Ch. 13: Gases
Sec. 13.1: The Gas Laws
Objectives
 State the relationships among pressure,
temperature, and volume of a constant
amount of gas.
 Apply the gas laws to problems involving
the pressure, temperature and volume of a
constant amount of gas.
Review: The Kinetic Theory
Ideally:
 Gas particles do not attract or repel each other.
 Gas particles are much smaller than the distances between
them. That is, they have essentially NO volume compared to
the space between them.
 Gas particles are in constant, random motion.
 No kinetic energy is lost when gas particles collide with
each other or their container.
 All gases have the same average kinetic energy at a given
temperature.
In Reality ….
 Actual gases don’t obey all the assumptions made by the
kinetic theory.
 Most gases DO approximate the behaviors assumed by the
kinetic theory. (At extremely high pressures and low
temperatures, gases do not behave ideally.)
 There are 3 factors that work together, when the amount of
a gas is constant, to determine the behavior of a gas in the
kinetic theory: temperature (T), volume (V), and pressure
(P).
What is the relationship between
pressure and volume that is pictured here?
Boyle’s Law
 If the number of particles and the temperature do not
change, when the gas particles are pushed closer
together, the number of collisions those particles have
increases (less room, more collisions). Therefore, the
pressure of the gas increases.
 If the volume is increased, the number of collisions
will decrease and gas pressure will decrease.
 P & V are inversely proportional.
Boyle’s Law:
The volume of a given
amount of gas held at a
constant temperature
varies inversely with
the pressure.
The plot of an inversely
proportional relationship
results in a downward
curve.
Boyle’s Law
 Mathematically, for two sets of conditions,
P1V1 = P2V2
 “1” represent the original conditions; “2” represent new
conditions.
 If a gas occupies 2.0 L at 2.5 atm., what volume will it
occupy at 4 atm.?
P1 = 2.5 atm
P2 = 4 atm
V1 = 2.0 L
V2 = ?
Solve for V2
Boyle’s Law Problems
 A sample of helium gas in a balloon 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?
 A sample of neon gas occupies 0.220 L at 0.860
atm. What will its volume be at 29.2 kPa of
pressure?
Charles’s Law
 As the temperature of a
gas increases, so does its
volume when the
amount of gas and
pressure do not change.
How does the KMT
explain this?
Charles’s Law
 Charles’s law states that the volume of a given mass of gas is
directly proportional to its Kelvin temperature at
constant pressure.
 Mathematically,
 To convert 0C into K, use the expression:
273.
K = C +
The Kelvin Scale
 The Kelvin scale is based on a concept called
absolute zero. Absolute zero is, theoretically, the
lowest possible temperature that can be reached.
 At absolute zero (K = 0 and C = -2730), it is
theorized that the motion of all particles of
matter ceases. The particles have no movement
and, so, the particles have no energy.
Charles’s Law
The graph of a
directly proportional
relationship is an
upward sloping
straight line.
Charles’s Law Problems
 A gas sample at 40 0C occupies a volume of 2.32 L.
If the temperature is raised to 75 0C, what will the
volume be, assuming the pressure remains constant?
 A gas at 89 0C occupies a volume of 0.67 L. At what
Celsius temperature will the volume be increased to
1.12 L?
 What is the volume of air in a balloon that occupies
0.620 L at 25 0C if the temperature is lowered to 0
0C?
Recall . . .
 Gas pressure results from the collisions of gas
particles with the walls of their container.
 If the temperature is increased, the particles will
move faster.
 This will increase the number of collisions (and
their force).
 So an increase in temperature will result in an
increase of gas pressure.
Gay-Lussac’s Law
 Gay-Lussac’s law states
that the pressure of a
given mass of gas varies
directly with the Kelvin
temperature when the
volume remains
constant.
Gay-Lussac’s Law
 Mathematically,
Gay-Lussac’s Law Problems
 The pressure of a gas in a tank is 3.20 atm at 22 0C. If the
temperature rises to 60 0C, what will be the gas pressure in
the tank?
 A gas in a sealed container has a pressure of 125 kPa at a
temperature of 30 0C. If the pressure in the container is
increased to 201 kPa, what is the new temperature?
 Helium gas in a 2 L cylinder is under 1.12 atm of pressure.
At 36.5 0C, that same gas sample has a pressure of 2.56 atm.
What was the initial temperature of the gas in the cylinder?
The Combined Gas Law
 Boyle’s, Charles’s and Gay-Lussac’s Laws can be
combined into a single law.
 The combined gas law states that the relationship
among pressure, volume and temperature of a
fixed amount of gas.
The Combined Gas Law
 Relationships between the variables do not
change. For example, P and V are still inversely
proportional.
 The equation for the combined gas law is:
P1V1 = P2V2
T1
T2
The Combined Gas Law Problems
 A gas at 110 kPa and 30 0C fills a flexible container with an
initial volume of 2.0 L. If the temperature is raised to 80 0C
and the pressure is increased to 440 kPa, what is the new
volume?
 At STP, a gas sample occupies 30 mL. If the temperature is
increased to 30 0C and the entire sample is transferred to a
20 mL container, what will be the gas pressure inside the
container?