### Gas Laws - Madison Public Schools

```Physical
Characteristics of
Gases
The Gas Laws
Objectives
• Students will be able to use Boyle’s Law to
calculate volume and pressure changes at
constant temperature.
• Students will be able to use Charles’ Law to
calculate volume and temperature changes at
constant pressure.
Class Warmup
1. A weather report gives the current atmospheric
pressure reading of 745.8 mm Hg. Express this
a. atmospheres
b. torr
c. kilopascals
2. What will happen to the pressure of a gas if the
volume of its container is decreases. Explain in
terms of gas particles.
Boyle’s Law
• 1662 – Robert Boyle
discovered the relationship
between pressure and
volume
• The volume of a fixed
amount of gas is inversely
proportional to the pressure
at constant temperature.
Boyle’s Law
Boyle’s Law:
PV = k
Or
P1V1=P2V2
Sample Problems
1. A helium-filled balloon contains 125 mL of gas at a
pressure of 0.974 atm. What volume will the gas
occupy at standard pressure?
2. A weather balloon with a volume of 1.375 L is
released from Earth’s surface at sea level. What
volume will the balloon occupy at an altitude of 20.0
km, where the air pressure is 10.0 kPa?
3. The piston of an internal combustion engine
compresses 450. mL of gas. The final pressure is 15
times greater than the initial pressure. What is the
final volume of the gas, assuming constant
temperature?
Charles’ Law
• The relationship between
volume and temperature
of a gas was discovered
by Jacques Charles in
1787.
• The volume of a fixed
mass of gas at constant
pressure is directly
proportional to the Kelvin
temperature.
Charles’ Law
• Charles Law:
V
 k
T
Or
V1
T1

V2
T2
Sample Problems
Assume constant pressure for #’s 1-2.
1. A balloon filled with oxygen gas occupies a volume
of 5.5 L at 25oC. What volume will the gas occupy
at 100.oC?
2. A sample of nitrogen gas is contained in a piston
with a freely moving cylinder. At 0.0oC, the volume
of the gas is 375 mL. To what temperature must the
gas be heated to occupy a volume of 500. mL?
3. An aerosol paint can has a warning label that advises
against storage at high temperatures. What is the
reason for this warning? Explain in terms of gas
particles
Gay-Lussac’s Law
Question:
What would happen if the temperature of a
sample of gas in a rigid, sealed container was
increased?
Gas particles gain kinetic energy and move faster.
This causes increased #’s of collisions and
collisions with greater intensity. As a result, the
pressure increases.
Gay-Lussac’s Law
• The relationship between
pressure and temperature
was recognized by Joseph
Gay-Lussac in 1802
• The pressure of fixed
amount of gas at constant
volume is directly
proportional to the Kelvin
temperature.
•Gay-Lussac’s Law
P
 k
T
P1
T1

P2
T2
Sample Problems
1. An empty aerosol-spray can at room temperature
(20oC) is thrown into an incinerator where the
temperature is 500oC. If the gas inside the empty
container was initially at a pressure of 1.0 atm, what
pressure did it reach inside the incinerator? Assume
the gas was at constant volume and the can did not
explode.
2. The temperature within an automobile tire at the
beginning of a long trip is 25oC. At the conclusion
of the trip, the tire has a pressure of 1.80 atm. What
is the final Celsius temperature within the tire if its
original pressure was 1.75 atm?
Next Question
What happens when gas particles are added to a
container that that is free to expand or
contract. Assume the temperature is constant.
• Discovered in 1811 by
• Equal volumes of a gas at
constant temperature and
pressure contain equal
number of particles.
• At constant temperature and
pressure the number of
moles of gas is directly
proportional to the volume.
V
 k
n
V1
n1

V2
n2
Sample Problems
1. 5.00 L of a gas is known to contain 0.965 mol. If the
amount of gas is increased to 1.80 mol, what new
volume will result (at an unchanged temperature and
pressure)?
2. A cylinder with a movable piston contains 2.00 g of
helium, He, at room temperature. More helium was
that the gas pressure remained the same. How many
grams of helium were added to the cylinder if the
volume was changed from 2.00 L to 2.70 L? (The
temperature was held constant.)
Combined Gas Law
•In many situations,
pressure, volume, and
temperature all change.
•Boyle’s Law, Charles’ Law,
and Gay-Lussac’s Law can
be combined.
•The combined gas law
expresses the relationship
between P, V, and T for a
constant amount of gas
PV
 k
T
P1V 1
T1

P2 V 2
T2
Sample Problems
1. The volume of a gas at 27.0oC and 0.200 atm is 80.0
mL. What volume will the same gas sample occupy
at standard conditions of temperature and pressure?
2. A gas occupying 75 mL at standard conditions is
heated to 17oC while the pressure is reduced to 0.97
atm. What is the new volume occupied by the gas?
Dalton’s Law of Partial Pressures
• The pressure of a mixture
of gases is equal to the
sum of the pressures of
each individual gas.
• Partial pressure- pressure
of an individual gas in a
gas mixture.
PT= P1 + P2 + P3 +….
Problem
Calculate the partial pressure in millimeters of mercury
exerted by the four main gases in air at 760 mm Hg:
nitrogen, oxygen, argon, carbon dioxide. Their
abundance by volume is 78.08 %, 20.95 %, 0.934 %,
and 0.035 %, respectively.
```