11.9 THE GAS LAWS – BOYLE’S LAW, GAY-LUSSAC’S LAW AND COMBINED GAS LAW
BOYLE’S LAW
Robert Boyle (1662) stated that the volume of a given amount of
gas varies inversely with pressure (provided the temperature and
amount of gas are constant). Consider a piston or syringe with the end
plugged. If it is pushed in, the pressure will
and
the volume will
(assuming the temperature
remains constant). The gas molecules are forced closer together. They
have little to travel before they strike the walls of the container. This
will
internal pressure. Conversely, if the piston is
pulled out the pressure will
and the volume will
.
Since these changes are inversely proportional, they can be expressed mathematically as:
Mathematically, V  1/P
PV = k (constant value) or V = 1 k
P
K differs depending on the gas. If you double the pressure, the volume will be halved
Table 1: Pressure and Volume of H2 at 25 °C
Pressure
(mm Hg)*
Volume
(mL)
PxV
760
23
1.75 x 104
912
19.2
1.75 x 104
1064
16.4
1.75 x 104
1216
14.4
1.75 x 104
1368
12.8
1.75 x 104
1520
11.5
1.75 x 104
Figure 1: Graph of Relationship in Boyle’s Law
We can also express Boyle’s law by initial conditions and
final conditions.
P1V1 = P2V2
Real-World Application: Breathing
During inhalation, your diaphragm contracts and ribcage
expands, so the volume of your lungs increases and the
pressure is decreased. During exhalation, your
diaphragm rises and ribcage contracts, so the volume of
your lungs decrease and the pressure is increased.
GAY-LUSSAC’S LAW
Gay Lussac’s Law states that the pressure of a gas is directly
proportional to its temperature. Consider a strong scuba tank. If it is
heated the pressure will
(assuming the volume remains
constant). Conversely, if the tank is cooled, the pressure will
.
Since these changes are proportional, they can be expressed
mathematically as:
P = k (constant value) or P = kT
T
Mathematically, P  T
We can also express Gay-Lussac’s law by initial conditions and final conditions.
P 1 = P2
T 1 T2
Example Problems – USE GRASS
1. Helium gas has a volume of 8.25 L at 446 kPa. What pressure must be applied to the gas when it
occupies 12 L?
Given: V1 = 8.25 L
V2 = 12 L
P1 = 446 kPa
Solution:
Required: P2
Analysis: P1V1= P2V2
P2 = P1V1
V2
2. Soccer balloons are typically inflated to between 60 and 110 kPa. A soccer ball is inflated
indoors with a pressure of 85 kPa at 25 C. If it is taken outside, where the temperature on the
playing field is -11.4 C, what is the pressure of the gas inside the soccer ball?
Given:
Required:
Analysis:
Solution:
THE COMBINED GAS LAW
A combination of:
Boyle’s Law
P1V1 = P2V2
Charles’ Law
V1 = V 2
T1 T2
Gay-Lussac’s Law
P1 = P 2
T1 T2
P1V1 = P2V2
T1
T2
gives us…
Mathematically, V 1 x T or V T . There is a proportionality constant: k = PV
P
P
T
Example 3:
A balloon at the top of Mount Logan occupies a volume of 775 mL at a temperature of -28°C and a
pressure of 92.5 kPa. What is the pressure at the bottom of the mountain if the same balloon has a
volume of 825 mL at a temperature of 15°C?
Given:
Required:
Analysis:
Solution:
Read Pages 554-561 and do Questions Pg 562 #2-4, 6-7, 10-11, 15