# Molar volume:

The molar volume, symbol $V_\mathrm m$ is the volume occupied by one mole of a substance (chemical element or chemical compound) at a given temperature and pressure.

At S.T.P conditions the molar volume of any ideal gas is $\pu{22.711 dm^3}$. My question is: how can two gases with giant difference in molecular size (say $\ce{He}$ and $\ce{Fe}$) have the same volume, considering that the size difference between them is huge, shouldn't the volume they occupy also be different?

Thanks to @MaxW for pointing out a fault.

• Most of the volume in a gas is empty space, not atoms. – orthocresol Sep 10 '18 at 15:15
• You have the wrong molar volume. Since 1982, STP is defined as a temperature of 273.15 K (0 °C, 32 °F) and an absolute pressure of exactly $10^5$ Pa (100 kPa, 1 bar) which gives a molar volume of $22.711 \mathrm{dm}^3\mathrm{/mol}$. – MaxW Sep 10 '18 at 15:19
• Calculate the average volume containing a single molecule at STP. It's about 36,000 nm3 (cubic nanometers). A single simple molecule (like CO2, SF6, etc) is about 0.03 nm3, meaning that at STP a volume of gas is about 99.9999% empty space. Even if the molecule in question becomes quite large it is still effectively occupying a similarly negligible amount of physical space. – J... Sep 10 '18 at 19:13

## 1 Answer

You have the right thought process; if two real gases have different sized molecules, they won't have the same molar volume. The issue is that your statement about gases at STP refers to ideal gases which by assumption are just point particles that only interact via elastic collisions. To get a better sense of the difference that considering the finite size of molecules and their electrostatic interactions can make, you will want to read up on the various real gas models used, such as the Van der Waals, Redlich-Kwong, and Peng-Robinson models.

As a small side note, MaxW is correct that the definition of STP you are using is out of date so the molar volume at STP with the new definition is slightly higher. Its still quite common to see people accidentally continuing to use the old definition, so be on the lookout for that.

• So, what you are saying is that they don't have same volume? I wasn't aware of the change regarding STP, will read into it as well. – Any3nymous user Sep 10 '18 at 15:31
• @Any3nymoususer they would not have the same volume, though in most cases the difference is very small because molecules don't take up a lot of space. The specifics of how much the molecular size matters depends on the model you are using to describe a real gas. – Tyberius Sep 10 '18 at 15:35
• Very small doesn't make them equal. Anyhow so lemme see if I understood correctly: The difference although really small (as atoms themselves are small), is there and in most events they won't be equal? – Any3nymous user Sep 10 '18 at 15:38
• Can you possibly give a reference read. It'd be great if I could read up on this? Thanks for taking the time to answer – Any3nymous user Sep 10 '18 at 15:40
• @Any3nymoususer remember that ideal gas law is even previous to the periodic table. It was found experimentally, and explains fairly well behaviour of gases. You can wonder about molecules' size, but take that into account i.e all microscopical interpretations come centuries later. – santimirandarp Sep 11 '18 at 1:48