States of matter & gas laws
The idea
Gases are the state where the particle model pays off most directly: molecules in constant random motion, far apart, colliding with the container walls — and each wall collision contributes to pressure. Four variables describe any gas sample: pressure P, volume V, temperature T, and amount n in moles. The named laws you may have met — Boyle (P and V inversely related), Charles (V grows with T) — are each just one slice of a single master relationship, the ideal gas law PV = nRT, where R is a constant (0.0821 L·atm/(mol·K) when pressure is in atmospheres).
Each connection is mechanical once you think in collisions. Squeeze the volume and the same molecules hit the walls more often: pressure rises. Heat the gas and molecules move faster, hitting harder and more often: pressure or volume must rise. Add moles and there are more colliders. Notably absent is the gas's identity — at ordinary conditions, ideal behavior depends only on how many particles there are, not what they are.
The non-negotiable rule: temperature must be in kelvin (K = °C + 273). Celsius has an arbitrary zero, so going from 10 °C to 20 °C is nowhere near doubling the molecular motion. Kelvin starts at absolute zero, where motion effectively stops, making temperature truly proportional to molecular kinetic energy — feed Celsius into a gas law and every answer comes out wrong.
Worked example
What volume does 0.500 mol of nitrogen gas occupy at 25 °C and a pressure of 1.20 atm? Use R = 0.0821 L·atm/(mol·K).
- List the variables and fix the units first: n = 0.500 mol, P = 1.20 atm, and T = 25 + 273 = 298 K — the Celsius-to-kelvin conversion is the step you must never skip.
- Rearrange the ideal gas law for the unknown: PV = nRT becomes V = nRT/P.
- Substitute and compute the numerator: 0.500 × 0.0821 × 298 = 12.2 L·atm.
- Divide by the pressure: V = 12.2 ÷ 1.20 = 10.2 L.
- Sanity-check against a benchmark: near 0 °C and 1 atm, one mole of any ideal gas fills about 22.4 L, so half a mole should be around 11 L; our sample is a bit warmer (more volume) but at higher pressure (less volume), so 10.2 L is exactly the right neighborhood.
Answer. The 0.500 mol of N₂ occupies about 10.2 L at 25 °C and 1.20 atm.
Check your understanding
- Why does every gas law demand kelvin, and what specifically breaks if you plug in Celsius?
- Using the collision picture, what happens to pressure when volume is halved at constant temperature, and why?
- Why does the identity of the gas not appear anywhere in PV = nRT?
- Under what conditions does a real gas stop behaving ideally, and which assumptions of the model fail there?
Build the foundations first
States of matter & gas laws builds on these concepts. If any feel shaky, start there.