NO2 and N2 O4 both have the same empirical (simplest)...

$\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ both have the same empirical (simplest) formula. At a temperature and pressure at which both substances are gases, can you tell without calculating which gas is more dense? Explain.

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Key Concepts

Empirical vs. Molecular Formulas

An empirical formula gives the simplest whole-number ratio of the elements in a compound, whereas the molecular formula reveals the actual number of atoms of each element present in a molecule. Two different substances can share the same empirical formula while having different molecular formulas, which in turn leads to differences in molecular weight and other physical properties.

Molar Mass and Gas Density

Under the same temperature and pressure conditions, the density of a gas is largely determined by its molar mass. Since density is mass per unit volume and the ideal gas law links these variables, a gas with a higher molar mass will be denser than a gas with a lower molar mass.

Ideal Gas Law

The ideal gas law (PV = nRT) illustrates that at constant temperature and pressure, the volume occupied by a gas is directly proportional to the amount of substance (n) and inversely related to its molar mass. This implies that, for gases under identical conditions, those with heavier molecules will have more mass in the same volume, hence a higher density.

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