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:
1. Perfectly elastic
collisions, no energy is
gained or lost when gas
molecules collide
2. Gas molecules take up
no space they are so
small
3. Gas molecules are in

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 = 101.3 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
P1V1 = P2V2
V↑ P↓
V
o
l
u
m
e
L
Pressure (kPa)
If you squeeze a
gas sample, you
make its volume
smaller.

10. Moveable
piston
↕
Now . . . a
container where
the volume can
change (syringe)
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. Boyle’s Law Example
2.00 L of a gas is at 740.0 mmHg pressure.
What is its volume at 760.0 mmHg pressure?
P1V1 =
P2V2
2.00L x 740.0 mmHg = 760.0 mm Hg x V2
2.00L x 740.0 mmHg = 760.0 mm Hg x V2
760.0 mm Hg 760.0 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.
V
o
l
u
m
e
L
Temperature (K)
V1 V2
T1 T2
=
• increasing the
temperature of a gas
increases the speed
of
gas particles which
collide more often and
with more force
causing the walls of a
flexible container
expand. Think of hot
air balloons!
Charles’ Law Video Example

13. Charles’ Law Example:
4.40 L of a gas is collected at 50.0°C. What will be
volume upon cooling to 25.0°C?
First you must convert temperatures from Celsius to
Kelvin. Temperature must always be in Kelvin
K = 273 + °C
T1 = 273 + 50.0°C = 323K
T2 = 273 + 25.0°C = 298K
V1 = V2
T1 T2
4.40L = V2
323K 298K V2 = 4.06L
(298K)
1
(298K)
1

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.
Pressure
(atm)
Temperature (K)
P1 P2
T1 T2
=
Gay-Lussac’s Law Video Example

15. Steel cylinder (2L)
contains 500
molecules of O2 at
400 K
Steel cylinder (2L)
contains 500
molecules of O2 at
800 K
1. In which system do the O2 molecules have the highest average
kinetic energy (temperature)?
2. In which system will the particles collide with the container walls
with the greatest force and the most often?
3. 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. What is the pressure of the gas if it is heated to
45°C?
P1 P2
T1 T2
First you must convert temperatures from Celsius to
Kelvin. Temperature must always be in Kelvin
K = 273 + °C
T1 = 273 + 25.0°C = 298K
T2 = 273 + 45.0°C = 318K
1.3 atm = P2
298K 318K
X (318K)
1
(318K) X
1 P2 = 1.39 atm
1.4 atm (2 sig figs)

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

18. Combined Gas Law
P1V1 P2V2
T1 T2
=
Note that all temperatures must be in
Kelvin!
A combination of Boyle’s, Charles’, and Gay-Lussac’s Laws

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?
P1V1 P2V2
T1 T2
P1 = 2.5 atm
V1 = 2.0L
T1 = 25 + 273 = 298K
P2 = 1.5 atm
V2 = ?
T2 = 33 + 273 = 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
T1 T2
P1 = 1.3 atm
V1 = 4.5L
T1 = 35 + 273 = 308K
P2 = 1.5 atm
V2 = 3.2L
T2 = ?K
(1.5 atm)(3.2L) (308K) = T2
(4.5L) (1.3 atm) T2 = 250K
(1.3 atm)(4.5L) = (1.5atm)(3.2L)
(308k) T2

21. What is STP?
STP is the abbreviation for
standard temperature and
pressure.
Standard temperature is 273K
Standard pressure is 1 atm
You must memorize the
meaning of STP.

22. Avogadro’s Law
Avogadro’s Law – equal volumes of gases
at the same temperature and pressure
contain equal numbers of molecules.
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!
H2
O2 CO2

23. 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?
One mole which is 6.022 x 1023

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

25. 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
◦ There are no intermolecular forces between the gas
molecules.
◦ The volume occupied by the molecules themselves
is entirely negligible relative to the volume of the
container.

26. Ideal Gas Law
PV = nRT
P = pressure in atmospheres (atm)
V = volume in Liters (L)
n = # of moles
T = temperature in Kelvin (K)
R =.08206 L·atm/mol·K

27. 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 = .123 moles of oxygen
n = (1.20)(2.50)
(.08206) (298K)
n = PV
RT

28. 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
n = 12.4g
1
x 1 mol
32.00g
n = .388 mol
V = (.388)(.08206) (290K)
.995 atm
P = 756 torr
1
X 1 atm
760.0 torr
P = .995 atm
V = 9.28L

29. 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
T1 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

30. 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

31. 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 + 44.7 kPa + 112 kPa =
PTOTAL = 179 kPa

32. Gas Stoichiometry
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 OR 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 excess hydrogen gas to produce .830L of NH3
in the reaction above?
22.4
.830L NH3
1 mol N2 22.4 L N2
1 22.4 L NH3 1 mol N2
= .415L N2
1 mol NH3
2 mol NH3

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

34. END