# Why 1 mole of H2 occupied the same volume occupied by 1 mole of O2?

I'm asking a question about the volume occupied by gasses in standard temperature and pressure.

My textbook said that a mole of any gas occupies $$\pu{22.4 L}$$ at standard temperature and pressure.

But $$\ce{O2}$$ is greater than $$\ce{H2}$$ in size

I asked my teacher why the volume occupied by 1 mole of $$\ce{H_2}$$ is equal to the volume occupied by $$\ce{O_2}$$ at standard temperature and pressure, but he seemed to not know the answer, and I remain confused.

• The basic assumption is ideal gas behavior. // PS -- STP changed in 1982. An ideal gas has a volume of 22.7 liters at STP. – MaxW Mar 25 '19 at 18:31
• Think of tennis and football balls in a very big hangar to see that the frequency of collision is basically the same, unless you pack the hangar with a lot more balls. What you refer to is the proper volume, which is not the volume of a gas. Reread what your book say about ideal gas, if the level of your class includes it. Else use my pictorial example. – Alchimista Mar 26 '19 at 8:37

The volume occupied by a gas has no relationship to the size of the molecules of the gas

This is one of the principles of the gas laws in chemistry. It is based on observation: in the early days of chemistry it is what chemists observed to be true. And it is a very important chemical law. But, of course, that doesn't explain why it is true.

There are several ways to gain some appreciation of this without too much theory. consider water as a liquid compared to water as a gas (I'm simplifying a bit but not by much). One mole of liquid water occupies about 18mL of space and this space is largely dominated by the size of the water molecule (again reality is a little more complex as the specific way the molecules interact makes a small difference to the volume occupied). As water vapour (the same substance but as a gas) 1 mole of water occupies over 22L of space (ignoring the fact that water is not a gas at STP, but bear with me as this is the space it would occupy if it were). That is well about 1200 times more space. This implies that very little of the space occupied has anything to do with how big the water molecule is.

The same broad idea applies to all gases.

So why does the molecular size not matter? A detailed understanding requires a fair few calculations about how gas molecules behave. But, the bottom line involves thinking about the molecular cause of pressure and the meaning of temperature. Pressure is caused by gas molecules bouncing off the walls of a vessel. Temperature is the average energy of those molecules which is a function of their speed and their mass. Doing the calculations shows the relationship between volume, pressure and temperature. This calculation explains the properties of gases but the volume of the molecules has no part.

Strictly speaking the ideal gas laws assume that the size of molecules don't matter. But this is a good approximation when the gases are far away from the point where they become liquids. The simplified theory matches actual observations well. And the fact that, in typical gases, the volume occupied by the molecules is less than 0.1% of the volume occupied by the gas shows why the molecular volume is usually irrelevant.

Let's take a look at the mean free path in a gas, which is defined by Wikipedia as

the average distance travelled by a moving particle (such as an atom, a molecule, a photon) between successive impacts (collisions)

On the same page, one can find a value of $$\pu{68 nm}$$ ($$\pu{6.8 \cdot 10^{-8} m}$$) for the mean free path at room temperature and a pressure of about 1 atmosphere. This is to be compared with the bond lengths of $$\ce{H2}$$ and $$\ce{O2}$$, which are about $$\pu{74 pm ( 0.74 \cdot 10^{-10} m)}$$ and $$\pu{121 pm ( 1.21 \cdot 10^{-10} m)}$$ respectively. Even if we generously assume and effective molecular diameter of three times the bond length, we can conclude that molecular size has little impact given that there are two orders of magnitude difference between size and mean free path.

This is true as long as we deal with a gas that is reasonably close to ideal. In reality, the size does matter indirectly. Larger and heavier molecules typically have more polarizable electron clouds, leading to stronger intermolecular forces. This is the reason why at low densities, gases with otherwise rather different boiling points (that are largely dependent on the strength of the intermolecular forces) still behave rather similar.

• I down voted this answer. The OP is obviously an absolute novice. I think you need to first explain the basic notions of ideal gas behavior. – MaxW Mar 25 '19 at 20:37
• I'd restructure that last paragraph since "This is the reason..." doesn't follow from the preceding sentence (it follows from the first sentence). Also, nonideality is probably unimportant except for charged particles, polarization being important only when you get to much higher densities compared to a gas at STP (maybe a dipole moment will have some effect). – Buck Thorn Mar 25 '19 at 21:19