KMT and Gas Laws
States of Matter, Kinetic Molecular
Theory, Diffusion,
Properties of Gases,
and
Gas Laws
Standards
4. The kinetic molecular theory describes the motion of atoms and molecules and explains the properties of
gases. As a basis for understanding this concept:
a. Students know the random motion of molecules and their collisions with a surface create the observable
pressure on that surface.
4. b. Students know the random motion of molecules explains the diffusion of gases.
4. c. Students know how to apply the gas laws to relations between the pressure, temperature, and volume of
any amount of an ideal gas or any mixture of ideal gases.
4. d. Students know the values and meanings of standard temperature and pressure (STP).
4. e. Students know how to convert between the Celsius and Kelvin temperature scales.
4. f. Students know there is no temperature lower than 0 Kelvin.
4. g.* Students know the kinetic theory of gases relates the absolute temperature of a gas to the average
kinetic energy of its molecules or atoms.
4. h.* Students know how to solve problems by using the ideal gas law in the form PV = nRT.
4. i. * Students know how to apply Dalton’s law of partial pressures to describe the composition of gases and
Graham’s law to predict diffusion of gases.
States of Matter
Plasma
Deposition
Sublimation
Gas
Solid
Liquid
Condensation (Gas  Liquid)
Boiling
(Liquid  Gas)
Sublimation (Solid  Gas)
Deposition
(Gas  Solid)
Freezing (Liquid  Solid)
Melting (Solid  Liquid)
Molecular Motion of Gases
Molecular Motion of Gases
KMT
KMT – Kinetic Molecular Theory
• The path of any individual
molecule could best be
described as random.
Molecular Motion
• The state of matter depends
on how much energy
(motion) the molecules,
atoms, or ions have.
• The state of matter also
depends on how attracted
the atoms, molecules, or
ions are to each other.
Molecular Motion
State of Matter
O
O
Gas
–
O
+
H
+
Na
Liquid
+
H
–
Cl
Solid
Nonpolar molecules
O
O
O
O
Polar molecules
–
O
+
H
+
H
Ionic compounds
–
+
Na
+
Na
–
Cl
Cl
–
Cl
+
Na
–
+
Na
+
Na
–
Cl
–
Cl
Cl
+
Na
Molecular Twist and Stretch
Diffusion
• Diffusion – when a substance spreads out in a
gas or liquid.
• Examples:
1. Perfume eventually reaching the far side of a
room.
2. Kool-Aid dissolving into water.
Diffusion of Gases
Diffusion of Gases
Diffusion of Liquids
Temperature (T)
• Kinetic energy is the energy of motion.
• Temperature is defined as a measure of the
average kinetic energy of the atoms or
molecules.
Temperature (T)
• There are two scales and an absolute unit.
(degrees Fahrenheit, degrees Celsius, and
Kelvin)
Temperature Scales
Water Boils
212°F
100°C
373K
Human Body
98.7°F
37°C
310K
Water Freezes
32°F
0°C
273K
Temperature Scales
Surface of Sun
9,941°F
5,505°C
5,778K
Room Temp.
70°F
21°C
294K
Absolute Zero
-460°F
-273°C
0K
Converting Temperatures
• Fahrenheit  Celsius
°C = (°F – 32)×(5/9)
• Celsius  Fahrenheit
°F = °C ×(9/5) + 32
• Celsius  Kelvin
K = °C + 273.15
Absolute Zero
• At Zero Kelvin (0 K or –273.15 °C), atoms
and molecules stop moving.
• There is no temperature lower than
absolute zero (0 K).
Volume (V)
• How much space is occupied by a fluid.
Liquid
Gas
• Usually gases are measured in Liters (L)
Pressure (P)
• Defined as force divided by area.
• The force comes from atoms’ or molecules’
collisions with the wall of the container.
• The greater the number of collisions or the
more energy with each collision, the greater
the pressure.
Pressure (P)
• Defined as force divided by area.
• The force comes from atoms’ or molecules’
collisions with the wall of the container.
• The greater the number of collisions or the
more energy with each collision, the greater
the pressure.
Pressure Units
Unit
Atmospheres
Unit
Symbol
atm
1 atm =
--
Pascals
Pa
101,325 Pa
Kilopascals
kPa
101.3 kPa
Pounds per
square inch
Millimeters
mercury
lbs. or psi 14.7 psi
in.2
mm Hg 760 mm Hg
Pressure
0 atm
Outer Space (a vacuum)
0.33 atm
Top of Mt. Everest
1 atm
Regular Atmosphere
(at sea level)
1,072 atm
At the Bottom of
Mariana Trench
Gas Properties
Property
Pressure
Usual
Unit
Symbol Unit
Symbol
P
kilopascal kPa
Volume
V
liters
L
Temperature
T
Kelvin
K
Moles
n
moles
mol
STP = Standard Temperature and Pressure
Temperature is 0°C = 273.15 K
and
Pressure is 1 atm = 101.3 kPa
Gas Laws
• Most of the gas laws deal with taking a
quantity of gas and changing one property
(pressure, temperature, or volume) and
predicting how the other properties will
change in response.
