Combined Gas Law
Pressure, volume, and temperature of gases are all related to each other. While we have been looking at
how each variable relate to each other separately, identifying our first three gas laws – Gay-Lussac’s
Law, Boyle’s Law, and Charles’s Law – each law cannot help us distinguish all three variables at once
within a lab environment. Thus, a fourth gas law has been developed to be able to identify the
relationship between pressure, volume, and temperature within the same system. This law is known as
the combined gas law.
Looking at the basic three gas laws, label each gas law shown below:
P1/T1 = P2/T2
P1V1 = P2V2
V1/T1 = V2/T2
Each law only focuses on two variables at once, assuming the third is held constant. However in the
combined gas law, the basic laws are merged into one simple equation:
P1V1 = P2V2
T1
T2
Each variable is represented in this culminating formula. In many real life scenarios, it is impossible to
control only one of these variables while only two change, thus the combined gas law provides a
solution that enables us to predict what is happening while all three variables are changing.
While each variable is represented, the basic math involved in solving combined gas law scenarios is
very similar to what you have practiced with the three basic gas laws. You must GUESS…
- Identify the GIVEN variables and their units
- Identify the UNKNOWN
- SET up the equation
- SOLVE for the unknown
Example 1:
A toy balloon has an internal pressure of 1.05atm and a volume of 5L. If the temperature where the
balloon is released is 20⁰C, what will happen to the volume when the balloon rises to an altitude where
the pressure is 0.65atm and the temperature is 5⁰C?
P1 =
P2 =
V1 =
V2 =
T1 =
T2 =
Example 2:
A gas that has a volume of 28 liters, a temperature of 45 0C, and an unknown pressure has its volume
increased to 34 liters and its temperature decreased to 35 0C. If I measure the pressure after
the change to be 2.0 atm, what was the original pressure of the gas?
Example 3:
If I have 2.9 L of gas at a pressure of 5 atm and a temperature of 50 0C, what will be the temperature of
the gas if I decrease the volume of the gas to 2.4 L and decrease the pressure to 3 atm?
Example 4:
Example 5: