1. The Gas Laws

2. Kinetic Molecular Theory (KMT)
Kinetic Molecular Theory of gases attempts to explain the properties of gases such as pressure, temperature, or volume, by looking at what they are made up of and how they move

3. Kinetic Molecular Theory (KMT)
Kinetic refers to motion
The energy an object has because of its motion is called kinetic energy
Example: A ball rolling down a hill has kinetic energy

4. Kinetic Molecular Theory (KMT)
There are three main components to kinetic theory:
Perfectly elastic collisions, no energy is gained or lost when gas molecules collide
Gas molecules take up no space they are so small
Gas molecules are in constant, linear, random motion

5. Kinetic Molecular Theory (KMT)
How does Kinetic Theory explain Gas Pressure?
Gas Pressure results from fast moving gas particles colliding with the sides of a container
More Collisions = Higher Pressure

6. Kinetic Molecular Theory (KMT)
How does Temperature relate to Kinetic Theory?
Temperature is a measure of the average kinetic energy of all the particles in a gas
Higher Energy = Higher Temperature

7. Kinetic Molecular Theory (KMT)
Through KMT, several Laws were developed to help calculate the changes in pressure, temperature, and volume of gases.
There are 6 Basic Laws:
1. Boyle’s Law
2. Charles’ Law
3. Gay-Lussac’s Law
4. Avogadro’s Law
5. Ideal Gas Law – volume liters only
6. Dalton’s Law
Combined Gas Law

8. Units used to describe gas samples:
Volume
Liter (L)
Milliliter (mL)
1000 mL = 1L
Temperature
Kelvin ONLY
K = ºC + 273
Pressure
Atmosphere (atm)
Kilopascale (kPa)
Torr (torr)
mm of mercury (mm Hg)
1 atm = kPa
1 atm = 760 mm Hg
1 atm = 760 torr
Standard Temperature and Pressure (STP)
Standard Temperature = 273K
Standard Pressure = 1 atm

9. Boyle’s Law
Boyle’s Law – at constant temperature, the volume of the gas increases as the pressure decreases. (and the volume of the gas decreases and the pressure increases). They are inversely related
V↑ P↓
Volume L
P1V1 = P2V2
If you squeeze a gas sample, you make its volume smaller.
Pressure (kPa)

10. ↕ Same temperature Moveable piston
Now a container where the volume can change (syringe)
Moveable piston ↕
Same temperature
Volume is 100 mL at 25°C
Volume is 50 mL at 25°C
In which system is the pressure higher? (Which has the greater number of collisions with the walls and each other?)
Boyle’s Law video example

11. P1V1 = P2V2 Boyle’s Law Example
2.00 L of a gas is at mmHg pressure. What is its volume at mmHg pressure?
P1V1 = P2V2
2.00L x mmHg = mm Hg x V2
2.00L x mmHg = mm Hg x V2
760.0 mm Hg mmHg
1.95 L = V2

12. Charles’ Law
Charles’ Law – at a constant pressure, the volume of a gas increases as the temperature of the gas increases (and the volume decreases when the temperature decreases). They are directly related.
increase the speed of
the particles collide more often and with more force causing the walls of a flexible container expand. Think of hot air balloons!
V V2
T T2 =
Volume L
Temperature (K)
Charles’ Law Video Example

13. V1 = V2 T1 T2 4.40L = V2 323K 298K (298K) x 4.40L = V2 (298K)
Charles’ Law Example:
4.40 L of a gas is collected at 50.0°C. What will be its volume upon cooling to 25.0°C?
First you must convert temperatures from Celsius to Kelvin. Temperature must always be in Kelvin
K = °C
T1 = °C = 323K
T2 = °C = 298K
V1 = V2
T1 T2
4.40L = V2
323K K
(298K) x 4.40L = V2 (298K)
323K K
V2 = 4.06L

14. Gay-Lussac’s Law
Gay-Lussac’s Law – at a constant volume, the pressure of a gas increases as the temperature of the gas increases (and the pressure decreases when the temperature decreases). They are directly related.
P P2
T T2
Pressure
(atm) =
Temperature (K)
Gay-Lussac’s Law Video Example

15. A B Steel cylinder (2L) contains 500 molecules of O2 at 400 K
In which system do the O2 molecules have the highest average kinetic energy (temperature)?
In which system will the particles collide with the container walls with the greatest force and the most often?
In which system is the pressure higher? B B B

16. Example: In a rigid container a gas has a pressure of 1. 3 atm at 25°C
Example: In a rigid container a gas has a pressure of 1.3 atm at 25°C. What is the pressure of the gas if it is heated to 45°C?
First you must convert temperatures from Celsius to Kelvin. Temperature must always be in Kelvin
K = °C
T1 = °C = 298K
T2 = °C = 318K
P P2
T T2
1.3 atm = P2
298K 318K
(318K) X 1
1.3 atm = P2
298K 318K
X (318K) 1
P2 = 1.39 atm
1.4 atm (2 sig figs)

17. Unit Conversions Practice
Convert 56.0 mL to L .056L Convert 65.6 g H2O to moles H2O 65.6g x 1mole H2O g 3.64 mole H2O Convert 788 torr to atm 788 x 1 atm 760 torr 1.04 atm

18. Note that all temperatures must be in Kelvin!
Combined Gas Law
A combination of Boyle’s, Charles’, and Gay-Lussac’s Laws
P1V P2V2
T T2 =
Note that all temperatures must be in Kelvin!

