1. Kinetic Molecular Theory and Gas Behavior

3. Definition
Theory – An attempt to explain scientific behavior and properties.
Kinetic Molecular Theory (KMT) – An attempt to explain gas behavior based upon the motion of molecules

4. Assumptions of the KMT 1
All gases are made of atoms or molecules 2
Gas particles are in constant, rapid, random motion
The temperature of a gas is proportional to the average kinetic energy of the particles 3
Gas particles are not attracted nor repelled from one another 4
All gas particle collisions are perfectly elastic (no kinetic energy is lost to other forms) 5
The volume of gas particles is so small compared to the space between the particles, that the volume of the particle itself is insignificant 6

5. What is a “real gas”?
Ideal Gas – a gas that is a gas under any conditions of temperature and pressure. There is no such thing as a real gas! Only Real gases that behave ideally!
Real Gas – 2 of the assumptions of the Kinetic Molecular Theory are not valid
Gas particles are not attracted nor repelled from one another
Gas particles do have attractions and repulsions towards one another
The volume of gas particles is so small compared to the space between the particles, that the volume of the particle itself is insignificant
Gas particles do take up space—thereby reducing the space available for other particles to be

6. What are the measurable quantities of a gas:
The Amount of the gas in Moles (n)
The Pressure of the gas (P)
The Temperature of the gas (T)
The Volume of the gas (V)

7. Pressure
Gas Pressure – Caused by the collisions of billions of gas particles against a surface
Watch the Can!

8. Pressure Units Several units are used when describing pressure Unit
Symbol
atmospheres
atm
Pascals, kiloPascals
Pa, kPa
millimeters of mercury
mm Hg
pounds per square inch
psi
1 atm = Pa = kPa = 760 mm Hg = 14.7 psi

9. What is Atmospheric Pressure?
Atmospheric Pressure – Pressure due to the layers of air in the atmosphere.
Climb in altitude
Less layers of air
Lower atmospheric pressure
As altitude increases, atmospheric pressure decreases.

10. Pressure In Versus Out
A container will expand or contract until the pressure inside = atmospheric pressure outside
Example:
A bag of chips is bagged at sea level. What happens if the bag is then brought up to the top of a mountain.
The internal pressure is from low altitude (high presser)
The external pressure is high altitude (low pressure).
Lower
pressure
Higher
pressure
Lower
pressure
The internal pressure is higher than the external pressure.
The bag will expand in order to reduce the internal pressure.

11. When Expansion Isn’t Possible
Rigid containers cannot expand
Example:
An aerosol can is left in a car trunk in the summer. What happens?
The temperature inside the can begins to rise.
As temperature increases, pressure increases.
Lower
pressure
Can
Explodes!
Higher
pressure
The internal pressure is higher than the external pressure.
The can is rigid—it cannot expand, it explodes!
Soft containers or “movable pistons” can expand and contract.
Rigid containers cannot.

12. Pressure and Volume
As volume increases, pressure decreases because the molecules have to travel farther before colliding with the container!

13. Boyles’ Law – Mathematical Relationship
Boyles’ Law relates pressure and volume
Where temperature and # of molecules are held constant
P = pressure
V = volume
The two pressure units must match and
the two volume units must match!
Example:
A gas sample is 1.05 atm in a 2.5 L container. What pressure is it if the volume is changed to 2.7 L?

14. Boyles’ Law Boyles’ Law relates pressure and volume
Where temperature and # of molecules are held constant
P = pressure
V = volume
The two pressure units must match and
the two volume units must match!
Example:
A gas sample is 1.05 atm in a 2.5 L container. What pressure is it if the volume is changed to 2.7 L?
P1 = 1.05 atm
V1 = 2.5 L
P2 = ? atm
V2 = 2.7 L
P2 = 0.98 atm

15. What is “Temperature”?
Temperature – proportional to the average kinetic energy of the molecules
Energy due to motion
(Related to how fast the molecules are moving)
As temperature increases
Molecular motion increases

16. Temperatures cannot fall below an absolute zero
Temperature Units
Kelvin (K)– temperature scale with an absolute zero
Temperatures cannot fall below an absolute zero
A temperature scale with absolute zero is needed in Gas Law calculations because you can’t have negative pressures or volumes

17. STP
Standard Temperature and Pressure (STP) – 1 atm (or the equivalent in another unit) and 0°C (273 K)
Problems often use “STP” to indicate quantities…don’t forget this “hidden” information when making your list!
1 atm = Pa = kPa = 760 mm Hg = 14.7 psi

18. Pressure and Temperature
As temperature increases, pressure increases because the particles are moving faster and can collide with the wall at a faster pace.