Boyle’s Law
When given a certain amount of gas, if you
increase the pressure, the volume decreases.
If you decrease the pressure, the volume
increases.
Mathematically: P1V1 = P2V2
P1V1 = P2 V2
Boyle’s Law
When given a certain amount of gas, if you
increase the pressure, the volume decreases.
If you decrease the pressure, the volume
increases.
Mathematically: P1V1 = P2V2
P1V1 = P2 V2
This assumes a constant temperature (T)
Boyle’s Law Example
Your nephew is playing with a balloon in the car as
your family drives over a mountain pass. The
balloon initially had a volume of 1 L when the car
was at the bottom of the mountain (and the air
pressure was 100 kPa).
Now that your family is at the top the air pressure is
70 kPa. What is the new volume of the balloon?
P1V1 = P2 V2
Boyle’s Law Example
P1 = 100 kPa
V1 = 1 L
P2 = 70 kPa
V2 = ?
P1V1 = P2V2
(100 kPa)(1 L) = (70 kPa)•V2
100 kPa•L = 70 kPa•V2
70 kPa
70 kPa
1.43 L = V2
Boyle’s Law Example
Low P
Normal P
Boyle’s Law Example
Normal P
V1 = 1 L
Low P
V2 = 1.43 L
Charles’ Law
When given a certain amount of gas, if you increase
the temperature, the volume increases.
If you decrease the temperature, the volume
decreases.
1
2
Mathematically:
You must use
Kelvin
temperatures!
V = V
T1
T2
V1 V 2
=
T1
T2
Charles’ Law
When given a certain amount of gas, if you increase
the temperature, the volume increases.
If you decrease the temperature, the volume
decreases.
1
2
Mathematically:
You must use
Kelvin
temperatures!
V = V
T1
T2
V1 V 2
=
T1
T2
This assumes a constant pressure (P)
Charles’ Law Example
If 1.0 L of gas is contained within a piston at
27 ˚C (300 K), what will new volume be if the
gas is cooled to -23 ˚C (250 K)? Assume that
the pressure is constant.
V 1 V2
=
T1
T2
Charles’ Law Example
V1 = 1.0 L
T1 = 300 K
V 1 V2
=
T1
T2
V2 = ?
T2 = 250 K
1.0 L
V2
=
300 K 250 K
1.0
V2
=
(250)
(250) V2 = 0.83 L
300 250
Charles’ Law
This assumes a constant pressure (P)
Charles’ Law
This assumes a constant pressure (P)
Which Law?
T1
V1
7) Oxygen
gasTat
2 47 ˚C occupies a volume
of 0.5 L. To what temperature should the
V2 gas be lowered to bring the volume
oxygen
to 0.2 L? Assume constant pressure.
V1 = V2
T1
T2
Charles’ Law
Which Law?
P1
V1 sample (N2O) occupies
9) A nitrous oxide
a
volume of 360 mL when
V2 under 70 kPa of
P2 How much volume will it occupy
pressure.
at 420 kPa? Assume constant temperature.
P1V1 = P2V2
Boyle’s Law
Gay–Lussac’s Law
When given a certain amount of gas, if you increase
the temperature, the pressure increases.
If you decrease the temperature, the pressure
decreases.
1
2
Mathematically:
You must use
Kelvin
temperatures!
P = P
T1
T2
P1
P2
=
T1
T2
Gay–Lussac’s Law
When given a certain amount of gas, if you increase
the temperature, the pressure increases.
If you decrease the temperature, the pressure
decreases.
1
2
Mathematically:
You must use
Kelvin
temperatures!
P = P
T1
T2
P1
P2
=
T1
T2
This assumes a constant volume (V)
Gay–Lussac’s Law Example
A tire that has already been inflated to its
maximum volume,T1begins a drive at a
P1
temperature
of 300K with an air pressure
2 air in the
of 36 psi. During the hot day Pthe
T2
tire’s pressure increases
to 42 psi. What
will the new temperature be?
Gay–Lussac’s Law Example
A tire that has already been inflated to its
maximum volume,T1begins a drive at a
P1
temperature
of 300K with an air pressure
2 air in the
of 36 psi. During the hot day Pthe
T2
tire’s pressure increases
to 42 psi. What
will the new temperature be?
