Gas Laws
The Gas Laws
• Describe HOW gases behave.
• Can be predicted by the The
Kinetic Theory
Kinetic Theory states that all
matter consists of tiny particles
that are in constant motion
Matter Review
• Solids: least motion, definite volume
definite shape
• Liquids: more motion, particles further
apart than solids (can pour), definite
volume but indefinite shape
• Gases: most motion of three states,
indefinite volume and indefinite shape
4 things
• In order to completely describe
a gas you need to measure 4
things
1.
2.
3.
4.
Pressure
Temperature
Volume
Number of particles
Gas Pressure
• Pressure is defined as force per unit area.
• Gas particles exert pressure when they
collide with the walls of their container.
• The SI unit of pressure is the pascal (Pa).
• However, there are several units of pressure
– Pascal (Pa)
– Kilopascal (KPa)
– Atmosphere (atm)
1 atm
4 Liters
• As the
pressure on
a gas
increases
2 atm
2 Liters
• …the
volume
decreases
• Pressure
and volume
are
inversely
related
Temperature
• Raising the temperature of a gas
increases the pressure if the
volume is held constant.
• The molecules hit the walls
harder.
• The only way to increase the
temperature at constant pressure
is to increase the volume.
300 K
• If you start with 1 liter of gas at 1
atm pressure and 300 K
• and heat it to 600 K one of 2 things
happens
600 K
300 K
• Either the volume will
increase to 2 liters at 1
atm
300 K
•Or the pressure will
increase to 2 atm.
•More collisions mean
greater pressure
600 K
Changing the Size of the
Container
• In a smaller container molecules
have less room to move
• Hit the sides of the container
more often
• As volume decreases pressure
increases.
The effect of adding gas
• When we blow up a balloon we are adding
gas molecules.
• Doubling the number of gas particles
doubles the pressure
More molecules means more collisions
Fewer molecules means fewer collisions.
• If you double the number of
molecules…
1 atm
• …You double the pressure
2 atm
4 atm
• As you remove
molecules from a
container……..
2 atm
• ….the pressure
decreases
2
Avogadro’s Hypothesis
Nitrogen, N2
Hydrogen, H2
Oxygen, O2
1 mole of each gas has the same number of molecules at STP
Boyle’s Law
• At a constant temperature, pressure and
volume are inversely related
• As one goes up the other goes down
• P1 x V1= P2 x V2
Example
• A balloon is filled with 25 L of air at 1.0
atm pressure. If the pressure is changed
to 1.5 atm what is the new volume?
P1= 1 atm
V1= 25 L
P2= 1.5 atm
V2= ?
(1 atm)(25 L)=(1.5 atm)(V2)
16.7 L
Example
• A balloon is filled with 73 L of air at 1.3
atm pressure. What pressure is needed to
change to volume to 43 L?
• A sample of Helium gas is compressed
from 4.0 L to 2.5 L at a constant
temperature. If the pressure of the gas in
the 4.0 L volume is 210 kPa, what will the
pressure be at 2.5 L?
Charles’s Law
• The volume of a gas is directly
proportional to the Kelvin temperature
when the pressure is held constant
Example
• A sample of gas at 40.0 °C occupies a
volume of 2.32 L. If the temperature is
raised to 75.0 °C what will the new volume
be?
V1= 2.32 L
T1= 40+273
V2= ?
T2= 75+273
V1 = V2
T1 T2
2.32 L = V2
313K 348 K
MUST CONVERT TEMP TO K!!!!!!!
2.58 L
Examples
• What is the pressure inside a 0.250
L can of deodorant that starts at
25ºC and 1.2 atm if the temperature
is raised to 100ºC?
• At what temperature will the can
above have a pressure of 2.2 atm?
Combined Gas Law
• The Combined Gas Law Deals
with the situation where only the
number of molecules stays
constant.
• P1 x V1 = P2 x V2
T1
T2
Example
• A gas at 110.0 kPa and 30.0°C
fills a flexible container to a
volume of 2.00 L. If the
temperature was raised to 80.0°C
and the pressure was increased
to 440.0 kPa, what is the new
volume?
Example
• P1V1 = P2V2
T1
T2
•
•
•
•
•
•
P1 = 110.0 kPa
V1 = 2.00 L
T1 = 30.0 °C = 303 K
P2 = 440.0 kPa
V2 = ?
T2 = 80.0 °C = 353 K
Example
• P1V1 = P2V2
T1
T2
• (110.0)(2.00L) = (440.0kPa)(V2)
303K
353K
• V2 = 0.583 L
Dalton’s Law of Partial
Pressures
• The total pressure inside a container
is equal to the sum of the partial
pressure due to each gas.
• The partial pressure of a gas is the
contribution by that gas hitting the
wall.
• PTotal = P1 + P2 + P3 + …
• We can find out the pressure in the
fourth container
• By adding up the pressure in the first 3
2 atm
1 atm
3 atm
6 atm
Dalton’s Law of Partial
Pressures
A gas mixture contains H2, He, Ne, and Ar.
The total pressure of the mixture is 93.6 kPa.
The partial pressures of He, Ne, and Ar are
15.4 kPa, 25.7 kPa, and 35.6 kPa
respectively. What is the pressure
exerted by H2?
PT = PH2 + PHe + PNe + PAr
PH2 = 16.9 kPa
Dalton’s Law of Partial
Pressures
A person using an oxygen mask is breathing
air with 33% Oxygen. What is the partial
pressure of the Oxygen when the air
pressure in the mask is 110 kPa?
33% of 110 kPa
36 kPa
Diffusion & Effusion
 Molecules
moving from areas of high
concentration to low concentration.
 Perfume molecules spreading across
the room.
 Effusion - Gas escaping through a tiny
hole in a container.
 Both depend on the speed of the
molecules
Diffusion
• Bigger molecules move
slower at the same temp.
• Bigger molecules effuse
and diffuse slower
• Helium effuses and diffuses
faster than air -escapes
from balloon.
Kinetic Molecular Theory
Three main points to the kinetic theory of
gases.
• Gases are made of small particles, which are
spread very far apart from each other and
behave independently of one another.
• Gas particles constantly move, randomly, yet
in a straight line until acted upon by an
outside force or barrier.
• All collisions are perfectly elastic which
means that no energy is gained or lost during
the collision.
Ideal Gases
• We are going to assume that gases
behave ideally
• Does not really exist
• Assume particles have no volume
• Assume no attractive forces between
molecules
ONLY 2 ELEMENTS TO BEHAVE MOST
LIKE AN IDEAL GAS ARE HYDROGEN
AND HELIUM
Ideal Gases vs Real Gases
Real Gases deviate from the Ideal Gases:
1) Volume of a gas is significant (22.4 L)
2) Gas particles can condense, so do
have forces of attraction between
particles
Real gases differ when at low
temp and high pressure