Kinetic Molecular Theory of
Gases and the Gas Laws
Mr. Nelson
Chemistry
Properties of Gases
 Gases
are fluids
◦ Fluids are any substance that flows
 Gases
are highly compressible
◦ Example: Tire pressure
 Gases
completely fill containers
 Gases have lower densities than
liquids and solids
Kinetic Molecular Theory
 KMT
describes the motion of
the particles
◦ Particles have the same motion
as billiard balls
http://intro.chem.okstate.edu/NSFCCLI/GasLa
w/GLP.htm
Kinetic Molecular Theory of Gases
 Assumptions:
◦ Gas molecules are in constant,
random motion
◦ Gas molecules are separated by
large distances
◦ Gas molecules have no
attractive/repulsive forces
Temperature of Gases

Temperature and energy of gases are
directly proportional
◦ As the temperature increases, kinetic energy
of the molecules increases
◦ As temperature decreases, kinetic energy will
also decrease
Pressure of Gases
At sea level, the standard gas pressure is 1
atmosphere
 Pressure is the force exerted by gas
molecules
 Standard Temperature and Pressure (STP)
is equal to 1 atm and 0 °C

Different Units of Pressure
Unit
Abbreviation
Atmosphere
atm
Millimeter of
mercury
mm Hg
Pascal
Pa
(Usually, kPa)
To convert,
1
atm = 760 mm Hg
1 atm = 101.3 kPa
Converting Pressure Example

Convert 72.7 atmospheres (atm) into
kilopascals (kPa)
The Gas Laws
 Variables
in Gas Equations:
◦ P = Pressure (kPa or atm)
◦ V = Volume (L)
◦ T = Temperature (K)
◦ n = amount of gas (moles)
Boyle’s Law

States that for a fixed amount of gas at
constant temperature the volume of the
gas is inversely proportional to the
pressure of a gas
P1V 1  P2V 2
Boyle’s Law

Example Problem
◦ The pressure on 2.50 L of anesthetic gas
changes from 105 kPa to 40.5 kPa. What will
be the new volume if the temperature
remains constant?
Boyle’s Law

Example Problem
◦ A high-altitude balloon contains 30.0 L of
helium gas at 103 kPa. As the balloon rises,
you record a new volume of 35.0 L. What is
the atmospheric pressure in kPa? (Assume
constant temperature)
Charles’s Law

States that the volume of a gas is directly
proportional to the Kelvin temperature if
the pressure remains constant
V1
T1

V2
T2
Charles’s Law

Example Problem
◦ The air in a hot air balloon has a volume of
400.0 L at 30.0°C (303 K). What will the
volume be if the temperature is raised to
120.0 °C (393 K)?
Charles’s Law

Example Problem
◦ An aerosol can has a volume of 3.00 x 102 mL
at 150.0°C is heated until its volume is 6.00 x
102 mL.What is the new temperature (in K)
of the gas if pressure remains constant?
Gay-Lussac’s Law

States that the pressure of a gas is directly
proportional to the Kelvin temperature if
the volume remains constant
Temperature
Pressure
P1
T1

P2
T2
Gay-Lussac’s Law

Example Problem
◦ The gas left in a used aerosol can is at a
pressure of 103 kPa at 25 °C. If this can is
thrown onto a fire, what is the pressure of
the gas when its temperature reaches 928 °C?
Gay-Lussac’s Law

Example Problem
◦ A sealed cylinder of gas contains nitrogen gas
at 1.00 x 103 kPa pressure and a temperature
of 20.0 °C. The cylinder is left in the sun, and
the temperature of the gas increases to 50.0
°C. What is the new pressure in the cylinder?
Combined Gas Law

A single equation that combines all the
gas laws:
Combined Gas Law

Example Problem
◦ A gas takes up a volume of 17 liters, has a
pressure of 2.3 atm, and a temperature of 299
K. If I raise the temperature to 350 K and
lower the pressure to 1.5 atm, what is the
new volume of the gas?
Ideal Gas Law
Relates the gas laws and the amount of
gas
 Requires the gas constant, R

◦ R can be a different number depending on the
units
R  8 . 31
kPa L
mol K
R  0 . 08205
atm L
mol K
PV = nRT

Example Problem
◦ A container of 3.0 L of nitrogen (N2) is at a
pressure of 4.5 x 102 kPa and a temperature
of 39 °C. How many grams of N2 are in the
container?
Ideal Gas Law

Example Problem
◦ What pressure will be exerted by 0.450 mol
of a gas at 25.0 °C if it is contained in a 0.650
L vessel?
Avogadro’s Hypothesis
 Equal
volumes of gases at the same
temperature and pressure contain
equal numbers of particles
 Due mainly to the large amount of
empty space between particles
◦ From this, scientists have determined
that 1 mol = 22.4 L at STP
This was not well accepted

Why?
◦ Tennis balls vs. Bowling balls
But its true!