Where does gas pressure come from?
A gas is made of tiny particles that move fast and in random directions. They hit each other and the walls of their container.
Each hit gives the wall a tiny push (a force). Pressure is the total force on each square metre of wall: P = F ÷ A. Its SI unit is the pascal (Pa); 1 kPa = 1000 Pa. Air around us is about 101 kPa.
Pressure goes up when particles hit more often or harder. Every gas law is just a way of changing one of these two things.
Boyle's law: pressure and volume
Keep the amount of gas and the temperature fixed. Squeeze the gas into half the space. The particles now have less room, so they hit the walls twice as often. Pressure doubles.
P × V = constant, or P₁V₁ = P₂V₂.
P and V are inversely proportional: one goes up as the other goes down. A graph of P against V is a curve; P against 1/V is a straight line through the origin.
Doing work on a gas
When you push a piston in, you do work on the gas. The particles bounce off a moving wall and speed up a little, so the gas warms. That is why a bicycle pump gets warm.
Charles's law and the pressure law
Heating a gas makes its particles move faster.
Charles's law (pressure fixed)
If the lid can move, faster particles push it up until the pressure is back to normal. Volume grows: V ÷ T = constant, or V₁/T₁ = V₂/T₂.
Pressure law, also called Gay-Lussac's law (volume fixed)
If the container is rigid, the particles hit harder and more often. Pressure grows: P ÷ T = constant, or P₁/T₁ = P₂/T₂.
Why kelvin?
These laws only work with the absolute (kelvin) temperature. T(K) = T(°C) + 273. At 0 K (−273 °C), called absolute zero, the particles would have the least possible motion. Using °C gives wrong answers because 0 °C is not "no motion".
Combined gas law
Put the three together: P₁V₁/T₁ = P₂V₂/T₂. With the amount of gas n as well, this becomes the ideal gas equation PV = nRT.
Dalton's law of partial pressures
In a mixture of gases that do not react, each gas behaves as if it were alone in the container.
The partial pressure of a gas is the pressure it would make on its own. Dalton's law: P(total) = P₁ + P₂ + P₃ + …
The mole fraction x of a gas is its moles divided by the total moles. Then P(gas) = x(gas) × P(total). Example: air is about 21% oxygen, so at 101 kPa oxygen's partial pressure is about 0.21 × 101 ≈ 21 kPa.
Gas collected over water contains water vapour too: P(dry gas) = P(total) − P(water vapour).
Try it: the 3D and at home
In the 3D: on the last step set volume to 10 L, note the pressure, then set 5 L. Predict first: what should the pressure be? Then change the temperature from 300 K to 600 K at a fixed volume.
At home: blow up a balloon a little and tie it. Put it in the fridge for 20 minutes, then in a bowl of warm water. Watch it shrink and swell (Charles's law). Hold your finger over the end of a syringe and push: feel the pressure rise (Boyle's law).
Limits and exam focus
The gas laws are exact only for an ideal gas. Real gases follow them well at low pressure and high temperature. At very high pressure or very low temperature, particles take up space and attract each other, so real gases differ.
Exam questions usually ask you to: state a law with its condition, sketch its graph, explain it with particles, and solve a two-state numerical (remember kelvin and same units on both sides).
Key formulas and definitions
- P = F ÷ A
- Boyle: P₁V₁ = P₂V₂ (n, T fixed)
- Charles: V₁/T₁ = V₂/T₂ (n, P fixed)
- Pressure law: P₁/T₁ = P₂/T₂ (n, V fixed)
- Combined: P₁V₁/T₁ = P₂V₂/T₂
- T(K) = T(°C) + 273
- Dalton: P(total) = P₁ + P₂ + …
- P(gas) = mole fraction × P(total)
Worked examples
1. A gas has volume 6 L at 100 kPa. It is squeezed to 2 L at the same temperature. Find the new pressure.
Boyle: P₁V₁ = P₂V₂ → 100 × 6 = P₂ × 2 → P₂ = 600 ÷ 2 = 300 kPa.
2. A balloon holds 3.0 L at 27 °C. What is its volume at 127 °C, pressure unchanged?
Change to kelvin: T₁ = 300 K, T₂ = 400 K. Charles: V₂ = V₁ × T₂/T₁ = 3.0 × 400/300 = 4.0 L.
3. A sealed can is at 200 kPa and 27 °C. It is heated to 327 °C. Find the pressure.
T₁ = 300 K, T₂ = 600 K. Pressure law: P₂ = 200 × 600/300 = 400 kPa. (This is why aerosol cans must not be heated.)
4. A gas occupies 500 mL at 100 kPa and 300 K. Find its volume at 150 kPa and 360 K.
Combined law: V₂ = V₁ × (P₁/P₂) × (T₂/T₁) = 500 × (100/150) × (360/300) = 500 × 0.667 × 1.2 = 400 mL.
5. A container holds 2 mol N₂ and 3 mol O₂ at total pressure 250 kPa. Find each partial pressure.
Total moles = 5. x(N₂) = 2/5 = 0.4, x(O₂) = 0.6. P(N₂) = 0.4 × 250 = 100 kPa; P(O₂) = 0.6 × 250 = 150 kPa. Check: 100 + 150 = 250 kPa.
6. Hydrogen is collected over water at 25 °C. Total pressure is 100.0 kPa and water vapour pressure at 25 °C is 3.2 kPa. Find the pressure of dry hydrogen.
Dalton: P(H₂) = P(total) − P(water) = 100.0 − 3.2 = 96.8 kPa.
Common mistakes
- Using °C in Charles's or the pressure law. Always add 273 to get kelvin first.
- Thinking pressure doubles when °C doubles. 20 °C → 40 °C is only 293 K → 313 K, a small rise.
- Mixing units: if V₁ is in mL, V₂ comes out in mL. Keep both sides in the same units.
- Forgetting which quantity is held constant: Boyle (T fixed), Charles (P fixed), pressure law (V fixed).