P1
P2
=
T1
T2
Gay–Lussac’s Law Example
P1 = 36 psi
T1 = 300 K
P1
P2
=
T1
T2
P2 = 42 psi
T2 = ?
36 psi 42 psi
=
300 K
T2
42
(T2) 0.12 =
(T2)
T2
0.12 (T2) = 42
T2 = 350 K
0.12
0.12
Before
After
P2 = 42 psi
P1 = 36 psi
T1 = 300 K
T2 = 350 K
Avogadro’s Law
The volume of a gas at Standard Temperature
and Pressure (STP) is directly proportional to
the moles of the gas.
V=kn
# of moles
At STP there are 22.4 L per mole of gas.
Avogadro’s Law Example
How many liters will 3 moles of gas occupy
at STP?
V=kn
L
V = (22.4 mol )(3 mol)
V = 67.2 L
Combined Gas Law
This combines Boyle’s, Charles’, and Gay-Lussac’s
Gas Laws.
Mathematically:
P1 V1 = P 2 V2
T1
T2
Cancel out the properties that remain constant.
Combined Gas Law
This combines Boyle’s, Charles’, and Gay-Lussac’s
Gas Laws.
Mathematically:
P1 V1 = P 2 V2
T1
T2
Cancel out the properties that remain constant.
Combined Gas Law Example
P1 = 50 kPa
V1 = ?
T1 = 300 K
P1V1 P2V2
=
T1
T2
P2 = 200 kPa
V2 = 0.12 L
T2 = 400 K
(50)V1 (200)(0.12)
=
300
(400)
(V1)0.167 = 0.06
0.167
0.167
V1 = 0.36 L
Ideal Gas Law
If we know 3 of the 4 gas properties (P, V, T, and n)
we can solve for the missing one by using the
formula:
PV = nRT
R is called the gas constant.
•L
kPa
R = 8.314
mol•K
Ideal Gas Law
A cylinder is filled with 0.2 moles of gas. The
sealed cylinder has a volume 3.0 L and is heated
with 3,000 J to a temperature of 300K. What is
the pressure inside the cylinder?
PV = nRT
kPa L
P•(3.0 L) = (0.2 mol)(8.314
)(300 K)
•
mol•K
P•(3.0 L) = 499 kPa•L
3.0 L
3.0 L
P = 166 kPa
Gas Law
Gas Laws Summary
Formula
Boyle’s Law
Charles’ Law
Gay-Lussac’s Law
Avogadro’s Law
Combined Gas Law
Ideal Gas Law
P1V1 = P2V2
V1
V2
=
T1
T2
P1
P2
=
T1
T2
V=kn
P1 V1 P2 V2
=
T1
T2
PV = nRT
What is the change in volume?
CH4(g) + H2O (g)  CO (g) + 3 H2 (g)
Methane
+
water
carbon
monoxide
hydrogen
+
Vapor Pressure
For a liquid as the temperature increases, its
vapor pressure increases.
When the vapor pressure is equal to the
external pressure, the liquid has reached its
boiling point.
Effects of Vapor Pressure:
• Warm water evaporates faster than cold
water.
• At higher altitudes, water boils at a lower
temperature.
Dynamic Equilibrium
Dynamic equilibrium occurs when the rate of
condensation equals the rate of evaporation.
evaporation
Liquid
condensation
Vapor
(or gas)
Note: the amounts of liquid and vapor can be
completely different.
Dalton’s Law of Partial Pressures
The total pressure exerted by a mixture of gases is
equal to the sum of all partial pressures exerted by
each individual gas.
Ptot = P1 + P2 + P3 + …
For example: our classroom
Ptot = PN2 + PO2 + PAr + PCO2 + PH2O + …
1 atm = 0.79 atm + 0.19 atm + 0.01 atm + 0.003 atm
+…
Graham’s Law of Diffusion
• From the simulations we saw, that lighter gas
molecules move faster than heavier gas
molecules.
• If we want to directly compare the speeds of
gas molecules we can use:
These are the
average
molecular
speeds
vA
=
vB
MB
MA
These are the
molar masses
H
He
Li Be B
C
N
O
F
Na Mg Al
Si
P
S
Cl Ar
K
Ca
Ne
Br Kr
I
Xe
H
He
Li Be B
C
N
O
F
Na Mg Al
Si
P
S
Cl Ar
K
Ca
Ne
Br Kr
I
Xe
4 e– in valence shell
Gas Laws Summary
Gas Law
Formula
Boyle’s Law
P1V1 = P2V2
Charles’ Law
Avogadro’s Law
V1
V2
=
T1
T2
P1 = P2
T1
T2
V=kn
Ideal Gas Law
PV = nRT
Gay-Lussac’s Law