Physical Characteristics

of GasesChapter 10

Chemistry Chapter 10 2

Kinetic-molecular theory• Particles of matter are always in

motion

Chemistry Chapter 10 3

Ideal 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.

Chemistry Chapter 10 4

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

Chemistry Chapter 10 5

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

Chemistry Chapter 10 6

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

Chemistry Chapter 10 7

Fluidity• Gas particles slide past each other.• They can flow

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

Chemistry Chapter 10 8

Diffusion• Spontaneous mixing of the particles

of two substances caused by their random motion.

• Gas particles spread out to fill their new container

Chemistry Chapter 10 9

Effusion• When gas particles pass through a

small opening• Particles leak out of the container

Chemistry Chapter 10 10

Real 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

Chemistry Chapter 10 11

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.

Chemistry Chapter 10 12

Describing gases• Needed:

– Volume– Temperature– Number of molecules– Pressure

• They are mathematically related.

Chemistry Chapter 10 13

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

area

forcepressure

Chemistry Chapter 10 14

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.

Chemistry Chapter 10 15

Chemistry Chapter 10 16

Pressure of gases• Gases exert pressure on any surface

with which they collide.– Depends on volume, temperature, and

number of molecules

Chemistry Chapter 10 17

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.

Chemistry Chapter 10 18

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.

h

Chemistry Chapter 10 19

Manometer• Used to measure

the pressure of gases.

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

Chemistry Chapter 10 20

Pressure Units

Chemistry Chapter 10 21

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

Chemistry Chapter 10 22

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

Chemistry Chapter 10 23

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

– 1.4999 atm

Chemistry Chapter 10 24

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

Chemistry Chapter 10 25

Boyle’s Law• Mathematically:

• Each sample of gas has its own k.

P

kV kPV

2211 VPVP

Chemistry Chapter 10 26

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

Chemistry Chapter 10 27

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

Chemistry Chapter 10 28

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.

Chemistry Chapter 10 29

Charles’s Law• Mathematically

2

2

1

1

T

V

T

V

kT

V

Chemistry Chapter 10 30

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.

Chemistry Chapter 10 31

Kelvin Scale• Absolute zero: lowest possible

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

• Often rounded to 273

CK 15.273

Chemistry Chapter 10 32

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

Chemistry Chapter 10 33

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

Chemistry Chapter 10 34

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.

Chemistry Chapter 10 35

Gay-Lussac’s Law• Mathematically:

kT

P

2

2

1

1

T

P

T

P

Chemistry Chapter 10 36

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

Chemistry Chapter 10 37

Combined 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

Chemistry Chapter 10 38

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

Chemistry Chapter 10 39

Dalton’s Law• The total pressure in a container is

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

...321 PPPPT

Chemistry Chapter 10 40

Application• 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

Chemistry Chapter 10 41

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

Chemistry Chapter 10 42

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