Molar Gas Volume

Gases push on their container because their particles are constantly bouncing off the walls. Change the volume or temperature and you change how often those collisions happen — which is the whole story behind the gas laws.

Where gas pressure comes from

Gas particles are in constant motion, so they’re forever bumping into the walls of their container. Each collision gives the wall a tiny push, and all those pushes together make up the pressure of the gas. Anything that changes how often particles hit the walls changes the pressure.

Boyle’s Law — pressure and volume

Squeeze a gas into a smaller space (keeping temperature constant) and the particles are packed closer together, so they hit the walls more often. Pressure goes up.

So pressure is inversely proportional to volume. This shows up three ways on a graph:

Charles’ Law — volume and temperature

Heat a gas at constant pressure and its particles gain kinetic energy, moving faster and hitting the walls harder and more often. To keep the pressure the same, the gas must expand — so volume rises with temperature.

Volume is directly proportional to temperature in Kelvin, so a graph of V against T (in K) is a straight line through the origin.

The Pressure Law — pressure and temperature

Now hold the volume fixed and heat the gas. The faster particles collide with the walls more frequently and more forcefully, so the pressure rises.

Pressure is directly proportional to temperature in Kelvin — a graph of P against T (in K) is a straight line.

Combining the three

Put the three relationships together and you get the seeds of the ideal gas equation:

• PV = constant
• V/T = constant
• P/T = constant

Combined, these give PV/T = constant, which leads directly to PV = nRT — the subject of the next note.