The document summarizes the kinetic molecular theory and gas laws. It explains that kinetic molecular theory models gases as particles in constant, random motion that exert pressure during collisions. It describes the gas laws of Boyle's law, Charles' law, Gay-Lussac's law, Avogadro's hypothesis, and Dalton's law of partial pressures which relate the variables of pressure, volume, temperature, and moles of gas. Examples are provided to illustrate applications of the gas laws.

1. Kinetic Molecular Theory
 Explains the behavior of gases

2. POSTULATES:
Gases are composed of a many particles that behave like
hard spherical objects in a state of constant, random
motion
These particles move in a straight line until they collide
with another particle or the walls of the container
These particles are much smaller than the distance
between particles, therefore the volume of a gas is mostly
empty space and the volume of the gas molecule
themselves is negligible

3.  There is no force of attraction between gas particles or
between the particles and the walls of the container
 Collisions between gas particles or collisions with the walls
of the container are elastic. That is, none of the energy of
the gas particle is lost in a collision.
The average kinetic energy of a collection of gas particles is
dependent only upon the temperature of the gas
 The average kinetic energy of a collection of gas particles
depends on the temperature of the gas and nothing else

4. Kinetic Energy
 The energy of motion
 Directly proportional to the mass of the object and to
square of its velocity
KE = _1_ mv2
2
where m = mass
v = velocity

5. GAS LAWS:
 Gases have various properties which we can
observe with our senses, including the
gas pressure, temperature, mass, and
the volume which contains the gas
 Scientific observation has determined that
these variables are related to one another, and
values of these properties determine the state of
the gas

6.  Pressure in a closed container changes if
1.temperature changes
2.number of molecules increases or decreases
3.volume changes

7.  Using the Kinetic Molecular Theory to explain
the Gas Laws
 The Relationship Between P and n
 Boyle's Law
 Amonton's Law
 Charles' Law
 Avogadro's Hypothesis
 Dalton's Law of Partial Pressures

8. Relationship between P and n
 Pressure (P) is the force exerted on the walls
of the container during a collision
 An increase in the number of particles (n)
increases the frequency of collisions with the
walls
 Therefore, P increases as n increases.

9. Boyle’s Law
 By Robert Boyle (1600s) - observed that the product
of the pressure and volume are observed to be nearly
constant
p (V) = C
Compressing a gas makes the V smaller but does not
alter the average KE of the molecules since
temperature is constant
Though the speed of the particles remains constant,
the frequency of collisions increases because the
container is smaller
 Therefore, P increases as V decreases.

10. Key Points:
•Temperature and moles of gas are constant
•Graph is hyperbolic and asymptotic to both axes
•Pressure and volume are inversely proportional to
each other

11. Equation:
P1V1 = P2V2
where P1 is the pressure of a quantity of gas with
a volume of V1
P2 is the pressure of the same quantity of
gas when it has a volume V2

13. Example:
1. Given a container of air with an initial volume of 28
L and pressure of 40 Pa, calculate the pressure if
the volume is changed to 141 L.
2. Sulfur dioxide (SO2) gas is a component of car exhaust
and power plant discharge, and it plays a major role in the
formation of acid rain. Consider a 3.0 L sample of gaseous
SO2at a pressure of 1.0 atm. If the pressure is changed to
1.5 atm at a constant temperature, what will be the new
volume of the gas?
3. Find the pressure on 5.25 L of gas that was originally 3.12
L at 1.54 atm

14. CHARLE’S LAW
 By Jacques Charles
The average KE of a gas particle is proportional
to T
 Since mass is constant, the average velocity of
the particles must increase (KE = 1/2mv2)
 At higher velocity, the particles exert greater
force which increases P
 If the walls are flexible, they will expand to
balance the atmospheric pressure outside
 Therefore, V is directly proportional to T

15. Key Points:
• Pressure and moles of gas are constant
• Graph is linear
• Volume and temperature are directly
proportional to each other

16. Equation:
_V1_ = V2_
T1 T2

17. Example:
1. A 5.0 L vessel of gas is held at 25°C. What will be the
new volume if the temperature is doubled?
2. What change in volume results if 60.0 mL of gas is
cooled from 33.0 °C to 5.00 °C?
3. Given a container of helium gas with an initial volume of
496 L and temperature of 6.4 °C,
calculate the volume if the temperature is changed to -
16.9 °C.

18. Gay-Lussac’s Law
 By Joseph Louis Gay-Lussac (1778-1850)
 Key Points:
-- Volume and moles of gas are constant
-- Graph is linear (see below)
-- Pressure and temperature are directly
proportional to each other

19. Equation:
_P1_ = P2_
T1 T2

20. Example:
1) 25.0 L of a gas is held in a fixed container at 1.25 atm at
20°C. What will be the pressure of the gas if the
is increased to 35°C?
2) If a gas is cooled from 323.0 K to 273.15 K and the volume
kept constant what final pressure would result if the
pressure was 750.0 mm Hg?

21. AMONTON’S LAW
 The pressure of a gas is directly proportional to the
Temperature (Kelvin) at a constant V and n

22.  Absolute Zero – The temperature (-273.15
degrees C or 0 Kelvin) at which the volume and
pressure of an ideal gas extrapolated to zero.
-- Proposed by Joseph Lambert in 1779
Where: TK is measured in Kelvin
T0C is measured in Celsius

23. DALTON'S LAW OF PARTIAL PRESSURES
Assumptions:
 Gases must be unreactive and follow ideal gas
behavior
 the total pressure of a gas mixture is equal to the
sum of the pressures of each individual gas
 By John Dalton

24. Example:
1. The pressure of a mixture of nitrogen, carbon dioxide, and
oxygen is 150 kPa. What is the partial pressure of oxygen if
the partial pressures of the nitrogen and carbon dioxide
100 kPA and 24 kPa, respectively?
2. A container holds three gases: oxygen, carbon dioxide,
helium. The partial pressures of the three gases are 2.00
atm, 3.00 atm, and 4.00 atm, respectively. What is the total
pressure inside the container?

25. AVOGADRO’S HYPOTHESIS
 By Amadeo Avogadro
 The volume of a gas is directly proportional to the
moles of the gas, n at constant P and T
 The hypothesis that equal volumes of different
gases at the same temperature and pressure
contain the same number of particles

26. Avogadro's law can be expressed by the formula:
_Vi_ = _Vf_
ni nf
Where:
Vi = initial volume
ni = initial number of moles
Vf = final volume
nf = final number of moles

27. Example:
1. A 6.0 L sample at 25 °C and 2.00 atm of pressure
contains 0.5 moles of a gas. If an additional 0.25
moles of gas at the same pressure and temperature
are added, what is the final total volume of the gas?