Boyle’s Law: Pressure and Volume
Boyle’s law states that for a fixed amount of gas at constant temperature, the pressure and volume are inversely proportional: P1V1 = P2V2. In brief: if 6.0 L of gas at 1.0 atm is compressed at constant temperature until the pressure is 3.0 atm, the new volume is 2.0 L.
Boyle’s law describes why a bicycle pump works, why a balloon expands as it rises and why divers must exhale on the way up. It is the simplest of the gas laws and the first to be stated mathematically. This article explains the relationship, shows the calculation step by step, gives a data table and covers the history and common mistakes.
What does Boyle’s law say?
For a fixed amount of gas at constant temperature, the product of pressure and volume is constant:
P × V = k, or P1V1 = P2V2
If the volume is halved, the pressure doubles. If the volume triples, the pressure falls to one third. The law holds when the number of moles of gas and the temperature do not change.
Why are pressure and volume inversely related?
According to kinetic molecular theory, pressure comes from particles colliding with the walls of the container. If the same number of particles is squeezed into half the volume, they hit each unit of wall area twice as often. The speed of the particles does not change, because the temperature is constant, so the pressure doubles.
How do you solve Boyle’s law problems?
- List the known values and decide which are P1, V1, P2 and V2.
- Check that the temperature and the amount of gas are constant.
- Make sure both pressures use the same unit and both volumes use the same unit.
- Rearrange: V2 = P1V1 / P2 or P2 = P1V1 / V2.
- Substitute, calculate and check whether the answer makes sense: a higher pressure must give a smaller volume.
Worked example 1: compressing a gas
A sample of helium occupies 5.60 L at 740 mmHg. What is its volume at 925 mmHg and the same temperature?
V2 = (740 mmHg × 5.60 L) / 925 mmHg = 4144 / 925 = 4.48 L. The pressure increased, so the volume decreased, as expected.
Worked example 2: a scuba diver’s lungs
A diver at a depth of 30 m, where the absolute pressure is about 4.0 atm, fills her lungs with 3.0 L of air. If she held her breath while rising to the surface at 1.0 atm, to what volume would the air expand?
V2 = (4.0 atm × 3.0 L) / 1.0 atm = 12 L. This is much more than the lungs can hold, which is why divers must never hold their breath while ascending: the expanding gas can seriously injure the lungs.
Boyle’s law data table
The table shows how a fixed sample of gas with P × V = 12.0 atm·L behaves as the pressure changes at constant temperature.
| Pressure (atm) | Volume (L) | 1/V (L−1) | P × V (atm·L) |
|---|---|---|---|
| 0.50 | 24.0 | 0.042 | 12.0 |
| 1.00 | 12.0 | 0.083 | 12.0 |
| 2.00 | 6.00 | 0.167 | 12.0 |
| 3.00 | 4.00 | 0.250 | 12.0 |
| 4.00 | 3.00 | 0.333 | 12.0 |
| 6.00 | 2.00 | 0.500 | 12.0 |
What do the graphs of Boyle’s law look like?
A plot of pressure against volume is a hyperbola that curves down from the upper left to the lower right. A plot of pressure against 1/V is a straight line through the origin, and its slope is the constant k. Chemists often use the straight-line version because it is easier to test against experimental data. A graph of P × V against P is a horizontal line.
Who discovered Boyle’s law?
Robert Boyle published the relationship in 1662 in the second edition of his work on the “spring of the air”, using a J-shaped glass tube in which mercury trapped a sample of air. Boyle credited his assistant Robert Hooke with much of the experimental work. In continental Europe the law is often called the Mariotte law, after Edme Mariotte, who described it independently in 1676 and emphasized that the temperature must stay constant. Earlier hints of the relationship were given by Richard Towneley and Henry Power.
Where is Boyle’s law used?
- Breathing: the diaphragm increases the volume of the chest, which lowers the pressure inside the lungs below atmospheric pressure, so air flows in.
- Syringes and pumps: pulling the plunger enlarges the volume and lowers the pressure, so liquid or air is drawn in.
- Diving: the volume of air spaces in the body changes with depth.
- Weather balloons: a balloon expands as it rises because the surrounding pressure falls.
- Engines and compressors: gas in a cylinder is compressed to a higher pressure by reducing its volume.
Which mistakes are common?
- Ignoring the conditions: the law only applies to a fixed amount of gas at constant temperature.
- Mixing units: P1 and P2 must be in the same unit, as must V1 and V2.
- Using gauge pressure: the law uses absolute pressure, so add atmospheric pressure to gauge readings.
- Inverting the ratio: after calculating, check the direction. More pressure always means less volume.
- Applying it to very high pressures: real gases deviate from the law when the particles are squeezed close together.