How important is it to check the weather?
Each day, hundreds of weather balloons are launched. Made of a synthetic rubber and carrying a box of instruments, the helium-filled balloon rises up into the sky. As it gains altitude, the atmospheric pressure becomes less and the balloon expands. At some point the balloon bursts due to the expansion, the instruments drop (aided by a parachute) to be retrieved and studied for information about the weather.
Boyle’s Law
Robert Boyle (1627-1691), an English chemist, is widely considered to be one of the founders of the modern experimental science of chemistry. He discovered that doubling the pressure of an enclosed sample of gas while keeping its temperature constant caused the volume of the gas to be reduced by half. Boyle’s law states that the volume of a given mass of gas varies inversely with the pressure when the temperature is kept constant. An inverse relationship is described in this way. As one variable increases in value, the other variable decreases.
Physically, what is happening? The gas molecules are moving and are a certain distance apart from one another. An increase in pressure pushes the molecules closer together, reducing the volume. If the pressure is decreased, the gases are free to move about in a larger volume.
Mathematically, Boyle’s law can be expressed by the equation:
The
Pressure (atm) | Volume (mL) | |
0.5 | 1000 | 500 |
0.625 | 800 | 500 |
1.0 | 500 |
500 |
2.0 | 250 |
500 |
5.0 | 100 | 500 |
8.0 | 62.5 | 500 |
10.0 | 50 | 500 |
A graph of the data in the table further illustrates the inverse relationship nature of Boyle’s Law (see Figure below). Volume is plotted on the
Boyle’s Law can be used to compare changing conditions for a gas. We use
This equation can be used to calculate any one of the four quantities if the other three are known.
Sample Problem: Boyle’s Law
A sample of oxygen gas has a volume of 425 mL when the pressure is equal to 387 kPa. The gas is allowed to expand into a 1.75 L container. Calculate the new pressure of the gas.
Step 1: List the known quantities and plan the problem.
Known
P1=387 kPa V1=425 mL V2=1.75 L=1750 mL
Unknown
P2=? kPa
Use Boyle’s Law to solve for the unknown pressure
Step 2: Solve.
First, rearrange the equation algebraically to solve for
Now substitute the known quantities into the equation and solve.
Step 3: Think about your result.
The volume has increased to slightly over 4 times its original value and so the pressure is decreased by about
Pressure vs. Volume
Have you ever wondered why your ears pop during airplane take offs and landings? Or why a balloon pops when you squeeze it too much? Find out in this MIT video.
Summary
- The volume of a gas is inversely proportional to temperature.
Review
- What does “inversely” mean in this law?
- Explain Boyle’s law in terms of the kinetic-molecular theory of gases.
- Does it matter what units are used?