CHARLES’S LAW
The Second Gas Law
Objectives
• Upon completion of this presentation, you will be able to
• describe the relationship between the volume and the
temperature of an ideal gas
• use Charles’s law to calculate the final volume of a gas
when given the initial temperature and volume and the
final temperature
• use Charles’s law to calculate the final temperature of a
gas when given the initial temperature and volume and
the final volume
Introduction
• In the 1780’s, Jacques Charles was investigating the
properties of gases.
• He found a relationship between volume, V, and
temperature, T, when the pressure, P, is held constant.
• Volume is directly related to temperature.
• As the temperature increases, the volume increases.
• As the temperature decreases, the volume decreases.
Introduction
• This behavior would be expected from the assumptions of
the kinetic theory.
• As the temperature increases, the average speed of the
gas particles also increases.
• This causes the collisions with the walls of the container
to be more forceful.
• More force over the same area gives more pressure.
• To keep the pressure constant, we would need to
increase the volume of the container.
Introduction
• We can write Charles’s law two different ways:
• V/T = k or V = kT
• where "k" is a constant.
• V1/T1 = V2/T2
• where V1 and T1 are initial volume and temperature
• where V2 and T2 are final volume and temperature
Introduction
• Charles stated his law using the first notation, V = kT.
• The change in volume of a gas is directly proportional to
the temperature when the pressure is held constant.
•V∝T
⇒
V = kT
• We most often use the second notation, V1/T1 = V2/T2, to
solve problems.
Application
• When we are trying to solve a Charles's law problem, we
will need to know three of the four variables.
• For V1/T1 = V2/T2 we can solve for:
V1 =
V2T1
T2
T1 =
T2V1
V2
V2 =
V1T2
T1
T2 =
T1V2
V1
Example 1 – Finding V2
What is the final volume, V2, of 2.00 L of helium gas at an
initial temperature of 300K, and a final temperature of 500 K?
V1 = 2.00 L
T1 = 300 K
V2 = ? L
T2 = 500 K
V2 =
V1T2
=
T1
(2.00 L)(500 K)
300 K
= 3.33 L
Sample Problems – Finding V2
1. What is the final volume of hydrogen gas with an initial
volume of 3.00 L, an initial temperature of 300 K, and
a final temperature of 400 K?
V2 = 4.00 L
2. What is the final volume of oxygen gas with an initial
volume of 0.120 L, an initial temperature of 500 K, and
a final temperature of 200 K?
V2 = 0.0480 L
3. What is the final volume of chlorine gas with an initial
volume of 2.40 L, an initial temperature of 200 K, and
a final temperature of 250 K?
V2 = 3.00 L
4. What is the final volume of carbon monoxide gas with
an initial volume of 0.0480 L, an initial temperature of
273 K, and a final temperature of 625 K?
V2 = 0.110 L
Example 2 – Finding T2
What is the final temperature, T2, of argon gas at an initial
volume of 4.20 L, an initial temperature of 250 K, and a
final volume of 4.80 L?
V1 = 4.20 L
T1 = 250 K
V2 = 4.80 L
T2 = ? L
T2 =
T1V2
=
V1
(250 K)(4.80 L)
= 285 K
4.20 L
Sample Problems – Finding T2
1. What is the final temperature of neon gas with an
initial volume of 4.00 L, an initial temperature of 350 K,
and a final volume of 0.100 L?
T2 = 8.75 K
2. What is the final temperature of helium gas with an
initial volume of 1.20 L, an initial temperature of 250 K,
and a final volume of 0.600 L?
T2 = 125 K
3. What is the final temperature of argon gas with an
initial volume of 480 L, an initial temperature of 300 K,
and a final volume of 1,200 L?
T2 = 750 K
4. What is the final temperature of fluorine gas with an
initial volume of 40.4 L, an initial temperature of 280 K,
and a final volume of 542 L?
T2 = 3,760 K
Example 3 – Finding V1
What was the initial volume, V1, of neon gas that had an
initial temperature of 200 K, a final volume of 0.500 L, and
a final temperature of 500 K?
V1 = ? L
T1 = 200 K
V2 = 0.500 L
T2 = 500 K
V1 =
V2T1
(0.500 L)(200 K)
=
= 0.200 L
T2
500 K
Sample Problems – Finding V1
1. What is the initial volume of nitrogen gas with an initial
temperature of 600 K, a final temperature of 300 K,
and a final volume of 0.100 L?
V1 = 0.200 L
2. What is the initial volume of oxygen gas with an initial
temperature of 250 K, a final temperature of 300 K,
and a final volume of 6.00 L?
V1 = 5.00 L
3. What is the initial volume of chlorine gas with an initial
temperature of 1,200 K, a final temperature of 400 K,
and a final volume of 3,500 L?
V1 = 10,500 L
4. What is the initial volume of fluorine gas with an initial
temperature of 294 K, a final temperature of 742 K,
and a final volume of 85.9 L?
V1 = 34.0 L
Example 4 – Finding T1
What was the initial temperature, T1, of argon gas at an
initial volume of 0.100 L, a final volume of 0.125 L, and a
final temperature of 298 K?
V1 = 0.100 L
T1 = ? L
V2 = 0.125 L
T2 = 298 K
T1 =
T2V1
=
V2
(298 K)(0.100 L)
= 238 K
0.125 L
Sample Problems – Finding T1
1. What is the initial temperature of radon gas with an
initial volume of 4.00 L, a final volume of 2.00 L, and a
final temperature of 250 K?
T1 = 500 K
2. What is the initial temperature of neon gas with an
initial volume of 12.0 L, a final volume of 15.0 L, and a
final temperature of 400 K?
T1 = 320 K
3. What is the initial temperature of helium gas with an
initial volume of 0.720 L, a final volume of 0.600 L, and
a final temperature of 350 K?
T1 = 420 K
4. What is the initial temperature of ammonia gas with an
initial volume of 0.235 L, a final volume of 0.123 L, and
a final temperature of 275 K?
T1 = 525 K
Summary
• Charles’s Law:
• At a constant pressure,
• the volume of a gas is directly proportional to its
volume.
• Equations:
• V/T = k or V = kT, where k is a constant
• V1/T1 = V2/T2