$PV = nRT$, read aloud P V equals n R T. $P$ is the absolute pressure in pascals — absolute, not gauge, because a gas at zero gauge still has atmosphere in it. $V$ is the volume in cubic metres, $n$ the amount of gas in moles, $T$ the absolute temperature in kelvin, and $R$ the molar gas constant, 8.314 J/(mol·K).

$R$ is the referee, and it only whistles in one set of units. There is a check that never fails: multiply your pressure unit by your volume unit and ask whether the answer is a joule. Pa·m³ is. kPa·L is. bar·m³ is a hundred thousand of them. And the resident trap of every gas problem is the temperature: $R$ is per kelvin, so 27 °C goes in as 300.15 K. Celsius fed into a gas law does not give a slightly wrong answer; at low temperatures it gives an absurd one, and at 0 °C it divides by zero.

At STP — 0 °C and 101.325 kPa — the whole of $R T / P$ has already been worked out and given a name: the molar volume $V_m$, 22.414 L/mol, which every exam paper prints as 22.4. Then $V = n\,V_m$, V equals n times V-m. The remarkable part is that $V_m$ is the same for every ideal gas: chlorine, ammonia, oxygen — one mole, one bucketful, whatever the molecule weighs. The fine print is the reference condition. Off STP the shortcut's contract is void, and 25 °C has its own molar volume of 24.5 L/mol, which is a perfectly good number quoted at the wrong temperature.

Density needs no new physics. Put $n = m/M$ into the gas law, divide through by $V$, and $\rho = \dfrac{PM}{RT}$ falls out — rho equals P M over R T — where $\rho$ (rho) is the density in kg/m³ and $M$ the molar mass, in kilograms per mole for SI to balance. Read its shape: at one pressure and temperature, density is simply proportional to molar mass.

That last line is a safety fact before it is a chemistry one. Chlorine at 71 g/mol is two and a half times as dense as air and pools in pits, trenches and sumps. Ammonia at 17 g/mol is lighter than air and goes for the ceiling. Where you put the detector follows directly from an equation you can write in eight characters.