directly proportional to its K temp.
V1
V2

T1
T2
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Example 3
A weather balloon contains 5.30 kL of He gas when
the temp is 12°C. At what temp will the balloon’s
volume have increased to 6.00 kL?
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Answer
50°C
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Applying Charles’s Law (2)
New Temp = 323 – 273 = 50°C
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Example 4 (Charles’s Law)
A balloon inflated in a room at 24°C has a
volume of 4.00 L. The balloon is then heated to
a temp of 58°C. What is the new volume if the
pressure remains constant?
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Gay-Lussac Law
Gay-Lussac’s law
• pressure of (g) is directly proportional to its K
temp (volume constant)
Pressure
P1
T1
=
α
temperature (K)
P2
T2
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Example 5 (Gay-Lussac’s Law)
The gas left in a used aerosol can is at a pressure of
103 kPa at 25°C. If it is thrown onto a fire, what
is the pressure of the gas when its temp reaches
928°C?
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Answer
415.1 kPa
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The Combined Gas Law (1)
combined gas law
• relating P, V, and T
P1V 1 P 2V 2

T1
T2
STP :
1 atm; 101 kPa;
0°C; 273K
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Factors Affecting Gas Pressure (1)
• If the (g) pressure increases until it exceeds the
strength of an enclosed, rigid container, the
container will burst.
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Factors Affecting Gas Pressure (2)
Aerosol Spray Paint
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Factors Affecting Gas Pressure (4)
When the volume of the container is halved, the
pressure the (g) exerts is doubled.
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Factors Affecting Gas Pressure (6)
When the K temp of the enclosed gas doubles, the
pressure of the enclosed (g) doubles.
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Avogadro’s Principle (1)
Avogadro Law
• = vol of all (g) at the same conditions of T
and P contain the same # of particles.
• one mole (6.02 x 1023 particles) of any (g) at
std temp and P (0°C and 1.00 atm pressure,
101 kPa, STP) occupies a vol of 22.4 L.
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Example 6 (combined gas law)
A sample of nitrogen monoxide has a volume of
72.6 mL at a temp of 16°C and a pressure of
104.1 kPa. What volume will the sample
occupy at 24°C and 99.3 kPa?
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Answer
78.2 mL
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Example 7 (combined gas law)
The volume of a gas-filled balloon is 30.0L at
40°C and 153 kPa pressure. What volume will
the balloon have at std temp and pressure
(STP)?
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CST problem 1
The volume of 400 mL of chlorine gas at 400
mm Hg is decreased to 200 mL at constant
temperature. What is the new gas pressure?
A 400 mm Hg
B 300 mm Hg
C 800 mm Hg
D 650 mm Hg
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CST problem 2
Standard temperature and pressure (STP) are
defined as
A 0°C and 1.0 atm pressure
B 0°C and 273 mm Hg pressure
C 0 K and 1.0 atm pressure
D 0 K and 760 mm Hg pressure
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CST problem 3
Under which of the following sets of conditions
will a 0.50 mole sample of He occupy a
volume of 11.2 L?
A 298 K and 0.90 atm
B 273 K and 1.10 atm
C 373 K and 0.50 atm
D 273 K and 1.00 atm
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CST problem 4
What is the equivalent of 423 K in °C?
A
B
C
D
-223°C
-23°C
150°C
696°C
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CST problem 5
Under what circumstance might a gas decrease in
volume when heated?
A The gas is held constant at STP.
B The gas remains under uniform temperature.
C The gas is placed under increasing pressure.
D The gas undergoes a decrease in pressure.
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CST problem 6
Theoretically, when an ideal gas in a closed container
cools, the pressure will drop steadily until the
pressure inside is essentially that of a vacuum. At
what temperature should this occur?
A 0 °C
B -460 °C
C -273 °C
D 0K
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Factors Affecting Gas Pressure (3)
Volume
 can raise the pressure exerted by a
contained (g) by reducing its volume.
The more a (g) is compressed, the > is the
pressure that the (g) exerts inside the
container.
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CST problem 1
A scientist observed changes in the gas pressure of one
mole of a gas in a sealed chamber with a fixed
volume. To identify the source of the changes, the
scientist should check for variations in the
A air pressure outside the chamber
B molecular formula of the gas
C temperature of the chamber
D isotopes of the gas
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CST problem 2
A weather balloon with a 2-m diameter at ambient
temperature holds 525 g of He. What type of
electronic probe could be used to determine the
pressure inside the balloon?
A barometric
B thermometric
C calorimetric
D spectrophotometric
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The End
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Question 4
What pressure will be needed to reduce the
vol of 77.4 L of He at 98.0 kPa to a vol of
60.0 L?
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Answer
126 kPa
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The Ideal Gas Law (1)
• The pressure, vol, temp, and # moles of gas can be
related as in the ideal gas law.
PV = nRT
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The Ideal Gas Law (2)
• The ideal gas constant, R, already contains
the molar vol of a gas at STP along with the
std temp and pressure conditions.
R = 0.082 L atm K−1 mol−1
R = 8.31 L kPa K−1 mol−1
62.36 L Torr K−1 mol−1
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Applying the Ideal Gas Law
• What pressure in atm will 18.6 mol of methane
exert when it is compressed in a 12.00-L tank at a
temp of 45°C?
• change the temp to K before doing anything else.
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Question 3
A 250.0-mL sample of a noble gas collected at
88.1 kPa and 7°C has a mass of 0.378 g. What is
the molar mass of the gas? Identify the sample.
Answer
40.0g/mol; argon
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Question 4
When potassium chlorate is heated, it decomposes to
produce potassium chloride and oxygen (g). Write a
balanced eqn for this rxn, and calculate the mass of
potassium chlorate needed to produce 5.00 x 102 mL
of oxygen (g) at 1.108 atm and 39°C.
Answer
2KClO3(s) → 2KCl(s) + 3O2
;
1,77g
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Factors Affecting Gas Pressure (5)
Temperature
• An increase in the temperature of an enclosed (g)
causes an increase in its pressure.
• As a (g) is heated, the average KE of the particles in
the (g) increases. Faster-moving particles strike the
walls of their container with more energy.
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