19. Gay Lussac’s Law – A mathematical relationship
Gay Lussac’s Law relates pressure to temperature
Where Volume and # of molecules are held constant
P = Pressure
T = Temperature in Kelvins
Example:
A gas at a pressure of 2.0 atm and 273K is heated to 285K. What is the new pressure of the gas?

20. Gay Lussac’s Law Gay Lussac’s Law relates pressure to temperature
Where Volume and # of molecules are held constant
P = Pressure
T = Temperature in Kelvins
Temperature must be in K and units must match!
Example:
A gas at a pressure of 2.0 atm and 273K is heated to 285K. What is the new pressure of the gas?
P1 = 2.0 atm
T1 = 273 K
T2 = 285 K
P2 = ? atm
P2 = 2.1 atm

21. Volume and Temperature
As the temperature of a gas increases the volume of the gas increases because the gas particles have more kinetic energy and will spread farther away from each other.

22. Charles’ Law Charles’ Law relates temperature and volume
Where pressure and # of molecules are held constant
V = Volume
T = Temperature
The two volume units must match and
temperature must be in Kelvin!
Example:
What is the final volume if a 10.5 L sample of gas is changed from 25C to 50C?
Temperature needs to be in Kelvin!
V1 = 10.5 L
T1 = 25C
V2 = ? L
T2 = 50C
25C = 298 K
50C = 323 K

23. Charles’ Law Charles’ Law relates temperature and pressure
Where pressure and # of molecules are held constant
V = Volume
T = Temperature
The two volume units must match and
temperature must be in Kelvin!
Example:
What is the final volume if a 10.5 L sample of gas is changed from 25C to 50C?
V1 = 10.5 L
T1 = 25C
V2 = ? L
T2 = 50C
= 298 K
= 323 K
V2 = 11.4 L

24. Moles What is a mole? A mole is a counting unit
Other counting units include
Dozen = 12
Gross = 144
Baker’s Dozen = 13
You can have half or part of a mole just like you can have half or part of a dozen

25. Volume and Moles
The volume of a gas increases as the moles of the gas increase because the more gas particles you have the larger the space they will take up.

26. Avogadro’s Law
Avogadro’s Law relates # of particles (counted in a unit called moles) and volume.
Where Temperature and Pressure are held constant
V = Volume
n = # of moles of gas (A mole is a counting term like a dozen)
The two volume units must match!
Example:
A sample with 0.15 moles of gas has a volume of 2.5 L. What is the volume if the sample is increased to 0.55 moles?

27. Avogadro’s Law
Avogadro’s Law relates # of particles (moles) and volume.
Where Temperature and Pressure are held constant
V = Volume
n = # of moles of gas
The two volume units must match!
Example:
A sample with 0.15 moles of gas has a volume of 2.5 L. What is the volume if the sample is increased to 0.55 moles?
n1 = 0.15 moles
V1 = 2.5 L
n2 = 0.55 moles
V2 = ? L
V2 = 9.2 L

28. Combined Gas Law P = Pressure Each “pair” of units must match and
V = Volume
n = # of moles
T = Temperature
Each “pair” of units must match and
temperature must be in Kelvin!
Example:
What is the final volume if a mole sample of gas at 1.7 atm, 1.5 L and 298 K is changed to STP and particles are added to mole?

29. Combined Gas Law P = Pressure Each “pair” of units must match and
V = Volume
n = # of moles
T = Temperature
Each “pair” of units must match and
temperature must be in Kelvin!
Example:
What is the final volume if a mole sample of gas at 1.7 atm, 1.5 L and 298 K is changed to STP and particles are added to mole?
P1 = 1.7 atm
V1 = 1.5 L
n1 = mole
T1 = 298 K
P2 = 1.0 atm
V2 = ? L
n2 = mole
T2 = 273 K
STP is standard temperature (273 K) and pressure (1 atm)
V2 = 4.2 L

30. Transforming the Combined Law
Watch as variables are held constant and the combined gas law “becomes” the other 3 laws
Hold pressure and temperature constant
Avogadro’s Law
Hold moles and temperature constant
Boyles’ Law
Hold pressure and moles constant
Charles’ Law
Can you show how to prove Gay Lussac’s Law? Which two variables are constant?

31. Effusion & Diffusion

32. Effusion Effusion –gas escapes from a tiny hole in the container
Effusion is why balloons deflate over time!

33. Diffusion Diffusion –gas moves across a space
Diffusion is the reason we can smell perfume across the room

34. Effusion, Diffusion & Particle Mass
How are particle size (mass) and these concepts related?
As mass of the particles increases, rate of effusion and diffusion is lowered because heavier particles, move slower.

35. Rate of Diffusion & Particle Mass
Watch as larger particles take longer to get to your nose