Grade 12 Chemistry · Molar mass from the gas
The balance, folded into the gas law
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The balance, folded into the gas law

Two definitions meet here. Density is mass per volume, ρ=mV\rho = \dfrac{m}{V}ρ\rho is the Greek letter rho, said “row”, and for a gas it is usually quoted in grams per litre. Molar mass is mass per mole, M=mnM = \dfrac{m}{n}, in grams per mole. Put n=mMn = \dfrac{m}{M} into PV=nRTPV = nRT, divide through by VV, and the mass turns into a density on its own:

ρ=PMRT\rho = \dfrac{PM}{RT} — read aloud rho equals P M over R T. Four letters, four jobs: ρ\rho is the gas's density in g/L, PP its absolute pressure in kPa, MM its molar mass in g/mol, and TT the absolute temperature in kelvin, with R=8.314 kPaL/(molK)R = 8.314\ \mathrm{kPa \cdot L/(mol \cdot K)} refereeing as always. Solved the other way, M=ρRTPM = \dfrac{\rho R T}{P}, it becomes the classic identification: weigh a known volume of an unknown gas, and its molar mass — and usually its name — falls out.

Two sanity rails worth carrying. Heavy molecules make dense gases at the same conditions, because ρ\rho is directly proportional to MM. And hot gas is thin gas: TT sits underneath, which is the entire operating principle of a hot-air balloon. If your answer says otherwise, something upstream is inverted.