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
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
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
constant, linear, random
motion
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
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
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
Combined Gas Law
3. Gay-Lussac’s Law
4. Avogadro’s Law
5. Ideal Gas Law – volume liters only
6. Dalton’s Law
Units used to describe gas
samples:
Volume
Temperature
Pressure
Liter (L)
Milliliter (mL)
Kelvin ONLY
1000 mL = 1L
K = ºC + 273
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
A. Avogadro’s Principle

Equal volumes of gases contain
equal numbers of moles
• at constant temp & pressure
• true for any gas
V
k
n
V
n
A. Avogadro’s Principle

Equal volumes of gases contain
equal numbers of moles
• at constant temp & pressure
• true for any gas
n1
n2
=
V1
V2
V
n
Avogadro’s Law
When the amount of
gas in a sample
increases at constant
temperature and
pressure, its volume
increases in direct
proportion because
the greater number
of gas particles fill
more space.
The volume of a gas sample increases linearly with the number
of moles of gas in the sample.
Avogadro’s Law
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
A. Avogadro’s Principle
If 2.45 mol of argon gas occupies
a volume of 89.0 L, what volume
will 2.10 mol of argon occupy
under the same conditions of
temperature and pressure?
76.3 L
Ideal Gas Law
Ideal Gas Law
Ideal Gas Law
Merge the Combined Gas Law with Avogadro’s Principle:
PV
V
k
=R
nT
T
n
UNIVERSAL GAS
CONSTANT
R=0.0821 Latm/molK
3kPa/molK
R=8.315
dm
You don’t need to memorize these values!
Ideal Gas Law
PV=nRT
UNIVERSAL GAS
CONSTANT
R=0.0821 Latm/molK
3kPa/molK
R=8.315
dm
You don’t need to memorize these values!
Ideal Gas Law Problems
 Calculate
the pressure in atmospheres
of 0.412 mol of He at 16°C & occupying
3.25 L.
GIVEN:
WORK:
P = ? atm
PV = nRT
n = 0.412 mol
P(3.25)=(0.412)(0.0821)(289)
L
mol Latm/molK K
T = 16°C = 289 K
V = 3.25 L
P = 3.01 atm
R = 0.0821Latm/molK
Ideal Gas Law Problems
 Find
the volume of 85 g of O2 at 25°C
and 104.5 kPa.
GIVEN:
WORK:
V=?
85 g 1 mol = 2.7 mol
n = 85 g = 2.7 mol
32.00 g
T = 25°C = 298 K PV = nRT
P = 104.5 kPa
(104.5)V=(2.7) (8.315) (298)
kPa
mol
dm3kPa/molK K
R = 8.315 dm3kPa/molK
V = 64 dm3
Molar Volume at STP
 Solving
the ideal gas equation for
the volume of 1 mol of gas at STP
gives 22.4 L.
6.022 × 1023 molecules of gas
 We
call the volume of 1 mole of gas
at STP the molar volume.
Molar Volume at STP
Molar Volume of an Ideal Gas
For 1 mole of an ideal gas at 0°C and 1 atm, the volume
of the gas is 22.42 L.

V=
nRT
P

=
1.000 mol0.08206 L  atm/K  mol 273.2 K 
1.000 atm
= 22.42 L
STP = standard temperature and pressure
• 273 K and 1 atm
• Therefore, the molar volume is 22.42 L at STP.
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21
EXERCISE!
A sample of oxygen gas has a volume of 2.50 L
at STP. How many grams of O2 are present?
3.57 g
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Density of a Gas at STP
 Density
is the ratio of mass to
volume.
 Density of a gas is generally given
in g/L.
 The mass of 1 mole = molar
mass.
 The volume of 1 mole at STP =
22.4 L.
Density of a Gas at STP
 For
example, the densities of
helium and nitrogen gas at STP
are as follows:
Gas Density
• Density is directly proportional to molar mass.
Molar Mass of a Gas
 g  L  atm 
K




dRT  L  mol  K 
g
Molar mass =
=
=
P
mol
 atm 
»
»
»
»
d = density of gas
T = temperature in Kelvin
P = pressure of gas
R = universal gas constant
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26
EXERCISE!
What is the density of F2 at STP (in g/L)?
1.70 g/L
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27