Gases

A gas is molecules flying around with lots of space between them. Its pressure is the push of those molecules hitting the walls, measured in pascals (Pa), kilopascals (kPa), atmospheres or bar: 1 atm = 101.325 kPa, and 1 bar = 100 kPa, close enough that they're often treated as about the same.

Gas laws need temperature in kelvin (K), which starts at absolute zero, the coldest anything can get: K = °C + 273.15 (273 is fine for most sums). At 0 K the molecules would stop moving; double the kelvin temperature and you double their average energy.

Squeeze a gas into half the space at the same temperature and the molecules hit the walls twice as often, so the pressure doubles: P₁V₁ = P₂V₂ (Boyle's law). Heat it at the same pressure and it expands in proportion to the kelvin temperature: V₁/T₁ = V₂/T₂ (Charles's law). 3 L at 300 K becomes 6 L at 600 K.

Both fit inside the ideal gas law: PV = nRT, where n is moles and R is the gas constant, 8.314 J/(mol·K), or 0.08206 L·atm/(mol·K) when pressure is in atm and volume in litres. It says one mole of any gas takes about 22.4 L at 0 °C and 1 atm, and about 24.5 L at 25 °C. Real gases follow it well at everyday conditions and drift from it at high pressure or close to condensing.

In a mixture each gas pushes as if it were alone, and the pressures add up (Dalton's law). A gas's share of the pressure is its share of the moles: air is about 21% oxygen, so at 1 atm the oxygen's partial pressure is about 0.21 atm.