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Physical Physical Characteristics Characteristics

of Gasesof GasesChapter 10Chapter 10

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Kinetic-molecular theoryKinetic-molecular theory• Particles of matter are always in

motion

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Ideal gasIdeal gas• An imaginary gas that perfectly fits

all the assumptions of the kinetic-molecular theory.

• We can often treat real gases as ideal gases and still get good results.

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Assumptions of KMT of Assumptions of KMT of gasesgases

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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ExpansionExpansion• 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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FluidityFluidity• Gas particles slide past each other.• They can flow

– Fluid: something that can flow (can be gas or liquid)

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DiffusionDiffusion• 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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EffusionEffusion• When gas particles pass through a

small opening• Particles leak out of the container

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Real gasesReal gases• Do not completely follow kinetic-

molecular 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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DiscussDiscuss• 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 gasesDescribing gases• Needed:

– Volume– Temperature– Number of molecules– Pressure

• They are mathematically related.

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PressurePressure• balloon• The force per unit area on a surface.

area

forcepressure

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ForceForce• 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 gasesPressure 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 pressureAtmospheric 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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BarometerBarometer• 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.

h

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ManometerManometer• Used to measure

the pressure of gases.

• The height difference between the two arms is the pressure.

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Pressure UnitsPressure Units

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STPSTP• Standard temperature and pressure.• 0 °C and 1 atm• Used to compare volumes of gases.

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ExampleExample• 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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DiscussDiscuss• Define pressure• What is STP?• Convert 151.98 kPa to atmospheres

– 1.4999 atm

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Boyle’s LawBoyle’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 LawBoyle’s Law• Mathematically:

• Each sample of gas has its own k.

P

kV kPV

2211 VPVP

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ExampleExample• 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 tryYou 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 LawCharles’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 LawCharles’s Law• Mathematically

2

2

1

1

T

V

T

V

kT

V

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Kelvin ScaleKelvin 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 ScaleKelvin Scale• Absolute zero: lowest possible

temperature– All particle motion stops– 0 K, -273.15 °C

• Often rounded to 273

CK 15.273

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ExampleExample• 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 tryYou 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 LawGay-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 LawGay-Lussac’s Law• Mathematically:

kT

P

2

2

1

1

T

P

T

P

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You tryYou 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 lawCombined gas law• Expresses the relationship between

pressure, volume, and temperature of a fixed amount of gas.

kT

PV

2

22

1

11

T

VP

T

VP

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You tryYou 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 LawDalton’s Law• The total pressure in a container is

the sum of the partial pressures of all the gases in the container.

...321 PPPPT

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ApplicationApplication• We can collect gases by displacing

water.• When we do this,

• Read Patm from the barometer. Look up Pwater in table A-8 in the appendix.

watergasatm PPP

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ExampleExample• 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 tryYou 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