Chapter 13States of Matter

Section 13.1: Nature of Gases

• Kinetic Theory and a Model for Gases

– Kinetic Energy: Energy that an object has because of its motion

– Kinetic Theory: All matter consists of tiny particles that are in constant motion

• Particles in a gas are usually atoms/molecules.

• There are three fundamentals to the kinetic theory of gases which we will review one by one.

Kinetic Theory

• Particles in a gas are considered to be small, hard spheres w/ insignificant volume.

- a lot of empty space between particles

- no attractive/repulsive forces b/w

particles

- Motion of 1 particle is independent

from the motion of other particles

Kinetic Theory

• Motion of particles in a gas is rapid, constant and random

- a gas will fill the shape of any container

- uncontained gas spreads out with no limit

- gas particles will travel in a straight path until they collide with something else

Why would individuals in Mexico not be able to smell pizza from a shop in Washington D.C? (Oxygen molecules can travel 1700 km/h at 20 degrees Celsius)

Kinetic Theory

• All Collisions between particles in a gas are perfectly elastic

- Elastic Collision

-Total kinetic energy remains constant between 2 molecules.

-No K.E. is lost, only transferred

Example:

How does the following steel ball toy work?

Layers of the Atmosphere

Components of Dry Troposphere AirSubstance Formula Percent of All

Gas MoleculesMajor ComponentsNitrogen and Oxygen

N2 O2

78%21%

Minor ComponentsArgon Carbon Dioxide

Ar CO2

.93%

.033%

Trace Amounts Ne NH3

He CH4

.0018%

.0010%

.0005%

.0002%

Atmospheric Pressure• -What is atmospheric pressure?

• Results from the collisions of atoms and molecules in air with objects

• Air exerts pressure on earth b/c gravity holds particles in the atmosphere.

As you climb higher up a

mountain, does atmospheric

pressure increase or

decrease and why?

Athletes and Higher Altitude

• Athletes and trainers often recommend high altitude training as a means to increase exercise endurance. At higher altitudes, less oxygen results in the heart working harder.

Atmospheric Pressure• How much pressure are you under? Earth's

atmosphere is pressing against each square inch of you with a force of 1 kilogram per square centimeter (14.7 pounds per square inch). The force on 1,000 square centimeters (a little larger than a square foot) is about a ton!

• Why doesn't all that pressure squash me? Remember that you have air inside your body too, that air balances out the pressure outside so you stay nice and firm and not squishy.

Atmospheric PressureWhy do my ears pop?• . As the number of molecules of air around you decreases, the

air pressure decreases. This causes your ears to pop in order to balance the pressure between the outside and inside of your ear.

• Since you are breathing fewer molecules of oxygen, you need to breathe faster to bring the few molecules there are into your lungs to make up for the deficit.

Measuring PressureBarometer: used to measure

atmospheric pressureThe SI units of pressure is Pascal (Pa)

other units: Millimeters of Mercury (mm Hg)

atmospheres (atm

1 atm = 760 mm Hg = 103.3 kPa

Old Mercury Barometer Is Shown to the Left.

Atmospheric pressure depends on weather and altitude.

Gas Pressure– Gas Pressure: result of simultaneous collisions of

billions of rapidly moving particles in a gas with an object.

– Vacuum: No pressure and No Particles • Why is there no pressure with no particles?

• Demonstration: Write a description of what is happening to the marshmallows

Gas Activity• Kinetic Molecular Theory

Gas particles are small hard spheres with insignificant volume, -far apart

Gas particles move in a random, rapid and constant motion

All collisions between gas particles are perfectly elastic

Properties of Gases• Compressibility : is the measure of how much the volume of matter decreases under pressure.

• Why can gases be compressed?Because of the empty space between gas particles. At room

temp; distance b/w particles in an enclosed gas is 10 x the diameter of the particle.

Why does a collision with an inflated air bag cause much less

damage than a collision with a steering wheel?When a person collides with an air bag, the impact forces the molecules

of gas to compress, which absorbs the energy of the impact.

• Four Variables Describe a Gas– Pressure (P) in Kilopascals– Temperature (T) in Kelvin– Volume (V) in Liters– Numbers of Moles (n)

Factors Affecting Gas Pressure

-gas

-volume

- temperature

Amount of Gas• Increase the number of particles, increase

number of collisions which leads to greater air pressure

Volume• How do you think volume will

affect gas pressure?

Increase the volume, decrease the pressure.

More volume gives the molecules more space to travel around and frequency of collisions is less

• How does an Aerosol Can Work?

Pressure in the can is higher

than the outside pressure.

