Gas pressure and Boyle's law
In 1662 Robert Boyle squeezed trapped air to a quarter of its volume and found that its pressure had gone up about four times.
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Cover the tip of a syringe with your finger and push the plunger. It moves a little, then pushes back harder and harder. Let go and it springs out again. The air inside has not changed in amount or temperature; only its volume has. This pushing back is gas pressure, the force the gas exerts on each square metre of the walls. It is measured in pascals; normal air pressure at sea level, 1 atm, is 101.325 kPa.
Where pressure comes from
Gas molecules fly in straight lines and bounce off the walls of their container. Each bounce gives the wall a tiny push. Billions of billions of them every second add up to a steady pressure. Squeeze the gas into half the volume and each part of the wall is hit twice as often, so the pressure doubles. Heat the gas and the molecules hit harder and more often, so the pressure rises too. The particle picture explains the gas laws, which were first found by experiment.
Boyle's law
For a fixed amount of gas at constant temperature, pressure and volume are inversely proportional: P × V stays the same. So P₁V₁ = P₂V₂. Double the pressure and the volume halves; triple it and the volume drops to a third. On a graph of P against V the points lie on a curve called a hyperbola. Plot P against 1/V instead and they fall on a straight line, which is easier to read and check. Switch the graph in the lab above to see both.
Robert Boyle published the relationship in 1662. He trapped air in the short, closed end of a J-shaped glass tube and poured mercury into the long open end, so that the weight of mercury squeezed the air. In his table the air was squeezed from 48 equal spaces of the tube down to 12, while the total pressure on it rose from 29 2/16 to 117 9/16 inches of mercury. A quarter of the volume, about four times the pressure. The French physicist Edme Mariotte found the same relation independently in 1676.
Boyle's law in the body and under water
Breathing uses Boyle's law about 20 times a minute. To breathe in, the diaphragm and the muscles between the ribs tighten, the chest gets bigger and the volume of the lungs increases. The pressure inside drops a little below the air outside, and air flows in. Breathing out reverses it. Every 33 feet (about 10 m) of sea water adds about 1 atm. For a fixed amount of air at constant temperature, 2 atm compresses it to half its volume at 1 atm. A scuba regulator supplies air at ambient pressure, so the lungs of a breathing scuba diver do not simply shrink to half their surface volume. This is a gas-law example, not diving guidance.
| Boyle's law | P₁V₁ = P₂V₂ at constant temperature and amount |
| 1 atm | 101.325 kPa |
| P against 1/V | A straight line for a gas obeying Boyle's law |
| Ideal gas law | PV = nRT |
- A gas fills 2.0 L at 100 kPa. At the same temperature it is squeezed to 0.50 L. What is the new pressure?
- A syringe holds 15.0 mL of air at 13.0 psi. What is the pressure at 7.5 mL?
- The same air at 6.5 psi fills 30.0 mL. What volume does it fill at 11.0 psi (1 decimal place)?
- In Boyle's law, which two quantities must stay the same?
- Amount of gas and temperature
- Pressure and volume
- Volume and temperature
- A graph of P against V for Boyle's law is…
- a curve (hyperbola)
- a straight line through the origin
- a horizontal line
- In particle terms, why does squeezing a gas raise its pressure?
- Molecules hit each part of the wall more often
- Molecules get bigger
- Molecules stop moving
- In Boyle's table, air at 48 spaces was under 29 2/16 in of mercury. Using P₁V₁ = P₂V₂, what pressure should it have at 12 spaces (2 decimal places)?
- A diver at 33 feet is under 2 atm. A balloon holding 4.0 L at the surface (1 atm) is taken down. What is its volume there?
- When you breathe in, the volume of your lungs increases. The pressure inside them…
- drops below the outside air, so air flows in
- rises, pushing air in
- does not change
- Who published the pressure-volume law in 1662?
- Robert Boyle
- Jacques Charles
- Amedeo Avogadro
- Gas pressure comes from molecules hitting the walls; 1 atm = 101.325 kPa.
- Boyle's law: P₁V₁ = P₂V₂ at constant amount and temperature.
- P against V is a curve; P against 1/V is a straight line.
- Breathing and diving both follow Boyle's law; every 33 ft of sea water adds 1 atm.
Sources for this course (8)
- OpenStax Chemistry 2e (openstax.org/books/chemistry-2e): 1.2 Phases and Classification of Matter (matter, three states, plasma, mass and weight, Moon 1/6, conservation of matter, sand and clouds)
- 9.2 gas laws (Boyle's law P1V1 = P2V2, syringe 15.0 mL 13.0 psi to 7.5 mL 26 psi, breathing, divers: every 33 ft of sea water adds 1 atm and halves the air volume at 33 ft, Amontons ~1700, Gay-Lussac ~1800, Charles, STP 273.15 K and 101.325 kPa, -273 °C absolute zero)
- 9.5 kinetic-molecular theory (average kinetic energy proportional to kelvin temperature, KEavg = 3/2 RT, urms = sqrt(3RT/M), N2 at 30 °C 519 m/s, O2 at -23 °C 441 m/s)
- 10.3 phase transitions (vapor pressure, normal boiling point at 1 atm = 101.3 kPa, Leadville 68 kPa about 90 °C, ΔHvap 44.01 kJ/mol at 25 °C and 40.67 kJ/mol at 100 °C, 1.5 L sweat 3600 kJ, ΔHfus 6.01 kJ/mol, ice at -12 °C staying at 0 °C while melting, CO2 sublimation 26.1 kJ/mol, frost is deposition, heating curve example 135 g ice -15 °C to steam 120 °C = 416 kJ with c ice 2.09, water 4.18, steam 1.86 J/g °C, burner turned up does not raise boiling temperature)
- NIST Chemistry WebBook phase change data (webbook.nist.gov: ethanol Tfus 159 K, Tboil 351.5 K; nitrogen Tfus 63.3 K, Tboil 77.34 K; oxygen Tfus 54.8 K, Tboil 90.2 K; mercury Tfus 234.31 K, Tboil 629.81 K; CO2 triple point 216.58 K at 5.185 bar, solid vapour-pressure equation Giauque and Egan 1937 giving 194.7 K at 1 atm)
- USGS Water Science School, Water Density (0.99987 g/cm³ at 0 °C, 1.00000 at 4 °C, 0.95865 at 100 °C; ice about 9% less dense)
- Britannica, Boyle's law (Robert Boyle 1662, air compressed by mercury; Edme Mariotte 1676)
- Boyle's 1662 table (48 spaces at 29 2/16 in, 12 spaces at 117 9/16 in of mercury) as reprinted in J. Appl. Physiol. 87 (1999) 1543.
Checked: 2026-10-17