Transcript wbm-chemistry

Physical
Characteristics
of Gases
Chapter 10
Kinetic-molecular theory
• Particles of matter are always in
motion
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Ideal gas
• An imaginary gas that perfectly fits
all the assumptions of the kineticmolecular theory.
• We can often treat real gases as
ideal gases and still get good results.
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Assumptions of KMT of
gases
1. Large numbers of tiny particles that
are far apart compared to their size
• Low density
• Easily compressed
2. Elastic collisions
• No kinetic energy is lost when gas particles
collide with each other or their container
• It can be transferred between particles,
but the total kinetic energy remains the
same
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3. Gas particles are in continuous,
rapid, random motion
4. There are no attractive or repulsive
forces between gas particles
• When they hit, they don’t stick together
5. The average kinetic energy of gas
particles depends on the
temperature of the gas
• Direct relationship
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Expansion
• Gases have indefinite shape and
volume.
• They completely fill any container
they are in.
• They also take the shape of that
container.
• Because:
– they move rapidly in all directions and
don’t stick together
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Fluidity
• Gas particles slide past each other.
• They can flow
– Fluid: something that can flow (can be
gas or liquid)
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Diffusion
• Spontaneous mixing of the particles
of two substances caused by their
random motion.
• Gas particles spread out to fill their
new container
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Effusion
• When gas particles pass through a
small opening
• Particles leak out of the container
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Real gases
• Do not completely follow kineticmolecular theory
• Especially deviant at high pressures
and low temperatures
• Noble gases are closest to ideal
• Very polar gases are farthest from
ideal
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Discuss
• Describe the conditions under which
a real gas is most likely to behave
ideally.
• Explain the following properties of
gases using the kinetic-molecular
theory: expansion, fluidity, low
density, compressibility, and
diffusion.
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Describing gases
• Needed:
– Volume
– Temperature
– Number of molecules
– Pressure
• They are mathematically related.
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Pressure
• balloon
• The force per unit area on a surface.
force
pressure 
area
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Force
• A push or a pull
• Measured in newtons (N).
• At the Earth’s surface, 1 kg of mass
exerts 9.8 N of force due to gravity.
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Pressure of gases
• Gases exert pressure on any surface
with which they collide.
– Depends on volume, temperature, and
number of molecules
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Atmospheric pressure
• Air around Earth exerts a pressure
on it’s surface and everything on it.
– Like the weight of all the molecules
pressing down.
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Barometer
• Used to measure
atmospheric pressure.
• Height of liquid (usually
mercury) in tube can be
used to express
atmospheric pressure.
• At sea level, the
average is 760 mm Hg.
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Manometer
• Used to measure
the pressure of
gases.
• The height
difference between
the two arms is the
pressure.
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Pressure Units
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STP
• Standard temperature and pressure.
• 0 °C and 1 atm
• Used to compare volumes of gases.
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Example
• A weather report gives a current
atmospheric pressure of
745.8 mm Hg. Convert this to
– Atmospheres
• 0.9813 atm
– Torr
• 745.8 torr
– Kilopascals
• 99.43 kPa
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Discuss
• Define pressure
• What is STP?
• Convert 151.98 kPa to atmospheres
– 1.4999 atm
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Boyle’s Law
• Fixed: mass and temperature
• The volume varies inversely with
pressure
– Less volume, means the particles hit the
walls more often.
– This increases the pressure
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Boyle’s Law
• Mathematically:
k
V
P
PV  k
• Each sample of gas has its own k.
P1V1  P2V2
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Example
• A helium-filled balloon contains
125 mL of gas at a pressure of
0.974 atm. What volume will the
gas occupy at standard pressure,
assuming constant temperature?
• 122 mL
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You try
• A weather balloon with a volume of
1.375 L is released from Earth’s
surface at sea level. What volume
will the balloon occupy at an altitude
of 20.0 km, where the air pressure is
10.0 kPa, assuming constant
temperature?
• 13.9 L
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Charles’s Law
• Fixed: mass and pressure
• Volume varies directly with
temperature.
– As temperature goes up, the particles
have more energy, so they hit the walls
more often and with more force
– This pushes the walls outward.
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Charles’s Law
• Mathematically
V
k
T
V1 V2

T1 T2
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Kelvin Scale
• Charles’s law works more elegantly
on the Kelvin Scale than the Celsius
Scale.
– If you double the temperature, the
volume doubles.
• Not true with Celsius
• We must use Kelvin for Charles’s
Law.
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Kelvin Scale
• Absolute zero: lowest possible
temperature
– All particle motion stops
– 0 K, -273.15 °C
K  273.15 C

• Often rounded to 273
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Example
• A balloon filled with oxygen gas
occupies a volume of 5.5 L at 25 °C.
What volume will the gas occupy at
100. °C, assuming constant
pressure?
• 6.9 L
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You try
• A sample of nitrogen gas is contained
in a piston with a freely moving
cylinder. At 0.0 °C, the volume of
the gas is 375 mL. To what
temperature must the gas be heated
to occupy a volume of 500. mL,
assuming constant pressure?
• 91 °C
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Gay-Lussac’s Law
• Fixed: mass and volume
• Pressure varies directly with
temperature (in Kelvin)
– As temperature goes up, energy of
particles goes up.
– They go faster and hit the walls harder.
– If the walls can’t move, the pressure
goes up.
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Gay-Lussac’s Law
• Mathematically:
P
k
T
P1 P2

T1 T2
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You try
• The temperature within an
automobile tire at the beginning of a
long trip is 25 °C. At the conclusion
of the trip, the tire has a pressure of
1.80 atm. What is the final Celsius
temperature within the tire if its
original pressure was 1.75 atm?
Assume constant volume.
• 34 °C
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Combined gas law
• Expresses the relationship between
pressure, volume, and temperature
of a fixed amount of gas.
PV
k
T
P1V1 P2V2

T1
T2
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You try
• The volume of a gas at 27.0 °C and
0.200 atm is 80.0 mL. What volume
will the same gas sample occupy at
standard conditions?
• 14.6 mL
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Dalton’s Law
• The total pressure in a container is
the sum of the partial pressures of
all the gases in the container.
PT  P1  P2  P3  ...
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Application
• We can collect gases by displacing
water.
• When we do this,
Patm  Pgas  Pwater
• Read Patm from the barometer. Look
up Pwater in table A-8 in the appendix.
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Example
• A student has stored 100.0 mL of
neon gas over water on a day when
the temperature is 27.0 °C. If the
barometer in the room reads
743.3 mm Hg, what is the pressure
of the neon gas in its container?
• 716.6 mm Hg
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You try
• A sample of nitrogen gas is collected
over water at a temperature of
23.0 °C. What is the pressure of the
nitrogen gas if atmospheric pressure
is 785 mm Hg?
• 764 mm Hg
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