Chapter 4: The Gas Laws
•
•
In this chapter, we’ll study the gas
laws which will allow us to predict the
properties of any gas
We’ll cover sections 1 through 11 over
the next three days
The Nature of Gases
• Eleven elements are gases under
normal conditions
• Despite the fact that the elements
are VERY different, their physical
properties in the gas phase are
very similar
• Gases are compressible examples
of bulk matter
– Gases fill the entirety of whatever
closed volume they occupy
– Gas molecules are in constant motion
Pressure
Pressure = Force per unit area
F
P
A
The pressure of a gas
exerted on the walls
of a container is a
result of the collisions
of gas molecules with
the surface of the
walls.
The SI Unit of Pressure is
the pascal, Pa
1 Pa = 1 kg·m-1·s-2
Pressure
Measuring Pressure
• The atmosphere of the
planet is filled with gas
molecules. These
molecules exert a force
on the surface of the
earth
• We use a barometer to
measure the pressure of
atmospheric gases.

Vacuum Gauges
• A manometer is a
device used to
measure the
pressure inside a
vessel
• We measure the
pressure on the
atmospheric side
and the pressure on
the device side
– The difference is the
pressure in the
device
The Gas Laws
•
Studies on the effect of temperature,
pressure and volume have been carried out
by many scientists, but 4 stand out:
1. Robert Boyle: (1662) Studied the relationship
between Volume and Pressure
2. Jacques Charles and Joseph-Louis Gay-Lussac:
(1810) Studied the relationship between Volume
and temperature while hot air ballooning over
Paris
3. Avedeo Avogadro: Helped prove atoms exist by
confirming the relationship between Volume and
the number of molecules of a gas
Boyle’s Law
• Took a closed tube
with an air bubble
on the closed end
and poured Hg into
the open end
– As he added more
Hg, the air bubble
shrank

Boyle’s Law
• Pressure is inversely
related to volume.
• V  1/P
• PV = constant (at constant n)
Boyle’s Law
Pressure is inversely related to volume.
V  1/P
PV = constant (at constant n and T)
P1V1  P2V2

Charles’s Law
• Charles and GayLussac were
balloonists and while
trying to improve their
balloons, they found
that:
At constant pressure, the
volume of a gas
increases with
temperature
Charles’s Law
•We could also state Charles’s
Law in terms of Pressure.
•The Pressure of a sample is
directly proportional to the
absolute temperature
Charles’s Law
Volume  absolute temperature
V=(constant) T
@ constant n, constant P
Pressure  absolute temperature
P=(constant) T
V1 V2

T1 T2
@ constant n, constant P
or
@ constant n, constant V
P1 P2

T1 T2
@ constant n, constant V
Absolute Temperature
• Note: The absolute temperature is the
temperature on the Kelvin scale
• For the remainder of the semester, whenever
you use a temperature, you may need to
convert it to the Kelvin scale
• Many of the constants and relationships that
use them will only be valid when temperature
is on the absolute, or Kelvin, scale
0C = 273.15 K
1 degree C = 1 Kelvin
25C = 298.15 K
Charles’s Law
• If we double the absolute temperature,
the volume of the gas doubles OR the
pressure of the gas doubles

Avogadro’s Principle
• Avogadro found that under the same
conditions of temperature and pressure, a
given number of gas molecules occupy the
same volume regardless of their chemical
identity
At 273.15K and 1 atm, all gases occupy
approximately 22.4L
Vm=Molar volume of gas = V/n
V=nVm

The Gas Laws: Summary
1. Boyle’s Law: P1V1=P2V2 @ constant n, constant T
2. Charles’s Law: V1/T1=V2/T2 @ constant n, constant P
P1/T1=P2/T2 @ constant n, constant V
3. Avogadro’s Law: As more molecules are
added to a sample of gas at constant
temperature and pressure, the volume must
increase
OR
As more molecules are added to a sample
of gas at constant temperature and volume,
the pressure must increase
Putting it all together:
The Ideal Gas Law
We can combine the relationships stated in the
three laws to create a single equation that will
allow us to predict the pressure, volume or
temperature of a certain number of moles of
gas
V= n • (constant) • P
V= n • (constant) • T
P= n • (constant) • T
PV= n • (constant) • T
The Ideal Gas Law
PV=nRT where R=8.314 J/Kmol
• The ideal gas law is an equation of state, an
equation that describes the pressure, volume
and temperature of a certain amount of a
substance
• We can use the equation by itself or we can
use it to determine the properties of an ideal
gas at 2 sets of conditions by using the
combined gas law
P1V1 P2V2

n1T1 n2T2