When the valve opens,

the air will rush out

towards the lower pressure

Air will travel from higher

pressure to lower pressure

Gas Laws• Boyles Law: for a given mass of gas at

constant temperature; the volume of gas varies inversely with pressure

• Mathematical Expression of Boyles Law:

– P1 × V1 = P2 × V2

A sample of chlorine gas occupies a volume of 946 mL at a pressure of 726 mmHg. What is the pressure of the gas (in mmHg) if the volume is reduced at constant temperature to 154 mL?

P1 x V1 = P2 x V2

P1 = 726 mmHg

V1 = 946 mL

P2 = ?

V2 = 154 mL

P2 = P1 x V1

V2

726 mmHg x 946 mL154 mL

= = 4460 mmHg

Graphing: Boyle’s Law• Prepare the following graph

• X axis = volume (L), intervals of .5,

0 to 4• Y axis = pressure (kPa) intervals of 25,

0 to 200

Plot the following point : Pressure(P1) = 200, Volume(V1) = .5

Using the equation : P1 × V1 = P2 × V2

Solve for P2 in the table to the right, and then

plot all of the points from the table on your graph.

P2 V2

1

1.5

2

2.5

3

Kinetic Energy and Temperature

• What’s the difference between Heat and Temperature?

• Heat = Energy• Temperature = measurement of heat

• When a substance is heated, its particles absorb energy- some is stored as P.E.

• The rest of the energy speeds up the particles and increases K.E.

•The faster the particles move, the higher the temperature!

Temperature• Why are an aerosol cans considered

extremely flammable and dangerous if heated?

• An increase in temperature of an enclosed gas causes an increase in its pressure.

• If an aerosol can is thrown in a fire, the pressure increases so dramatically because of the heat, the can explodes

Kinetic TheoryAll atoms and particles are in constant motion, however,

is it possible for particles to have absolutely no motion?

Absolute Zero is the temperature at which the motion of particles theoretically ceases. (-273.15 degrees C)

Absolute Zero has never been produced in a laboratory, but scientists have been close

Charles’s Law: Temp and Vol.• Charles’s Law: states that the volume of a

fixed mass of gas is directly proportional to its Kelvin temperature if the pressure is kept constant.

• Reminder Celsius to Kelvin, + 273 degrees.

Mathematical Representation

V1 = V2

T1 T2

A sample of carbon monoxide gas occupies 3.20 L at 125 0C. At what temperature will the gas occupy a volume of 1.54 L if the pressure remains constant?

V1 = 3.20 L

T1 = 398.15 K

V2 = 1.54 L

T2 = ?

T2 = V2 x T1

V1

1.54 L x 398.15 K3.20 L= = 192 K

V1/T1 = V2/T2

Graphing Charles Law• Prepare the following graph

• X axis = temperature (K), intervals of 100, 0 to 1000

• Y axis = Volume (L) intervals of 1 0 to 4

Plot the following point : Volume = 1, Temp = 300 K

Plot the rest of the graph by completing the following

calculations using : V1 = V2

T1 T2

T2 (x) V2 (y)

300 1

1.5

2

2.5

3

How does a hot air balloon work?

Hot air is lighter than cold air, which makes the balloon float.

Gay-Lussac’s Law:

• States that the pressure of a gas is directly proportional to the Kelvin temperature if the volume remains constant.

• Mathematical Representation P1 = P2

T1 T2

– Example: The gas in a used aerosol can is at a pressure of 103 kPa at 25 degrees Celsius. If the can is thrown into a fire, what is the pressure at 928 degrees Celsius.

Why should you never measure the pressure of your tires after a long trip?• After a long trip, the air in your

tires heats up which increases

the pressure.

• Tire inflation pressures fluctuate with changes in the outside air temperature. This occurs at a rate of about 1 psi for every 10°F (plus or minus).

• If you add the variations of time and temperature together, it is easy to understand why a tire's inflation pressure should be checked frequently. Improper inflation can cause tires to wear irregularly

Summary of Three Gas Law’sLAWLAW RELAT-RELAT-

IONSHIPIONSHIP LAWLAW CON-CON-STANTSTANT

Boyle’sBoyle’s PP V V PP11VV1 1 = P= P22VV22 T, nT, n

Charles’Charles’ VV T T VV11/T/T11 = V = V22/T/T22 P, nP, n

Gay-Gay-Lussac’sLussac’s PP T T PP11/T/T11 = P = P22/T/T22 V, nV, n

Combined Gas Law• Single expression that combines all of the

previous gas laws into one.• The combined gas law allows you to do

calculations for situations in which only the amount of gas is constant

• Mathematical Expression:P1 V1 P2P1×V1 = P2×V2

T1 T2

= T1 T2

Combined Gas Law Problem

A sample of helium gas has a volume of 0.180 L, a pressure of

0.800 atm and a temperature of 29°C. What is the new temperature of the gas at a volume of 90.0 mL and a pressure of 3.20 atm?