19. Example:
A gas occupies 2.0 L at 2.5 atm and 25ºC. What is it’s volume if the temperature is increased to 33ºC and the pressure is decreased to 1.5 atm?
P1V P2V2
T T2
P1 = 2.5 atm
V1 = 2.0L
T1 = = 298K
P2 = 1.5 atm
V2 = ?
T2 = = 306K
(2.5 atm)(2.0L) (306K) = V2
(298K) (1.5 tm)
V2 = 3.4 L

20. Example:
A gas occupies 4.5 L at 1.3 atm and 35ºC. What is the final temperature if the final volume of the gas is 3.2 L with a pressure of 1.5 atm?
P1V1 = P2V2
T T2
P1 = 1.3 atm
V1 = 4.5L
T1 = = 308K
P2 = 1.5 atm
V2 = 3.2L
T2 = ?K
(1.5 atm)(3.2L) (308K) = T2
(4.5L) (1.3 atm)
T2 = 250K

21. Avogadro’s Law (Hypothesis pg 320)
Avogadro’s Law – equal volumes of gases at the same temperature and pressure contain equal numbers of molecules. H2 O2
CO2
1 mole of ANY gas takes up a volume of 22.4 L at STP. This is called Molar Volume
22.4L = 1 mole of gas at STP
Memorize this!

22. One mole of ANY gas takes up a volume of 22.4 L at STP.
Avogadro’s Law:
One mole of ANY gas takes up a volume of 22.4 L at STP.
So how many molecules of any gas are there in 22.4 L at STP?
6.022 x 1023

23. Avogadro’s Law: At STP, 1.0 L of Helium gas contains the
same number of atoms as:
2.0 L of Kr
1.0 L of Ne
0.5 L of Rn
1.5 L of Ar
Therefore equal _______________ of gas
contain equal numbers of __________ or
______________________.
volumes
atoms
molecules

24. Ideal Gases
Gases whose behavior can be predicted by the kinetic molecular theory are called ideal, or perfect, gases. No gases are truly ideal because no gas totally obeys all of the gas laws.
An ideal gas is an imaginary gas that is perfect and does follow everything perfectly.
We assume that all gases behave like ideal gases so there is an ideal gas law

25. Ideal Gas Law P = pressure in atmospheres (atm)
PV = nRT
P = pressure in atmospheres (atm)
V = volume in Liters (L)
n = # of moles
T = temperature in Kelvin (K)
R = L·atm/mol·K

26. Ideal Gas Law Example:
How many moles of oxygen will occupy a volume of 2.50 L at 1.20 atm and 25°C?
PV = nRT
n = PV RT
n = (1.20)(2.50)
(.08206) (298K)
n = .123 moles of oxygen

27. Ideal Gas Law Example:
What volume will 12.4 grams of O2 gas occupy at 756 torr and 17°C?
PV = nRT
V = nRT P
P = 756 torr
X 1 atm
760.0 torr
P = .995 atm
n = 12.4g 1
x 1 mol
32.00g
n = .388 mol
V = (.388)(.08206) (290.0K)
.995 atm
V = 9.28L

28. What is STP. STP stands for standard temperature and pressure
What is STP? STP stands for standard temperature and pressure. Standard temperature is always 273K. Standard pressure is always 1.00 atm.
Examples using STP:
At 1.80 atm of pressure and 30.0 °C temperature, a gas occupies a volume of 65.5 mL. What will be the volume of the same gas at STP?
Which gas law should we use?
Combined Gas Law
P1V1 = P2V2
T T2
(1.80 atm) (65.5 mL) = (1.00 atm) V2
(303K) 273K
(1.80 atm) (65.5 mL) (273K) = V2
(303K) (1.00 atm)
V2 = 106 mL

29. One More Law!! Dalton’s Law of Partial Pressures -
In a mixture of gases, each gas exerts a certain pressure as if it were alone. The pressure of each one of these gases is called the partial pressure. The total pressure of a mixture of gases is the sum of all of the partial pressures.
Ptotal = P1 + P2 + P3 …….
Pair = PO2 + PN2 + Par + PH2O + PCO2

30. Ptotal = P1 + P2 + P3 PTOTAL = 179 kPa
Example:
What is the total pressure of a mixture of gases made up of CO2, O2, and H2 if the partial pressures are 22.3 kPa, 44.7 kPa, and 112 kPa, respectively?
Ptotal = P1 + P2 + P3
PTOTAL = 22.3kPa kPa kPa =
PTOTAL = 179 kPa

31. YouTube - MythBusters - Fun With Gas

32. Gas Stoichiometry 0.100 mol H2 1 mol N2 22.4 L N2 = .747 L N2 1
Example 1: One mole of any gas at STP occupies a volume of ___________ L .
How do you write this as a conversion factor? 
22.4 L 1 mol
1mol 22.4L
For the following reaction:
N2(g) +3H2 (g) 2NH3(g)
What volume of nitrogen gas at STP would be required to react with mol of hydrogen gas in the reaction above?
22.4
0.100 mol H2
1 mol N2
22.4 L N2
= .747 L N2 1
3 mol H2
1 mol N2

33. Gas Stoichiometry N2(g) +3H2 (g) 2NH3(g)   
What volume of nitrogen gas at STP would be required to react with grams of hydrogen gas in the reaction above?
22.4 L N2
0.100 g H2
1 mol H2
1 mol N2
3 mol H2 1
2.02 g H2
1 mol N2
= .370 L N2

34. END