# Why are certain gases with higher molar masses less dense than the ones that have a lower one?

Neon, despite having a larger molar mass than nitrogen, oxygen and fluorine, is less dense than all of them. This also goes that fluorine (again) and chlorine are both denser than argon, even though argon has a higher molar mass than both of the halogens. The table below lists densities at standard pressure and temperature:

$$\begin{array}{lrr} \hline \text{Gas} & M/\pu{g mol^-1} & \rho/\pu{g l^-1} \\ \hline \text{Nitrogen} & 14.007 & 1.165 \\ \text{Oxygen} & 15.999 & 1.292 \\ \text{Fluorine} & 18.998 & 1.696 \\ \text{Neon} & 20.180 & \color{red}{0.900} \\ \text{Chlorine} & 35.453 & 3.214 \\ \text{Argon} & 39.498 & \color{red}{1.664} \\ \hline \end{array}$$

According to the ideal gas law, under equal pressure and temperature gases with higher molar mass should be denser:

$$\frac{M_1}{\rho_1}=\frac{M_2}{\rho_2}$$

Why isn't this the case for neon and argon?

• Because a nitrogen molecule is N2, not N, and Ne is just plain Ne. Commented Feb 16, 2022 at 4:09
• You list molar masses for elements, whereas nitrogen, oxygen, fluorine and chlorine are diatomic gases (noble gases are monoatomic). Commented Feb 16, 2022 at 4:12
• In analogy, a molar mass is like a mass of a dozen ( $N_\mathrm{A}$ ) of the paper bags with the exactly same content, which may be 1 or more pieces of various fruits. Commented Feb 16, 2022 at 13:37

As the comments imply,the molar masses you quote are for atoms of each element, whereas the observed gas density is determined by the masses of molecules.

Most elemental gases have two atoms per molecule, so for example nitrogen is $$\ce{N2}$$ and thus, properly, the molar mass of the molecules is $$2×14.007=28.014\text{ g/mol}$$.

The noble gases helium, neon, argon, krypton , xenon and radon (we do not know the ambient state of oganesson, element 118) are exceptions: with their filled atomic valence shell these have only one atom per molecule in the gas phase, and so the molar mass of neon truly is $$20.018\text{ g/mol}$$.

Thus the molar mass of neon is less than that of nitrogen after all when you count molecules, so neon will come out less dense.

A more curious example is hydrogen fluoride, whose density at 25°C is $$1.15\text{ g/L}$$ despite apparently having a molar mass of only $$20.006\text{ g/mol}$$. Neon, as seen above, has nearly the same molar mass but its ambient density is $$0.900\text{ g/L}$$. This happens because some hydrogen fluoride molecules are joined together by hydrogen bonds, even in the low-pressure gas phase, to effectively make bigger molecules. It's a rare example of a gas showing significant non-ideal behavior at normal atmospheric pressure. But we may expect other gases with hydrogen bonding, such as steam, to act the same way at higher gas pressure (which means higher temperature at least for steam).

• Ok,thank you. I never really thought of that. All the answers on google said " higher molar mass=higher density" Commented Feb 16, 2022 at 12:56
• ...these have only one atom per molecule in the gas phase... By IUPAC Goldbook definition, molecules must consist of at least 2 atoms, so elementary noble gases do not consist of molecules. (I personally do not like it, thinking it could be formally like a molecule as the least amount of particular compound or allotrope. E.g. O3 as ozone molecule, O2 as molecule of "normal" oxygen and O as a molecule of atomary oxygen, being also an atom of element oxygen.) Commented Feb 16, 2022 at 13:15
• @poutnik then please offer another way to describe the concept that fits with the definitions. I am apparently not as good at nomenclature as I am at physics Commented Feb 16, 2022 at 13:26
• @OscarLanzi Neither am I, nor it was my idea. I knew this because I was in past corrected myself. I have not received a positive answer to my question if there is any official common term for "an atom or molecule". Perhaps a particle, what can be an atom, or molecule, or a ion, or whatever. Commented Feb 16, 2022 at 13:32
• The definition of molecule that is really appropriate is "The form of the compound or element that exists in the system under consideration" instead of making a Text book definition. It is what is used for n in PV= nRT or what should be used to calculate molality or mole fraction or partial pressures. A helium atom is a molecule until it is cold enough to become super fluid etc. Similarly, in space the hydrogen molecule is the H atom or possibly H+. Commented Dec 13, 2022 at 18:36